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guanjihuan
2025-09-22 17:49:02 +08:00
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52
2025.09.22_cpp_with_eigen_package/Eigen/AccelerateSupport Normal file
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_ACCELERATESUPPORT_MODULE_H
#define EIGEN_ACCELERATESUPPORT_MODULE_H
#include "SparseCore"
#include "src/Core/util/DisableStupidWarnings.h"
/** \ingroup Support_modules
* \defgroup AccelerateSupport_Module AccelerateSupport module
*
* This module provides an interface to the Apple Accelerate library.
* It provides the seven following main factorization classes:
* - class AccelerateLLT: a Cholesky (LL^T) factorization.
* - class AccelerateLDLT: the default LDL^T factorization.
* - class AccelerateLDLTUnpivoted: a Cholesky-like LDL^T factorization with only 1x1 pivots and no pivoting
* - class AccelerateLDLTSBK: an LDL^T factorization with Supernode Bunch-Kaufman and static pivoting
* - class AccelerateLDLTTPP: an LDL^T factorization with full threshold partial pivoting
* - class AccelerateQR: a QR factorization
* - class AccelerateCholeskyAtA: a QR factorization without storing Q (equivalent to A^TA = R^T R)
*
* \code
* #include <Eigen/AccelerateSupport>
* \endcode
*
* In order to use this module, the Accelerate headers must be accessible from
* the include paths, and your binary must be linked to the Accelerate framework.
* The Accelerate library is only available on Apple hardware.
*
* Note that many of the algorithms can be influenced by the UpLo template
* argument. All matrices are assumed to be symmetric. For example, the following
* creates an LDLT factorization where your matrix is symmetric (implicit) and
* uses the lower triangle:
*
* \code
* AccelerateLDLT<SparseMatrix<float>, Lower> ldlt;
* \endcode
*/
// IWYU pragma: begin_exports
#include "src/AccelerateSupport/AccelerateSupport.h"
// IWYU pragma: end_exports
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_ACCELERATESUPPORT_MODULE_H

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2025.09.22_cpp_with_eigen_package/Eigen/Cholesky Normal file
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_CHOLESKY_MODULE_H
#define EIGEN_CHOLESKY_MODULE_H
#include "Core"
#include "Jacobi"
#include "src/Core/util/DisableStupidWarnings.h"
/** \defgroup Cholesky_Module Cholesky module
*
*
*
* This module provides two variants of the Cholesky decomposition for selfadjoint (hermitian) matrices.
* Those decompositions are also accessible via the following methods:
* - MatrixBase::llt()
* - MatrixBase::ldlt()
* - SelfAdjointView::llt()
* - SelfAdjointView::ldlt()
*
* \code
* #include <Eigen/Cholesky>
* \endcode
*/
// IWYU pragma: begin_exports
#include "src/Cholesky/LLT.h"
#include "src/Cholesky/LDLT.h"
#ifdef EIGEN_USE_LAPACKE
#include "src/misc/lapacke_helpers.h"
#include "src/Cholesky/LLT_LAPACKE.h"
#endif
// IWYU pragma: end_exports
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_CHOLESKY_MODULE_H

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2025.09.22_cpp_with_eigen_package/Eigen/CholmodSupport Normal file
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_CHOLMODSUPPORT_MODULE_H
#define EIGEN_CHOLMODSUPPORT_MODULE_H
#include "SparseCore"
#include "src/Core/util/DisableStupidWarnings.h"
#include <cholmod.h>
/** \ingroup Support_modules
* \defgroup CholmodSupport_Module CholmodSupport module
*
* This module provides an interface to the Cholmod library which is part of the <a
* href="http://www.suitesparse.com">suitesparse</a> package. It provides the two following main factorization classes:
* - class CholmodSupernodalLLT: a supernodal LLT Cholesky factorization.
* - class CholmodDecomposition: a general L(D)LT Cholesky factorization with automatic or explicit runtime selection of
* the underlying factorization method (supernodal or simplicial).
*
* For the sake of completeness, this module also propose the two following classes:
* - class CholmodSimplicialLLT
* - class CholmodSimplicialLDLT
* Note that these classes does not bring any particular advantage compared to the built-in
* SimplicialLLT and SimplicialLDLT factorization classes.
*
* \code
* #include <Eigen/CholmodSupport>
* \endcode
*
* In order to use this module, the cholmod headers must be accessible from the include paths, and your binary must be
* linked to the cholmod library and its dependencies. The dependencies depend on how cholmod has been compiled. For a
* cmake based project, you can use our FindCholmod.cmake module to help you in this task.
*
*/
// IWYU pragma: begin_exports
#include "src/CholmodSupport/CholmodSupport.h"
// IWYU pragma: end_exports
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_CHOLMODSUPPORT_MODULE_H

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2025.09.22_cpp_with_eigen_package/Eigen/Core Normal file
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2007-2011 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_CORE_MODULE_H
#define EIGEN_CORE_MODULE_H
// Eigen version information.
#include "Version"
// first thing Eigen does: stop the compiler from reporting useless warnings.
#include "src/Core/util/DisableStupidWarnings.h"
// then include this file where all our macros are defined. It's really important to do it first because
// it's where we do all the compiler/OS/arch detections and define most defaults.
#include "src/Core/util/Macros.h"
// This detects SSE/AVX/NEON/etc. and configure alignment settings
#include "src/Core/util/ConfigureVectorization.h"
// We need cuda_runtime.h/hip_runtime.h to ensure that
// the EIGEN_USING_STD macro works properly on the device side
#if defined(EIGEN_CUDACC)
#include <cuda_runtime.h>
#elif defined(EIGEN_HIPCC)
#include <hip/hip_runtime.h>
#endif
#ifdef EIGEN_EXCEPTIONS
#include <new>
#endif
// Disable the ipa-cp-clone optimization flag with MinGW 6.x or older (enabled by default with -O3)
// See http://eigen.tuxfamily.org/bz/show_bug.cgi?id=556 for details.
#if EIGEN_COMP_MINGW && EIGEN_GNUC_STRICT_LESS_THAN(6, 0, 0)
#pragma GCC optimize("-fno-ipa-cp-clone")
#endif
// Prevent ICC from specializing std::complex operators that silently fail
// on device. This allows us to use our own device-compatible specializations
// instead.
#if EIGEN_COMP_ICC && defined(EIGEN_GPU_COMPILE_PHASE) && !defined(_OVERRIDE_COMPLEX_SPECIALIZATION_)
#define _OVERRIDE_COMPLEX_SPECIALIZATION_ 1
#endif
#include <complex>
// this include file manages BLAS and MKL related macros
// and inclusion of their respective header files
#include "src/Core/util/MKL_support.h"
#if defined(EIGEN_HAS_CUDA_FP16) || defined(EIGEN_HAS_HIP_FP16)
#define EIGEN_HAS_GPU_FP16
#endif
#if defined(EIGEN_HAS_CUDA_BF16) || defined(EIGEN_HAS_HIP_BF16)
#define EIGEN_HAS_GPU_BF16
#endif
#if (defined _OPENMP) && (!defined EIGEN_DONT_PARALLELIZE)
#define EIGEN_HAS_OPENMP
#endif
#ifdef EIGEN_HAS_OPENMP
#include <atomic>
#include <omp.h>
#endif
// MSVC for windows mobile does not have the errno.h file
#if !(EIGEN_COMP_MSVC && EIGEN_OS_WINCE) && !EIGEN_COMP_ARM
#define EIGEN_HAS_ERRNO
#endif
#ifdef EIGEN_HAS_ERRNO
#include <cerrno>
#endif
#include <cstddef>
#include <cstdlib>
#include <cmath>
#include <functional>
#ifndef EIGEN_NO_IO
#include <sstream>
#include <iosfwd>
#endif
#include <cstring>
#include <string>
#include <limits>
#include <climits> // for CHAR_BIT
// for min/max:
#include <algorithm>
#include <array>
#include <memory>
#include <vector>
// for std::is_nothrow_move_assignable
#include <type_traits>
// for std::this_thread::yield().
#if !defined(EIGEN_USE_BLAS) && (defined(EIGEN_HAS_OPENMP) || defined(EIGEN_GEMM_THREADPOOL))
#include <thread>
#endif
// for std::bit_cast()
#if defined(__cpp_lib_bit_cast) && __cpp_lib_bit_cast >= 201806L
#include <bit>
#endif
// for outputting debug info
#ifdef EIGEN_DEBUG_ASSIGN
#include <iostream>
#endif
// required for __cpuid, needs to be included after cmath
// also required for _BitScanReverse on Windows on ARM
#if EIGEN_COMP_MSVC && (EIGEN_ARCH_i386_OR_x86_64 || EIGEN_ARCH_ARM64) && !EIGEN_OS_WINCE
#include <intrin.h>
#endif
#if defined(EIGEN_USE_SYCL)
#undef min
#undef max
#undef isnan
#undef isinf
#undef isfinite
#include <CL/sycl.hpp>
#include <map>
#include <thread>
#include <utility>
#ifndef EIGEN_SYCL_LOCAL_THREAD_DIM0
#define EIGEN_SYCL_LOCAL_THREAD_DIM0 16
#endif
#ifndef EIGEN_SYCL_LOCAL_THREAD_DIM1
#define EIGEN_SYCL_LOCAL_THREAD_DIM1 16
#endif
#endif
#if defined EIGEN2_SUPPORT_STAGE40_FULL_EIGEN3_STRICTNESS || defined EIGEN2_SUPPORT_STAGE30_FULL_EIGEN3_API || \
defined EIGEN2_SUPPORT_STAGE20_RESOLVE_API_CONFLICTS || defined EIGEN2_SUPPORT_STAGE10_FULL_EIGEN2_API || \
defined EIGEN2_SUPPORT
// This will generate an error message:
#error Eigen2-support is only available up to version 3.2. Please go to "http://eigen.tuxfamily.org/index.php?title=Eigen2" for further information
#endif
namespace Eigen {
// we use size_t frequently and we'll never remember to prepend it with std:: every time just to
// ensure QNX/QCC support
using std::size_t;
// gcc 4.6.0 wants std:: for ptrdiff_t
using std::ptrdiff_t;
} // namespace Eigen
/** \defgroup Core_Module Core module
* This is the main module of Eigen providing dense matrix and vector support
* (both fixed and dynamic size) with all the features corresponding to a BLAS library
* and much more...
*
* \code
* #include <Eigen/Core>
* \endcode
*/
#ifdef EIGEN_USE_LAPACKE
#ifdef EIGEN_USE_MKL
#include "mkl_lapacke.h"
#else
#include "src/misc/lapacke.h"
#endif
#endif
// IWYU pragma: begin_exports
#include "src/Core/util/Constants.h"
#include "src/Core/util/Meta.h"
#include "src/Core/util/Assert.h"
#include "src/Core/util/ForwardDeclarations.h"
#include "src/Core/util/StaticAssert.h"
#include "src/Core/util/XprHelper.h"
#include "src/Core/util/Memory.h"
#include "src/Core/util/IntegralConstant.h"
#include "src/Core/util/Serializer.h"
#include "src/Core/util/SymbolicIndex.h"
#include "src/Core/util/EmulateArray.h"
#include "src/Core/util/MoreMeta.h"
#include "src/Core/NumTraits.h"
#include "src/Core/MathFunctions.h"
#include "src/Core/RandomImpl.h"
#include "src/Core/GenericPacketMath.h"
#include "src/Core/MathFunctionsImpl.h"
#include "src/Core/arch/Default/ConjHelper.h"
// Generic half float support
#include "src/Core/arch/Default/Half.h"
#include "src/Core/arch/Default/BFloat16.h"
#include "src/Core/arch/Default/GenericPacketMathFunctionsFwd.h"
#if defined EIGEN_VECTORIZE_AVX512
#include "src/Core/arch/SSE/PacketMath.h"
#include "src/Core/arch/SSE/Reductions.h"
#include "src/Core/arch/AVX/PacketMath.h"
#include "src/Core/arch/AVX/Reductions.h"
#include "src/Core/arch/AVX512/PacketMath.h"
#include "src/Core/arch/AVX512/Reductions.h"
#if defined EIGEN_VECTORIZE_AVX512FP16
#include "src/Core/arch/AVX512/PacketMathFP16.h"
#endif
#include "src/Core/arch/SSE/TypeCasting.h"
#include "src/Core/arch/AVX/TypeCasting.h"
#include "src/Core/arch/AVX512/TypeCasting.h"
#if defined EIGEN_VECTORIZE_AVX512FP16
#include "src/Core/arch/AVX512/TypeCastingFP16.h"
#endif
#include "src/Core/arch/SSE/Complex.h"
#include "src/Core/arch/AVX/Complex.h"
#include "src/Core/arch/AVX512/Complex.h"
#include "src/Core/arch/SSE/MathFunctions.h"
#include "src/Core/arch/AVX/MathFunctions.h"
#include "src/Core/arch/AVX512/MathFunctions.h"
#if defined EIGEN_VECTORIZE_AVX512FP16
#include "src/Core/arch/AVX512/MathFunctionsFP16.h"
#endif
#include "src/Core/arch/AVX512/TrsmKernel.h"
#elif defined EIGEN_VECTORIZE_AVX
// Use AVX for floats and doubles, SSE for integers
#include "src/Core/arch/SSE/PacketMath.h"
#include "src/Core/arch/SSE/Reductions.h"
#include "src/Core/arch/SSE/TypeCasting.h"
#include "src/Core/arch/SSE/Complex.h"
#include "src/Core/arch/AVX/PacketMath.h"
#include "src/Core/arch/AVX/Reductions.h"
#include "src/Core/arch/AVX/TypeCasting.h"
#include "src/Core/arch/AVX/Complex.h"
#include "src/Core/arch/SSE/MathFunctions.h"
#include "src/Core/arch/AVX/MathFunctions.h"
#elif defined EIGEN_VECTORIZE_SSE
#include "src/Core/arch/SSE/PacketMath.h"
#include "src/Core/arch/SSE/Reductions.h"
#include "src/Core/arch/SSE/TypeCasting.h"
#include "src/Core/arch/SSE/MathFunctions.h"
#include "src/Core/arch/SSE/Complex.h"
#endif
#if defined(EIGEN_VECTORIZE_ALTIVEC) || defined(EIGEN_VECTORIZE_VSX)
#include "src/Core/arch/AltiVec/PacketMath.h"
#include "src/Core/arch/AltiVec/TypeCasting.h"
#include "src/Core/arch/AltiVec/MathFunctions.h"
#include "src/Core/arch/AltiVec/Complex.h"
#elif defined EIGEN_VECTORIZE_NEON
#include "src/Core/arch/NEON/PacketMath.h"
#include "src/Core/arch/NEON/TypeCasting.h"
#include "src/Core/arch/NEON/MathFunctions.h"
#include "src/Core/arch/NEON/Complex.h"
#elif defined EIGEN_VECTORIZE_LSX
#include "src/Core/arch/LSX/PacketMath.h"
#include "src/Core/arch/LSX/TypeCasting.h"
#include "src/Core/arch/LSX/MathFunctions.h"
#include "src/Core/arch/LSX/Complex.h"
#elif defined EIGEN_VECTORIZE_SVE
#include "src/Core/arch/SVE/PacketMath.h"
#include "src/Core/arch/SVE/TypeCasting.h"
#include "src/Core/arch/SVE/MathFunctions.h"
#elif defined EIGEN_VECTORIZE_ZVECTOR
#include "src/Core/arch/ZVector/PacketMath.h"
#include "src/Core/arch/ZVector/MathFunctions.h"
#include "src/Core/arch/ZVector/Complex.h"
#elif defined EIGEN_VECTORIZE_MSA
#include "src/Core/arch/MSA/PacketMath.h"
#include "src/Core/arch/MSA/MathFunctions.h"
#include "src/Core/arch/MSA/Complex.h"
#elif defined EIGEN_VECTORIZE_HVX
#include "src/Core/arch/HVX/PacketMath.h"
#endif
#if defined EIGEN_VECTORIZE_GPU
#include "src/Core/arch/GPU/PacketMath.h"
#include "src/Core/arch/GPU/MathFunctions.h"
#include "src/Core/arch/GPU/TypeCasting.h"
#endif
#if defined(EIGEN_USE_SYCL)
#include "src/Core/arch/SYCL/InteropHeaders.h"
#if !defined(EIGEN_DONT_VECTORIZE_SYCL)
#include "src/Core/arch/SYCL/PacketMath.h"
#include "src/Core/arch/SYCL/MathFunctions.h"
#include "src/Core/arch/SYCL/TypeCasting.h"
#endif
#endif
#include "src/Core/arch/Default/Settings.h"
// This file provides generic implementations valid for scalar as well
#include "src/Core/arch/Default/GenericPacketMathFunctions.h"
#include "src/Core/functors/TernaryFunctors.h"
#include "src/Core/functors/BinaryFunctors.h"
#include "src/Core/functors/UnaryFunctors.h"
#include "src/Core/functors/NullaryFunctors.h"
#include "src/Core/functors/StlFunctors.h"
#include "src/Core/functors/AssignmentFunctors.h"
// Specialized functors for GPU.
#ifdef EIGEN_GPUCC
#include "src/Core/arch/GPU/Complex.h"
#endif
// Specializations of vectorized activation functions for NEON.
#ifdef EIGEN_VECTORIZE_NEON
#include "src/Core/arch/NEON/UnaryFunctors.h"
#endif
#include "src/Core/util/IndexedViewHelper.h"
#include "src/Core/util/ReshapedHelper.h"
#include "src/Core/ArithmeticSequence.h"
#ifndef EIGEN_NO_IO
#include "src/Core/IO.h"
#endif
#include "src/Core/DenseCoeffsBase.h"
#include "src/Core/DenseBase.h"
#include "src/Core/MatrixBase.h"
#include "src/Core/EigenBase.h"
#include "src/Core/Product.h"
#include "src/Core/CoreEvaluators.h"
#include "src/Core/AssignEvaluator.h"
#include "src/Core/RealView.h"
#include "src/Core/Assign.h"
#include "src/Core/ArrayBase.h"
#include "src/Core/util/BlasUtil.h"
#include "src/Core/DenseStorage.h"
#include "src/Core/NestByValue.h"
// #include "src/Core/ForceAlignedAccess.h"
#include "src/Core/ReturnByValue.h"
#include "src/Core/NoAlias.h"
#include "src/Core/PlainObjectBase.h"
#include "src/Core/Matrix.h"
#include "src/Core/Array.h"
#include "src/Core/Fill.h"
#include "src/Core/CwiseTernaryOp.h"
#include "src/Core/CwiseBinaryOp.h"
#include "src/Core/CwiseUnaryOp.h"
#include "src/Core/CwiseNullaryOp.h"
#include "src/Core/CwiseUnaryView.h"
#include "src/Core/SelfCwiseBinaryOp.h"
#include "src/Core/InnerProduct.h"
#include "src/Core/Dot.h"
#include "src/Core/StableNorm.h"
#include "src/Core/Stride.h"
#include "src/Core/MapBase.h"
#include "src/Core/Map.h"
#include "src/Core/Ref.h"
#include "src/Core/Block.h"
#include "src/Core/VectorBlock.h"
#include "src/Core/IndexedView.h"
#include "src/Core/Reshaped.h"
#include "src/Core/Transpose.h"
#include "src/Core/DiagonalMatrix.h"
#include "src/Core/Diagonal.h"
#include "src/Core/DiagonalProduct.h"
#include "src/Core/SkewSymmetricMatrix3.h"
#include "src/Core/Redux.h"
#include "src/Core/Visitor.h"
#include "src/Core/FindCoeff.h"
#include "src/Core/Fuzzy.h"
#include "src/Core/Swap.h"
#include "src/Core/CommaInitializer.h"
#include "src/Core/GeneralProduct.h"
#include "src/Core/Solve.h"
#include "src/Core/Inverse.h"
#include "src/Core/SolverBase.h"
#include "src/Core/PermutationMatrix.h"
#include "src/Core/Transpositions.h"
#include "src/Core/TriangularMatrix.h"
#include "src/Core/SelfAdjointView.h"
#include "src/Core/products/GeneralBlockPanelKernel.h"
#include "src/Core/DeviceWrapper.h"
#ifdef EIGEN_GEMM_THREADPOOL
#include "ThreadPool"
#endif
#include "src/Core/products/Parallelizer.h"
#include "src/Core/ProductEvaluators.h"
#include "src/Core/products/GeneralMatrixVector.h"
#include "src/Core/products/GeneralMatrixMatrix.h"
#include "src/Core/SolveTriangular.h"
#include "src/Core/products/GeneralMatrixMatrixTriangular.h"
#include "src/Core/products/SelfadjointMatrixVector.h"
#include "src/Core/products/SelfadjointMatrixMatrix.h"
#include "src/Core/products/SelfadjointProduct.h"
#include "src/Core/products/SelfadjointRank2Update.h"
#include "src/Core/products/TriangularMatrixVector.h"
#include "src/Core/products/TriangularMatrixMatrix.h"
#include "src/Core/products/TriangularSolverMatrix.h"
#include "src/Core/products/TriangularSolverVector.h"
#include "src/Core/BandMatrix.h"
#include "src/Core/CoreIterators.h"
#include "src/Core/ConditionEstimator.h"
#if defined(EIGEN_VECTORIZE_VSX)
#include "src/Core/arch/AltiVec/MatrixProduct.h"
#elif defined EIGEN_VECTORIZE_NEON
#include "src/Core/arch/NEON/GeneralBlockPanelKernel.h"
#elif defined EIGEN_VECTORIZE_LSX
#include "src/Core/arch/LSX/GeneralBlockPanelKernel.h"
#endif
#if defined(EIGEN_VECTORIZE_AVX512)
#include "src/Core/arch/AVX512/GemmKernel.h"
#endif
#include "src/Core/Select.h"
#include "src/Core/VectorwiseOp.h"
#include "src/Core/PartialReduxEvaluator.h"
#include "src/Core/Random.h"
#include "src/Core/Replicate.h"
#include "src/Core/Reverse.h"
#include "src/Core/ArrayWrapper.h"
#include "src/Core/StlIterators.h"
#ifdef EIGEN_USE_BLAS
#include "src/Core/products/GeneralMatrixMatrix_BLAS.h"
#include "src/Core/products/GeneralMatrixVector_BLAS.h"
#include "src/Core/products/GeneralMatrixMatrixTriangular_BLAS.h"
#include "src/Core/products/SelfadjointMatrixMatrix_BLAS.h"
#include "src/Core/products/SelfadjointMatrixVector_BLAS.h"
#include "src/Core/products/TriangularMatrixMatrix_BLAS.h"
#include "src/Core/products/TriangularMatrixVector_BLAS.h"
#include "src/Core/products/TriangularSolverMatrix_BLAS.h"
#endif // EIGEN_USE_BLAS
#ifdef EIGEN_USE_MKL_VML
#include "src/Core/Assign_MKL.h"
#endif
#include "src/Core/GlobalFunctions.h"
// IWYU pragma: end_exports
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_CORE_MODULE_H

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#include "Core"
#include "LU"
#include "Cholesky"
#include "QR"
#include "SVD"
#include "Geometry"
#include "Eigenvalues"

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2025.09.22_cpp_with_eigen_package/Eigen/Eigen Normal file
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#include "Dense"
#include "Sparse"

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_EIGENVALUES_MODULE_H
#define EIGEN_EIGENVALUES_MODULE_H
#include "Core"
#include "Cholesky"
#include "Jacobi"
#include "Householder"
#include "LU"
#include "Geometry"
#include "src/Core/util/DisableStupidWarnings.h"
/** \defgroup Eigenvalues_Module Eigenvalues module
*
*
*
* This module mainly provides various eigenvalue solvers.
* This module also provides some MatrixBase methods, including:
* - MatrixBase::eigenvalues(),
* - MatrixBase::operatorNorm()
*
* \code
* #include <Eigen/Eigenvalues>
* \endcode
*/
#include "src/misc/RealSvd2x2.h"
// IWYU pragma: begin_exports
#include "src/Eigenvalues/Tridiagonalization.h"
#include "src/Eigenvalues/RealSchur.h"
#include "src/Eigenvalues/EigenSolver.h"
#include "src/Eigenvalues/SelfAdjointEigenSolver.h"
#include "src/Eigenvalues/GeneralizedSelfAdjointEigenSolver.h"
#include "src/Eigenvalues/HessenbergDecomposition.h"
#include "src/Eigenvalues/ComplexSchur.h"
#include "src/Eigenvalues/ComplexEigenSolver.h"
#include "src/Eigenvalues/RealQZ.h"
#include "src/Eigenvalues/GeneralizedEigenSolver.h"
#include "src/Eigenvalues/MatrixBaseEigenvalues.h"
#ifdef EIGEN_USE_LAPACKE
#ifdef EIGEN_USE_MKL
#include "mkl_lapacke.h"
#else
#include "src/misc/lapacke.h"
#endif
#include "src/Eigenvalues/RealSchur_LAPACKE.h"
#include "src/Eigenvalues/ComplexSchur_LAPACKE.h"
#include "src/Eigenvalues/SelfAdjointEigenSolver_LAPACKE.h"
#endif
// IWYU pragma: end_exports
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_EIGENVALUES_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_GEOMETRY_MODULE_H
#define EIGEN_GEOMETRY_MODULE_H
#include "Core"
#include "SVD"
#include "LU"
#include <limits>
#include "src/Core/util/DisableStupidWarnings.h"
/** \defgroup Geometry_Module Geometry module
*
* This module provides support for:
* - fixed-size homogeneous transformations
* - translation, scaling, 2D and 3D rotations
* - \link Quaternion quaternions \endlink
* - cross products (\ref MatrixBase::cross(), \ref MatrixBase::cross3())
* - orthogonal vector generation (MatrixBase::unitOrthogonal)
* - some linear components: \link ParametrizedLine parametrized-lines \endlink and \link Hyperplane hyperplanes \endlink
* - \link AlignedBox axis aligned bounding boxes \endlink
* - \link umeyama() least-square transformation fitting \endlink
* \code
* #include <Eigen/Geometry>
* \endcode
*/
// IWYU pragma: begin_exports
#include "src/Geometry/OrthoMethods.h"
#include "src/Geometry/EulerAngles.h"
#include "src/Geometry/Homogeneous.h"
#include "src/Geometry/RotationBase.h"
#include "src/Geometry/Rotation2D.h"
#include "src/Geometry/Quaternion.h"
#include "src/Geometry/AngleAxis.h"
#include "src/Geometry/Transform.h"
#include "src/Geometry/Translation.h"
#include "src/Geometry/Scaling.h"
#include "src/Geometry/Hyperplane.h"
#include "src/Geometry/ParametrizedLine.h"
#include "src/Geometry/AlignedBox.h"
#include "src/Geometry/Umeyama.h"
// Use the SSE optimized version whenever possible.
#if (defined EIGEN_VECTORIZE_SSE) || (defined EIGEN_VECTORIZE_NEON)
#include "src/Geometry/arch/Geometry_SIMD.h"
#endif
// IWYU pragma: end_exports
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_GEOMETRY_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_HOUSEHOLDER_MODULE_H
#define EIGEN_HOUSEHOLDER_MODULE_H
#include "Core"
#include "src/Core/util/DisableStupidWarnings.h"
/** \defgroup Householder_Module Householder module
* This module provides Householder transformations.
*
* \code
* #include <Eigen/Householder>
* \endcode
*/
// IWYU pragma: begin_exports
#include "src/Householder/Householder.h"
#include "src/Householder/HouseholderSequence.h"
#include "src/Householder/BlockHouseholder.h"
// IWYU pragma: end_exports
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_HOUSEHOLDER_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_ITERATIVELINEARSOLVERS_MODULE_H
#define EIGEN_ITERATIVELINEARSOLVERS_MODULE_H
#include "SparseCore"
#include "OrderingMethods"
#include "src/Core/util/DisableStupidWarnings.h"
/**
* \defgroup IterativeLinearSolvers_Module IterativeLinearSolvers module
*
* This module currently provides iterative methods to solve problems of the form \c A \c x = \c b, where \c A is a
squared matrix, usually very large and sparse.
* Those solvers are accessible via the following classes:
* - ConjugateGradient for selfadjoint (hermitian) matrices,
* - LeastSquaresConjugateGradient for rectangular least-square problems,
* - BiCGSTAB for general square matrices.
*
* These iterative solvers are associated with some preconditioners:
* - IdentityPreconditioner - not really useful
* - DiagonalPreconditioner - also called Jacobi preconditioner, work very well on diagonal dominant matrices.
* - IncompleteLUT - incomplete LU factorization with dual thresholding
*
* Such problems can also be solved using the direct sparse decomposition modules: SparseCholesky, CholmodSupport,
UmfPackSupport, SuperLUSupport, AccelerateSupport.
*
\code
#include <Eigen/IterativeLinearSolvers>
\endcode
*/
// IWYU pragma: begin_exports
#include "src/IterativeLinearSolvers/SolveWithGuess.h"
#include "src/IterativeLinearSolvers/IterativeSolverBase.h"
#include "src/IterativeLinearSolvers/BasicPreconditioners.h"
#include "src/IterativeLinearSolvers/ConjugateGradient.h"
#include "src/IterativeLinearSolvers/LeastSquareConjugateGradient.h"
#include "src/IterativeLinearSolvers/BiCGSTAB.h"
#include "src/IterativeLinearSolvers/IncompleteLUT.h"
#include "src/IterativeLinearSolvers/IncompleteCholesky.h"
// IWYU pragma: end_exports
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_ITERATIVELINEARSOLVERS_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_JACOBI_MODULE_H
#define EIGEN_JACOBI_MODULE_H
#include "Core"
#include "src/Core/util/DisableStupidWarnings.h"
/** \defgroup Jacobi_Module Jacobi module
* This module provides Jacobi and Givens rotations.
*
* \code
* #include <Eigen/Jacobi>
* \endcode
*
* In addition to listed classes, it defines the two following MatrixBase methods to apply a Jacobi or Givens rotation:
* - MatrixBase::applyOnTheLeft()
* - MatrixBase::applyOnTheRight().
*/
// IWYU pragma: begin_exports
#include "src/Jacobi/Jacobi.h"
// IWYU pragma: end_exports
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_JACOBI_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_KLUSUPPORT_MODULE_H
#define EIGEN_KLUSUPPORT_MODULE_H
#include "SparseCore"
#include "src/Core/util/DisableStupidWarnings.h"
extern "C" {
#include <btf.h>
#include <klu.h>
}
/** \ingroup Support_modules
* \defgroup KLUSupport_Module KLUSupport module
*
* This module provides an interface to the KLU library which is part of the <a
* href="http://www.suitesparse.com">suitesparse</a> package. It provides the following factorization class:
* - class KLU: a sparse LU factorization, well-suited for circuit simulation.
*
* \code
* #include <Eigen/KLUSupport>
* \endcode
*
* In order to use this module, the klu and btf headers must be accessible from the include paths, and your binary must
* be linked to the klu library and its dependencies. The dependencies depend on how umfpack has been compiled. For a
* cmake based project, you can use our FindKLU.cmake module to help you in this task.
*
*/
// IWYU pragma: begin_exports
#include "src/KLUSupport/KLUSupport.h"
// IWYU pragma: end_exports
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_KLUSUPPORT_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_LU_MODULE_H
#define EIGEN_LU_MODULE_H
#include "Core"
#include "src/Core/util/DisableStupidWarnings.h"
/** \defgroup LU_Module LU module
* This module includes %LU decomposition and related notions such as matrix inversion and determinant.
* This module defines the following MatrixBase methods:
* - MatrixBase::inverse()
* - MatrixBase::determinant()
*
* \code
* #include <Eigen/LU>
* \endcode
*/
#include "src/misc/Kernel.h"
#include "src/misc/Image.h"
// IWYU pragma: begin_exports
#include "src/LU/FullPivLU.h"
#include "src/LU/PartialPivLU.h"
#ifdef EIGEN_USE_LAPACKE
#include "src/misc/lapacke_helpers.h"
#include "src/LU/PartialPivLU_LAPACKE.h"
#endif
#include "src/LU/Determinant.h"
#include "src/LU/InverseImpl.h"
#if defined EIGEN_VECTORIZE_SSE || defined EIGEN_VECTORIZE_NEON
#include "src/LU/arch/InverseSize4.h"
#endif
// IWYU pragma: end_exports
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_LU_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_METISSUPPORT_MODULE_H
#define EIGEN_METISSUPPORT_MODULE_H
#include "SparseCore"
#include "src/Core/util/DisableStupidWarnings.h"
extern "C" {
#include <metis.h>
}
/** \ingroup Support_modules
* \defgroup MetisSupport_Module MetisSupport module
*
* \code
* #include <Eigen/MetisSupport>
* \endcode
* This module defines an interface to the METIS reordering package (http://glaros.dtc.umn.edu/gkhome/views/metis).
* It can be used just as any other built-in method as explained in \link OrderingMethods_Module here. \endlink
*/
// IWYU pragma: begin_exports
#include "src/MetisSupport/MetisSupport.h"
// IWYU pragma: end_exports
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_METISSUPPORT_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_ORDERINGMETHODS_MODULE_H
#define EIGEN_ORDERINGMETHODS_MODULE_H
#include "SparseCore"
#include "src/Core/util/DisableStupidWarnings.h"
/**
* \defgroup OrderingMethods_Module OrderingMethods module
*
* This module is currently for internal use only
*
* It defines various built-in and external ordering methods for sparse matrices.
* They are typically used to reduce the number of elements during
* the sparse matrix decomposition (LLT, LU, QR).
* Precisely, in a preprocessing step, a permutation matrix P is computed using
* those ordering methods and applied to the columns of the matrix.
* Using for instance the sparse Cholesky decomposition, it is expected that
* the nonzeros elements in LLT(A*P) will be much smaller than that in LLT(A).
*
*
* Usage :
* \code
* #include <Eigen/OrderingMethods>
* \endcode
*
* A simple usage is as a template parameter in the sparse decomposition classes :
*
* \code
* SparseLU<MatrixType, COLAMDOrdering<int> > solver;
* \endcode
*
* \code
* SparseQR<MatrixType, COLAMDOrdering<int> > solver;
* \endcode
*
* It is possible as well to call directly a particular ordering method for your own purpose,
* \code
* AMDOrdering<int> ordering;
* PermutationMatrix<Dynamic, Dynamic, int> perm;
* SparseMatrix<double> A;
* //Fill the matrix ...
*
* ordering(A, perm); // Call AMD
* \endcode
*
* \note Some of these methods (like AMD or METIS), need the sparsity pattern
* of the input matrix to be symmetric. When the matrix is structurally unsymmetric,
* Eigen computes internally the pattern of \f$A^T*A\f$ before calling the method.
* If your matrix is already symmetric (at least in structure), you can avoid that
* by calling the method with a SelfAdjointView type.
*
* \code
* // Call the ordering on the pattern of the lower triangular matrix A
* ordering(A.selfadjointView<Lower>(), perm);
* \endcode
*/
// IWYU pragma: begin_exports
#include "src/OrderingMethods/Amd.h"
#include "src/OrderingMethods/Ordering.h"
// IWYU pragma: end_exports
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_ORDERINGMETHODS_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_PASTIXSUPPORT_MODULE_H
#define EIGEN_PASTIXSUPPORT_MODULE_H
#include "SparseCore"
#include "src/Core/util/DisableStupidWarnings.h"
extern "C" {
#include <pastix_nompi.h>
#include <pastix.h>
}
#ifdef complex
#undef complex
#endif
/** \ingroup Support_modules
* \defgroup PaStiXSupport_Module PaStiXSupport module
*
* This module provides an interface to the <a href="http://pastix.gforge.inria.fr/">PaSTiX</a> library.
* PaSTiX is a general \b supernodal, \b parallel and \b opensource sparse solver.
* It provides the two following main factorization classes:
* - class PastixLLT : a supernodal, parallel LLt Cholesky factorization.
* - class PastixLDLT: a supernodal, parallel LDLt Cholesky factorization.
* - class PastixLU : a supernodal, parallel LU factorization (optimized for a symmetric pattern).
*
* \code
* #include <Eigen/PaStiXSupport>
* \endcode
*
* In order to use this module, the PaSTiX headers must be accessible from the include paths, and your binary must be
* linked to the PaSTiX library and its dependencies. This wrapper resuires PaStiX version 5.x compiled without MPI
* support. The dependencies depend on how PaSTiX has been compiled. For a cmake based project, you can use our
* FindPaSTiX.cmake module to help you in this task.
*
*/
// IWYU pragma: begin_exports
#include "src/PaStiXSupport/PaStiXSupport.h"
// IWYU pragma: end_exports
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_PASTIXSUPPORT_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_PARDISOSUPPORT_MODULE_H
#define EIGEN_PARDISOSUPPORT_MODULE_H
#include "SparseCore"
#include "src/Core/util/DisableStupidWarnings.h"
#include <mkl_pardiso.h>
/** \ingroup Support_modules
* \defgroup PardisoSupport_Module PardisoSupport module
*
* This module brings support for the Intel(R) MKL PARDISO direct sparse solvers.
*
* \code
* #include <Eigen/PardisoSupport>
* \endcode
*
* In order to use this module, the MKL headers must be accessible from the include paths, and your binary must be
* linked to the MKL library and its dependencies. See this \ref TopicUsingIntelMKL "page" for more information on
* MKL-Eigen integration.
*
*/
// IWYU pragma: begin_exports
#include "src/PardisoSupport/PardisoSupport.h"
// IWYU pragma: end_exports
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_PARDISOSUPPORT_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_QR_MODULE_H
#define EIGEN_QR_MODULE_H
#include "Core"
#include "Cholesky"
#include "Jacobi"
#include "Householder"
#include "src/Core/util/DisableStupidWarnings.h"
/** \defgroup QR_Module QR module
*
*
*
* This module provides various QR decompositions
* This module also provides some MatrixBase methods, including:
* - MatrixBase::householderQr()
* - MatrixBase::colPivHouseholderQr()
* - MatrixBase::fullPivHouseholderQr()
*
* \code
* #include <Eigen/QR>
* \endcode
*/
// IWYU pragma: begin_exports
#include "src/QR/HouseholderQR.h"
#include "src/QR/FullPivHouseholderQR.h"
#include "src/QR/ColPivHouseholderQR.h"
#include "src/QR/CompleteOrthogonalDecomposition.h"
#ifdef EIGEN_USE_LAPACKE
#include "src/misc/lapacke_helpers.h"
#include "src/QR/HouseholderQR_LAPACKE.h"
#include "src/QR/ColPivHouseholderQR_LAPACKE.h"
#endif
// IWYU pragma: end_exports
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_QR_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_QTMALLOC_MODULE_H
#define EIGEN_QTMALLOC_MODULE_H
#include "Core"
#if (!EIGEN_MALLOC_ALREADY_ALIGNED)
#include "src/Core/util/DisableStupidWarnings.h"
void *qMalloc(std::size_t size) { return Eigen::internal::aligned_malloc(size); }
void qFree(void *ptr) { Eigen::internal::aligned_free(ptr); }
void *qRealloc(void *ptr, std::size_t size) {
void *newPtr = Eigen::internal::aligned_malloc(size);
std::memcpy(newPtr, ptr, size);
Eigen::internal::aligned_free(ptr);
return newPtr;
}
#include "src/Core/util/ReenableStupidWarnings.h"
#endif
#endif // EIGEN_QTMALLOC_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_SPQRSUPPORT_MODULE_H
#define EIGEN_SPQRSUPPORT_MODULE_H
#include "SparseCore"
#include "src/Core/util/DisableStupidWarnings.h"
#include "SuiteSparseQR.hpp"
/** \ingroup Support_modules
* \defgroup SPQRSupport_Module SuiteSparseQR module
*
* This module provides an interface to the SPQR library, which is part of the <a
* href="http://www.suitesparse.com">suitesparse</a> package.
*
* \code
* #include <Eigen/SPQRSupport>
* \endcode
*
* In order to use this module, the SPQR headers must be accessible from the include paths, and your binary must be
* linked to the SPQR library and its dependencies (Cholmod, AMD, COLAMD,...). For a cmake based project, you can use
* our FindSPQR.cmake and FindCholmod.Cmake modules
*
*/
#include "CholmodSupport"
// IWYU pragma: begin_exports
#include "src/SPQRSupport/SuiteSparseQRSupport.h"
// IWYU pragma: end_exports
#include "src/Core/util/ReenableStupidWarnings.h"
#endif

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_SVD_MODULE_H
#define EIGEN_SVD_MODULE_H
#include "QR"
#include "Householder"
#include "Jacobi"
#include "src/Core/util/DisableStupidWarnings.h"
/** \defgroup SVD_Module SVD module
*
*
*
* This module provides SVD decomposition for matrices (both real and complex).
* Two decomposition algorithms are provided:
* - JacobiSVD implementing two-sided Jacobi iterations is numerically very accurate, fast for small matrices, but very
* slow for larger ones.
* - BDCSVD implementing a recursive divide & conquer strategy on top of an upper-bidiagonalization which remains fast
* for large problems. These decompositions are accessible via the respective classes and following MatrixBase methods:
* - MatrixBase::jacobiSvd()
* - MatrixBase::bdcSvd()
*
* \code
* #include <Eigen/SVD>
* \endcode
*/
// IWYU pragma: begin_exports
#include "src/misc/RealSvd2x2.h"
#include "src/SVD/UpperBidiagonalization.h"
#include "src/SVD/SVDBase.h"
#include "src/SVD/JacobiSVD.h"
#include "src/SVD/BDCSVD.h"
#ifdef EIGEN_USE_LAPACKE
#ifdef EIGEN_USE_MKL
#include "mkl_lapacke.h"
#else
#include "src/misc/lapacke.h"
#endif
#ifndef EIGEN_USE_LAPACKE_STRICT
#include "src/SVD/JacobiSVD_LAPACKE.h"
#endif
#include "src/SVD/BDCSVD_LAPACKE.h"
#endif
// IWYU pragma: end_exports
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_SVD_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_SPARSE_MODULE_H
#define EIGEN_SPARSE_MODULE_H
/** \defgroup Sparse_Module Sparse meta-module
*
* Meta-module including all related modules:
* - \ref SparseCore_Module
* - \ref OrderingMethods_Module
* - \ref SparseCholesky_Module
* - \ref SparseLU_Module
* - \ref SparseQR_Module
* - \ref IterativeLinearSolvers_Module
*
\code
#include <Eigen/Sparse>
\endcode
*/
#include "SparseCore"
#include "OrderingMethods"
#include "SparseCholesky"
#include "SparseLU"
#include "SparseQR"
#include "IterativeLinearSolvers"
#endif // EIGEN_SPARSE_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2013 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_SPARSECHOLESKY_MODULE_H
#define EIGEN_SPARSECHOLESKY_MODULE_H
#include "SparseCore"
#include "OrderingMethods"
#include "src/Core/util/DisableStupidWarnings.h"
/**
* \defgroup SparseCholesky_Module SparseCholesky module
*
* This module currently provides two variants of the direct sparse Cholesky decomposition for selfadjoint (hermitian)
* matrices. Those decompositions are accessible via the following classes:
* - SimplicialLLt,
* - SimplicialLDLt
*
* Such problems can also be solved using the ConjugateGradient solver from the IterativeLinearSolvers module.
*
* \code
* #include <Eigen/SparseCholesky>
* \endcode
*/
// IWYU pragma: begin_exports
#include "src/SparseCholesky/SimplicialCholesky.h"
#include "src/SparseCholesky/SimplicialCholesky_impl.h"
// IWYU pragma: end_exports
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_SPARSECHOLESKY_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_SPARSECORE_MODULE_H
#define EIGEN_SPARSECORE_MODULE_H
#include "Core"
#include "src/Core/util/DisableStupidWarnings.h"
#include <vector>
#include <map>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <numeric>
/**
* \defgroup SparseCore_Module SparseCore module
*
* This module provides a sparse matrix representation, and basic associated matrix manipulations
* and operations.
*
* See the \ref TutorialSparse "Sparse tutorial"
*
* \code
* #include <Eigen/SparseCore>
* \endcode
*
* This module depends on: Core.
*/
// IWYU pragma: begin_exports
#include "src/SparseCore/SparseUtil.h"
#include "src/SparseCore/SparseMatrixBase.h"
#include "src/SparseCore/SparseAssign.h"
#include "src/SparseCore/CompressedStorage.h"
#include "src/SparseCore/AmbiVector.h"
#include "src/SparseCore/SparseCompressedBase.h"
#include "src/SparseCore/SparseMatrix.h"
#include "src/SparseCore/SparseMap.h"
#include "src/SparseCore/SparseVector.h"
#include "src/SparseCore/SparseRef.h"
#include "src/SparseCore/SparseCwiseUnaryOp.h"
#include "src/SparseCore/SparseCwiseBinaryOp.h"
#include "src/SparseCore/SparseTranspose.h"
#include "src/SparseCore/SparseBlock.h"
#include "src/SparseCore/SparseDot.h"
#include "src/SparseCore/SparseRedux.h"
#include "src/SparseCore/SparseView.h"
#include "src/SparseCore/SparseDiagonalProduct.h"
#include "src/SparseCore/ConservativeSparseSparseProduct.h"
#include "src/SparseCore/SparseSparseProductWithPruning.h"
#include "src/SparseCore/SparseProduct.h"
#include "src/SparseCore/SparseDenseProduct.h"
#include "src/SparseCore/SparseSelfAdjointView.h"
#include "src/SparseCore/SparseTriangularView.h"
#include "src/SparseCore/TriangularSolver.h"
#include "src/SparseCore/SparsePermutation.h"
#include "src/SparseCore/SparseFuzzy.h"
#include "src/SparseCore/SparseSolverBase.h"
// IWYU pragma: end_exports
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_SPARSECORE_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_SPARSELU_MODULE_H
#define EIGEN_SPARSELU_MODULE_H
#include "SparseCore"
/**
* \defgroup SparseLU_Module SparseLU module
* This module defines a supernodal factorization of general sparse matrices.
* The code is fully optimized for supernode-panel updates with specialized kernels.
* Please, see the documentation of the SparseLU class for more details.
*/
// Ordering interface
#include "OrderingMethods"
#include "src/Core/util/DisableStupidWarnings.h"
// IWYU pragma: begin_exports
#include "src/SparseLU/SparseLU_Structs.h"
#include "src/SparseLU/SparseLU_SupernodalMatrix.h"
#include "src/SparseLU/SparseLUImpl.h"
#include "src/SparseCore/SparseColEtree.h"
#include "src/SparseLU/SparseLU_Memory.h"
#include "src/SparseLU/SparseLU_heap_relax_snode.h"
#include "src/SparseLU/SparseLU_relax_snode.h"
#include "src/SparseLU/SparseLU_pivotL.h"
#include "src/SparseLU/SparseLU_panel_dfs.h"
#include "src/SparseLU/SparseLU_kernel_bmod.h"
#include "src/SparseLU/SparseLU_panel_bmod.h"
#include "src/SparseLU/SparseLU_column_dfs.h"
#include "src/SparseLU/SparseLU_column_bmod.h"
#include "src/SparseLU/SparseLU_copy_to_ucol.h"
#include "src/SparseLU/SparseLU_pruneL.h"
#include "src/SparseLU/SparseLU_Utils.h"
#include "src/SparseLU/SparseLU.h"
// IWYU pragma: end_exports
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_SPARSELU_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_SPARSEQR_MODULE_H
#define EIGEN_SPARSEQR_MODULE_H
#include "SparseCore"
#include "OrderingMethods"
#include "src/Core/util/DisableStupidWarnings.h"
/** \defgroup SparseQR_Module SparseQR module
* \brief Provides QR decomposition for sparse matrices
*
* This module provides a simplicial version of the left-looking Sparse QR decomposition.
* The columns of the input matrix should be reordered to limit the fill-in during the
* decomposition. Built-in methods (COLAMD, AMD) or external methods (METIS) can be used to this end.
* See the \link OrderingMethods_Module OrderingMethods\endlink module for the list
* of built-in and external ordering methods.
*
* \code
* #include <Eigen/SparseQR>
* \endcode
*
*
*/
// IWYU pragma: begin_exports
#include "src/SparseCore/SparseColEtree.h"
#include "src/SparseQR/SparseQR.h"
// IWYU pragma: end_exports
#include "src/Core/util/ReenableStupidWarnings.h"
#endif

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_STDDEQUE_MODULE_H
#define EIGEN_STDDEQUE_MODULE_H
#include "Core"
#include <deque>
#if EIGEN_COMP_MSVC && EIGEN_OS_WIN64 && \
(EIGEN_MAX_STATIC_ALIGN_BYTES <= 16) /* MSVC auto aligns up to 16 bytes in 64 bit builds */
#define EIGEN_DEFINE_STL_DEQUE_SPECIALIZATION(...)
#else
// IWYU pragma: begin_exports
#include "src/StlSupport/StdDeque.h"
// IWYU pragma: end_exports
#endif
#endif // EIGEN_STDDEQUE_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_STDLIST_MODULE_H
#define EIGEN_STDLIST_MODULE_H
#include "Core"
#include <list>
#if EIGEN_COMP_MSVC && EIGEN_OS_WIN64 && \
(EIGEN_MAX_STATIC_ALIGN_BYTES <= 16) /* MSVC auto aligns up to 16 bytes in 64 bit builds */
#define EIGEN_DEFINE_STL_LIST_SPECIALIZATION(...)
#else
// IWYU pragma: begin_exports
#include "src/StlSupport/StdList.h"
// IWYU pragma: end_exports
#endif
#endif // EIGEN_STDLIST_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_STDVECTOR_MODULE_H
#define EIGEN_STDVECTOR_MODULE_H
#include "Core"
#include <vector>
#if EIGEN_COMP_MSVC && EIGEN_OS_WIN64 && \
(EIGEN_MAX_STATIC_ALIGN_BYTES <= 16) /* MSVC auto aligns up to 16 bytes in 64 bit builds */
#define EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION(...)
#else
// IWYU pragma: begin_exports
#include "src/StlSupport/StdVector.h"
// IWYU pragma: end_exports
#endif
#endif // EIGEN_STDVECTOR_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_SUPERLUSUPPORT_MODULE_H
#define EIGEN_SUPERLUSUPPORT_MODULE_H
#include "SparseCore"
#include "src/Core/util/DisableStupidWarnings.h"
#ifdef EMPTY
#define EIGEN_EMPTY_WAS_ALREADY_DEFINED
#endif
typedef int int_t;
#include <slu_Cnames.h>
#include <supermatrix.h>
#include <slu_util.h>
// slu_util.h defines a preprocessor token named EMPTY which is really polluting,
// so we remove it in favor of a SUPERLU_EMPTY token.
// If EMPTY was already defined then we don't undef it.
#if defined(EIGEN_EMPTY_WAS_ALREADY_DEFINED)
#undef EIGEN_EMPTY_WAS_ALREADY_DEFINED
#elif defined(EMPTY)
#undef EMPTY
#endif
#define SUPERLU_EMPTY (-1)
namespace Eigen {
struct SluMatrix;
}
/** \ingroup Support_modules
* \defgroup SuperLUSupport_Module SuperLUSupport module
*
* This module provides an interface to the <a href="http://crd-legacy.lbl.gov/~xiaoye/SuperLU/">SuperLU</a> library.
* It provides the following factorization class:
* - class SuperLU: a supernodal sequential LU factorization.
* - class SuperILU: a supernodal sequential incomplete LU factorization (to be used as a preconditioner for iterative
* methods).
*
* \warning This wrapper requires at least versions 4.0 of SuperLU. The 3.x versions are not supported.
*
* \warning When including this module, you have to use SUPERLU_EMPTY instead of EMPTY which is no longer defined
* because it is too polluting.
*
* \code
* #include <Eigen/SuperLUSupport>
* \endcode
*
* In order to use this module, the superlu headers must be accessible from the include paths, and your binary must be
* linked to the superlu library and its dependencies. The dependencies depend on how superlu has been compiled. For a
* cmake based project, you can use our FindSuperLU.cmake module to help you in this task.
*
*/
// IWYU pragma: begin_exports
#include "src/SuperLUSupport/SuperLUSupport.h"
// IWYU pragma: end_exports
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_SUPERLUSUPPORT_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_THREADPOOL_MODULE_H
#define EIGEN_THREADPOOL_MODULE_H
#include "Core"
#include "src/Core/util/DisableStupidWarnings.h"
/** \defgroup ThreadPool_Module ThreadPool Module
*
* This module provides 2 threadpool implementations
* - a simple reference implementation
* - a faster non blocking implementation
*
* \code
* #include <Eigen/ThreadPool>
* \endcode
*/
#include <cstddef>
#include <cstring>
#include <time.h>
#include <vector>
#include <atomic>
#include <condition_variable>
#include <deque>
#include <mutex>
#include <thread>
#include <functional>
#include <memory>
#include <utility>
// There are non-parenthesized calls to "max" in the <unordered_map> header,
// which trigger a check in test/main.h causing compilation to fail.
// We work around the check here by removing the check for max in
// the case where we have to emulate thread_local.
#ifdef max
#undef max
#endif
#include <unordered_map>
#include "src/Core/util/Meta.h"
#include "src/Core/util/MaxSizeVector.h"
#ifndef EIGEN_MUTEX
#define EIGEN_MUTEX std::mutex
#endif
#ifndef EIGEN_MUTEX_LOCK
#define EIGEN_MUTEX_LOCK std::unique_lock<std::mutex>
#endif
#ifndef EIGEN_CONDVAR
#define EIGEN_CONDVAR std::condition_variable
#endif
// IWYU pragma: begin_exports
#include "src/ThreadPool/ThreadLocal.h"
#include "src/ThreadPool/ThreadYield.h"
#include "src/ThreadPool/ThreadCancel.h"
#include "src/ThreadPool/EventCount.h"
#include "src/ThreadPool/RunQueue.h"
#include "src/ThreadPool/ThreadPoolInterface.h"
#include "src/ThreadPool/ThreadEnvironment.h"
#include "src/ThreadPool/Barrier.h"
#include "src/ThreadPool/NonBlockingThreadPool.h"
#include "src/ThreadPool/CoreThreadPoolDevice.h"
#include "src/ThreadPool/ForkJoin.h"
// IWYU pragma: end_exports
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_CXX11_THREADPOOL_MODULE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_UMFPACKSUPPORT_MODULE_H
#define EIGEN_UMFPACKSUPPORT_MODULE_H
#include "SparseCore"
#include "src/Core/util/DisableStupidWarnings.h"
extern "C" {
#include <umfpack.h>
}
/** \ingroup Support_modules
* \defgroup UmfPackSupport_Module UmfPackSupport module
*
* This module provides an interface to the UmfPack library which is part of the <a
* href="http://www.suitesparse.com">suitesparse</a> package. It provides the following factorization class:
* - class UmfPackLU: a multifrontal sequential LU factorization.
*
* \code
* #include <Eigen/UmfPackSupport>
* \endcode
*
* In order to use this module, the umfpack headers must be accessible from the include paths, and your binary must be
* linked to the umfpack library and its dependencies. The dependencies depend on how umfpack has been compiled. For a
* cmake based project, you can use our FindUmfPack.cmake module to help you in this task.
*
*/
// IWYU pragma: begin_exports
#include "src/UmfPackSupport/UmfPackSupport.h"
// IWYU pragma: endexports
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_UMFPACKSUPPORT_MODULE_H

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#ifndef EIGEN_VERSION_H
#define EIGEN_VERSION_H
// The "WORLD" version will forever remain "3" for the "Eigen3" library.
#define EIGEN_WORLD_VERSION 3
// As of Eigen3 5.0.0, we have moved to Semantic Versioning (semver.org).
#define EIGEN_MAJOR_VERSION 5
#define EIGEN_MINOR_VERSION 0
#define EIGEN_PATCH_VERSION 0
#define EIGEN_PRERELEASE_VERSION "dev"
#define EIGEN_BUILD_VERSION "master"
#define EIGEN_VERSION_STRING "5.0.0-dev+master"
#endif // EIGEN_VERSION_H

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#ifndef EIGEN_ACCELERATESUPPORT_H
#define EIGEN_ACCELERATESUPPORT_H
#include <Accelerate/Accelerate.h>
#include <Eigen/Sparse>
namespace Eigen {
template <typename MatrixType_, int UpLo_, SparseFactorization_t Solver_, bool EnforceSquare_>
class AccelerateImpl;
/** \ingroup AccelerateSupport_Module
* \typedef AccelerateLLT
* \brief A direct Cholesky (LLT) factorization and solver based on Accelerate
*
* \warning Only single and double precision real scalar types are supported by Accelerate
*
* \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
* \tparam UpLo_ additional information about the matrix structure. Default is Lower.
*
* \sa \ref TutorialSparseSolverConcept, class AccelerateLLT
*/
template <typename MatrixType, int UpLo = Lower>
using AccelerateLLT = AccelerateImpl<MatrixType, UpLo | Symmetric, SparseFactorizationCholesky, true>;
/** \ingroup AccelerateSupport_Module
* \typedef AccelerateLDLT
* \brief The default Cholesky (LDLT) factorization and solver based on Accelerate
*
* \warning Only single and double precision real scalar types are supported by Accelerate
*
* \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
* \tparam UpLo_ additional information about the matrix structure. Default is Lower.
*
* \sa \ref TutorialSparseSolverConcept, class AccelerateLDLT
*/
template <typename MatrixType, int UpLo = Lower>
using AccelerateLDLT = AccelerateImpl<MatrixType, UpLo | Symmetric, SparseFactorizationLDLT, true>;
/** \ingroup AccelerateSupport_Module
* \typedef AccelerateLDLTUnpivoted
* \brief A direct Cholesky-like LDL^T factorization and solver based on Accelerate with only 1x1 pivots and no pivoting
*
* \warning Only single and double precision real scalar types are supported by Accelerate
*
* \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
* \tparam UpLo_ additional information about the matrix structure. Default is Lower.
*
* \sa \ref TutorialSparseSolverConcept, class AccelerateLDLTUnpivoted
*/
template <typename MatrixType, int UpLo = Lower>
using AccelerateLDLTUnpivoted = AccelerateImpl<MatrixType, UpLo | Symmetric, SparseFactorizationLDLTUnpivoted, true>;
/** \ingroup AccelerateSupport_Module
* \typedef AccelerateLDLTSBK
* \brief A direct Cholesky (LDLT) factorization and solver based on Accelerate with Supernode Bunch-Kaufman and static
* pivoting
*
* \warning Only single and double precision real scalar types are supported by Accelerate
*
* \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
* \tparam UpLo_ additional information about the matrix structure. Default is Lower.
*
* \sa \ref TutorialSparseSolverConcept, class AccelerateLDLTSBK
*/
template <typename MatrixType, int UpLo = Lower>
using AccelerateLDLTSBK = AccelerateImpl<MatrixType, UpLo | Symmetric, SparseFactorizationLDLTSBK, true>;
/** \ingroup AccelerateSupport_Module
* \typedef AccelerateLDLTTPP
* \brief A direct Cholesky (LDLT) factorization and solver based on Accelerate with full threshold partial pivoting
*
* \warning Only single and double precision real scalar types are supported by Accelerate
*
* \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
* \tparam UpLo_ additional information about the matrix structure. Default is Lower.
*
* \sa \ref TutorialSparseSolverConcept, class AccelerateLDLTTPP
*/
template <typename MatrixType, int UpLo = Lower>
using AccelerateLDLTTPP = AccelerateImpl<MatrixType, UpLo | Symmetric, SparseFactorizationLDLTTPP, true>;
/** \ingroup AccelerateSupport_Module
* \typedef AccelerateQR
* \brief A QR factorization and solver based on Accelerate
*
* \warning Only single and double precision real scalar types are supported by Accelerate
*
* \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
*
* \sa \ref TutorialSparseSolverConcept, class AccelerateQR
*/
template <typename MatrixType>
using AccelerateQR = AccelerateImpl<MatrixType, 0, SparseFactorizationQR, false>;
/** \ingroup AccelerateSupport_Module
* \typedef AccelerateCholeskyAtA
* \brief A QR factorization and solver based on Accelerate without storing Q (equivalent to A^TA = R^T R)
*
* \warning Only single and double precision real scalar types are supported by Accelerate
*
* \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
*
* \sa \ref TutorialSparseSolverConcept, class AccelerateCholeskyAtA
*/
template <typename MatrixType>
using AccelerateCholeskyAtA = AccelerateImpl<MatrixType, 0, SparseFactorizationCholeskyAtA, false>;
namespace internal {
template <typename T>
struct AccelFactorizationDeleter {
void operator()(T* sym) {
if (sym) {
SparseCleanup(*sym);
delete sym;
sym = nullptr;
}
}
};
template <typename DenseVecT, typename DenseMatT, typename SparseMatT, typename NumFactT>
struct SparseTypesTraitBase {
typedef DenseVecT AccelDenseVector;
typedef DenseMatT AccelDenseMatrix;
typedef SparseMatT AccelSparseMatrix;
typedef SparseOpaqueSymbolicFactorization SymbolicFactorization;
typedef NumFactT NumericFactorization;
typedef AccelFactorizationDeleter<SymbolicFactorization> SymbolicFactorizationDeleter;
typedef AccelFactorizationDeleter<NumericFactorization> NumericFactorizationDeleter;
};
template <typename Scalar>
struct SparseTypesTrait {};
template <>
struct SparseTypesTrait<double> : SparseTypesTraitBase<DenseVector_Double, DenseMatrix_Double, SparseMatrix_Double,
SparseOpaqueFactorization_Double> {};
template <>
struct SparseTypesTrait<float>
: SparseTypesTraitBase<DenseVector_Float, DenseMatrix_Float, SparseMatrix_Float, SparseOpaqueFactorization_Float> {
};
} // end namespace internal
template <typename MatrixType_, int UpLo_, SparseFactorization_t Solver_, bool EnforceSquare_>
class AccelerateImpl : public SparseSolverBase<AccelerateImpl<MatrixType_, UpLo_, Solver_, EnforceSquare_> > {
protected:
using Base = SparseSolverBase<AccelerateImpl>;
using Base::derived;
using Base::m_isInitialized;
public:
using Base::_solve_impl;
typedef MatrixType_ MatrixType;
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::StorageIndex StorageIndex;
enum { ColsAtCompileTime = Dynamic, MaxColsAtCompileTime = Dynamic };
enum { UpLo = UpLo_ };
using AccelDenseVector = typename internal::SparseTypesTrait<Scalar>::AccelDenseVector;
using AccelDenseMatrix = typename internal::SparseTypesTrait<Scalar>::AccelDenseMatrix;
using AccelSparseMatrix = typename internal::SparseTypesTrait<Scalar>::AccelSparseMatrix;
using SymbolicFactorization = typename internal::SparseTypesTrait<Scalar>::SymbolicFactorization;
using NumericFactorization = typename internal::SparseTypesTrait<Scalar>::NumericFactorization;
using SymbolicFactorizationDeleter = typename internal::SparseTypesTrait<Scalar>::SymbolicFactorizationDeleter;
using NumericFactorizationDeleter = typename internal::SparseTypesTrait<Scalar>::NumericFactorizationDeleter;
AccelerateImpl() {
m_isInitialized = false;
auto check_flag_set = [](int value, int flag) { return ((value & flag) == flag); };
if (check_flag_set(UpLo_, Symmetric)) {
m_sparseKind = SparseSymmetric;
m_triType = (UpLo_ & Lower) ? SparseLowerTriangle : SparseUpperTriangle;
} else if (check_flag_set(UpLo_, UnitLower)) {
m_sparseKind = SparseUnitTriangular;
m_triType = SparseLowerTriangle;
} else if (check_flag_set(UpLo_, UnitUpper)) {
m_sparseKind = SparseUnitTriangular;
m_triType = SparseUpperTriangle;
} else if (check_flag_set(UpLo_, StrictlyLower)) {
m_sparseKind = SparseTriangular;
m_triType = SparseLowerTriangle;
} else if (check_flag_set(UpLo_, StrictlyUpper)) {
m_sparseKind = SparseTriangular;
m_triType = SparseUpperTriangle;
} else if (check_flag_set(UpLo_, Lower)) {
m_sparseKind = SparseTriangular;
m_triType = SparseLowerTriangle;
} else if (check_flag_set(UpLo_, Upper)) {
m_sparseKind = SparseTriangular;
m_triType = SparseUpperTriangle;
} else {
m_sparseKind = SparseOrdinary;
m_triType = (UpLo_ & Lower) ? SparseLowerTriangle : SparseUpperTriangle;
}
m_order = SparseOrderDefault;
}
explicit AccelerateImpl(const MatrixType& matrix) : AccelerateImpl() { compute(matrix); }
~AccelerateImpl() {}
inline Index cols() const { return m_nCols; }
inline Index rows() const { return m_nRows; }
ComputationInfo info() const {
eigen_assert(m_isInitialized && "Decomposition is not initialized.");
return m_info;
}
void analyzePattern(const MatrixType& matrix);
void factorize(const MatrixType& matrix);
void compute(const MatrixType& matrix);
template <typename Rhs, typename Dest>
void _solve_impl(const MatrixBase<Rhs>& b, MatrixBase<Dest>& dest) const;
/** Sets the ordering algorithm to use. */
void setOrder(SparseOrder_t order) { m_order = order; }
private:
template <typename T>
void buildAccelSparseMatrix(const SparseMatrix<T>& a, AccelSparseMatrix& A, std::vector<long>& columnStarts) {
const Index nColumnsStarts = a.cols() + 1;
columnStarts.resize(nColumnsStarts);
for (Index i = 0; i < nColumnsStarts; i++) columnStarts[i] = a.outerIndexPtr()[i];
SparseAttributes_t attributes{};
attributes.transpose = false;
attributes.triangle = m_triType;
attributes.kind = m_sparseKind;
SparseMatrixStructure structure{};
structure.attributes = attributes;
structure.rowCount = static_cast<int>(a.rows());
structure.columnCount = static_cast<int>(a.cols());
structure.blockSize = 1;
structure.columnStarts = columnStarts.data();
structure.rowIndices = const_cast<int*>(a.innerIndexPtr());
A.structure = structure;
A.data = const_cast<T*>(a.valuePtr());
}
void doAnalysis(AccelSparseMatrix& A) {
m_numericFactorization.reset(nullptr);
SparseSymbolicFactorOptions opts{};
opts.control = SparseDefaultControl;
opts.orderMethod = m_order;
opts.order = nullptr;
opts.ignoreRowsAndColumns = nullptr;
opts.malloc = malloc;
opts.free = free;
opts.reportError = nullptr;
m_symbolicFactorization.reset(new SymbolicFactorization(SparseFactor(Solver_, A.structure, opts)));
SparseStatus_t status = m_symbolicFactorization->status;
updateInfoStatus(status);
if (status != SparseStatusOK) m_symbolicFactorization.reset(nullptr);
}
void doFactorization(AccelSparseMatrix& A) {
SparseStatus_t status = SparseStatusReleased;
if (m_symbolicFactorization) {
m_numericFactorization.reset(new NumericFactorization(SparseFactor(*m_symbolicFactorization, A)));
status = m_numericFactorization->status;
if (status != SparseStatusOK) m_numericFactorization.reset(nullptr);
}
updateInfoStatus(status);
}
protected:
void updateInfoStatus(SparseStatus_t status) const {
switch (status) {
case SparseStatusOK:
m_info = Success;
break;
case SparseFactorizationFailed:
case SparseMatrixIsSingular:
m_info = NumericalIssue;
break;
case SparseInternalError:
case SparseParameterError:
case SparseStatusReleased:
default:
m_info = InvalidInput;
break;
}
}
mutable ComputationInfo m_info;
Index m_nRows, m_nCols;
std::unique_ptr<SymbolicFactorization, SymbolicFactorizationDeleter> m_symbolicFactorization;
std::unique_ptr<NumericFactorization, NumericFactorizationDeleter> m_numericFactorization;
SparseKind_t m_sparseKind;
SparseTriangle_t m_triType;
SparseOrder_t m_order;
};
/** Computes the symbolic and numeric decomposition of matrix \a a */
template <typename MatrixType_, int UpLo_, SparseFactorization_t Solver_, bool EnforceSquare_>
void AccelerateImpl<MatrixType_, UpLo_, Solver_, EnforceSquare_>::compute(const MatrixType& a) {
if (EnforceSquare_) eigen_assert(a.rows() == a.cols());
m_nRows = a.rows();
m_nCols = a.cols();
AccelSparseMatrix A{};
std::vector<long> columnStarts;
buildAccelSparseMatrix(a, A, columnStarts);
doAnalysis(A);
if (m_symbolicFactorization) doFactorization(A);
m_isInitialized = true;
}
/** Performs a symbolic decomposition on the sparsity pattern of matrix \a a.
*
* This function is particularly useful when solving for several problems having the same structure.
*
* \sa factorize()
*/
template <typename MatrixType_, int UpLo_, SparseFactorization_t Solver_, bool EnforceSquare_>
void AccelerateImpl<MatrixType_, UpLo_, Solver_, EnforceSquare_>::analyzePattern(const MatrixType& a) {
if (EnforceSquare_) eigen_assert(a.rows() == a.cols());
m_nRows = a.rows();
m_nCols = a.cols();
AccelSparseMatrix A{};
std::vector<long> columnStarts;
buildAccelSparseMatrix(a, A, columnStarts);
doAnalysis(A);
m_isInitialized = true;
}
/** Performs a numeric decomposition of matrix \a a.
*
* The given matrix must have the same sparsity pattern as the matrix on which the symbolic decomposition has been
* performed.
*
* \sa analyzePattern()
*/
template <typename MatrixType_, int UpLo_, SparseFactorization_t Solver_, bool EnforceSquare_>
void AccelerateImpl<MatrixType_, UpLo_, Solver_, EnforceSquare_>::factorize(const MatrixType& a) {
eigen_assert(m_symbolicFactorization && "You must first call analyzePattern()");
eigen_assert(m_nRows == a.rows() && m_nCols == a.cols());
if (EnforceSquare_) eigen_assert(a.rows() == a.cols());
AccelSparseMatrix A{};
std::vector<long> columnStarts;
buildAccelSparseMatrix(a, A, columnStarts);
doFactorization(A);
}
template <typename MatrixType_, int UpLo_, SparseFactorization_t Solver_, bool EnforceSquare_>
template <typename Rhs, typename Dest>
void AccelerateImpl<MatrixType_, UpLo_, Solver_, EnforceSquare_>::_solve_impl(const MatrixBase<Rhs>& b,
MatrixBase<Dest>& x) const {
if (!m_numericFactorization) {
m_info = InvalidInput;
return;
}
eigen_assert(m_nRows == b.rows());
eigen_assert(((b.cols() == 1) || b.outerStride() == b.rows()));
SparseStatus_t status = SparseStatusOK;
Scalar* b_ptr = const_cast<Scalar*>(b.derived().data());
Scalar* x_ptr = const_cast<Scalar*>(x.derived().data());
AccelDenseMatrix xmat{};
xmat.attributes = SparseAttributes_t();
xmat.columnCount = static_cast<int>(x.cols());
xmat.rowCount = static_cast<int>(x.rows());
xmat.columnStride = xmat.rowCount;
xmat.data = x_ptr;
AccelDenseMatrix bmat{};
bmat.attributes = SparseAttributes_t();
bmat.columnCount = static_cast<int>(b.cols());
bmat.rowCount = static_cast<int>(b.rows());
bmat.columnStride = bmat.rowCount;
bmat.data = b_ptr;
SparseSolve(*m_numericFactorization, bmat, xmat);
updateInfoStatus(status);
}
} // end namespace Eigen
#endif // EIGEN_ACCELERATESUPPORT_H

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#ifndef EIGEN_ACCELERATESUPPORT_MODULE_H
#error "Please include Eigen/AccelerateSupport instead of including headers inside the src directory directly."
#endif

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#ifndef EIGEN_CHOLESKY_MODULE_H
#error "Please include Eigen/Cholesky instead of including headers inside the src directory directly."
#endif

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2009 Keir Mierle <mierle@gmail.com>
// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2011 Timothy E. Holy <tim.holy@gmail.com >
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_LDLT_H
#define EIGEN_LDLT_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
template <typename MatrixType_, int UpLo_>
struct traits<LDLT<MatrixType_, UpLo_> > : traits<MatrixType_> {
typedef MatrixXpr XprKind;
typedef SolverStorage StorageKind;
typedef int StorageIndex;
enum { Flags = 0 };
};
template <typename MatrixType, int UpLo>
struct LDLT_Traits;
// PositiveSemiDef means positive semi-definite and non-zero; same for NegativeSemiDef
enum SignMatrix { PositiveSemiDef, NegativeSemiDef, ZeroSign, Indefinite };
} // namespace internal
/** \ingroup Cholesky_Module
*
* \class LDLT
*
* \brief Robust Cholesky decomposition of a matrix with pivoting
*
* \tparam MatrixType_ the type of the matrix of which to compute the LDL^T Cholesky decomposition
* \tparam UpLo_ the triangular part that will be used for the decomposition: Lower (default) or Upper.
* The other triangular part won't be read.
*
* Perform a robust Cholesky decomposition of a positive semidefinite or negative semidefinite
* matrix \f$ A \f$ such that \f$ A = P^TLDL^*P \f$, where P is a permutation matrix, L
* is lower triangular with a unit diagonal and D is a diagonal matrix.
*
* The decomposition uses pivoting to ensure stability, so that D will have
* zeros in the bottom right rank(A) - n submatrix. Avoiding the square root
* on D also stabilizes the computation.
*
* Remember that Cholesky decompositions are not rank-revealing. Also, do not use a Cholesky
* decomposition to determine whether a system of equations has a solution.
*
* This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism.
*
* \sa MatrixBase::ldlt(), SelfAdjointView::ldlt(), class LLT
*/
template <typename MatrixType_, int UpLo_>
class LDLT : public SolverBase<LDLT<MatrixType_, UpLo_> > {
public:
typedef MatrixType_ MatrixType;
typedef SolverBase<LDLT> Base;
friend class SolverBase<LDLT>;
EIGEN_GENERIC_PUBLIC_INTERFACE(LDLT)
enum {
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
UpLo = UpLo_
};
typedef Matrix<Scalar, RowsAtCompileTime, 1, 0, MaxRowsAtCompileTime, 1> TmpMatrixType;
typedef Transpositions<RowsAtCompileTime, MaxRowsAtCompileTime> TranspositionType;
typedef PermutationMatrix<RowsAtCompileTime, MaxRowsAtCompileTime> PermutationType;
typedef internal::LDLT_Traits<MatrixType, UpLo> Traits;
/** \brief Default Constructor.
*
* The default constructor is useful in cases in which the user intends to
* perform decompositions via LDLT::compute(const MatrixType&).
*/
LDLT() : m_matrix(), m_transpositions(), m_sign(internal::ZeroSign), m_isInitialized(false) {}
/** \brief Default Constructor with memory preallocation
*
* Like the default constructor but with preallocation of the internal data
* according to the specified problem \a size.
* \sa LDLT()
*/
explicit LDLT(Index size)
: m_matrix(size, size),
m_transpositions(size),
m_temporary(size),
m_sign(internal::ZeroSign),
m_isInitialized(false) {}
/** \brief Constructor with decomposition
*
* This calculates the decomposition for the input \a matrix.
*
* \sa LDLT(Index size)
*/
template <typename InputType>
explicit LDLT(const EigenBase<InputType>& matrix)
: m_matrix(matrix.rows(), matrix.cols()),
m_transpositions(matrix.rows()),
m_temporary(matrix.rows()),
m_sign(internal::ZeroSign),
m_isInitialized(false) {
compute(matrix.derived());
}
/** \brief Constructs a LDLT factorization from a given matrix
*
* This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when \c
* MatrixType is a Eigen::Ref.
*
* \sa LDLT(const EigenBase&)
*/
template <typename InputType>
explicit LDLT(EigenBase<InputType>& matrix)
: m_matrix(matrix.derived()),
m_transpositions(matrix.rows()),
m_temporary(matrix.rows()),
m_sign(internal::ZeroSign),
m_isInitialized(false) {
compute(matrix.derived());
}
/** Clear any existing decomposition
* \sa rankUpdate(w,sigma)
*/
void setZero() { m_isInitialized = false; }
/** \returns a view of the upper triangular matrix U */
inline typename Traits::MatrixU matrixU() const {
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return Traits::getU(m_matrix);
}
/** \returns a view of the lower triangular matrix L */
inline typename Traits::MatrixL matrixL() const {
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return Traits::getL(m_matrix);
}
/** \returns the permutation matrix P as a transposition sequence.
*/
inline const TranspositionType& transpositionsP() const {
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return m_transpositions;
}
/** \returns the coefficients of the diagonal matrix D */
inline Diagonal<const MatrixType> vectorD() const {
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return m_matrix.diagonal();
}
/** \returns true if the matrix is positive (semidefinite) */
inline bool isPositive() const {
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return m_sign == internal::PositiveSemiDef || m_sign == internal::ZeroSign;
}
/** \returns true if the matrix is negative (semidefinite) */
inline bool isNegative(void) const {
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return m_sign == internal::NegativeSemiDef || m_sign == internal::ZeroSign;
}
#ifdef EIGEN_PARSED_BY_DOXYGEN
/** \returns a solution x of \f$ A x = b \f$ using the current decomposition of A.
*
* This function also supports in-place solves using the syntax <tt>x = decompositionObject.solve(x)</tt> .
*
* \note_about_checking_solutions
*
* More precisely, this method solves \f$ A x = b \f$ using the decomposition \f$ A = P^T L D L^* P \f$
* by solving the systems \f$ P^T y_1 = b \f$, \f$ L y_2 = y_1 \f$, \f$ D y_3 = y_2 \f$,
* \f$ L^* y_4 = y_3 \f$ and \f$ P x = y_4 \f$ in succession. If the matrix \f$ A \f$ is singular, then
* \f$ D \f$ will also be singular (all the other matrices are invertible). In that case, the
* least-square solution of \f$ D y_3 = y_2 \f$ is computed. This does not mean that this function
* computes the least-square solution of \f$ A x = b \f$ if \f$ A \f$ is singular.
*
* \sa MatrixBase::ldlt(), SelfAdjointView::ldlt()
*/
template <typename Rhs>
inline const Solve<LDLT, Rhs> solve(const MatrixBase<Rhs>& b) const;
#endif
template <typename Derived>
bool solveInPlace(MatrixBase<Derived>& bAndX) const;
template <typename InputType>
LDLT& compute(const EigenBase<InputType>& matrix);
/** \returns an estimate of the reciprocal condition number of the matrix of
* which \c *this is the LDLT decomposition.
*/
RealScalar rcond() const {
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return internal::rcond_estimate_helper(m_l1_norm, *this);
}
template <typename Derived>
LDLT& rankUpdate(const MatrixBase<Derived>& w, const RealScalar& alpha = 1);
/** \returns the internal LDLT decomposition matrix
*
* TODO: document the storage layout
*/
inline const MatrixType& matrixLDLT() const {
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return m_matrix;
}
MatrixType reconstructedMatrix() const;
/** \returns the adjoint of \c *this, that is, a const reference to the decomposition itself as the underlying matrix
* is self-adjoint.
*
* This method is provided for compatibility with other matrix decompositions, thus enabling generic code such as:
* \code x = decomposition.adjoint().solve(b) \endcode
*/
const LDLT& adjoint() const { return *this; }
EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return m_matrix.rows(); }
EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return m_matrix.cols(); }
/** \brief Reports whether previous computation was successful.
*
* \returns \c Success if computation was successful,
* \c NumericalIssue if the factorization failed because of a zero pivot.
*/
ComputationInfo info() const {
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return m_info;
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
template <typename RhsType, typename DstType>
void _solve_impl(const RhsType& rhs, DstType& dst) const;
template <bool Conjugate, typename RhsType, typename DstType>
void _solve_impl_transposed(const RhsType& rhs, DstType& dst) const;
#endif
protected:
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
/** \internal
* Used to compute and store the Cholesky decomposition A = L D L^* = U^* D U.
* The strict upper part is used during the decomposition, the strict lower
* part correspond to the coefficients of L (its diagonal is equal to 1 and
* is not stored), and the diagonal entries correspond to D.
*/
MatrixType m_matrix;
RealScalar m_l1_norm;
TranspositionType m_transpositions;
TmpMatrixType m_temporary;
internal::SignMatrix m_sign;
bool m_isInitialized;
ComputationInfo m_info;
};
namespace internal {
template <int UpLo>
struct ldlt_inplace;
template <>
struct ldlt_inplace<Lower> {
template <typename MatrixType, typename TranspositionType, typename Workspace>
static bool unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp, SignMatrix& sign) {
using std::abs;
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
typedef typename TranspositionType::StorageIndex IndexType;
eigen_assert(mat.rows() == mat.cols());
const Index size = mat.rows();
bool found_zero_pivot = false;
bool ret = true;
if (size <= 1) {
transpositions.setIdentity();
if (size == 0)
sign = ZeroSign;
else if (numext::real(mat.coeff(0, 0)) > static_cast<RealScalar>(0))
sign = PositiveSemiDef;
else if (numext::real(mat.coeff(0, 0)) < static_cast<RealScalar>(0))
sign = NegativeSemiDef;
else
sign = ZeroSign;
return true;
}
for (Index k = 0; k < size; ++k) {
// Find largest diagonal element
Index index_of_biggest_in_corner;
mat.diagonal().tail(size - k).cwiseAbs().maxCoeff(&index_of_biggest_in_corner);
index_of_biggest_in_corner += k;
transpositions.coeffRef(k) = IndexType(index_of_biggest_in_corner);
if (k != index_of_biggest_in_corner) {
// apply the transposition while taking care to consider only
// the lower triangular part
Index s = size - index_of_biggest_in_corner - 1; // trailing size after the biggest element
mat.row(k).head(k).swap(mat.row(index_of_biggest_in_corner).head(k));
mat.col(k).tail(s).swap(mat.col(index_of_biggest_in_corner).tail(s));
std::swap(mat.coeffRef(k, k), mat.coeffRef(index_of_biggest_in_corner, index_of_biggest_in_corner));
for (Index i = k + 1; i < index_of_biggest_in_corner; ++i) {
Scalar tmp = mat.coeffRef(i, k);
mat.coeffRef(i, k) = numext::conj(mat.coeffRef(index_of_biggest_in_corner, i));
mat.coeffRef(index_of_biggest_in_corner, i) = numext::conj(tmp);
}
if (NumTraits<Scalar>::IsComplex)
mat.coeffRef(index_of_biggest_in_corner, k) = numext::conj(mat.coeff(index_of_biggest_in_corner, k));
}
// partition the matrix:
// A00 | - | -
// lu = A10 | A11 | -
// A20 | A21 | A22
Index rs = size - k - 1;
Block<MatrixType, Dynamic, 1> A21(mat, k + 1, k, rs, 1);
Block<MatrixType, 1, Dynamic> A10(mat, k, 0, 1, k);
Block<MatrixType, Dynamic, Dynamic> A20(mat, k + 1, 0, rs, k);
if (k > 0) {
temp.head(k) = mat.diagonal().real().head(k).asDiagonal() * A10.adjoint();
mat.coeffRef(k, k) -= (A10 * temp.head(k)).value();
if (rs > 0) A21.noalias() -= A20 * temp.head(k);
}
// In some previous versions of Eigen (e.g., 3.2.1), the scaling was omitted if the pivot
// was smaller than the cutoff value. However, since LDLT is not rank-revealing
// we should only make sure that we do not introduce INF or NaN values.
// Remark that LAPACK also uses 0 as the cutoff value.
RealScalar realAkk = numext::real(mat.coeffRef(k, k));
bool pivot_is_valid = (abs(realAkk) > RealScalar(0));
if (k == 0 && !pivot_is_valid) {
// The entire diagonal is zero, there is nothing more to do
// except filling the transpositions, and checking whether the matrix is zero.
sign = ZeroSign;
for (Index j = 0; j < size; ++j) {
transpositions.coeffRef(j) = IndexType(j);
ret = ret && (mat.col(j).tail(size - j - 1).array() == Scalar(0)).all();
}
return ret;
}
if ((rs > 0) && pivot_is_valid)
A21 /= realAkk;
else if (rs > 0)
ret = ret && (A21.array() == Scalar(0)).all();
if (found_zero_pivot && pivot_is_valid)
ret = false; // factorization failed
else if (!pivot_is_valid)
found_zero_pivot = true;
if (sign == PositiveSemiDef) {
if (realAkk < static_cast<RealScalar>(0)) sign = Indefinite;
} else if (sign == NegativeSemiDef) {
if (realAkk > static_cast<RealScalar>(0)) sign = Indefinite;
} else if (sign == ZeroSign) {
if (realAkk > static_cast<RealScalar>(0))
sign = PositiveSemiDef;
else if (realAkk < static_cast<RealScalar>(0))
sign = NegativeSemiDef;
}
}
return ret;
}
// Reference for the algorithm: Davis and Hager, "Multiple Rank
// Modifications of a Sparse Cholesky Factorization" (Algorithm 1)
// Trivial rearrangements of their computations (Timothy E. Holy)
// allow their algorithm to work for rank-1 updates even if the
// original matrix is not of full rank.
// Here only rank-1 updates are implemented, to reduce the
// requirement for intermediate storage and improve accuracy
template <typename MatrixType, typename WDerived>
static bool updateInPlace(MatrixType& mat, MatrixBase<WDerived>& w,
const typename MatrixType::RealScalar& sigma = 1) {
using numext::isfinite;
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
const Index size = mat.rows();
eigen_assert(mat.cols() == size && w.size() == size);
RealScalar alpha = 1;
// Apply the update
for (Index j = 0; j < size; j++) {
// Check for termination due to an original decomposition of low-rank
if (!(isfinite)(alpha)) break;
// Update the diagonal terms
RealScalar dj = numext::real(mat.coeff(j, j));
Scalar wj = w.coeff(j);
RealScalar swj2 = sigma * numext::abs2(wj);
RealScalar gamma = dj * alpha + swj2;
mat.coeffRef(j, j) += swj2 / alpha;
alpha += swj2 / dj;
// Update the terms of L
Index rs = size - j - 1;
w.tail(rs) -= wj * mat.col(j).tail(rs);
if (!numext::is_exactly_zero(gamma)) mat.col(j).tail(rs) += (sigma * numext::conj(wj) / gamma) * w.tail(rs);
}
return true;
}
template <typename MatrixType, typename TranspositionType, typename Workspace, typename WType>
static bool update(MatrixType& mat, const TranspositionType& transpositions, Workspace& tmp, const WType& w,
const typename MatrixType::RealScalar& sigma = 1) {
// Apply the permutation to the input w
tmp = transpositions * w;
return ldlt_inplace<Lower>::updateInPlace(mat, tmp, sigma);
}
};
template <>
struct ldlt_inplace<Upper> {
template <typename MatrixType, typename TranspositionType, typename Workspace>
static EIGEN_STRONG_INLINE bool unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp,
SignMatrix& sign) {
Transpose<MatrixType> matt(mat);
return ldlt_inplace<Lower>::unblocked(matt, transpositions, temp, sign);
}
template <typename MatrixType, typename TranspositionType, typename Workspace, typename WType>
static EIGEN_STRONG_INLINE bool update(MatrixType& mat, TranspositionType& transpositions, Workspace& tmp, WType& w,
const typename MatrixType::RealScalar& sigma = 1) {
Transpose<MatrixType> matt(mat);
return ldlt_inplace<Lower>::update(matt, transpositions, tmp, w.conjugate(), sigma);
}
};
template <typename MatrixType>
struct LDLT_Traits<MatrixType, Lower> {
typedef const TriangularView<const MatrixType, UnitLower> MatrixL;
typedef const TriangularView<const typename MatrixType::AdjointReturnType, UnitUpper> MatrixU;
static inline MatrixL getL(const MatrixType& m) { return MatrixL(m); }
static inline MatrixU getU(const MatrixType& m) { return MatrixU(m.adjoint()); }
};
template <typename MatrixType>
struct LDLT_Traits<MatrixType, Upper> {
typedef const TriangularView<const typename MatrixType::AdjointReturnType, UnitLower> MatrixL;
typedef const TriangularView<const MatrixType, UnitUpper> MatrixU;
static inline MatrixL getL(const MatrixType& m) { return MatrixL(m.adjoint()); }
static inline MatrixU getU(const MatrixType& m) { return MatrixU(m); }
};
} // end namespace internal
/** Compute / recompute the LDLT decomposition A = L D L^* = U^* D U of \a matrix
*/
template <typename MatrixType, int UpLo_>
template <typename InputType>
LDLT<MatrixType, UpLo_>& LDLT<MatrixType, UpLo_>::compute(const EigenBase<InputType>& a) {
eigen_assert(a.rows() == a.cols());
const Index size = a.rows();
m_matrix = a.derived();
// Compute matrix L1 norm = max abs column sum.
m_l1_norm = RealScalar(0);
// TODO move this code to SelfAdjointView
for (Index col = 0; col < size; ++col) {
RealScalar abs_col_sum;
if (UpLo_ == Lower)
abs_col_sum =
m_matrix.col(col).tail(size - col).template lpNorm<1>() + m_matrix.row(col).head(col).template lpNorm<1>();
else
abs_col_sum =
m_matrix.col(col).head(col).template lpNorm<1>() + m_matrix.row(col).tail(size - col).template lpNorm<1>();
if (abs_col_sum > m_l1_norm) m_l1_norm = abs_col_sum;
}
m_transpositions.resize(size);
m_isInitialized = false;
m_temporary.resize(size);
m_sign = internal::ZeroSign;
m_info = internal::ldlt_inplace<UpLo>::unblocked(m_matrix, m_transpositions, m_temporary, m_sign) ? Success
: NumericalIssue;
m_isInitialized = true;
return *this;
}
/** Update the LDLT decomposition: given A = L D L^T, efficiently compute the decomposition of A + sigma w w^T.
* \param w a vector to be incorporated into the decomposition.
* \param sigma a scalar, +1 for updates and -1 for "downdates," which correspond to removing previously-added column
* vectors. Optional; default value is +1. \sa setZero()
*/
template <typename MatrixType, int UpLo_>
template <typename Derived>
LDLT<MatrixType, UpLo_>& LDLT<MatrixType, UpLo_>::rankUpdate(
const MatrixBase<Derived>& w, const typename LDLT<MatrixType, UpLo_>::RealScalar& sigma) {
typedef typename TranspositionType::StorageIndex IndexType;
const Index size = w.rows();
if (m_isInitialized) {
eigen_assert(m_matrix.rows() == size);
} else {
m_matrix.resize(size, size);
m_matrix.setZero();
m_transpositions.resize(size);
for (Index i = 0; i < size; i++) m_transpositions.coeffRef(i) = IndexType(i);
m_temporary.resize(size);
m_sign = sigma >= 0 ? internal::PositiveSemiDef : internal::NegativeSemiDef;
m_isInitialized = true;
}
internal::ldlt_inplace<UpLo>::update(m_matrix, m_transpositions, m_temporary, w, sigma);
return *this;
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
template <typename MatrixType_, int UpLo_>
template <typename RhsType, typename DstType>
void LDLT<MatrixType_, UpLo_>::_solve_impl(const RhsType& rhs, DstType& dst) const {
_solve_impl_transposed<true>(rhs, dst);
}
template <typename MatrixType_, int UpLo_>
template <bool Conjugate, typename RhsType, typename DstType>
void LDLT<MatrixType_, UpLo_>::_solve_impl_transposed(const RhsType& rhs, DstType& dst) const {
// dst = P b
dst = m_transpositions * rhs;
// dst = L^-1 (P b)
// dst = L^-*T (P b)
matrixL().template conjugateIf<!Conjugate>().solveInPlace(dst);
// dst = D^-* (L^-1 P b)
// dst = D^-1 (L^-*T P b)
// more precisely, use pseudo-inverse of D (see bug 241)
using std::abs;
const typename Diagonal<const MatrixType>::RealReturnType vecD(vectorD());
// In some previous versions, tolerance was set to the max of 1/highest (or rather numeric_limits::min())
// and the maximal diagonal entry * epsilon as motivated by LAPACK's xGELSS:
// RealScalar tolerance = numext::maxi(vecD.array().abs().maxCoeff() * NumTraits<RealScalar>::epsilon(),RealScalar(1)
// / NumTraits<RealScalar>::highest()); However, LDLT is not rank revealing, and so adjusting the tolerance wrt to the
// highest diagonal element is not well justified and leads to numerical issues in some cases. Moreover, Lapack's
// xSYTRS routines use 0 for the tolerance. Using numeric_limits::min() gives us more robustness to denormals.
RealScalar tolerance = (std::numeric_limits<RealScalar>::min)();
for (Index i = 0; i < vecD.size(); ++i) {
if (abs(vecD(i)) > tolerance)
dst.row(i) /= vecD(i);
else
dst.row(i).setZero();
}
// dst = L^-* (D^-* L^-1 P b)
// dst = L^-T (D^-1 L^-*T P b)
matrixL().transpose().template conjugateIf<Conjugate>().solveInPlace(dst);
// dst = P^T (L^-* D^-* L^-1 P b) = A^-1 b
// dst = P^-T (L^-T D^-1 L^-*T P b) = A^-1 b
dst = m_transpositions.transpose() * dst;
}
#endif
/** \internal use x = ldlt_object.solve(x);
*
* This is the \em in-place version of solve().
*
* \param bAndX represents both the right-hand side matrix b and result x.
*
* \returns true always! If you need to check for existence of solutions, use another decomposition like LU, QR, or SVD.
*
* This version avoids a copy when the right hand side matrix b is not
* needed anymore.
*
* \sa LDLT::solve(), MatrixBase::ldlt()
*/
template <typename MatrixType, int UpLo_>
template <typename Derived>
bool LDLT<MatrixType, UpLo_>::solveInPlace(MatrixBase<Derived>& bAndX) const {
eigen_assert(m_isInitialized && "LDLT is not initialized.");
eigen_assert(m_matrix.rows() == bAndX.rows());
bAndX = this->solve(bAndX);
return true;
}
/** \returns the matrix represented by the decomposition,
* i.e., it returns the product: P^T L D L^* P.
* This function is provided for debug purpose. */
template <typename MatrixType, int UpLo_>
MatrixType LDLT<MatrixType, UpLo_>::reconstructedMatrix() const {
eigen_assert(m_isInitialized && "LDLT is not initialized.");
const Index size = m_matrix.rows();
MatrixType res(size, size);
// P
res.setIdentity();
res = transpositionsP() * res;
// L^* P
res = matrixU() * res;
// D(L^*P)
res = vectorD().real().asDiagonal() * res;
// L(DL^*P)
res = matrixL() * res;
// P^T (LDL^*P)
res = transpositionsP().transpose() * res;
return res;
}
/** \cholesky_module
* \returns the Cholesky decomposition with full pivoting without square root of \c *this
* \sa MatrixBase::ldlt()
*/
template <typename MatrixType, unsigned int UpLo>
inline const LDLT<typename SelfAdjointView<MatrixType, UpLo>::PlainObject, UpLo>
SelfAdjointView<MatrixType, UpLo>::ldlt() const {
return LDLT<PlainObject, UpLo>(m_matrix);
}
/** \cholesky_module
* \returns the Cholesky decomposition with full pivoting without square root of \c *this
* \sa SelfAdjointView::ldlt()
*/
template <typename Derived>
inline const LDLT<typename MatrixBase<Derived>::PlainObject> MatrixBase<Derived>::ldlt() const {
return LDLT<PlainObject>(derived());
}
} // end namespace Eigen
#endif // EIGEN_LDLT_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_LLT_H
#define EIGEN_LLT_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
template <typename MatrixType_, int UpLo_>
struct traits<LLT<MatrixType_, UpLo_> > : traits<MatrixType_> {
typedef MatrixXpr XprKind;
typedef SolverStorage StorageKind;
typedef int StorageIndex;
enum { Flags = 0 };
};
template <typename MatrixType, int UpLo>
struct LLT_Traits;
} // namespace internal
/** \ingroup Cholesky_Module
*
* \class LLT
*
* \brief Standard Cholesky decomposition (LL^T) of a matrix and associated features
*
* \tparam MatrixType_ the type of the matrix of which we are computing the LL^T Cholesky decomposition
* \tparam UpLo_ the triangular part that will be used for the decomposition: Lower (default) or Upper.
* The other triangular part won't be read.
*
* This class performs a LL^T Cholesky decomposition of a symmetric, positive definite
* matrix A such that A = LL^* = U^*U, where L is lower triangular.
*
* While the Cholesky decomposition is particularly useful to solve selfadjoint problems like D^*D x = b,
* for that purpose, we recommend the Cholesky decomposition without square root which is more stable
* and even faster. Nevertheless, this standard Cholesky decomposition remains useful in many other
* situations like generalised eigen problems with hermitian matrices.
*
* Remember that Cholesky decompositions are not rank-revealing. This LLT decomposition is only stable on positive
* definite matrices, use LDLT instead for the semidefinite case. Also, do not use a Cholesky decomposition to determine
* whether a system of equations has a solution.
*
* Example: \include LLT_example.cpp
* Output: \verbinclude LLT_example.out
*
* \b Performance: for best performance, it is recommended to use a column-major storage format
* with the Lower triangular part (the default), or, equivalently, a row-major storage format
* with the Upper triangular part. Otherwise, you might get a 20% slowdown for the full factorization
* step, and rank-updates can be up to 3 times slower.
*
* This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism.
*
* Note that during the decomposition, only the lower (or upper, as defined by UpLo_) triangular part of A is
* considered. Therefore, the strict lower part does not have to store correct values.
*
* \sa MatrixBase::llt(), SelfAdjointView::llt(), class LDLT
*/
template <typename MatrixType_, int UpLo_>
class LLT : public SolverBase<LLT<MatrixType_, UpLo_> > {
public:
typedef MatrixType_ MatrixType;
typedef SolverBase<LLT> Base;
friend class SolverBase<LLT>;
EIGEN_GENERIC_PUBLIC_INTERFACE(LLT)
enum { MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime };
enum { PacketSize = internal::packet_traits<Scalar>::size, AlignmentMask = int(PacketSize) - 1, UpLo = UpLo_ };
typedef internal::LLT_Traits<MatrixType, UpLo> Traits;
/**
* \brief Default Constructor.
*
* The default constructor is useful in cases in which the user intends to
* perform decompositions via LLT::compute(const MatrixType&).
*/
LLT() : m_matrix(), m_isInitialized(false) {}
/** \brief Default Constructor with memory preallocation
*
* Like the default constructor but with preallocation of the internal data
* according to the specified problem \a size.
* \sa LLT()
*/
explicit LLT(Index size) : m_matrix(size, size), m_isInitialized(false) {}
template <typename InputType>
explicit LLT(const EigenBase<InputType>& matrix) : m_matrix(matrix.rows(), matrix.cols()), m_isInitialized(false) {
compute(matrix.derived());
}
/** \brief Constructs a LLT factorization from a given matrix
*
* This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when
* \c MatrixType is a Eigen::Ref.
*
* \sa LLT(const EigenBase&)
*/
template <typename InputType>
explicit LLT(EigenBase<InputType>& matrix) : m_matrix(matrix.derived()), m_isInitialized(false) {
compute(matrix.derived());
}
/** \returns a view of the upper triangular matrix U */
inline typename Traits::MatrixU matrixU() const {
eigen_assert(m_isInitialized && "LLT is not initialized.");
return Traits::getU(m_matrix);
}
/** \returns a view of the lower triangular matrix L */
inline typename Traits::MatrixL matrixL() const {
eigen_assert(m_isInitialized && "LLT is not initialized.");
return Traits::getL(m_matrix);
}
#ifdef EIGEN_PARSED_BY_DOXYGEN
/** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
*
* Since this LLT class assumes anyway that the matrix A is invertible, the solution
* theoretically exists and is unique regardless of b.
*
* Example: \include LLT_solve.cpp
* Output: \verbinclude LLT_solve.out
*
* \sa solveInPlace(), MatrixBase::llt(), SelfAdjointView::llt()
*/
template <typename Rhs>
inline const Solve<LLT, Rhs> solve(const MatrixBase<Rhs>& b) const;
#endif
template <typename Derived>
void solveInPlace(const MatrixBase<Derived>& bAndX) const;
template <typename InputType>
LLT& compute(const EigenBase<InputType>& matrix);
/** \returns an estimate of the reciprocal condition number of the matrix of
* which \c *this is the Cholesky decomposition.
*/
RealScalar rcond() const {
eigen_assert(m_isInitialized && "LLT is not initialized.");
eigen_assert(m_info == Success && "LLT failed because matrix appears to be negative");
return internal::rcond_estimate_helper(m_l1_norm, *this);
}
/** \returns the LLT decomposition matrix
*
* TODO: document the storage layout
*/
inline const MatrixType& matrixLLT() const {
eigen_assert(m_isInitialized && "LLT is not initialized.");
return m_matrix;
}
MatrixType reconstructedMatrix() const;
/** \brief Reports whether previous computation was successful.
*
* \returns \c Success if computation was successful,
* \c NumericalIssue if the matrix.appears not to be positive definite.
*/
ComputationInfo info() const {
eigen_assert(m_isInitialized && "LLT is not initialized.");
return m_info;
}
/** \returns the adjoint of \c *this, that is, a const reference to the decomposition itself as the underlying matrix
* is self-adjoint.
*
* This method is provided for compatibility with other matrix decompositions, thus enabling generic code such as:
* \code x = decomposition.adjoint().solve(b) \endcode
*/
const LLT& adjoint() const noexcept { return *this; }
constexpr Index rows() const noexcept { return m_matrix.rows(); }
constexpr Index cols() const noexcept { return m_matrix.cols(); }
template <typename VectorType>
LLT& rankUpdate(const VectorType& vec, const RealScalar& sigma = 1);
#ifndef EIGEN_PARSED_BY_DOXYGEN
template <typename RhsType, typename DstType>
void _solve_impl(const RhsType& rhs, DstType& dst) const;
template <bool Conjugate, typename RhsType, typename DstType>
void _solve_impl_transposed(const RhsType& rhs, DstType& dst) const;
#endif
protected:
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
/** \internal
* Used to compute and store L
* The strict upper part is not used and even not initialized.
*/
MatrixType m_matrix;
RealScalar m_l1_norm;
bool m_isInitialized;
ComputationInfo m_info;
};
namespace internal {
template <typename Scalar, int UpLo>
struct llt_inplace;
template <typename MatrixType, typename VectorType>
static Index llt_rank_update_lower(MatrixType& mat, const VectorType& vec,
const typename MatrixType::RealScalar& sigma) {
using std::sqrt;
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
typedef typename MatrixType::ColXpr ColXpr;
typedef internal::remove_all_t<ColXpr> ColXprCleaned;
typedef typename ColXprCleaned::SegmentReturnType ColXprSegment;
typedef Matrix<Scalar, Dynamic, 1> TempVectorType;
typedef typename TempVectorType::SegmentReturnType TempVecSegment;
Index n = mat.cols();
eigen_assert(mat.rows() == n && vec.size() == n);
TempVectorType temp;
if (sigma > 0) {
// This version is based on Givens rotations.
// It is faster than the other one below, but only works for updates,
// i.e., for sigma > 0
temp = sqrt(sigma) * vec;
for (Index i = 0; i < n; ++i) {
JacobiRotation<Scalar> g;
g.makeGivens(mat(i, i), -temp(i), &mat(i, i));
Index rs = n - i - 1;
if (rs > 0) {
ColXprSegment x(mat.col(i).tail(rs));
TempVecSegment y(temp.tail(rs));
apply_rotation_in_the_plane(x, y, g);
}
}
} else {
temp = vec;
RealScalar beta = 1;
for (Index j = 0; j < n; ++j) {
RealScalar Ljj = numext::real(mat.coeff(j, j));
RealScalar dj = numext::abs2(Ljj);
Scalar wj = temp.coeff(j);
RealScalar swj2 = sigma * numext::abs2(wj);
RealScalar gamma = dj * beta + swj2;
RealScalar x = dj + swj2 / beta;
if (x <= RealScalar(0)) return j;
RealScalar nLjj = sqrt(x);
mat.coeffRef(j, j) = nLjj;
beta += swj2 / dj;
// Update the terms of L
Index rs = n - j - 1;
if (rs) {
temp.tail(rs) -= (wj / Ljj) * mat.col(j).tail(rs);
if (!numext::is_exactly_zero(gamma))
mat.col(j).tail(rs) =
(nLjj / Ljj) * mat.col(j).tail(rs) + (nLjj * sigma * numext::conj(wj) / gamma) * temp.tail(rs);
}
}
}
return -1;
}
template <typename Scalar>
struct llt_inplace<Scalar, Lower> {
typedef typename NumTraits<Scalar>::Real RealScalar;
template <typename MatrixType>
static Index unblocked(MatrixType& mat) {
using std::sqrt;
eigen_assert(mat.rows() == mat.cols());
const Index size = mat.rows();
for (Index k = 0; k < size; ++k) {
Index rs = size - k - 1; // remaining size
Block<MatrixType, Dynamic, 1> A21(mat, k + 1, k, rs, 1);
Block<MatrixType, 1, Dynamic> A10(mat, k, 0, 1, k);
Block<MatrixType, Dynamic, Dynamic> A20(mat, k + 1, 0, rs, k);
RealScalar x = numext::real(mat.coeff(k, k));
if (k > 0) x -= A10.squaredNorm();
if (x <= RealScalar(0)) return k;
mat.coeffRef(k, k) = x = sqrt(x);
if (k > 0 && rs > 0) A21.noalias() -= A20 * A10.adjoint();
if (rs > 0) A21 /= x;
}
return -1;
}
template <typename MatrixType>
static Index blocked(MatrixType& m) {
eigen_assert(m.rows() == m.cols());
Index size = m.rows();
if (size < 32) return unblocked(m);
Index blockSize = size / 8;
blockSize = (blockSize / 16) * 16;
blockSize = (std::min)((std::max)(blockSize, Index(8)), Index(128));
for (Index k = 0; k < size; k += blockSize) {
// partition the matrix:
// A00 | - | -
// lu = A10 | A11 | -
// A20 | A21 | A22
Index bs = (std::min)(blockSize, size - k);
Index rs = size - k - bs;
Block<MatrixType, Dynamic, Dynamic> A11(m, k, k, bs, bs);
Block<MatrixType, Dynamic, Dynamic> A21(m, k + bs, k, rs, bs);
Block<MatrixType, Dynamic, Dynamic> A22(m, k + bs, k + bs, rs, rs);
Index ret;
if ((ret = unblocked(A11)) >= 0) return k + ret;
if (rs > 0) A11.adjoint().template triangularView<Upper>().template solveInPlace<OnTheRight>(A21);
if (rs > 0)
A22.template selfadjointView<Lower>().rankUpdate(A21,
typename NumTraits<RealScalar>::Literal(-1)); // bottleneck
}
return -1;
}
template <typename MatrixType, typename VectorType>
static Index rankUpdate(MatrixType& mat, const VectorType& vec, const RealScalar& sigma) {
return Eigen::internal::llt_rank_update_lower(mat, vec, sigma);
}
};
template <typename Scalar>
struct llt_inplace<Scalar, Upper> {
typedef typename NumTraits<Scalar>::Real RealScalar;
template <typename MatrixType>
static EIGEN_STRONG_INLINE Index unblocked(MatrixType& mat) {
Transpose<MatrixType> matt(mat);
return llt_inplace<Scalar, Lower>::unblocked(matt);
}
template <typename MatrixType>
static EIGEN_STRONG_INLINE Index blocked(MatrixType& mat) {
Transpose<MatrixType> matt(mat);
return llt_inplace<Scalar, Lower>::blocked(matt);
}
template <typename MatrixType, typename VectorType>
static Index rankUpdate(MatrixType& mat, const VectorType& vec, const RealScalar& sigma) {
Transpose<MatrixType> matt(mat);
return llt_inplace<Scalar, Lower>::rankUpdate(matt, vec.conjugate(), sigma);
}
};
template <typename MatrixType>
struct LLT_Traits<MatrixType, Lower> {
typedef const TriangularView<const MatrixType, Lower> MatrixL;
typedef const TriangularView<const typename MatrixType::AdjointReturnType, Upper> MatrixU;
static inline MatrixL getL(const MatrixType& m) { return MatrixL(m); }
static inline MatrixU getU(const MatrixType& m) { return MatrixU(m.adjoint()); }
static bool inplace_decomposition(MatrixType& m) {
return llt_inplace<typename MatrixType::Scalar, Lower>::blocked(m) == -1;
}
};
template <typename MatrixType>
struct LLT_Traits<MatrixType, Upper> {
typedef const TriangularView<const typename MatrixType::AdjointReturnType, Lower> MatrixL;
typedef const TriangularView<const MatrixType, Upper> MatrixU;
static inline MatrixL getL(const MatrixType& m) { return MatrixL(m.adjoint()); }
static inline MatrixU getU(const MatrixType& m) { return MatrixU(m); }
static bool inplace_decomposition(MatrixType& m) {
return llt_inplace<typename MatrixType::Scalar, Upper>::blocked(m) == -1;
}
};
} // end namespace internal
/** Computes / recomputes the Cholesky decomposition A = LL^* = U^*U of \a matrix
*
* \returns a reference to *this
*
* Example: \include TutorialLinAlgComputeTwice.cpp
* Output: \verbinclude TutorialLinAlgComputeTwice.out
*/
template <typename MatrixType, int UpLo_>
template <typename InputType>
LLT<MatrixType, UpLo_>& LLT<MatrixType, UpLo_>::compute(const EigenBase<InputType>& a) {
eigen_assert(a.rows() == a.cols());
const Index size = a.rows();
m_matrix.resize(size, size);
if (!internal::is_same_dense(m_matrix, a.derived())) m_matrix = a.derived();
// Compute matrix L1 norm = max abs column sum.
m_l1_norm = RealScalar(0);
// TODO move this code to SelfAdjointView
for (Index col = 0; col < size; ++col) {
RealScalar abs_col_sum;
if (UpLo_ == Lower)
abs_col_sum =
m_matrix.col(col).tail(size - col).template lpNorm<1>() + m_matrix.row(col).head(col).template lpNorm<1>();
else
abs_col_sum =
m_matrix.col(col).head(col).template lpNorm<1>() + m_matrix.row(col).tail(size - col).template lpNorm<1>();
if (abs_col_sum > m_l1_norm) m_l1_norm = abs_col_sum;
}
m_isInitialized = true;
bool ok = Traits::inplace_decomposition(m_matrix);
m_info = ok ? Success : NumericalIssue;
return *this;
}
/** Performs a rank one update (or dowdate) of the current decomposition.
* If A = LL^* before the rank one update,
* then after it we have LL^* = A + sigma * v v^* where \a v must be a vector
* of same dimension.
*/
template <typename MatrixType_, int UpLo_>
template <typename VectorType>
LLT<MatrixType_, UpLo_>& LLT<MatrixType_, UpLo_>::rankUpdate(const VectorType& v, const RealScalar& sigma) {
EIGEN_STATIC_ASSERT_VECTOR_ONLY(VectorType);
eigen_assert(v.size() == m_matrix.cols());
eigen_assert(m_isInitialized);
if (internal::llt_inplace<typename MatrixType::Scalar, UpLo>::rankUpdate(m_matrix, v, sigma) >= 0)
m_info = NumericalIssue;
else
m_info = Success;
return *this;
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
template <typename MatrixType_, int UpLo_>
template <typename RhsType, typename DstType>
void LLT<MatrixType_, UpLo_>::_solve_impl(const RhsType& rhs, DstType& dst) const {
_solve_impl_transposed<true>(rhs, dst);
}
template <typename MatrixType_, int UpLo_>
template <bool Conjugate, typename RhsType, typename DstType>
void LLT<MatrixType_, UpLo_>::_solve_impl_transposed(const RhsType& rhs, DstType& dst) const {
dst = rhs;
matrixL().template conjugateIf<!Conjugate>().solveInPlace(dst);
matrixU().template conjugateIf<!Conjugate>().solveInPlace(dst);
}
#endif
/** \internal use x = llt_object.solve(x);
*
* This is the \em in-place version of solve().
*
* \param bAndX represents both the right-hand side matrix b and result x.
*
* This version avoids a copy when the right hand side matrix b is not needed anymore.
*
* \warning The parameter is only marked 'const' to make the C++ compiler accept a temporary expression here.
* This function will const_cast it, so constness isn't honored here.
*
* \sa LLT::solve(), MatrixBase::llt()
*/
template <typename MatrixType, int UpLo_>
template <typename Derived>
void LLT<MatrixType, UpLo_>::solveInPlace(const MatrixBase<Derived>& bAndX) const {
eigen_assert(m_isInitialized && "LLT is not initialized.");
eigen_assert(m_matrix.rows() == bAndX.rows());
matrixL().solveInPlace(bAndX);
matrixU().solveInPlace(bAndX);
}
/** \returns the matrix represented by the decomposition,
* i.e., it returns the product: L L^*.
* This function is provided for debug purpose. */
template <typename MatrixType, int UpLo_>
MatrixType LLT<MatrixType, UpLo_>::reconstructedMatrix() const {
eigen_assert(m_isInitialized && "LLT is not initialized.");
return matrixL() * matrixL().adjoint().toDenseMatrix();
}
/** \cholesky_module
* \returns the LLT decomposition of \c *this
* \sa SelfAdjointView::llt()
*/
template <typename Derived>
inline const LLT<typename MatrixBase<Derived>::PlainObject> MatrixBase<Derived>::llt() const {
return LLT<PlainObject>(derived());
}
/** \cholesky_module
* \returns the LLT decomposition of \c *this
* \sa SelfAdjointView::llt()
*/
template <typename MatrixType, unsigned int UpLo>
inline const LLT<typename SelfAdjointView<MatrixType, UpLo>::PlainObject, UpLo> SelfAdjointView<MatrixType, UpLo>::llt()
const {
return LLT<PlainObject, UpLo>(m_matrix);
}
} // end namespace Eigen
#endif // EIGEN_LLT_H

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/*
Copyright (c) 2011, Intel Corporation. All rights reserved.
Redistribution and use in source and binary forms, with or without modification,
are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright notice, this
list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation
and/or other materials provided with the distribution.
* Neither the name of Intel Corporation nor the names of its contributors may
be used to endorse or promote products derived from this software without
specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
********************************************************************************
* Content : Eigen bindings to LAPACKe
* LLt decomposition based on LAPACKE_?potrf function.
********************************************************************************
*/
#ifndef EIGEN_LLT_LAPACKE_H
#define EIGEN_LLT_LAPACKE_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
namespace lapacke_helpers {
// -------------------------------------------------------------------------------------------------------------------
// Dispatch for rank update handling upper and lower parts
// -------------------------------------------------------------------------------------------------------------------
template <UpLoType Mode>
struct rank_update {};
template <>
struct rank_update<Lower> {
template <typename MatrixType, typename VectorType>
static Index run(MatrixType &mat, const VectorType &vec, const typename MatrixType::RealScalar &sigma) {
return Eigen::internal::llt_rank_update_lower(mat, vec, sigma);
}
};
template <>
struct rank_update<Upper> {
template <typename MatrixType, typename VectorType>
static Index run(MatrixType &mat, const VectorType &vec, const typename MatrixType::RealScalar &sigma) {
Transpose<MatrixType> matt(mat);
return Eigen::internal::llt_rank_update_lower(matt, vec.conjugate(), sigma);
}
};
// -------------------------------------------------------------------------------------------------------------------
// Generic lapacke llt implementation that hands of to the dispatches
// -------------------------------------------------------------------------------------------------------------------
template <typename Scalar, UpLoType Mode>
struct lapacke_llt {
EIGEN_STATIC_ASSERT(((Mode == Lower) || (Mode == Upper)), MODE_MUST_BE_UPPER_OR_LOWER)
template <typename MatrixType>
static Index blocked(MatrixType &m) {
eigen_assert(m.rows() == m.cols());
if (m.rows() == 0) {
return -1;
}
/* Set up parameters for ?potrf */
lapack_int size = to_lapack(m.rows());
lapack_int matrix_order = lapack_storage_of(m);
constexpr char uplo = Mode == Upper ? 'U' : 'L';
Scalar *a = &(m.coeffRef(0, 0));
lapack_int lda = to_lapack(m.outerStride());
lapack_int info = potrf(matrix_order, uplo, size, to_lapack(a), lda);
info = (info == 0) ? -1 : info > 0 ? info - 1 : size;
return info;
}
template <typename MatrixType, typename VectorType>
static Index rankUpdate(MatrixType &mat, const VectorType &vec, const typename MatrixType::RealScalar &sigma) {
return rank_update<Mode>::run(mat, vec, sigma);
}
};
} // namespace lapacke_helpers
// end namespace lapacke_helpers
/*
* Here, we just put the generic implementation from lapacke_llt into a full specialization of the llt_inplace
* type. By being a full specialization, the versions defined here thus get precedence over the generic implementation
* in LLT.h for double, float and complex double, complex float types.
*/
#define EIGEN_LAPACKE_LLT(EIGTYPE) \
template <> \
struct llt_inplace<EIGTYPE, Lower> : public lapacke_helpers::lapacke_llt<EIGTYPE, Lower> {}; \
template <> \
struct llt_inplace<EIGTYPE, Upper> : public lapacke_helpers::lapacke_llt<EIGTYPE, Upper> {};
EIGEN_LAPACKE_LLT(double)
EIGEN_LAPACKE_LLT(float)
EIGEN_LAPACKE_LLT(std::complex<double>)
EIGEN_LAPACKE_LLT(std::complex<float>)
#undef EIGEN_LAPACKE_LLT
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_LLT_LAPACKE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_CHOLMODSUPPORT_H
#define EIGEN_CHOLMODSUPPORT_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
template <typename Scalar>
struct cholmod_configure_matrix;
template <>
struct cholmod_configure_matrix<double> {
template <typename CholmodType>
static void run(CholmodType& mat) {
mat.xtype = CHOLMOD_REAL;
mat.dtype = CHOLMOD_DOUBLE;
}
};
template <>
struct cholmod_configure_matrix<std::complex<double> > {
template <typename CholmodType>
static void run(CholmodType& mat) {
mat.xtype = CHOLMOD_COMPLEX;
mat.dtype = CHOLMOD_DOUBLE;
}
};
// Other scalar types are not yet supported by Cholmod
// template<> struct cholmod_configure_matrix<float> {
// template<typename CholmodType>
// static void run(CholmodType& mat) {
// mat.xtype = CHOLMOD_REAL;
// mat.dtype = CHOLMOD_SINGLE;
// }
// };
//
// template<> struct cholmod_configure_matrix<std::complex<float> > {
// template<typename CholmodType>
// static void run(CholmodType& mat) {
// mat.xtype = CHOLMOD_COMPLEX;
// mat.dtype = CHOLMOD_SINGLE;
// }
// };
} // namespace internal
/** Wraps the Eigen sparse matrix \a mat into a Cholmod sparse matrix object.
* Note that the data are shared.
*/
template <typename Scalar_, int Options_, typename StorageIndex_>
cholmod_sparse viewAsCholmod(Ref<SparseMatrix<Scalar_, Options_, StorageIndex_> > mat) {
cholmod_sparse res;
res.nzmax = mat.nonZeros();
res.nrow = mat.rows();
res.ncol = mat.cols();
res.p = mat.outerIndexPtr();
res.i = mat.innerIndexPtr();
res.x = mat.valuePtr();
res.z = 0;
res.sorted = 1;
if (mat.isCompressed()) {
res.packed = 1;
res.nz = 0;
} else {
res.packed = 0;
res.nz = mat.innerNonZeroPtr();
}
res.dtype = 0;
res.stype = -1;
if (internal::is_same<StorageIndex_, int>::value) {
res.itype = CHOLMOD_INT;
} else if (internal::is_same<StorageIndex_, SuiteSparse_long>::value) {
res.itype = CHOLMOD_LONG;
} else {
eigen_assert(false && "Index type not supported yet");
}
// setup res.xtype
internal::cholmod_configure_matrix<Scalar_>::run(res);
res.stype = 0;
return res;
}
template <typename Scalar_, int Options_, typename Index_>
const cholmod_sparse viewAsCholmod(const SparseMatrix<Scalar_, Options_, Index_>& mat) {
cholmod_sparse res = viewAsCholmod(Ref<SparseMatrix<Scalar_, Options_, Index_> >(mat.const_cast_derived()));
return res;
}
template <typename Scalar_, int Options_, typename Index_>
const cholmod_sparse viewAsCholmod(const SparseVector<Scalar_, Options_, Index_>& mat) {
cholmod_sparse res = viewAsCholmod(Ref<SparseMatrix<Scalar_, Options_, Index_> >(mat.const_cast_derived()));
return res;
}
/** Returns a view of the Eigen sparse matrix \a mat as Cholmod sparse matrix.
* The data are not copied but shared. */
template <typename Scalar_, int Options_, typename Index_, unsigned int UpLo>
cholmod_sparse viewAsCholmod(const SparseSelfAdjointView<const SparseMatrix<Scalar_, Options_, Index_>, UpLo>& mat) {
cholmod_sparse res = viewAsCholmod(Ref<SparseMatrix<Scalar_, Options_, Index_> >(mat.matrix().const_cast_derived()));
if (UpLo == Upper) res.stype = 1;
if (UpLo == Lower) res.stype = -1;
// swap stype for rowmajor matrices (only works for real matrices)
EIGEN_STATIC_ASSERT((Options_ & RowMajorBit) == 0 || NumTraits<Scalar_>::IsComplex == 0,
THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
if (Options_ & RowMajorBit) res.stype *= -1;
return res;
}
/** Returns a view of the Eigen \b dense matrix \a mat as Cholmod dense matrix.
* The data are not copied but shared. */
template <typename Derived>
cholmod_dense viewAsCholmod(MatrixBase<Derived>& mat) {
EIGEN_STATIC_ASSERT((internal::traits<Derived>::Flags & RowMajorBit) == 0,
THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
typedef typename Derived::Scalar Scalar;
cholmod_dense res;
res.nrow = mat.rows();
res.ncol = mat.cols();
res.nzmax = res.nrow * res.ncol;
res.d = Derived::IsVectorAtCompileTime ? mat.derived().size() : mat.derived().outerStride();
res.x = (void*)(mat.derived().data());
res.z = 0;
internal::cholmod_configure_matrix<Scalar>::run(res);
return res;
}
/** Returns a view of the Cholmod sparse matrix \a cm as an Eigen sparse matrix.
* The data are not copied but shared. */
template <typename Scalar, typename StorageIndex>
Map<const SparseMatrix<Scalar, ColMajor, StorageIndex> > viewAsEigen(cholmod_sparse& cm) {
return Map<const SparseMatrix<Scalar, ColMajor, StorageIndex> >(
cm.nrow, cm.ncol, static_cast<StorageIndex*>(cm.p)[cm.ncol], static_cast<StorageIndex*>(cm.p),
static_cast<StorageIndex*>(cm.i), static_cast<Scalar*>(cm.x));
}
/** Returns a view of the Cholmod sparse matrix factor \a cm as an Eigen sparse matrix.
* The data are not copied but shared. */
template <typename Scalar, typename StorageIndex>
Map<const SparseMatrix<Scalar, ColMajor, StorageIndex> > viewAsEigen(cholmod_factor& cm) {
return Map<const SparseMatrix<Scalar, ColMajor, StorageIndex> >(
cm.n, cm.n, static_cast<StorageIndex*>(cm.p)[cm.n], static_cast<StorageIndex*>(cm.p),
static_cast<StorageIndex*>(cm.i), static_cast<Scalar*>(cm.x));
}
namespace internal {
// template specializations for int and long that call the correct cholmod method
#define EIGEN_CHOLMOD_SPECIALIZE0(ret, name) \
template <typename StorageIndex_> \
inline ret cm_##name(cholmod_common& Common) { \
return cholmod_##name(&Common); \
} \
template <> \
inline ret cm_##name<SuiteSparse_long>(cholmod_common & Common) { \
return cholmod_l_##name(&Common); \
}
#define EIGEN_CHOLMOD_SPECIALIZE1(ret, name, t1, a1) \
template <typename StorageIndex_> \
inline ret cm_##name(t1& a1, cholmod_common& Common) { \
return cholmod_##name(&a1, &Common); \
} \
template <> \
inline ret cm_##name<SuiteSparse_long>(t1 & a1, cholmod_common & Common) { \
return cholmod_l_##name(&a1, &Common); \
}
EIGEN_CHOLMOD_SPECIALIZE0(int, start)
EIGEN_CHOLMOD_SPECIALIZE0(int, finish)
EIGEN_CHOLMOD_SPECIALIZE1(int, free_factor, cholmod_factor*, L)
EIGEN_CHOLMOD_SPECIALIZE1(int, free_dense, cholmod_dense*, X)
EIGEN_CHOLMOD_SPECIALIZE1(int, free_sparse, cholmod_sparse*, A)
EIGEN_CHOLMOD_SPECIALIZE1(cholmod_factor*, analyze, cholmod_sparse, A)
EIGEN_CHOLMOD_SPECIALIZE1(cholmod_sparse*, factor_to_sparse, cholmod_factor, L)
template <typename StorageIndex_>
inline cholmod_dense* cm_solve(int sys, cholmod_factor& L, cholmod_dense& B, cholmod_common& Common) {
return cholmod_solve(sys, &L, &B, &Common);
}
template <>
inline cholmod_dense* cm_solve<SuiteSparse_long>(int sys, cholmod_factor& L, cholmod_dense& B, cholmod_common& Common) {
return cholmod_l_solve(sys, &L, &B, &Common);
}
template <typename StorageIndex_>
inline cholmod_sparse* cm_spsolve(int sys, cholmod_factor& L, cholmod_sparse& B, cholmod_common& Common) {
return cholmod_spsolve(sys, &L, &B, &Common);
}
template <>
inline cholmod_sparse* cm_spsolve<SuiteSparse_long>(int sys, cholmod_factor& L, cholmod_sparse& B,
cholmod_common& Common) {
return cholmod_l_spsolve(sys, &L, &B, &Common);
}
template <typename StorageIndex_>
inline int cm_factorize_p(cholmod_sparse* A, double beta[2], StorageIndex_* fset, std::size_t fsize, cholmod_factor* L,
cholmod_common& Common) {
return cholmod_factorize_p(A, beta, fset, fsize, L, &Common);
}
template <>
inline int cm_factorize_p<SuiteSparse_long>(cholmod_sparse* A, double beta[2], SuiteSparse_long* fset,
std::size_t fsize, cholmod_factor* L, cholmod_common& Common) {
return cholmod_l_factorize_p(A, beta, fset, fsize, L, &Common);
}
#undef EIGEN_CHOLMOD_SPECIALIZE0
#undef EIGEN_CHOLMOD_SPECIALIZE1
} // namespace internal
enum CholmodMode { CholmodAuto, CholmodSimplicialLLt, CholmodSupernodalLLt, CholmodLDLt };
/** \ingroup CholmodSupport_Module
* \class CholmodBase
* \brief The base class for the direct Cholesky factorization of Cholmod
* \sa class CholmodSupernodalLLT, class CholmodSimplicialLDLT, class CholmodSimplicialLLT
*/
template <typename MatrixType_, int UpLo_, typename Derived>
class CholmodBase : public SparseSolverBase<Derived> {
protected:
typedef SparseSolverBase<Derived> Base;
using Base::derived;
using Base::m_isInitialized;
public:
typedef MatrixType_ MatrixType;
enum { UpLo = UpLo_ };
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
typedef MatrixType CholMatrixType;
typedef typename MatrixType::StorageIndex StorageIndex;
enum { ColsAtCompileTime = MatrixType::ColsAtCompileTime, MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime };
public:
CholmodBase() : m_cholmodFactor(0), m_info(Success), m_factorizationIsOk(false), m_analysisIsOk(false) {
EIGEN_STATIC_ASSERT((internal::is_same<double, RealScalar>::value), CHOLMOD_SUPPORTS_DOUBLE_PRECISION_ONLY);
m_shiftOffset[0] = m_shiftOffset[1] = 0.0;
internal::cm_start<StorageIndex>(m_cholmod);
}
explicit CholmodBase(const MatrixType& matrix)
: m_cholmodFactor(0), m_info(Success), m_factorizationIsOk(false), m_analysisIsOk(false) {
EIGEN_STATIC_ASSERT((internal::is_same<double, RealScalar>::value), CHOLMOD_SUPPORTS_DOUBLE_PRECISION_ONLY);
m_shiftOffset[0] = m_shiftOffset[1] = 0.0;
internal::cm_start<StorageIndex>(m_cholmod);
compute(matrix);
}
~CholmodBase() {
if (m_cholmodFactor) internal::cm_free_factor<StorageIndex>(m_cholmodFactor, m_cholmod);
internal::cm_finish<StorageIndex>(m_cholmod);
}
inline StorageIndex cols() const { return internal::convert_index<StorageIndex, Index>(m_cholmodFactor->n); }
inline StorageIndex rows() const { return internal::convert_index<StorageIndex, Index>(m_cholmodFactor->n); }
/** \brief Reports whether previous computation was successful.
*
* \returns \c Success if computation was successful,
* \c NumericalIssue if the matrix.appears to be negative.
*/
ComputationInfo info() const {
eigen_assert(m_isInitialized && "Decomposition is not initialized.");
return m_info;
}
/** Computes the sparse Cholesky decomposition of \a matrix */
Derived& compute(const MatrixType& matrix) {
analyzePattern(matrix);
factorize(matrix);
return derived();
}
/** Performs a symbolic decomposition on the sparsity pattern of \a matrix.
*
* This function is particularly useful when solving for several problems having the same structure.
*
* \sa factorize()
*/
void analyzePattern(const MatrixType& matrix) {
if (m_cholmodFactor) {
internal::cm_free_factor<StorageIndex>(m_cholmodFactor, m_cholmod);
m_cholmodFactor = 0;
}
cholmod_sparse A = viewAsCholmod(matrix.template selfadjointView<UpLo>());
m_cholmodFactor = internal::cm_analyze<StorageIndex>(A, m_cholmod);
this->m_isInitialized = true;
this->m_info = Success;
m_analysisIsOk = true;
m_factorizationIsOk = false;
}
/** Performs a numeric decomposition of \a matrix
*
* The given matrix must have the same sparsity pattern as the matrix on which the symbolic decomposition has been
* performed.
*
* \sa analyzePattern()
*/
void factorize(const MatrixType& matrix) {
eigen_assert(m_analysisIsOk && "You must first call analyzePattern()");
cholmod_sparse A = viewAsCholmod(matrix.template selfadjointView<UpLo>());
internal::cm_factorize_p<StorageIndex>(&A, m_shiftOffset, 0, 0, m_cholmodFactor, m_cholmod);
// If the factorization failed, either the input matrix was zero (so m_cholmodFactor == nullptr), or minor is the
// column at which it failed. On success minor == n.
this->m_info =
(m_cholmodFactor != nullptr && m_cholmodFactor->minor == m_cholmodFactor->n ? Success : NumericalIssue);
m_factorizationIsOk = true;
}
/** Returns a reference to the Cholmod's configuration structure to get a full control over the performed operations.
* See the Cholmod user guide for details. */
cholmod_common& cholmod() { return m_cholmod; }
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** \internal */
template <typename Rhs, typename Dest>
void _solve_impl(const MatrixBase<Rhs>& b, MatrixBase<Dest>& dest) const {
eigen_assert(m_factorizationIsOk &&
"The decomposition is not in a valid state for solving, you must first call either compute() or "
"symbolic()/numeric()");
const Index size = m_cholmodFactor->n;
EIGEN_UNUSED_VARIABLE(size);
eigen_assert(size == b.rows());
// Cholmod needs column-major storage without inner-stride, which corresponds to the default behavior of Ref.
Ref<const Matrix<typename Rhs::Scalar, Dynamic, Dynamic, ColMajor> > b_ref(b.derived());
cholmod_dense b_cd = viewAsCholmod(b_ref);
cholmod_dense* x_cd = internal::cm_solve<StorageIndex>(CHOLMOD_A, *m_cholmodFactor, b_cd, m_cholmod);
if (!x_cd) {
this->m_info = NumericalIssue;
return;
}
// TODO optimize this copy by swapping when possible (be careful with alignment, etc.)
// NOTE Actually, the copy can be avoided by calling cholmod_solve2 instead of cholmod_solve
dest = Matrix<Scalar, Dest::RowsAtCompileTime, Dest::ColsAtCompileTime>::Map(reinterpret_cast<Scalar*>(x_cd->x),
b.rows(), b.cols());
internal::cm_free_dense<StorageIndex>(x_cd, m_cholmod);
}
/** \internal */
template <typename RhsDerived, typename DestDerived>
void _solve_impl(const SparseMatrixBase<RhsDerived>& b, SparseMatrixBase<DestDerived>& dest) const {
eigen_assert(m_factorizationIsOk &&
"The decomposition is not in a valid state for solving, you must first call either compute() or "
"symbolic()/numeric()");
const Index size = m_cholmodFactor->n;
EIGEN_UNUSED_VARIABLE(size);
eigen_assert(size == b.rows());
// note: cs stands for Cholmod Sparse
Ref<SparseMatrix<typename RhsDerived::Scalar, ColMajor, typename RhsDerived::StorageIndex> > b_ref(
b.const_cast_derived());
cholmod_sparse b_cs = viewAsCholmod(b_ref);
cholmod_sparse* x_cs = internal::cm_spsolve<StorageIndex>(CHOLMOD_A, *m_cholmodFactor, b_cs, m_cholmod);
if (!x_cs) {
this->m_info = NumericalIssue;
return;
}
// TODO optimize this copy by swapping when possible (be careful with alignment, etc.)
// NOTE cholmod_spsolve in fact just calls the dense solver for blocks of 4 columns at a time (similar to Eigen's
// sparse solver)
dest.derived() = viewAsEigen<typename DestDerived::Scalar, typename DestDerived::StorageIndex>(*x_cs);
internal::cm_free_sparse<StorageIndex>(x_cs, m_cholmod);
}
#endif // EIGEN_PARSED_BY_DOXYGEN
/** Sets the shift parameter that will be used to adjust the diagonal coefficients during the numerical factorization.
*
* During the numerical factorization, an offset term is added to the diagonal coefficients:\n
* \c d_ii = \a offset + \c d_ii
*
* The default is \a offset=0.
*
* \returns a reference to \c *this.
*/
Derived& setShift(const RealScalar& offset) {
m_shiftOffset[0] = double(offset);
return derived();
}
/** \returns the determinant of the underlying matrix from the current factorization */
Scalar determinant() const {
using std::exp;
return exp(logDeterminant());
}
/** \returns the log determinant of the underlying matrix from the current factorization */
Scalar logDeterminant() const {
using numext::real;
using std::log;
eigen_assert(m_factorizationIsOk &&
"The decomposition is not in a valid state for solving, you must first call either compute() or "
"symbolic()/numeric()");
RealScalar logDet = 0;
Scalar* x = static_cast<Scalar*>(m_cholmodFactor->x);
if (m_cholmodFactor->is_super) {
// Supernodal factorization stored as a packed list of dense column-major blocks,
// as described by the following structure:
// super[k] == index of the first column of the j-th super node
StorageIndex* super = static_cast<StorageIndex*>(m_cholmodFactor->super);
// pi[k] == offset to the description of row indices
StorageIndex* pi = static_cast<StorageIndex*>(m_cholmodFactor->pi);
// px[k] == offset to the respective dense block
StorageIndex* px = static_cast<StorageIndex*>(m_cholmodFactor->px);
Index nb_super_nodes = m_cholmodFactor->nsuper;
for (Index k = 0; k < nb_super_nodes; ++k) {
StorageIndex ncols = super[k + 1] - super[k];
StorageIndex nrows = pi[k + 1] - pi[k];
Map<const Array<Scalar, 1, Dynamic>, 0, InnerStride<> > sk(x + px[k], ncols, InnerStride<>(nrows + 1));
logDet += sk.real().log().sum();
}
} else {
// Simplicial factorization stored as standard CSC matrix.
StorageIndex* p = static_cast<StorageIndex*>(m_cholmodFactor->p);
Index size = m_cholmodFactor->n;
for (Index k = 0; k < size; ++k) logDet += log(real(x[p[k]]));
}
if (m_cholmodFactor->is_ll) logDet *= 2.0;
return logDet;
}
template <typename Stream>
void dumpMemory(Stream& /*s*/) {}
protected:
mutable cholmod_common m_cholmod;
cholmod_factor* m_cholmodFactor;
double m_shiftOffset[2];
mutable ComputationInfo m_info;
int m_factorizationIsOk;
int m_analysisIsOk;
};
/** \ingroup CholmodSupport_Module
* \class CholmodSimplicialLLT
* \brief A simplicial direct Cholesky (LLT) factorization and solver based on Cholmod
*
* This class allows to solve for A.X = B sparse linear problems via a simplicial LL^T Cholesky factorization
* using the Cholmod library.
* This simplicial variant is equivalent to Eigen's built-in SimplicialLLT class. Therefore, it has little practical
* interest. The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices X and B can be
* either dense or sparse.
*
* \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
* \tparam UpLo_ the triangular part that will be used for the computations. It can be Lower
* or Upper. Default is Lower.
*
* \implsparsesolverconcept
*
* This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non
* compressed.
*
* \warning Only double precision real and complex scalar types are supported by Cholmod.
*
* \sa \ref TutorialSparseSolverConcept, class CholmodSupernodalLLT, class SimplicialLLT
*/
template <typename MatrixType_, int UpLo_ = Lower>
class CholmodSimplicialLLT : public CholmodBase<MatrixType_, UpLo_, CholmodSimplicialLLT<MatrixType_, UpLo_> > {
typedef CholmodBase<MatrixType_, UpLo_, CholmodSimplicialLLT> Base;
using Base::m_cholmod;
public:
typedef MatrixType_ MatrixType;
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
typedef typename MatrixType::StorageIndex StorageIndex;
typedef TriangularView<const MatrixType, Eigen::Lower> MatrixL;
typedef TriangularView<const typename MatrixType::AdjointReturnType, Eigen::Upper> MatrixU;
CholmodSimplicialLLT() : Base() { init(); }
CholmodSimplicialLLT(const MatrixType& matrix) : Base() {
init();
this->compute(matrix);
}
~CholmodSimplicialLLT() {}
/** \returns an expression of the factor L */
inline MatrixL matrixL() const { return viewAsEigen<Scalar, StorageIndex>(*Base::m_cholmodFactor); }
/** \returns an expression of the factor U (= L^*) */
inline MatrixU matrixU() const { return matrixL().adjoint(); }
protected:
void init() {
m_cholmod.final_asis = 0;
m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
m_cholmod.final_ll = 1;
}
};
/** \ingroup CholmodSupport_Module
* \class CholmodSimplicialLDLT
* \brief A simplicial direct Cholesky (LDLT) factorization and solver based on Cholmod
*
* This class allows to solve for A.X = B sparse linear problems via a simplicial LDL^T Cholesky factorization
* using the Cholmod library.
* This simplicial variant is equivalent to Eigen's built-in SimplicialLDLT class. Therefore, it has little practical
* interest. The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices X and B can be
* either dense or sparse.
*
* \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
* \tparam UpLo_ the triangular part that will be used for the computations. It can be Lower
* or Upper. Default is Lower.
*
* \implsparsesolverconcept
*
* This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non
* compressed.
*
* \warning Only double precision real and complex scalar types are supported by Cholmod.
*
* \sa \ref TutorialSparseSolverConcept, class CholmodSupernodalLLT, class SimplicialLDLT
*/
template <typename MatrixType_, int UpLo_ = Lower>
class CholmodSimplicialLDLT : public CholmodBase<MatrixType_, UpLo_, CholmodSimplicialLDLT<MatrixType_, UpLo_> > {
typedef CholmodBase<MatrixType_, UpLo_, CholmodSimplicialLDLT> Base;
using Base::m_cholmod;
public:
typedef MatrixType_ MatrixType;
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
typedef typename MatrixType::StorageIndex StorageIndex;
typedef Matrix<Scalar, Dynamic, 1> VectorType;
typedef TriangularView<const MatrixType, Eigen::UnitLower> MatrixL;
typedef TriangularView<const typename MatrixType::AdjointReturnType, Eigen::UnitUpper> MatrixU;
CholmodSimplicialLDLT() : Base() { init(); }
CholmodSimplicialLDLT(const MatrixType& matrix) : Base() {
init();
this->compute(matrix);
}
~CholmodSimplicialLDLT() {}
/** \returns a vector expression of the diagonal D */
inline VectorType vectorD() const {
auto cholmodL = viewAsEigen<Scalar, StorageIndex>(*Base::m_cholmodFactor);
VectorType D{cholmodL.rows()};
for (Index k = 0; k < cholmodL.outerSize(); ++k) {
typename decltype(cholmodL)::InnerIterator it{cholmodL, k};
D(k) = it.value();
}
return D;
}
/** \returns an expression of the factor L */
inline MatrixL matrixL() const { return viewAsEigen<Scalar, StorageIndex>(*Base::m_cholmodFactor); }
/** \returns an expression of the factor U (= L^*) */
inline MatrixU matrixU() const { return matrixL().adjoint(); }
protected:
void init() {
m_cholmod.final_asis = 1;
m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
}
};
/** \ingroup CholmodSupport_Module
* \class CholmodSupernodalLLT
* \brief A supernodal Cholesky (LLT) factorization and solver based on Cholmod
*
* This class allows to solve for A.X = B sparse linear problems via a supernodal LL^T Cholesky factorization
* using the Cholmod library.
* This supernodal variant performs best on dense enough problems, e.g., 3D FEM, or very high order 2D FEM.
* The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices
* X and B can be either dense or sparse.
*
* \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
* \tparam UpLo_ the triangular part that will be used for the computations. It can be Lower
* or Upper. Default is Lower.
*
* \implsparsesolverconcept
*
* This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non
* compressed.
*
* \warning Only double precision real and complex scalar types are supported by Cholmod.
*
* \sa \ref TutorialSparseSolverConcept
*/
template <typename MatrixType_, int UpLo_ = Lower>
class CholmodSupernodalLLT : public CholmodBase<MatrixType_, UpLo_, CholmodSupernodalLLT<MatrixType_, UpLo_> > {
typedef CholmodBase<MatrixType_, UpLo_, CholmodSupernodalLLT> Base;
using Base::m_cholmod;
public:
typedef MatrixType_ MatrixType;
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
typedef typename MatrixType::StorageIndex StorageIndex;
CholmodSupernodalLLT() : Base() { init(); }
CholmodSupernodalLLT(const MatrixType& matrix) : Base() {
init();
this->compute(matrix);
}
~CholmodSupernodalLLT() {}
/** \returns an expression of the factor L */
inline MatrixType matrixL() const {
// Convert Cholmod factor's supernodal storage format to Eigen's CSC storage format
cholmod_sparse* cholmodL = internal::cm_factor_to_sparse(*Base::m_cholmodFactor, m_cholmod);
MatrixType L = viewAsEigen<Scalar, StorageIndex>(*cholmodL);
internal::cm_free_sparse<StorageIndex>(cholmodL, m_cholmod);
return L;
}
/** \returns an expression of the factor U (= L^*) */
inline MatrixType matrixU() const { return matrixL().adjoint(); }
protected:
void init() {
m_cholmod.final_asis = 1;
m_cholmod.supernodal = CHOLMOD_SUPERNODAL;
}
};
/** \ingroup CholmodSupport_Module
* \class CholmodDecomposition
* \brief A general Cholesky factorization and solver based on Cholmod
*
* This class allows to solve for A.X = B sparse linear problems via a LL^T or LDL^T Cholesky factorization
* using the Cholmod library. The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices
* X and B can be either dense or sparse.
*
* This variant permits to change the underlying Cholesky method at runtime.
* On the other hand, it does not provide access to the result of the factorization.
* The default is to let Cholmod automatically choose between a simplicial and supernodal factorization.
*
* \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
* \tparam UpLo_ the triangular part that will be used for the computations. It can be Lower
* or Upper. Default is Lower.
*
* \implsparsesolverconcept
*
* This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non
* compressed.
*
* \warning Only double precision real and complex scalar types are supported by Cholmod.
*
* \sa \ref TutorialSparseSolverConcept
*/
template <typename MatrixType_, int UpLo_ = Lower>
class CholmodDecomposition : public CholmodBase<MatrixType_, UpLo_, CholmodDecomposition<MatrixType_, UpLo_> > {
typedef CholmodBase<MatrixType_, UpLo_, CholmodDecomposition> Base;
using Base::m_cholmod;
public:
typedef MatrixType_ MatrixType;
CholmodDecomposition() : Base() { init(); }
CholmodDecomposition(const MatrixType& matrix) : Base() {
init();
this->compute(matrix);
}
~CholmodDecomposition() {}
void setMode(CholmodMode mode) {
switch (mode) {
case CholmodAuto:
m_cholmod.final_asis = 1;
m_cholmod.supernodal = CHOLMOD_AUTO;
break;
case CholmodSimplicialLLt:
m_cholmod.final_asis = 0;
m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
m_cholmod.final_ll = 1;
break;
case CholmodSupernodalLLt:
m_cholmod.final_asis = 1;
m_cholmod.supernodal = CHOLMOD_SUPERNODAL;
break;
case CholmodLDLt:
m_cholmod.final_asis = 1;
m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
break;
default:
break;
}
}
protected:
void init() {
m_cholmod.final_asis = 1;
m_cholmod.supernodal = CHOLMOD_AUTO;
}
};
} // end namespace Eigen
#endif // EIGEN_CHOLMODSUPPORT_H

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#ifndef EIGEN_CHOLMODSUPPORT_MODULE_H
#error "Please include Eigen/CholmodSupport instead of including headers inside the src directory directly."
#endif

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2017 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_ARITHMETIC_SEQUENCE_H
#define EIGEN_ARITHMETIC_SEQUENCE_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
// Helper to cleanup the type of the increment:
template <typename T>
struct cleanup_seq_incr {
typedef typename cleanup_index_type<T, DynamicIndex>::type type;
};
} // namespace internal
//--------------------------------------------------------------------------------
// seq(first,last,incr) and seqN(first,size,incr)
//--------------------------------------------------------------------------------
template <typename FirstType = Index, typename SizeType = Index, typename IncrType = internal::FixedInt<1> >
class ArithmeticSequence;
template <typename FirstType, typename SizeType, typename IncrType>
ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type,
typename internal::cleanup_index_type<SizeType>::type,
typename internal::cleanup_seq_incr<IncrType>::type>
seqN(FirstType first, SizeType size, IncrType incr);
/** \class ArithmeticSequence
* \ingroup Core_Module
*
* This class represents an arithmetic progression \f$ a_0, a_1, a_2, ..., a_{n-1}\f$ defined by
* its \em first value \f$ a_0 \f$, its \em size (aka length) \em n, and the \em increment (aka stride)
* that is equal to \f$ a_{i+1}-a_{i}\f$ for any \em i.
*
* It is internally used as the return type of the Eigen::seq and Eigen::seqN functions, and as the input arguments
* of DenseBase::operator()(const RowIndices&, const ColIndices&), and most of the time this is the
* only way it is used.
*
* \tparam FirstType type of the first element, usually an Index,
* but internally it can be a symbolic expression
* \tparam SizeType type representing the size of the sequence, usually an Index
* or a compile time integral constant. Internally, it can also be a symbolic expression
* \tparam IncrType type of the increment, can be a runtime Index, or a compile time integral constant (default is
* compile-time 1)
*
* \sa Eigen::seq, Eigen::seqN, DenseBase::operator()(const RowIndices&, const ColIndices&), class IndexedView
*/
template <typename FirstType, typename SizeType, typename IncrType>
class ArithmeticSequence {
public:
constexpr ArithmeticSequence() = default;
constexpr ArithmeticSequence(FirstType first, SizeType size) : m_first(first), m_size(size) {}
constexpr ArithmeticSequence(FirstType first, SizeType size, IncrType incr)
: m_first(first), m_size(size), m_incr(incr) {}
enum {
// SizeAtCompileTime = internal::get_fixed_value<SizeType>::value,
IncrAtCompileTime = internal::get_fixed_value<IncrType, DynamicIndex>::value
};
/** \returns the size, i.e., number of elements, of the sequence */
constexpr Index size() const { return m_size; }
/** \returns the first element \f$ a_0 \f$ in the sequence */
constexpr Index first() const { return m_first; }
/** \returns the value \f$ a_i \f$ at index \a i in the sequence. */
constexpr Index operator[](Index i) const { return m_first + i * m_incr; }
constexpr const FirstType& firstObject() const { return m_first; }
constexpr const SizeType& sizeObject() const { return m_size; }
constexpr const IncrType& incrObject() const { return m_incr; }
protected:
FirstType m_first;
SizeType m_size;
IncrType m_incr;
public:
constexpr auto reverse() const -> decltype(Eigen::seqN(m_first + (m_size + fix<-1>()) * m_incr, m_size, -m_incr)) {
return seqN(m_first + (m_size + fix<-1>()) * m_incr, m_size, -m_incr);
}
};
/** \returns an ArithmeticSequence starting at \a first, of length \a size, and increment \a incr
*
* \sa seqN(FirstType,SizeType), seq(FirstType,LastType,IncrType) */
template <typename FirstType, typename SizeType, typename IncrType>
ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type,
typename internal::cleanup_index_type<SizeType>::type,
typename internal::cleanup_seq_incr<IncrType>::type>
seqN(FirstType first, SizeType size, IncrType incr) {
return ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type,
typename internal::cleanup_index_type<SizeType>::type,
typename internal::cleanup_seq_incr<IncrType>::type>(first, size, incr);
}
/** \returns an ArithmeticSequence starting at \a first, of length \a size, and unit increment
*
* \sa seqN(FirstType,SizeType,IncrType), seq(FirstType,LastType) */
template <typename FirstType, typename SizeType>
ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type,
typename internal::cleanup_index_type<SizeType>::type>
seqN(FirstType first, SizeType size) {
return ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type,
typename internal::cleanup_index_type<SizeType>::type>(first, size);
}
#ifdef EIGEN_PARSED_BY_DOXYGEN
/** \returns an ArithmeticSequence starting at \a f, up (or down) to \a l, and with positive (or negative) increment \a
* incr
*
* It is essentially an alias to:
* \code
* seqN(f, (l-f+incr)/incr, incr);
* \endcode
*
* \sa seqN(FirstType,SizeType,IncrType), seq(FirstType,LastType)
*/
template <typename FirstType, typename LastType, typename IncrType>
auto seq(FirstType f, LastType l, IncrType incr);
/** \returns an ArithmeticSequence starting at \a f, up (or down) to \a l, and unit increment
*
* It is essentially an alias to:
* \code
* seqN(f,l-f+1);
* \endcode
*
* \sa seqN(FirstType,SizeType), seq(FirstType,LastType,IncrType)
*/
template <typename FirstType, typename LastType>
auto seq(FirstType f, LastType l);
#else // EIGEN_PARSED_BY_DOXYGEN
template <typename FirstType, typename LastType>
auto seq(FirstType f, LastType l)
-> decltype(seqN(typename internal::cleanup_index_type<FirstType>::type(f),
(typename internal::cleanup_index_type<LastType>::type(l) -
typename internal::cleanup_index_type<FirstType>::type(f) + fix<1>()))) {
return seqN(typename internal::cleanup_index_type<FirstType>::type(f),
(typename internal::cleanup_index_type<LastType>::type(l) -
typename internal::cleanup_index_type<FirstType>::type(f) + fix<1>()));
}
template <typename FirstType, typename LastType, typename IncrType>
auto seq(FirstType f, LastType l, IncrType incr)
-> decltype(seqN(typename internal::cleanup_index_type<FirstType>::type(f),
(typename internal::cleanup_index_type<LastType>::type(l) -
typename internal::cleanup_index_type<FirstType>::type(f) +
typename internal::cleanup_seq_incr<IncrType>::type(incr)) /
typename internal::cleanup_seq_incr<IncrType>::type(incr),
typename internal::cleanup_seq_incr<IncrType>::type(incr))) {
typedef typename internal::cleanup_seq_incr<IncrType>::type CleanedIncrType;
return seqN(typename internal::cleanup_index_type<FirstType>::type(f),
(typename internal::cleanup_index_type<LastType>::type(l) -
typename internal::cleanup_index_type<FirstType>::type(f) + CleanedIncrType(incr)) /
CleanedIncrType(incr),
CleanedIncrType(incr));
}
#endif // EIGEN_PARSED_BY_DOXYGEN
namespace placeholders {
/** \cpp11
* \returns a symbolic ArithmeticSequence representing the last \a size elements with increment \a incr.
*
* It is a shortcut for: \code seqN(last-(size-fix<1>)*incr, size, incr) \endcode
*
* \sa lastN(SizeType), seqN(FirstType,SizeType), seq(FirstType,LastType,IncrType) */
template <typename SizeType, typename IncrType>
auto lastN(SizeType size, IncrType incr)
-> decltype(seqN(Eigen::placeholders::last - (size - fix<1>()) * incr, size, incr)) {
return seqN(Eigen::placeholders::last - (size - fix<1>()) * incr, size, incr);
}
/** \cpp11
* \returns a symbolic ArithmeticSequence representing the last \a size elements with a unit increment.
*
* It is a shortcut for: \code seq(last+fix<1>-size, last) \endcode
*
* \sa lastN(SizeType,IncrType, seqN(FirstType,SizeType), seq(FirstType,LastType) */
template <typename SizeType>
auto lastN(SizeType size) -> decltype(seqN(Eigen::placeholders::last + fix<1>() - size, size)) {
return seqN(Eigen::placeholders::last + fix<1>() - size, size);
}
} // namespace placeholders
/** \namespace Eigen::indexing
* \ingroup Core_Module
*
* The sole purpose of this namespace is to be able to import all functions
* and symbols that are expected to be used within operator() for indexing
* and slicing. If you already imported the whole Eigen namespace:
* \code using namespace Eigen; \endcode
* then you are already all set. Otherwise, if you don't want/cannot import
* the whole Eigen namespace, the following line:
* \code using namespace Eigen::indexing; \endcode
* is equivalent to:
* \code
using Eigen::fix;
using Eigen::seq;
using Eigen::seqN;
using Eigen::placeholders::all;
using Eigen::placeholders::last;
using Eigen::placeholders::lastN; // c++11 only
using Eigen::placeholders::lastp1;
\endcode
*/
namespace indexing {
using Eigen::fix;
using Eigen::seq;
using Eigen::seqN;
using Eigen::placeholders::all;
using Eigen::placeholders::last;
using Eigen::placeholders::lastN;
using Eigen::placeholders::lastp1;
} // namespace indexing
} // end namespace Eigen
#endif // EIGEN_ARITHMETIC_SEQUENCE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_ARRAY_H
#define EIGEN_ARRAY_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
template <typename Scalar_, int Rows_, int Cols_, int Options_, int MaxRows_, int MaxCols_>
struct traits<Array<Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_>>
: traits<Matrix<Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_>> {
typedef ArrayXpr XprKind;
typedef ArrayBase<Array<Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_>> XprBase;
};
} // namespace internal
/** \class Array
* \ingroup Core_Module
*
* \brief General-purpose arrays with easy API for coefficient-wise operations
*
* The %Array class is very similar to the Matrix class. It provides
* general-purpose one- and two-dimensional arrays. The difference between the
* %Array and the %Matrix class is primarily in the API: the API for the
* %Array class provides easy access to coefficient-wise operations, while the
* API for the %Matrix class provides easy access to linear-algebra
* operations.
*
* See documentation of class Matrix for detailed information on the template parameters
* storage layout.
*
* This class can be extended with the help of the plugin mechanism described on the page
* \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_ARRAY_PLUGIN.
*
* \sa \blank \ref TutorialArrayClass, \ref TopicClassHierarchy
*/
template <typename Scalar_, int Rows_, int Cols_, int Options_, int MaxRows_, int MaxCols_>
class Array : public PlainObjectBase<Array<Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_>> {
public:
typedef PlainObjectBase<Array> Base;
EIGEN_DENSE_PUBLIC_INTERFACE(Array)
enum { Options = Options_ };
typedef typename Base::PlainObject PlainObject;
protected:
template <typename Derived, typename OtherDerived, bool IsVector>
friend struct internal::conservative_resize_like_impl;
using Base::m_storage;
public:
using Base::base;
using Base::coeff;
using Base::coeffRef;
/**
* The usage of
* using Base::operator=;
* fails on MSVC. Since the code below is working with GCC and MSVC, we skipped
* the usage of 'using'. This should be done only for operator=.
*/
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Array& operator=(const EigenBase<OtherDerived>& other) {
return Base::operator=(other);
}
/** Set all the entries to \a value.
* \sa DenseBase::setConstant(), DenseBase::fill()
*/
/* This overload is needed because the usage of
* using Base::operator=;
* fails on MSVC. Since the code below is working with GCC and MSVC, we skipped
* the usage of 'using'. This should be done only for operator=.
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Array& operator=(const Scalar& value) {
Base::setConstant(value);
return *this;
}
/** Copies the value of the expression \a other into \c *this with automatic resizing.
*
* *this might be resized to match the dimensions of \a other. If *this was a null matrix (not already initialized),
* it will be initialized.
*
* Note that copying a row-vector into a vector (and conversely) is allowed.
* The resizing, if any, is then done in the appropriate way so that row-vectors
* remain row-vectors and vectors remain vectors.
*/
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Array& operator=(const DenseBase<OtherDerived>& other) {
return Base::_set(other);
}
/**
* \brief Assigns arrays to each other.
*
* \note This is a special case of the templated operator=. Its purpose is
* to prevent a default operator= from hiding the templated operator=.
*
* \callgraph
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Array& operator=(const Array& other) { return Base::_set(other); }
/** Default constructor.
*
* For fixed-size matrices, does nothing.
*
* For dynamic-size matrices, creates an empty matrix of size 0. Does not allocate any array. Such a matrix
* is called a null matrix. This constructor is the unique way to create null matrices: resizing
* a matrix to 0 is not supported.
*
* \sa resize(Index,Index)
*/
#ifdef EIGEN_INITIALIZE_COEFFS
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Array() : Base() { EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED }
#else
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Array() = default;
#endif
/** \brief Move constructor */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Array(Array&&) = default;
EIGEN_DEVICE_FUNC Array& operator=(Array&& other) noexcept(std::is_nothrow_move_assignable<Scalar>::value) {
Base::operator=(std::move(other));
return *this;
}
/** \brief Construct a row of column vector with fixed size from an arbitrary number of coefficients.
*
* \only_for_vectors
*
* This constructor is for 1D array or vectors with more than 4 coefficients.
*
* \warning To construct a column (resp. row) vector of fixed length, the number of values passed to this
* constructor must match the the fixed number of rows (resp. columns) of \c *this.
*
*
* Example: \include Array_variadic_ctor_cxx11.cpp
* Output: \verbinclude Array_variadic_ctor_cxx11.out
*
* \sa Array(const std::initializer_list<std::initializer_list<Scalar>>&)
* \sa Array(const Scalar&), Array(const Scalar&,const Scalar&)
*/
template <typename... ArgTypes>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Array(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3,
const ArgTypes&... args)
: Base(a0, a1, a2, a3, args...) {}
/** \brief Constructs an array and initializes it from the coefficients given as initializer-lists grouped by row.
* \cpp11
*
* In the general case, the constructor takes a list of rows, each row being represented as a list of coefficients:
*
* Example: \include Array_initializer_list_23_cxx11.cpp
* Output: \verbinclude Array_initializer_list_23_cxx11.out
*
* Each of the inner initializer lists must contain the exact same number of elements, otherwise an assertion is
* triggered.
*
* In the case of a compile-time column 1D array, implicit transposition from a single row is allowed.
* Therefore <code> Array<int,Dynamic,1>{{1,2,3,4,5}}</code> is legal and the more verbose syntax
* <code>Array<int,Dynamic,1>{{1},{2},{3},{4},{5}}</code> can be avoided:
*
* Example: \include Array_initializer_list_vector_cxx11.cpp
* Output: \verbinclude Array_initializer_list_vector_cxx11.out
*
* In the case of fixed-sized arrays, the initializer list sizes must exactly match the array sizes,
* and implicit transposition is allowed for compile-time 1D arrays only.
*
* \sa Array(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args)
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Array(
const std::initializer_list<std::initializer_list<Scalar>>& list)
: Base(list) {}
#ifndef EIGEN_PARSED_BY_DOXYGEN
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit Array(const T& x) {
Base::template _init1<T>(x);
}
template <typename T0, typename T1>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Array(const T0& val0, const T1& val1) {
this->template _init2<T0, T1>(val0, val1);
}
#else
/** \brief Constructs a fixed-sized array initialized with coefficients starting at \a data */
EIGEN_DEVICE_FUNC explicit Array(const Scalar* data);
/** Constructs a vector or row-vector with given dimension. \only_for_vectors
*
* Note that this is only useful for dynamic-size vectors. For fixed-size vectors,
* it is redundant to pass the dimension here, so it makes more sense to use the default
* constructor Array() instead.
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit Array(Index dim);
/** constructs an initialized 1x1 Array with the given coefficient
* \sa const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args */
Array(const Scalar& value);
/** constructs an uninitialized array with \a rows rows and \a cols columns.
*
* This is useful for dynamic-size arrays. For fixed-size arrays,
* it is redundant to pass these parameters, so one should use the default constructor
* Array() instead. */
Array(Index rows, Index cols);
/** constructs an initialized 2D vector with given coefficients
* \sa Array(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args) */
Array(const Scalar& val0, const Scalar& val1);
#endif // end EIGEN_PARSED_BY_DOXYGEN
/** constructs an initialized 3D vector with given coefficients
* \sa Array(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args)
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Array(const Scalar& val0, const Scalar& val1, const Scalar& val2) {
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Array, 3)
m_storage.data()[0] = val0;
m_storage.data()[1] = val1;
m_storage.data()[2] = val2;
}
/** constructs an initialized 4D vector with given coefficients
* \sa Array(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args)
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Array(const Scalar& val0, const Scalar& val1, const Scalar& val2,
const Scalar& val3) {
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Array, 4)
m_storage.data()[0] = val0;
m_storage.data()[1] = val1;
m_storage.data()[2] = val2;
m_storage.data()[3] = val3;
}
/** Copy constructor */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Array(const Array&) = default;
private:
struct PrivateType {};
public:
/** \sa MatrixBase::operator=(const EigenBase<OtherDerived>&) */
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Array(
const EigenBase<OtherDerived>& other,
std::enable_if_t<internal::is_convertible<typename OtherDerived::Scalar, Scalar>::value, PrivateType> =
PrivateType())
: Base(other.derived()) {}
EIGEN_DEVICE_FUNC constexpr Index innerStride() const noexcept { return 1; }
EIGEN_DEVICE_FUNC constexpr Index outerStride() const noexcept { return this->innerSize(); }
#ifdef EIGEN_ARRAY_PLUGIN
#include EIGEN_ARRAY_PLUGIN
#endif
private:
template <typename MatrixType, typename OtherDerived, bool SwapPointers>
friend struct internal::matrix_swap_impl;
};
/** \defgroup arraytypedefs Global array typedefs
* \ingroup Core_Module
*
* %Eigen defines several typedef shortcuts for most common 1D and 2D array types.
*
* The general patterns are the following:
*
* \c ArrayRowsColsType where \c Rows and \c Cols can be \c 2,\c 3,\c 4 for fixed size square matrices or \c X for
* dynamic size, and where \c Type can be \c i for integer, \c f for float, \c d for double, \c cf for complex float, \c
* cd for complex double.
*
* For example, \c Array33d is a fixed-size 3x3 array type of doubles, and \c ArrayXXf is a dynamic-size matrix of
* floats.
*
* There are also \c ArraySizeType which are self-explanatory. For example, \c Array4cf is
* a fixed-size 1D array of 4 complex floats.
*
* With \cpp11, template alias are also defined for common sizes.
* They follow the same pattern as above except that the scalar type suffix is replaced by a
* template parameter, i.e.:
* - `ArrayRowsCols<Type>` where `Rows` and `Cols` can be \c 2,\c 3,\c 4, or \c X for fixed or dynamic size.
* - `ArraySize<Type>` where `Size` can be \c 2,\c 3,\c 4 or \c X for fixed or dynamic size 1D arrays.
*
* \sa class Array
*/
#define EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix) \
/** \ingroup arraytypedefs */ \
typedef Array<Type, Size, Size> Array##SizeSuffix##SizeSuffix##TypeSuffix; \
/** \ingroup arraytypedefs */ \
typedef Array<Type, Size, 1> Array##SizeSuffix##TypeSuffix;
#define EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, Size) \
/** \ingroup arraytypedefs */ \
typedef Array<Type, Size, Dynamic> Array##Size##X##TypeSuffix; \
/** \ingroup arraytypedefs */ \
typedef Array<Type, Dynamic, Size> Array##X##Size##TypeSuffix;
#define EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \
EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, 2, 2) \
EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, 3, 3) \
EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, 4, 4) \
EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, Dynamic, X) \
EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, 2) \
EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, 3) \
EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, 4)
EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(int, i)
EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(float, f)
EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(double, d)
EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(std::complex<float>, cf)
EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(std::complex<double>, cd)
#undef EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES
#undef EIGEN_MAKE_ARRAY_TYPEDEFS
#undef EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS
#define EIGEN_MAKE_ARRAY_TYPEDEFS(Size, SizeSuffix) \
/** \ingroup arraytypedefs */ \
/** \brief \cpp11 */ \
template <typename Type> \
using Array##SizeSuffix##SizeSuffix = Array<Type, Size, Size>; \
/** \ingroup arraytypedefs */ \
/** \brief \cpp11 */ \
template <typename Type> \
using Array##SizeSuffix = Array<Type, Size, 1>;
#define EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Size) \
/** \ingroup arraytypedefs */ \
/** \brief \cpp11 */ \
template <typename Type> \
using Array##Size##X = Array<Type, Size, Dynamic>; \
/** \ingroup arraytypedefs */ \
/** \brief \cpp11 */ \
template <typename Type> \
using Array##X##Size = Array<Type, Dynamic, Size>;
EIGEN_MAKE_ARRAY_TYPEDEFS(2, 2)
EIGEN_MAKE_ARRAY_TYPEDEFS(3, 3)
EIGEN_MAKE_ARRAY_TYPEDEFS(4, 4)
EIGEN_MAKE_ARRAY_TYPEDEFS(Dynamic, X)
EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(2)
EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(3)
EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(4)
#undef EIGEN_MAKE_ARRAY_TYPEDEFS
#undef EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS
#define EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, SizeSuffix) \
using Eigen::Matrix##SizeSuffix##TypeSuffix; \
using Eigen::Vector##SizeSuffix##TypeSuffix; \
using Eigen::RowVector##SizeSuffix##TypeSuffix;
#define EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(TypeSuffix) \
EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 2) \
EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 3) \
EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 4) \
EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, X)
#define EIGEN_USING_ARRAY_TYPEDEFS \
EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(i) \
EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(f) \
EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(d) \
EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(cf) \
EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(cd)
} // end namespace Eigen
#endif // EIGEN_ARRAY_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_ARRAYBASE_H
#define EIGEN_ARRAYBASE_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
template <typename ExpressionType>
class MatrixWrapper;
/** \class ArrayBase
* \ingroup Core_Module
*
* \brief Base class for all 1D and 2D array, and related expressions
*
* An array is similar to a dense vector or matrix. While matrices are mathematical
* objects with well defined linear algebra operators, an array is just a collection
* of scalar values arranged in a one or two dimensional fashion. As the main consequence,
* all operations applied to an array are performed coefficient wise. Furthermore,
* arrays support scalar math functions of the c++ standard library (e.g., std::sin(x)), and convenient
* constructors allowing to easily write generic code working for both scalar values
* and arrays.
*
* This class is the base that is inherited by all array expression types.
*
* \tparam Derived is the derived type, e.g., an array or an expression type.
*
* This class can be extended with the help of the plugin mechanism described on the page
* \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_ARRAYBASE_PLUGIN.
*
* \sa class MatrixBase, \ref TopicClassHierarchy
*/
template <typename Derived>
class ArrayBase : public DenseBase<Derived> {
public:
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** The base class for a given storage type. */
typedef ArrayBase StorageBaseType;
typedef ArrayBase Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl;
typedef typename internal::traits<Derived>::StorageKind StorageKind;
typedef typename internal::traits<Derived>::Scalar Scalar;
typedef typename internal::packet_traits<Scalar>::type PacketScalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef DenseBase<Derived> Base;
using Base::ColsAtCompileTime;
using Base::Flags;
using Base::IsVectorAtCompileTime;
using Base::MaxColsAtCompileTime;
using Base::MaxRowsAtCompileTime;
using Base::MaxSizeAtCompileTime;
using Base::RowsAtCompileTime;
using Base::SizeAtCompileTime;
using Base::coeff;
using Base::coeffRef;
using Base::cols;
using Base::const_cast_derived;
using Base::derived;
using Base::lazyAssign;
using Base::rows;
using Base::size;
using Base::operator-;
using Base::operator=;
using Base::operator+=;
using Base::operator-=;
using Base::operator*=;
using Base::operator/=;
typedef typename Base::CoeffReturnType CoeffReturnType;
typedef typename Base::PlainObject PlainObject;
/** \internal Represents a matrix with all coefficients equal to one another*/
typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject> ConstantReturnType;
#endif // not EIGEN_PARSED_BY_DOXYGEN
#define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::ArrayBase
#define EIGEN_DOC_UNARY_ADDONS(X, Y)
#include "../plugins/MatrixCwiseUnaryOps.inc"
#include "../plugins/ArrayCwiseUnaryOps.inc"
#include "../plugins/CommonCwiseBinaryOps.inc"
#include "../plugins/MatrixCwiseBinaryOps.inc"
#include "../plugins/ArrayCwiseBinaryOps.inc"
#ifdef EIGEN_ARRAYBASE_PLUGIN
#include EIGEN_ARRAYBASE_PLUGIN
#endif
#undef EIGEN_CURRENT_STORAGE_BASE_CLASS
#undef EIGEN_DOC_UNARY_ADDONS
/** Special case of the template operator=, in order to prevent the compiler
* from generating a default operator= (issue hit with g++ 4.1)
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const ArrayBase& other) {
internal::call_assignment(derived(), other.derived());
return derived();
}
/** Set all the entries to \a value.
* \sa DenseBase::setConstant(), DenseBase::fill() */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const Scalar& value) {
Base::setConstant(value);
return derived();
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator+=(const Scalar& other) {
internal::call_assignment(this->derived(), PlainObject::Constant(rows(), cols(), other),
internal::add_assign_op<Scalar, Scalar>());
return derived();
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator-=(const Scalar& other) {
internal::call_assignment(this->derived(), PlainObject::Constant(rows(), cols(), other),
internal::sub_assign_op<Scalar, Scalar>());
return derived();
}
/** replaces \c *this by \c *this + \a other.
*
* \returns a reference to \c *this
*/
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator+=(const ArrayBase<OtherDerived>& other) {
call_assignment(derived(), other.derived(), internal::add_assign_op<Scalar, typename OtherDerived::Scalar>());
return derived();
}
/** replaces \c *this by \c *this - \a other.
*
* \returns a reference to \c *this
*/
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator-=(const ArrayBase<OtherDerived>& other) {
call_assignment(derived(), other.derived(), internal::sub_assign_op<Scalar, typename OtherDerived::Scalar>());
return derived();
}
/** replaces \c *this by \c *this * \a other coefficient wise.
*
* \returns a reference to \c *this
*/
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator*=(const ArrayBase<OtherDerived>& other) {
call_assignment(derived(), other.derived(), internal::mul_assign_op<Scalar, typename OtherDerived::Scalar>());
return derived();
}
/** replaces \c *this by \c *this / \a other coefficient wise.
*
* \returns a reference to \c *this
*/
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator/=(const ArrayBase<OtherDerived>& other) {
call_assignment(derived(), other.derived(), internal::div_assign_op<Scalar, typename OtherDerived::Scalar>());
return derived();
}
public:
EIGEN_DEVICE_FUNC ArrayBase<Derived>& array() { return *this; }
EIGEN_DEVICE_FUNC const ArrayBase<Derived>& array() const { return *this; }
/** \returns an \link Eigen::MatrixBase Matrix \endlink expression of this array
* \sa MatrixBase::array() */
EIGEN_DEVICE_FUNC MatrixWrapper<Derived> matrix() { return MatrixWrapper<Derived>(derived()); }
EIGEN_DEVICE_FUNC const MatrixWrapper<const Derived> matrix() const {
return MatrixWrapper<const Derived>(derived());
}
// template<typename Dest>
// inline void evalTo(Dest& dst) const { dst = matrix(); }
protected:
EIGEN_DEFAULT_COPY_CONSTRUCTOR(ArrayBase)
EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(ArrayBase)
private:
explicit ArrayBase(Index);
ArrayBase(Index, Index);
template <typename OtherDerived>
explicit ArrayBase(const ArrayBase<OtherDerived>&);
protected:
// mixing arrays and matrices is not legal
template <typename OtherDerived>
Derived& operator+=(const MatrixBase<OtherDerived>&) {
EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar)) == -1,
YOU_CANNOT_MIX_ARRAYS_AND_MATRICES);
return *this;
}
// mixing arrays and matrices is not legal
template <typename OtherDerived>
Derived& operator-=(const MatrixBase<OtherDerived>&) {
EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar)) == -1,
YOU_CANNOT_MIX_ARRAYS_AND_MATRICES);
return *this;
}
};
} // end namespace Eigen
#endif // EIGEN_ARRAYBASE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_ARRAYWRAPPER_H
#define EIGEN_ARRAYWRAPPER_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
/** \class ArrayWrapper
* \ingroup Core_Module
*
* \brief Expression of a mathematical vector or matrix as an array object
*
* This class is the return type of MatrixBase::array(), and most of the time
* this is the only way it is use.
*
* \sa MatrixBase::array(), class MatrixWrapper
*/
namespace internal {
template <typename ExpressionType>
struct traits<ArrayWrapper<ExpressionType> > : public traits<remove_all_t<typename ExpressionType::Nested> > {
typedef ArrayXpr XprKind;
// Let's remove NestByRefBit
enum {
Flags0 = traits<remove_all_t<typename ExpressionType::Nested> >::Flags,
LvalueBitFlag = is_lvalue<ExpressionType>::value ? LvalueBit : 0,
Flags = (Flags0 & ~(NestByRefBit | LvalueBit)) | LvalueBitFlag
};
};
} // namespace internal
template <typename ExpressionType>
class ArrayWrapper : public ArrayBase<ArrayWrapper<ExpressionType> > {
public:
typedef ArrayBase<ArrayWrapper> Base;
EIGEN_DENSE_PUBLIC_INTERFACE(ArrayWrapper)
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(ArrayWrapper)
typedef internal::remove_all_t<ExpressionType> NestedExpression;
typedef std::conditional_t<internal::is_lvalue<ExpressionType>::value, Scalar, const Scalar>
ScalarWithConstIfNotLvalue;
typedef typename internal::ref_selector<ExpressionType>::non_const_type NestedExpressionType;
using Base::coeffRef;
EIGEN_DEVICE_FUNC explicit EIGEN_STRONG_INLINE ArrayWrapper(ExpressionType& matrix) : m_expression(matrix) {}
EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return m_expression.rows(); }
EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return m_expression.cols(); }
EIGEN_DEVICE_FUNC constexpr Index outerStride() const noexcept { return m_expression.outerStride(); }
EIGEN_DEVICE_FUNC constexpr Index innerStride() const noexcept { return m_expression.innerStride(); }
EIGEN_DEVICE_FUNC constexpr ScalarWithConstIfNotLvalue* data() { return m_expression.data(); }
EIGEN_DEVICE_FUNC constexpr const Scalar* data() const { return m_expression.data(); }
EIGEN_DEVICE_FUNC inline const Scalar& coeffRef(Index rowId, Index colId) const {
return m_expression.coeffRef(rowId, colId);
}
EIGEN_DEVICE_FUNC inline const Scalar& coeffRef(Index index) const { return m_expression.coeffRef(index); }
template <typename Dest>
EIGEN_DEVICE_FUNC inline void evalTo(Dest& dst) const {
dst = m_expression;
}
EIGEN_DEVICE_FUNC const internal::remove_all_t<NestedExpressionType>& nestedExpression() const {
return m_expression;
}
/** Forwards the resizing request to the nested expression
* \sa DenseBase::resize(Index) */
EIGEN_DEVICE_FUNC void resize(Index newSize) { m_expression.resize(newSize); }
/** Forwards the resizing request to the nested expression
* \sa DenseBase::resize(Index,Index)*/
EIGEN_DEVICE_FUNC void resize(Index rows, Index cols) { m_expression.resize(rows, cols); }
protected:
NestedExpressionType m_expression;
};
/** \class MatrixWrapper
* \ingroup Core_Module
*
* \brief Expression of an array as a mathematical vector or matrix
*
* This class is the return type of ArrayBase::matrix(), and most of the time
* this is the only way it is use.
*
* \sa MatrixBase::matrix(), class ArrayWrapper
*/
namespace internal {
template <typename ExpressionType>
struct traits<MatrixWrapper<ExpressionType> > : public traits<remove_all_t<typename ExpressionType::Nested> > {
typedef MatrixXpr XprKind;
// Let's remove NestByRefBit
enum {
Flags0 = traits<remove_all_t<typename ExpressionType::Nested> >::Flags,
LvalueBitFlag = is_lvalue<ExpressionType>::value ? LvalueBit : 0,
Flags = (Flags0 & ~(NestByRefBit | LvalueBit)) | LvalueBitFlag
};
};
} // namespace internal
template <typename ExpressionType>
class MatrixWrapper : public MatrixBase<MatrixWrapper<ExpressionType> > {
public:
typedef MatrixBase<MatrixWrapper<ExpressionType> > Base;
EIGEN_DENSE_PUBLIC_INTERFACE(MatrixWrapper)
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(MatrixWrapper)
typedef internal::remove_all_t<ExpressionType> NestedExpression;
typedef std::conditional_t<internal::is_lvalue<ExpressionType>::value, Scalar, const Scalar>
ScalarWithConstIfNotLvalue;
typedef typename internal::ref_selector<ExpressionType>::non_const_type NestedExpressionType;
using Base::coeffRef;
EIGEN_DEVICE_FUNC explicit inline MatrixWrapper(ExpressionType& matrix) : m_expression(matrix) {}
EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return m_expression.rows(); }
EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return m_expression.cols(); }
EIGEN_DEVICE_FUNC constexpr Index outerStride() const noexcept { return m_expression.outerStride(); }
EIGEN_DEVICE_FUNC constexpr Index innerStride() const noexcept { return m_expression.innerStride(); }
EIGEN_DEVICE_FUNC constexpr ScalarWithConstIfNotLvalue* data() { return m_expression.data(); }
EIGEN_DEVICE_FUNC constexpr const Scalar* data() const { return m_expression.data(); }
EIGEN_DEVICE_FUNC inline const Scalar& coeffRef(Index rowId, Index colId) const {
return m_expression.derived().coeffRef(rowId, colId);
}
EIGEN_DEVICE_FUNC inline const Scalar& coeffRef(Index index) const { return m_expression.coeffRef(index); }
EIGEN_DEVICE_FUNC const internal::remove_all_t<NestedExpressionType>& nestedExpression() const {
return m_expression;
}
/** Forwards the resizing request to the nested expression
* \sa DenseBase::resize(Index) */
EIGEN_DEVICE_FUNC void resize(Index newSize) { m_expression.resize(newSize); }
/** Forwards the resizing request to the nested expression
* \sa DenseBase::resize(Index,Index)*/
EIGEN_DEVICE_FUNC void resize(Index rows, Index cols) { m_expression.resize(rows, cols); }
protected:
NestedExpressionType m_expression;
};
} // end namespace Eigen
#endif // EIGEN_ARRAYWRAPPER_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2007 Michael Olbrich <michael.olbrich@gmx.net>
// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_ASSIGN_H
#define EIGEN_ASSIGN_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
template <typename Derived>
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::lazyAssign(const DenseBase<OtherDerived>& other) {
enum { SameType = internal::is_same<typename Derived::Scalar, typename OtherDerived::Scalar>::value };
EIGEN_STATIC_ASSERT_LVALUE(Derived)
EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Derived, OtherDerived)
EIGEN_STATIC_ASSERT(
SameType,
YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
eigen_assert(rows() == other.rows() && cols() == other.cols());
internal::call_assignment_no_alias(derived(), other.derived());
return derived();
}
template <typename Derived>
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::operator=(const DenseBase<OtherDerived>& other) {
internal::call_assignment(derived(), other.derived());
return derived();
}
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::operator=(const DenseBase& other) {
internal::call_assignment(derived(), other.derived());
return derived();
}
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const MatrixBase& other) {
internal::call_assignment(derived(), other.derived());
return derived();
}
template <typename Derived>
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const DenseBase<OtherDerived>& other) {
internal::call_assignment(derived(), other.derived());
return derived();
}
template <typename Derived>
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const EigenBase<OtherDerived>& other) {
internal::call_assignment(derived(), other.derived());
return derived();
}
template <typename Derived>
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(
const ReturnByValue<OtherDerived>& other) {
other.derived().evalTo(derived());
return derived();
}
} // end namespace Eigen
#endif // EIGEN_ASSIGN_H

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/*
Copyright (c) 2011, Intel Corporation. All rights reserved.
Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>
Redistribution and use in source and binary forms, with or without modification,
are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright notice, this
list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation
and/or other materials provided with the distribution.
* Neither the name of Intel Corporation nor the names of its contributors may
be used to endorse or promote products derived from this software without
specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
********************************************************************************
* Content : Eigen bindings to Intel(R) MKL
* MKL VML support for coefficient-wise unary Eigen expressions like a=b.sin()
********************************************************************************
*/
#ifndef EIGEN_ASSIGN_VML_H
#define EIGEN_ASSIGN_VML_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
template <typename Dst, typename Src>
class vml_assign_traits {
private:
enum {
DstHasDirectAccess = Dst::Flags & DirectAccessBit,
SrcHasDirectAccess = Src::Flags & DirectAccessBit,
StorageOrdersAgree = (int(Dst::IsRowMajor) == int(Src::IsRowMajor)),
InnerSize = int(Dst::IsVectorAtCompileTime) ? int(Dst::SizeAtCompileTime)
: int(Dst::Flags) & RowMajorBit ? int(Dst::ColsAtCompileTime)
: int(Dst::RowsAtCompileTime),
InnerMaxSize = int(Dst::IsVectorAtCompileTime) ? int(Dst::MaxSizeAtCompileTime)
: int(Dst::Flags) & RowMajorBit ? int(Dst::MaxColsAtCompileTime)
: int(Dst::MaxRowsAtCompileTime),
MaxSizeAtCompileTime = Dst::SizeAtCompileTime,
MightEnableVml = StorageOrdersAgree && DstHasDirectAccess && SrcHasDirectAccess &&
Src::InnerStrideAtCompileTime == 1 && Dst::InnerStrideAtCompileTime == 1,
MightLinearize = MightEnableVml && (int(Dst::Flags) & int(Src::Flags) & LinearAccessBit),
VmlSize = MightLinearize ? MaxSizeAtCompileTime : InnerMaxSize,
LargeEnough = VmlSize == Dynamic || VmlSize >= EIGEN_MKL_VML_THRESHOLD
};
public:
enum { EnableVml = MightEnableVml && LargeEnough, Traversal = MightLinearize ? LinearTraversal : DefaultTraversal };
};
#define EIGEN_PP_EXPAND(ARG) ARG
#if !defined(EIGEN_FAST_MATH) || (EIGEN_FAST_MATH != 1)
#define EIGEN_VMLMODE_EXPAND_xLA , VML_HA
#else
#define EIGEN_VMLMODE_EXPAND_xLA , VML_LA
#endif
#define EIGEN_VMLMODE_EXPAND_x_
#define EIGEN_VMLMODE_PREFIX_xLA vm
#define EIGEN_VMLMODE_PREFIX_x_ v
#define EIGEN_VMLMODE_PREFIX(VMLMODE) EIGEN_CAT(EIGEN_VMLMODE_PREFIX_x, VMLMODE)
#define EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, VMLOP, EIGENTYPE, VMLTYPE, VMLMODE) \
template <typename DstXprType, typename SrcXprNested> \
struct Assignment<DstXprType, CwiseUnaryOp<scalar_##EIGENOP##_op<EIGENTYPE>, SrcXprNested>, \
assign_op<EIGENTYPE, EIGENTYPE>, Dense2Dense, \
std::enable_if_t<vml_assign_traits<DstXprType, SrcXprNested>::EnableVml>> { \
typedef CwiseUnaryOp<scalar_##EIGENOP##_op<EIGENTYPE>, SrcXprNested> SrcXprType; \
static void run(DstXprType &dst, const SrcXprType &src, const assign_op<EIGENTYPE, EIGENTYPE> &func) { \
resize_if_allowed(dst, src, func); \
eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols()); \
if (vml_assign_traits<DstXprType, SrcXprNested>::Traversal == (int)LinearTraversal) { \
VMLOP(dst.size(), (const VMLTYPE *)src.nestedExpression().data(), \
(VMLTYPE *)dst.data() EIGEN_PP_EXPAND(EIGEN_VMLMODE_EXPAND_x##VMLMODE)); \
} else { \
const Index outerSize = dst.outerSize(); \
for (Index outer = 0; outer < outerSize; ++outer) { \
const EIGENTYPE *src_ptr = src.IsRowMajor ? &(src.nestedExpression().coeffRef(outer, 0)) \
: &(src.nestedExpression().coeffRef(0, outer)); \
EIGENTYPE *dst_ptr = dst.IsRowMajor ? &(dst.coeffRef(outer, 0)) : &(dst.coeffRef(0, outer)); \
VMLOP(dst.innerSize(), (const VMLTYPE *)src_ptr, \
(VMLTYPE *)dst_ptr EIGEN_PP_EXPAND(EIGEN_VMLMODE_EXPAND_x##VMLMODE)); \
} \
} \
} \
};
#define EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(EIGENOP, VMLOP, VMLMODE) \
EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, EIGEN_CAT(EIGEN_VMLMODE_PREFIX(VMLMODE), s##VMLOP), float, float, VMLMODE) \
EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, EIGEN_CAT(EIGEN_VMLMODE_PREFIX(VMLMODE), d##VMLOP), double, double, VMLMODE)
#define EIGEN_MKL_VML_DECLARE_UNARY_CALLS_CPLX(EIGENOP, VMLOP, VMLMODE) \
EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, EIGEN_CAT(EIGEN_VMLMODE_PREFIX(VMLMODE), c##VMLOP), scomplex, \
MKL_Complex8, VMLMODE) \
EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, EIGEN_CAT(EIGEN_VMLMODE_PREFIX(VMLMODE), z##VMLOP), dcomplex, \
MKL_Complex16, VMLMODE)
#define EIGEN_MKL_VML_DECLARE_UNARY_CALLS(EIGENOP, VMLOP, VMLMODE) \
EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(EIGENOP, VMLOP, VMLMODE) \
EIGEN_MKL_VML_DECLARE_UNARY_CALLS_CPLX(EIGENOP, VMLOP, VMLMODE)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS(sin, Sin, LA)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS(asin, Asin, LA)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS(sinh, Sinh, LA)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS(cos, Cos, LA)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS(acos, Acos, LA)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS(cosh, Cosh, LA)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS(tan, Tan, LA)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS(atan, Atan, LA)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS(tanh, Tanh, LA)
// EIGEN_MKL_VML_DECLARE_UNARY_CALLS(abs, Abs, _)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS(exp, Exp, LA)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS(log, Ln, LA)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS(log10, Log10, LA)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS(sqrt, Sqrt, _)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(square, Sqr, _)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS_CPLX(arg, Arg, _)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(round, Round, _)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(floor, Floor, _)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(ceil, Ceil, _)
EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(cbrt, Cbrt, _)
#define EIGEN_MKL_VML_DECLARE_POW_CALL(EIGENOP, VMLOP, EIGENTYPE, VMLTYPE, VMLMODE) \
template <typename DstXprType, typename SrcXprNested, typename Plain> \
struct Assignment<DstXprType, \
CwiseBinaryOp<scalar_##EIGENOP##_op<EIGENTYPE, EIGENTYPE>, SrcXprNested, \
const CwiseNullaryOp<internal::scalar_constant_op<EIGENTYPE>, Plain>>, \
assign_op<EIGENTYPE, EIGENTYPE>, Dense2Dense, \
std::enable_if_t<vml_assign_traits<DstXprType, SrcXprNested>::EnableVml>> { \
typedef CwiseBinaryOp<scalar_##EIGENOP##_op<EIGENTYPE, EIGENTYPE>, SrcXprNested, \
const CwiseNullaryOp<internal::scalar_constant_op<EIGENTYPE>, Plain>> \
SrcXprType; \
static void run(DstXprType &dst, const SrcXprType &src, const assign_op<EIGENTYPE, EIGENTYPE> &func) { \
resize_if_allowed(dst, src, func); \
eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols()); \
VMLTYPE exponent = reinterpret_cast<const VMLTYPE &>(src.rhs().functor().m_other); \
if (vml_assign_traits<DstXprType, SrcXprNested>::Traversal == LinearTraversal) { \
VMLOP(dst.size(), (const VMLTYPE *)src.lhs().data(), exponent, \
(VMLTYPE *)dst.data() EIGEN_PP_EXPAND(EIGEN_VMLMODE_EXPAND_x##VMLMODE)); \
} else { \
const Index outerSize = dst.outerSize(); \
for (Index outer = 0; outer < outerSize; ++outer) { \
const EIGENTYPE *src_ptr = \
src.IsRowMajor ? &(src.lhs().coeffRef(outer, 0)) : &(src.lhs().coeffRef(0, outer)); \
EIGENTYPE *dst_ptr = dst.IsRowMajor ? &(dst.coeffRef(outer, 0)) : &(dst.coeffRef(0, outer)); \
VMLOP(dst.innerSize(), (const VMLTYPE *)src_ptr, exponent, \
(VMLTYPE *)dst_ptr EIGEN_PP_EXPAND(EIGEN_VMLMODE_EXPAND_x##VMLMODE)); \
} \
} \
} \
};
EIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmsPowx, float, float, LA)
EIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmdPowx, double, double, LA)
EIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmcPowx, scomplex, MKL_Complex8, LA)
EIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmzPowx, dcomplex, MKL_Complex16, LA)
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_ASSIGN_VML_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_BANDMATRIX_H
#define EIGEN_BANDMATRIX_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
template <typename Derived>
class BandMatrixBase : public EigenBase<Derived> {
public:
enum {
Flags = internal::traits<Derived>::Flags,
CoeffReadCost = internal::traits<Derived>::CoeffReadCost,
RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime,
MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime,
Supers = internal::traits<Derived>::Supers,
Subs = internal::traits<Derived>::Subs,
Options = internal::traits<Derived>::Options
};
typedef typename internal::traits<Derived>::Scalar Scalar;
typedef Matrix<Scalar, RowsAtCompileTime, ColsAtCompileTime> DenseMatrixType;
typedef typename DenseMatrixType::StorageIndex StorageIndex;
typedef typename internal::traits<Derived>::CoefficientsType CoefficientsType;
typedef EigenBase<Derived> Base;
protected:
enum {
DataRowsAtCompileTime = ((Supers != Dynamic) && (Subs != Dynamic)) ? 1 + Supers + Subs : Dynamic,
SizeAtCompileTime = min_size_prefer_dynamic(RowsAtCompileTime, ColsAtCompileTime)
};
public:
using Base::cols;
using Base::derived;
using Base::rows;
/** \returns the number of super diagonals */
inline Index supers() const { return derived().supers(); }
/** \returns the number of sub diagonals */
inline Index subs() const { return derived().subs(); }
/** \returns an expression of the underlying coefficient matrix */
inline const CoefficientsType& coeffs() const { return derived().coeffs(); }
/** \returns an expression of the underlying coefficient matrix */
inline CoefficientsType& coeffs() { return derived().coeffs(); }
/** \returns a vector expression of the \a i -th column,
* only the meaningful part is returned.
* \warning the internal storage must be column major. */
inline Block<CoefficientsType, Dynamic, 1> col(Index i) {
EIGEN_STATIC_ASSERT((int(Options) & int(RowMajor)) == 0, THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
Index start = 0;
Index len = coeffs().rows();
if (i <= supers()) {
start = supers() - i;
len = (std::min)(rows(), std::max<Index>(0, coeffs().rows() - (supers() - i)));
} else if (i >= rows() - subs())
len = std::max<Index>(0, coeffs().rows() - (i + 1 - rows() + subs()));
return Block<CoefficientsType, Dynamic, 1>(coeffs(), start, i, len, 1);
}
/** \returns a vector expression of the main diagonal */
inline Block<CoefficientsType, 1, SizeAtCompileTime> diagonal() {
return Block<CoefficientsType, 1, SizeAtCompileTime>(coeffs(), supers(), 0, 1, (std::min)(rows(), cols()));
}
/** \returns a vector expression of the main diagonal (const version) */
inline const Block<const CoefficientsType, 1, SizeAtCompileTime> diagonal() const {
return Block<const CoefficientsType, 1, SizeAtCompileTime>(coeffs(), supers(), 0, 1, (std::min)(rows(), cols()));
}
template <int Index>
struct DiagonalIntReturnType {
enum {
ReturnOpposite =
(int(Options) & int(SelfAdjoint)) && (((Index) > 0 && Supers == 0) || ((Index) < 0 && Subs == 0)),
Conjugate = ReturnOpposite && NumTraits<Scalar>::IsComplex,
ActualIndex = ReturnOpposite ? -Index : Index,
DiagonalSize =
(RowsAtCompileTime == Dynamic || ColsAtCompileTime == Dynamic)
? Dynamic
: (ActualIndex < 0 ? min_size_prefer_dynamic(ColsAtCompileTime, RowsAtCompileTime + ActualIndex)
: min_size_prefer_dynamic(RowsAtCompileTime, ColsAtCompileTime - ActualIndex))
};
typedef Block<CoefficientsType, 1, DiagonalSize> BuildType;
typedef std::conditional_t<Conjugate, CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, BuildType>, BuildType>
Type;
};
/** \returns a vector expression of the \a N -th sub or super diagonal */
template <int N>
inline typename DiagonalIntReturnType<N>::Type diagonal() {
return typename DiagonalIntReturnType<N>::BuildType(coeffs(), supers() - N, (std::max)(0, N), 1, diagonalLength(N));
}
/** \returns a vector expression of the \a N -th sub or super diagonal */
template <int N>
inline const typename DiagonalIntReturnType<N>::Type diagonal() const {
return typename DiagonalIntReturnType<N>::BuildType(coeffs(), supers() - N, (std::max)(0, N), 1, diagonalLength(N));
}
/** \returns a vector expression of the \a i -th sub or super diagonal */
inline Block<CoefficientsType, 1, Dynamic> diagonal(Index i) {
eigen_assert((i < 0 && -i <= subs()) || (i >= 0 && i <= supers()));
return Block<CoefficientsType, 1, Dynamic>(coeffs(), supers() - i, std::max<Index>(0, i), 1, diagonalLength(i));
}
/** \returns a vector expression of the \a i -th sub or super diagonal */
inline const Block<const CoefficientsType, 1, Dynamic> diagonal(Index i) const {
eigen_assert((i < 0 && -i <= subs()) || (i >= 0 && i <= supers()));
return Block<const CoefficientsType, 1, Dynamic>(coeffs(), supers() - i, std::max<Index>(0, i), 1,
diagonalLength(i));
}
template <typename Dest>
inline void evalTo(Dest& dst) const {
dst.resize(rows(), cols());
dst.setZero();
dst.diagonal() = diagonal();
for (Index i = 1; i <= supers(); ++i) dst.diagonal(i) = diagonal(i);
for (Index i = 1; i <= subs(); ++i) dst.diagonal(-i) = diagonal(-i);
}
DenseMatrixType toDenseMatrix() const {
DenseMatrixType res(rows(), cols());
evalTo(res);
return res;
}
protected:
inline Index diagonalLength(Index i) const {
return i < 0 ? (std::min)(cols(), rows() + i) : (std::min)(rows(), cols() - i);
}
};
/**
* \class BandMatrix
* \ingroup Core_Module
*
* \brief Represents a rectangular matrix with a banded storage
*
* \tparam Scalar_ Numeric type, i.e. float, double, int
* \tparam Rows_ Number of rows, or \b Dynamic
* \tparam Cols_ Number of columns, or \b Dynamic
* \tparam Supers_ Number of super diagonal
* \tparam Subs_ Number of sub diagonal
* \tparam Options_ A combination of either \b #RowMajor or \b #ColMajor, and of \b #SelfAdjoint
* The former controls \ref TopicStorageOrders "storage order", and defaults to
* column-major. The latter controls whether the matrix represents a selfadjoint
* matrix in which case either Supers of Subs have to be null.
*
* \sa class TridiagonalMatrix
*/
template <typename Scalar_, int Rows_, int Cols_, int Supers_, int Subs_, int Options_>
struct traits<BandMatrix<Scalar_, Rows_, Cols_, Supers_, Subs_, Options_> > {
typedef Scalar_ Scalar;
typedef Dense StorageKind;
typedef Eigen::Index StorageIndex;
enum {
CoeffReadCost = NumTraits<Scalar>::ReadCost,
RowsAtCompileTime = Rows_,
ColsAtCompileTime = Cols_,
MaxRowsAtCompileTime = Rows_,
MaxColsAtCompileTime = Cols_,
Flags = LvalueBit,
Supers = Supers_,
Subs = Subs_,
Options = Options_,
DataRowsAtCompileTime = ((Supers != Dynamic) && (Subs != Dynamic)) ? 1 + Supers + Subs : Dynamic
};
typedef Matrix<Scalar, DataRowsAtCompileTime, ColsAtCompileTime, int(Options) & int(RowMajor) ? RowMajor : ColMajor>
CoefficientsType;
};
template <typename Scalar_, int Rows, int Cols, int Supers, int Subs, int Options>
class BandMatrix : public BandMatrixBase<BandMatrix<Scalar_, Rows, Cols, Supers, Subs, Options> > {
public:
typedef typename internal::traits<BandMatrix>::Scalar Scalar;
typedef typename internal::traits<BandMatrix>::StorageIndex StorageIndex;
typedef typename internal::traits<BandMatrix>::CoefficientsType CoefficientsType;
explicit inline BandMatrix(Index rows = Rows, Index cols = Cols, Index supers = Supers, Index subs = Subs)
: m_coeffs(1 + supers + subs, cols), m_rows(rows), m_supers(supers), m_subs(subs) {}
/** \returns the number of columns */
constexpr Index rows() const { return m_rows.value(); }
/** \returns the number of rows */
constexpr Index cols() const { return m_coeffs.cols(); }
/** \returns the number of super diagonals */
constexpr Index supers() const { return m_supers.value(); }
/** \returns the number of sub diagonals */
constexpr Index subs() const { return m_subs.value(); }
inline const CoefficientsType& coeffs() const { return m_coeffs; }
inline CoefficientsType& coeffs() { return m_coeffs; }
protected:
CoefficientsType m_coeffs;
internal::variable_if_dynamic<Index, Rows> m_rows;
internal::variable_if_dynamic<Index, Supers> m_supers;
internal::variable_if_dynamic<Index, Subs> m_subs;
};
template <typename CoefficientsType_, int Rows_, int Cols_, int Supers_, int Subs_, int Options_>
class BandMatrixWrapper;
template <typename CoefficientsType_, int Rows_, int Cols_, int Supers_, int Subs_, int Options_>
struct traits<BandMatrixWrapper<CoefficientsType_, Rows_, Cols_, Supers_, Subs_, Options_> > {
typedef typename CoefficientsType_::Scalar Scalar;
typedef typename CoefficientsType_::StorageKind StorageKind;
typedef typename CoefficientsType_::StorageIndex StorageIndex;
enum {
CoeffReadCost = internal::traits<CoefficientsType_>::CoeffReadCost,
RowsAtCompileTime = Rows_,
ColsAtCompileTime = Cols_,
MaxRowsAtCompileTime = Rows_,
MaxColsAtCompileTime = Cols_,
Flags = LvalueBit,
Supers = Supers_,
Subs = Subs_,
Options = Options_,
DataRowsAtCompileTime = ((Supers != Dynamic) && (Subs != Dynamic)) ? 1 + Supers + Subs : Dynamic
};
typedef CoefficientsType_ CoefficientsType;
};
template <typename CoefficientsType_, int Rows_, int Cols_, int Supers_, int Subs_, int Options_>
class BandMatrixWrapper
: public BandMatrixBase<BandMatrixWrapper<CoefficientsType_, Rows_, Cols_, Supers_, Subs_, Options_> > {
public:
typedef typename internal::traits<BandMatrixWrapper>::Scalar Scalar;
typedef typename internal::traits<BandMatrixWrapper>::CoefficientsType CoefficientsType;
typedef typename internal::traits<BandMatrixWrapper>::StorageIndex StorageIndex;
explicit inline BandMatrixWrapper(const CoefficientsType& coeffs, Index rows = Rows_, Index cols = Cols_,
Index supers = Supers_, Index subs = Subs_)
: m_coeffs(coeffs), m_rows(rows), m_supers(supers), m_subs(subs) {
EIGEN_UNUSED_VARIABLE(cols);
// eigen_assert(coeffs.cols()==cols() && (supers()+subs()+1)==coeffs.rows());
}
/** \returns the number of columns */
constexpr Index rows() const { return m_rows.value(); }
/** \returns the number of rows */
constexpr Index cols() const { return m_coeffs.cols(); }
/** \returns the number of super diagonals */
constexpr Index supers() const { return m_supers.value(); }
/** \returns the number of sub diagonals */
constexpr Index subs() const { return m_subs.value(); }
inline const CoefficientsType& coeffs() const { return m_coeffs; }
protected:
const CoefficientsType& m_coeffs;
internal::variable_if_dynamic<Index, Rows_> m_rows;
internal::variable_if_dynamic<Index, Supers_> m_supers;
internal::variable_if_dynamic<Index, Subs_> m_subs;
};
/**
* \class TridiagonalMatrix
* \ingroup Core_Module
*
* \brief Represents a tridiagonal matrix with a compact banded storage
*
* \tparam Scalar Numeric type, i.e. float, double, int
* \tparam Size Number of rows and cols, or \b Dynamic
* \tparam Options Can be 0 or \b SelfAdjoint
*
* \sa class BandMatrix
*/
template <typename Scalar, int Size, int Options>
class TridiagonalMatrix : public BandMatrix<Scalar, Size, Size, Options & SelfAdjoint ? 0 : 1, 1, Options | RowMajor> {
typedef BandMatrix<Scalar, Size, Size, Options & SelfAdjoint ? 0 : 1, 1, Options | RowMajor> Base;
typedef typename Base::StorageIndex StorageIndex;
public:
explicit TridiagonalMatrix(Index size = Size) : Base(size, size, Options & SelfAdjoint ? 0 : 1, 1) {}
inline typename Base::template DiagonalIntReturnType<1>::Type super() { return Base::template diagonal<1>(); }
inline const typename Base::template DiagonalIntReturnType<1>::Type super() const {
return Base::template diagonal<1>();
}
inline typename Base::template DiagonalIntReturnType<-1>::Type sub() { return Base::template diagonal<-1>(); }
inline const typename Base::template DiagonalIntReturnType<-1>::Type sub() const {
return Base::template diagonal<-1>();
}
protected:
};
struct BandShape {};
template <typename Scalar_, int Rows_, int Cols_, int Supers_, int Subs_, int Options_>
struct evaluator_traits<BandMatrix<Scalar_, Rows_, Cols_, Supers_, Subs_, Options_> >
: public evaluator_traits_base<BandMatrix<Scalar_, Rows_, Cols_, Supers_, Subs_, Options_> > {
typedef BandShape Shape;
};
template <typename CoefficientsType_, int Rows_, int Cols_, int Supers_, int Subs_, int Options_>
struct evaluator_traits<BandMatrixWrapper<CoefficientsType_, Rows_, Cols_, Supers_, Subs_, Options_> >
: public evaluator_traits_base<BandMatrixWrapper<CoefficientsType_, Rows_, Cols_, Supers_, Subs_, Options_> > {
typedef BandShape Shape;
};
template <>
struct AssignmentKind<DenseShape, BandShape> {
typedef EigenBase2EigenBase Kind;
};
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_BANDMATRIX_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_BLOCK_H
#define EIGEN_BLOCK_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
template <typename XprType_, int BlockRows, int BlockCols, bool InnerPanel_>
struct traits<Block<XprType_, BlockRows, BlockCols, InnerPanel_>> : traits<XprType_> {
typedef typename traits<XprType_>::Scalar Scalar;
typedef typename traits<XprType_>::StorageKind StorageKind;
typedef typename traits<XprType_>::XprKind XprKind;
typedef typename ref_selector<XprType_>::type XprTypeNested;
typedef std::remove_reference_t<XprTypeNested> XprTypeNested_;
enum {
MatrixRows = traits<XprType_>::RowsAtCompileTime,
MatrixCols = traits<XprType_>::ColsAtCompileTime,
RowsAtCompileTime = MatrixRows == 0 ? 0 : BlockRows,
ColsAtCompileTime = MatrixCols == 0 ? 0 : BlockCols,
MaxRowsAtCompileTime = BlockRows == 0 ? 0
: RowsAtCompileTime != Dynamic ? int(RowsAtCompileTime)
: int(traits<XprType_>::MaxRowsAtCompileTime),
MaxColsAtCompileTime = BlockCols == 0 ? 0
: ColsAtCompileTime != Dynamic ? int(ColsAtCompileTime)
: int(traits<XprType_>::MaxColsAtCompileTime),
XprTypeIsRowMajor = (int(traits<XprType_>::Flags) & RowMajorBit) != 0,
IsRowMajor = (MaxRowsAtCompileTime == 1 && MaxColsAtCompileTime != 1) ? 1
: (MaxColsAtCompileTime == 1 && MaxRowsAtCompileTime != 1) ? 0
: XprTypeIsRowMajor,
HasSameStorageOrderAsXprType = (IsRowMajor == XprTypeIsRowMajor),
InnerSize = IsRowMajor ? int(ColsAtCompileTime) : int(RowsAtCompileTime),
InnerStrideAtCompileTime = HasSameStorageOrderAsXprType ? int(inner_stride_at_compile_time<XprType_>::ret)
: int(outer_stride_at_compile_time<XprType_>::ret),
OuterStrideAtCompileTime = HasSameStorageOrderAsXprType ? int(outer_stride_at_compile_time<XprType_>::ret)
: int(inner_stride_at_compile_time<XprType_>::ret),
// FIXME, this traits is rather specialized for dense object and it needs to be cleaned further
FlagsLvalueBit = is_lvalue<XprType_>::value ? LvalueBit : 0,
FlagsRowMajorBit = IsRowMajor ? RowMajorBit : 0,
Flags = (traits<XprType_>::Flags & (DirectAccessBit | (InnerPanel_ ? CompressedAccessBit : 0))) | FlagsLvalueBit |
FlagsRowMajorBit,
// FIXME DirectAccessBit should not be handled by expressions
//
// Alignment is needed by MapBase's assertions
// We can sefely set it to false here. Internal alignment errors will be detected by an eigen_internal_assert in the
// respective evaluator
Alignment = 0,
InnerPanel = InnerPanel_ ? 1 : 0
};
};
template <typename XprType, int BlockRows = Dynamic, int BlockCols = Dynamic, bool InnerPanel = false,
bool HasDirectAccess = internal::has_direct_access<XprType>::ret>
class BlockImpl_dense;
} // end namespace internal
template <typename XprType, int BlockRows, int BlockCols, bool InnerPanel, typename StorageKind>
class BlockImpl;
/** \class Block
* \ingroup Core_Module
*
* \brief Expression of a fixed-size or dynamic-size block
*
* \tparam XprType the type of the expression in which we are taking a block
* \tparam BlockRows the number of rows of the block we are taking at compile time (optional)
* \tparam BlockCols the number of columns of the block we are taking at compile time (optional)
* \tparam InnerPanel is true, if the block maps to a set of rows of a row major matrix or
* to set of columns of a column major matrix (optional). The parameter allows to determine
* at compile time whether aligned access is possible on the block expression.
*
* This class represents an expression of either a fixed-size or dynamic-size block. It is the return
* type of DenseBase::block(Index,Index,Index,Index) and DenseBase::block<int,int>(Index,Index) and
* most of the time this is the only way it is used.
*
* However, if you want to directly manipulate block expressions,
* for instance if you want to write a function returning such an expression, you
* will need to use this class.
*
* Here is an example illustrating the dynamic case:
* \include class_Block.cpp
* Output: \verbinclude class_Block.out
*
* \note Even though this expression has dynamic size, in the case where \a XprType
* has fixed size, this expression inherits a fixed maximal size which means that evaluating
* it does not cause a dynamic memory allocation.
*
* Here is an example illustrating the fixed-size case:
* \include class_FixedBlock.cpp
* Output: \verbinclude class_FixedBlock.out
*
* \sa DenseBase::block(Index,Index,Index,Index), DenseBase::block(Index,Index), class VectorBlock
*/
template <typename XprType, int BlockRows, int BlockCols, bool InnerPanel>
class Block
: public BlockImpl<XprType, BlockRows, BlockCols, InnerPanel, typename internal::traits<XprType>::StorageKind> {
typedef BlockImpl<XprType, BlockRows, BlockCols, InnerPanel, typename internal::traits<XprType>::StorageKind> Impl;
using BlockHelper = internal::block_xpr_helper<Block>;
public:
// typedef typename Impl::Base Base;
typedef Impl Base;
EIGEN_GENERIC_PUBLIC_INTERFACE(Block)
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Block)
typedef internal::remove_all_t<XprType> NestedExpression;
/** Column or Row constructor
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Block(XprType& xpr, Index i) : Impl(xpr, i) {
eigen_assert((i >= 0) && (((BlockRows == 1) && (BlockCols == XprType::ColsAtCompileTime) && i < xpr.rows()) ||
((BlockRows == XprType::RowsAtCompileTime) && (BlockCols == 1) && i < xpr.cols())));
}
/** Fixed-size constructor
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Block(XprType& xpr, Index startRow, Index startCol)
: Impl(xpr, startRow, startCol) {
EIGEN_STATIC_ASSERT(RowsAtCompileTime != Dynamic && ColsAtCompileTime != Dynamic,
THIS_METHOD_IS_ONLY_FOR_FIXED_SIZE)
eigen_assert(startRow >= 0 && BlockRows >= 0 && startRow + BlockRows <= xpr.rows() && startCol >= 0 &&
BlockCols >= 0 && startCol + BlockCols <= xpr.cols());
}
/** Dynamic-size constructor
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Block(XprType& xpr, Index startRow, Index startCol, Index blockRows,
Index blockCols)
: Impl(xpr, startRow, startCol, blockRows, blockCols) {
eigen_assert((RowsAtCompileTime == Dynamic || RowsAtCompileTime == blockRows) &&
(ColsAtCompileTime == Dynamic || ColsAtCompileTime == blockCols));
eigen_assert(startRow >= 0 && blockRows >= 0 && startRow <= xpr.rows() - blockRows && startCol >= 0 &&
blockCols >= 0 && startCol <= xpr.cols() - blockCols);
}
// convert nested blocks (e.g. Block<Block<MatrixType>>) to a simple block expression (Block<MatrixType>)
using ConstUnwindReturnType = Block<const typename BlockHelper::BaseType, BlockRows, BlockCols, InnerPanel>;
using UnwindReturnType = Block<typename BlockHelper::BaseType, BlockRows, BlockCols, InnerPanel>;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ConstUnwindReturnType unwind() const {
return ConstUnwindReturnType(BlockHelper::base(*this), BlockHelper::row(*this, 0), BlockHelper::col(*this, 0),
this->rows(), this->cols());
}
template <typename T = Block, typename EnableIf = std::enable_if_t<!std::is_const<T>::value>>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE UnwindReturnType unwind() {
return UnwindReturnType(BlockHelper::base(*this), BlockHelper::row(*this, 0), BlockHelper::col(*this, 0),
this->rows(), this->cols());
}
};
// The generic default implementation for dense block simply forward to the internal::BlockImpl_dense
// that must be specialized for direct and non-direct access...
template <typename XprType, int BlockRows, int BlockCols, bool InnerPanel>
class BlockImpl<XprType, BlockRows, BlockCols, InnerPanel, Dense>
: public internal::BlockImpl_dense<XprType, BlockRows, BlockCols, InnerPanel> {
typedef internal::BlockImpl_dense<XprType, BlockRows, BlockCols, InnerPanel> Impl;
typedef typename XprType::StorageIndex StorageIndex;
public:
typedef Impl Base;
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(BlockImpl)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE BlockImpl(XprType& xpr, Index i) : Impl(xpr, i) {}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE BlockImpl(XprType& xpr, Index startRow, Index startCol)
: Impl(xpr, startRow, startCol) {}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE BlockImpl(XprType& xpr, Index startRow, Index startCol, Index blockRows,
Index blockCols)
: Impl(xpr, startRow, startCol, blockRows, blockCols) {}
};
namespace internal {
/** \internal Internal implementation of dense Blocks in the general case. */
template <typename XprType, int BlockRows, int BlockCols, bool InnerPanel, bool HasDirectAccess>
class BlockImpl_dense : public internal::dense_xpr_base<Block<XprType, BlockRows, BlockCols, InnerPanel>>::type {
typedef Block<XprType, BlockRows, BlockCols, InnerPanel> BlockType;
typedef typename internal::ref_selector<XprType>::non_const_type XprTypeNested;
public:
typedef typename internal::dense_xpr_base<BlockType>::type Base;
EIGEN_DENSE_PUBLIC_INTERFACE(BlockType)
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(BlockImpl_dense)
// class InnerIterator; // FIXME apparently never used
/** Column or Row constructor
*/
EIGEN_DEVICE_FUNC inline BlockImpl_dense(XprType& xpr, Index i)
: m_xpr(xpr),
// It is a row if and only if BlockRows==1 and BlockCols==XprType::ColsAtCompileTime,
// and it is a column if and only if BlockRows==XprType::RowsAtCompileTime and BlockCols==1,
// all other cases are invalid.
// The case a 1x1 matrix seems ambiguous, but the result is the same anyway.
m_startRow((BlockRows == 1) && (BlockCols == XprType::ColsAtCompileTime) ? i : 0),
m_startCol((BlockRows == XprType::RowsAtCompileTime) && (BlockCols == 1) ? i : 0),
m_blockRows(BlockRows == 1 ? 1 : xpr.rows()),
m_blockCols(BlockCols == 1 ? 1 : xpr.cols()) {}
/** Fixed-size constructor
*/
EIGEN_DEVICE_FUNC inline BlockImpl_dense(XprType& xpr, Index startRow, Index startCol)
: m_xpr(xpr), m_startRow(startRow), m_startCol(startCol), m_blockRows(BlockRows), m_blockCols(BlockCols) {}
/** Dynamic-size constructor
*/
EIGEN_DEVICE_FUNC inline BlockImpl_dense(XprType& xpr, Index startRow, Index startCol, Index blockRows,
Index blockCols)
: m_xpr(xpr), m_startRow(startRow), m_startCol(startCol), m_blockRows(blockRows), m_blockCols(blockCols) {}
EIGEN_DEVICE_FUNC inline Index rows() const { return m_blockRows.value(); }
EIGEN_DEVICE_FUNC inline Index cols() const { return m_blockCols.value(); }
EIGEN_DEVICE_FUNC inline Scalar& coeffRef(Index rowId, Index colId) {
EIGEN_STATIC_ASSERT_LVALUE(XprType)
return m_xpr.coeffRef(rowId + m_startRow.value(), colId + m_startCol.value());
}
EIGEN_DEVICE_FUNC inline const Scalar& coeffRef(Index rowId, Index colId) const {
return m_xpr.derived().coeffRef(rowId + m_startRow.value(), colId + m_startCol.value());
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CoeffReturnType coeff(Index rowId, Index colId) const {
return m_xpr.coeff(rowId + m_startRow.value(), colId + m_startCol.value());
}
EIGEN_DEVICE_FUNC inline Scalar& coeffRef(Index index) {
EIGEN_STATIC_ASSERT_LVALUE(XprType)
return m_xpr.coeffRef(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
}
EIGEN_DEVICE_FUNC inline const Scalar& coeffRef(Index index) const {
return m_xpr.coeffRef(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
}
EIGEN_DEVICE_FUNC inline const CoeffReturnType coeff(Index index) const {
return m_xpr.coeff(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
}
template <int LoadMode>
EIGEN_DEVICE_FUNC inline PacketScalar packet(Index rowId, Index colId) const {
return m_xpr.template packet<Unaligned>(rowId + m_startRow.value(), colId + m_startCol.value());
}
template <int LoadMode>
EIGEN_DEVICE_FUNC inline void writePacket(Index rowId, Index colId, const PacketScalar& val) {
m_xpr.template writePacket<Unaligned>(rowId + m_startRow.value(), colId + m_startCol.value(), val);
}
template <int LoadMode>
EIGEN_DEVICE_FUNC inline PacketScalar packet(Index index) const {
return m_xpr.template packet<Unaligned>(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
}
template <int LoadMode>
EIGEN_DEVICE_FUNC inline void writePacket(Index index, const PacketScalar& val) {
m_xpr.template writePacket<Unaligned>(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0), val);
}
#ifdef EIGEN_PARSED_BY_DOXYGEN
/** \sa MapBase::data() */
EIGEN_DEVICE_FUNC constexpr const Scalar* data() const;
EIGEN_DEVICE_FUNC inline Index innerStride() const;
EIGEN_DEVICE_FUNC inline Index outerStride() const;
#endif
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const internal::remove_all_t<XprTypeNested>& nestedExpression() const {
return m_xpr;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE XprType& nestedExpression() { return m_xpr; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr StorageIndex startRow() const noexcept { return m_startRow.value(); }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr StorageIndex startCol() const noexcept { return m_startCol.value(); }
protected:
XprTypeNested m_xpr;
const internal::variable_if_dynamic<StorageIndex, (XprType::RowsAtCompileTime == 1 && BlockRows == 1) ? 0 : Dynamic>
m_startRow;
const internal::variable_if_dynamic<StorageIndex, (XprType::ColsAtCompileTime == 1 && BlockCols == 1) ? 0 : Dynamic>
m_startCol;
const internal::variable_if_dynamic<StorageIndex, RowsAtCompileTime> m_blockRows;
const internal::variable_if_dynamic<StorageIndex, ColsAtCompileTime> m_blockCols;
};
/** \internal Internal implementation of dense Blocks in the direct access case.*/
template <typename XprType, int BlockRows, int BlockCols, bool InnerPanel>
class BlockImpl_dense<XprType, BlockRows, BlockCols, InnerPanel, true>
: public MapBase<Block<XprType, BlockRows, BlockCols, InnerPanel>> {
typedef Block<XprType, BlockRows, BlockCols, InnerPanel> BlockType;
typedef typename internal::ref_selector<XprType>::non_const_type XprTypeNested;
enum { XprTypeIsRowMajor = (int(traits<XprType>::Flags) & RowMajorBit) != 0 };
/** \internal Returns base+offset (unless base is null, in which case returns null).
* Adding an offset to nullptr is undefined behavior, so we must avoid it.
*/
template <typename Scalar>
EIGEN_DEVICE_FUNC constexpr EIGEN_ALWAYS_INLINE static Scalar* add_to_nullable_pointer(Scalar* base, Index offset) {
return base != nullptr ? base + offset : nullptr;
}
public:
typedef MapBase<BlockType> Base;
EIGEN_DENSE_PUBLIC_INTERFACE(BlockType)
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(BlockImpl_dense)
/** Column or Row constructor
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE BlockImpl_dense(XprType& xpr, Index i)
: Base((BlockRows == 0 || BlockCols == 0)
? nullptr
: add_to_nullable_pointer(
xpr.data(),
i * (((BlockRows == 1) && (BlockCols == XprType::ColsAtCompileTime) && (!XprTypeIsRowMajor)) ||
((BlockRows == XprType::RowsAtCompileTime) && (BlockCols == 1) &&
(XprTypeIsRowMajor))
? xpr.innerStride()
: xpr.outerStride())),
BlockRows == 1 ? 1 : xpr.rows(), BlockCols == 1 ? 1 : xpr.cols()),
m_xpr(xpr),
m_startRow((BlockRows == 1) && (BlockCols == XprType::ColsAtCompileTime) ? i : 0),
m_startCol((BlockRows == XprType::RowsAtCompileTime) && (BlockCols == 1) ? i : 0) {
init();
}
/** Fixed-size constructor
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE BlockImpl_dense(XprType& xpr, Index startRow, Index startCol)
: Base((BlockRows == 0 || BlockCols == 0)
? nullptr
: add_to_nullable_pointer(xpr.data(),
xpr.innerStride() * (XprTypeIsRowMajor ? startCol : startRow) +
xpr.outerStride() * (XprTypeIsRowMajor ? startRow : startCol))),
m_xpr(xpr),
m_startRow(startRow),
m_startCol(startCol) {
init();
}
/** Dynamic-size constructor
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE BlockImpl_dense(XprType& xpr, Index startRow, Index startCol, Index blockRows,
Index blockCols)
: Base((blockRows == 0 || blockCols == 0)
? nullptr
: add_to_nullable_pointer(xpr.data(),
xpr.innerStride() * (XprTypeIsRowMajor ? startCol : startRow) +
xpr.outerStride() * (XprTypeIsRowMajor ? startRow : startCol)),
blockRows, blockCols),
m_xpr(xpr),
m_startRow(startRow),
m_startCol(startCol) {
init();
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const internal::remove_all_t<XprTypeNested>& nestedExpression() const noexcept {
return m_xpr;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE XprType& nestedExpression() { return m_xpr; }
/** \sa MapBase::innerStride() */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index innerStride() const noexcept {
return internal::traits<BlockType>::HasSameStorageOrderAsXprType ? m_xpr.innerStride() : m_xpr.outerStride();
}
/** \sa MapBase::outerStride() */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index outerStride() const noexcept {
return internal::traits<BlockType>::HasSameStorageOrderAsXprType ? m_xpr.outerStride() : m_xpr.innerStride();
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr StorageIndex startRow() const noexcept { return m_startRow.value(); }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr StorageIndex startCol() const noexcept { return m_startCol.value(); }
#ifndef __SUNPRO_CC
// FIXME sunstudio is not friendly with the above friend...
// META-FIXME there is no 'friend' keyword around here. Is this obsolete?
protected:
#endif
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** \internal used by allowAligned() */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE BlockImpl_dense(XprType& xpr, const Scalar* data, Index blockRows,
Index blockCols)
: Base(data, blockRows, blockCols), m_xpr(xpr) {
init();
}
#endif
protected:
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void init() {
m_outerStride =
internal::traits<BlockType>::HasSameStorageOrderAsXprType ? m_xpr.outerStride() : m_xpr.innerStride();
}
XprTypeNested m_xpr;
const internal::variable_if_dynamic<StorageIndex, (XprType::RowsAtCompileTime == 1 && BlockRows == 1) ? 0 : Dynamic>
m_startRow;
const internal::variable_if_dynamic<StorageIndex, (XprType::ColsAtCompileTime == 1 && BlockCols == 1) ? 0 : Dynamic>
m_startCol;
Index m_outerStride;
};
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_BLOCK_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_COMMAINITIALIZER_H
#define EIGEN_COMMAINITIALIZER_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
/** \class CommaInitializer
* \ingroup Core_Module
*
* \brief Helper class used by the comma initializer operator
*
* This class is internally used to implement the comma initializer feature. It is
* the return type of MatrixBase::operator<<, and most of the time this is the only
* way it is used.
*
* \sa \blank \ref MatrixBaseCommaInitRef "MatrixBase::operator<<", CommaInitializer::finished()
*/
template <typename XprType>
struct CommaInitializer {
typedef typename XprType::Scalar Scalar;
EIGEN_DEVICE_FUNC inline CommaInitializer(XprType& xpr, const Scalar& s)
: m_xpr(xpr), m_row(0), m_col(1), m_currentBlockRows(1) {
eigen_assert(m_xpr.rows() > 0 && m_xpr.cols() > 0 && "Cannot comma-initialize a 0x0 matrix (operator<<)");
m_xpr.coeffRef(0, 0) = s;
}
template <typename OtherDerived>
EIGEN_DEVICE_FUNC inline CommaInitializer(XprType& xpr, const DenseBase<OtherDerived>& other)
: m_xpr(xpr), m_row(0), m_col(other.cols()), m_currentBlockRows(other.rows()) {
eigen_assert(m_xpr.rows() >= other.rows() && m_xpr.cols() >= other.cols() &&
"Cannot comma-initialize a 0x0 matrix (operator<<)");
m_xpr.template block<OtherDerived::RowsAtCompileTime, OtherDerived::ColsAtCompileTime>(0, 0, other.rows(),
other.cols()) = other;
}
/* Copy/Move constructor which transfers ownership. This is crucial in
* absence of return value optimization to avoid assertions during destruction. */
// FIXME in C++11 mode this could be replaced by a proper RValue constructor
EIGEN_DEVICE_FUNC inline CommaInitializer(const CommaInitializer& o)
: m_xpr(o.m_xpr), m_row(o.m_row), m_col(o.m_col), m_currentBlockRows(o.m_currentBlockRows) {
// Mark original object as finished. In absence of R-value references we need to const_cast:
const_cast<CommaInitializer&>(o).m_row = m_xpr.rows();
const_cast<CommaInitializer&>(o).m_col = m_xpr.cols();
const_cast<CommaInitializer&>(o).m_currentBlockRows = 0;
}
/* inserts a scalar value in the target matrix */
EIGEN_DEVICE_FUNC CommaInitializer &operator,(const Scalar& s) {
if (m_col == m_xpr.cols()) {
m_row += m_currentBlockRows;
m_col = 0;
m_currentBlockRows = 1;
eigen_assert(m_row < m_xpr.rows() && "Too many rows passed to comma initializer (operator<<)");
}
eigen_assert(m_col < m_xpr.cols() && "Too many coefficients passed to comma initializer (operator<<)");
eigen_assert(m_currentBlockRows == 1);
m_xpr.coeffRef(m_row, m_col++) = s;
return *this;
}
/* inserts a matrix expression in the target matrix */
template <typename OtherDerived>
EIGEN_DEVICE_FUNC CommaInitializer &operator,(const DenseBase<OtherDerived>& other) {
if (m_col == m_xpr.cols() && (other.cols() != 0 || other.rows() != m_currentBlockRows)) {
m_row += m_currentBlockRows;
m_col = 0;
m_currentBlockRows = other.rows();
eigen_assert(m_row + m_currentBlockRows <= m_xpr.rows() &&
"Too many rows passed to comma initializer (operator<<)");
}
eigen_assert((m_col + other.cols() <= m_xpr.cols()) &&
"Too many coefficients passed to comma initializer (operator<<)");
eigen_assert(m_currentBlockRows == other.rows());
m_xpr.template block<OtherDerived::RowsAtCompileTime, OtherDerived::ColsAtCompileTime>(m_row, m_col, other.rows(),
other.cols()) = other;
m_col += other.cols();
return *this;
}
EIGEN_DEVICE_FUNC inline ~CommaInitializer()
#if defined VERIFY_RAISES_ASSERT && (!defined EIGEN_NO_ASSERTION_CHECKING) && defined EIGEN_EXCEPTIONS
noexcept(false) // Eigen::eigen_assert_exception
#endif
{
finished();
}
/** \returns the built matrix once all its coefficients have been set.
* Calling finished is 100% optional. Its purpose is to write expressions
* like this:
* \code
* quaternion.fromRotationMatrix((Matrix3f() << axis0, axis1, axis2).finished());
* \endcode
*/
EIGEN_DEVICE_FUNC inline XprType& finished() {
eigen_assert(((m_row + m_currentBlockRows) == m_xpr.rows() || m_xpr.cols() == 0) && m_col == m_xpr.cols() &&
"Too few coefficients passed to comma initializer (operator<<)");
return m_xpr;
}
XprType& m_xpr; // target expression
Index m_row; // current row id
Index m_col; // current col id
Index m_currentBlockRows; // current block height
};
/** \anchor MatrixBaseCommaInitRef
* Convenient operator to set the coefficients of a matrix.
*
* The coefficients must be provided in a row major order and exactly match
* the size of the matrix. Otherwise an assertion is raised.
*
* Example: \include MatrixBase_set.cpp
* Output: \verbinclude MatrixBase_set.out
*
* \note According the c++ standard, the argument expressions of this comma initializer are evaluated in arbitrary
* order.
*
* \sa CommaInitializer::finished(), class CommaInitializer
*/
template <typename Derived>
EIGEN_DEVICE_FUNC inline CommaInitializer<Derived> DenseBase<Derived>::operator<<(const Scalar& s) {
return CommaInitializer<Derived>(*static_cast<Derived*>(this), s);
}
/** \sa operator<<(const Scalar&) */
template <typename Derived>
template <typename OtherDerived>
EIGEN_DEVICE_FUNC inline CommaInitializer<Derived> DenseBase<Derived>::operator<<(
const DenseBase<OtherDerived>& other) {
return CommaInitializer<Derived>(*static_cast<Derived*>(this), other);
}
} // end namespace Eigen
#endif // EIGEN_COMMAINITIALIZER_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2016 Rasmus Munk Larsen (rmlarsen@google.com)
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_CONDITIONESTIMATOR_H
#define EIGEN_CONDITIONESTIMATOR_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
template <typename Vector, typename RealVector, bool IsComplex>
struct rcond_compute_sign {
static inline Vector run(const Vector& v) {
const RealVector v_abs = v.cwiseAbs();
return (v_abs.array() == static_cast<typename Vector::RealScalar>(0))
.select(Vector::Ones(v.size()), v.cwiseQuotient(v_abs));
}
};
// Partial specialization to avoid elementwise division for real vectors.
template <typename Vector>
struct rcond_compute_sign<Vector, Vector, false> {
static inline Vector run(const Vector& v) {
return (v.array() < static_cast<typename Vector::RealScalar>(0))
.select(-Vector::Ones(v.size()), Vector::Ones(v.size()));
}
};
/**
* \returns an estimate of ||inv(matrix)||_1 given a decomposition of
* \a matrix that implements .solve() and .adjoint().solve() methods.
*
* This function implements Algorithms 4.1 and 5.1 from
* http://www.maths.manchester.ac.uk/~higham/narep/narep135.pdf
* which also forms the basis for the condition number estimators in
* LAPACK. Since at most 10 calls to the solve method of dec are
* performed, the total cost is O(dims^2), as opposed to O(dims^3)
* needed to compute the inverse matrix explicitly.
*
* The most common usage is in estimating the condition number
* ||matrix||_1 * ||inv(matrix)||_1. The first term ||matrix||_1 can be
* computed directly in O(n^2) operations.
*
* Supports the following decompositions: FullPivLU, PartialPivLU, LDLT, and
* LLT.
*
* \sa FullPivLU, PartialPivLU, LDLT, LLT.
*/
template <typename Decomposition>
typename Decomposition::RealScalar rcond_invmatrix_L1_norm_estimate(const Decomposition& dec) {
typedef typename Decomposition::MatrixType MatrixType;
typedef typename Decomposition::Scalar Scalar;
typedef typename Decomposition::RealScalar RealScalar;
typedef typename internal::plain_col_type<MatrixType>::type Vector;
typedef typename internal::plain_col_type<MatrixType, RealScalar>::type RealVector;
const bool is_complex = (NumTraits<Scalar>::IsComplex != 0);
eigen_assert(dec.rows() == dec.cols());
const Index n = dec.rows();
if (n == 0) return 0;
// Disable Index to float conversion warning
#ifdef __INTEL_COMPILER
#pragma warning push
#pragma warning(disable : 2259)
#endif
Vector v = dec.solve(Vector::Ones(n) / Scalar(n));
#ifdef __INTEL_COMPILER
#pragma warning pop
#endif
// lower_bound is a lower bound on
// ||inv(matrix)||_1 = sup_v ||inv(matrix) v||_1 / ||v||_1
// and is the objective maximized by the ("super-") gradient ascent
// algorithm below.
RealScalar lower_bound = v.template lpNorm<1>();
if (n == 1) return lower_bound;
// Gradient ascent algorithm follows: We know that the optimum is achieved at
// one of the simplices v = e_i, so in each iteration we follow a
// super-gradient to move towards the optimal one.
RealScalar old_lower_bound = lower_bound;
Vector sign_vector(n);
Vector old_sign_vector;
Index v_max_abs_index = -1;
Index old_v_max_abs_index = v_max_abs_index;
for (int k = 0; k < 4; ++k) {
sign_vector = internal::rcond_compute_sign<Vector, RealVector, is_complex>::run(v);
if (k > 0 && !is_complex && sign_vector == old_sign_vector) {
// Break if the solution stagnated.
break;
}
// v_max_abs_index = argmax |real( inv(matrix)^T * sign_vector )|
v = dec.adjoint().solve(sign_vector);
v.real().cwiseAbs().maxCoeff(&v_max_abs_index);
if (v_max_abs_index == old_v_max_abs_index) {
// Break if the solution stagnated.
break;
}
// Move to the new simplex e_j, where j = v_max_abs_index.
v = dec.solve(Vector::Unit(n, v_max_abs_index)); // v = inv(matrix) * e_j.
lower_bound = v.template lpNorm<1>();
if (lower_bound <= old_lower_bound) {
// Break if the gradient step did not increase the lower_bound.
break;
}
if (!is_complex) {
old_sign_vector = sign_vector;
}
old_v_max_abs_index = v_max_abs_index;
old_lower_bound = lower_bound;
}
// The following calculates an independent estimate of ||matrix||_1 by
// multiplying matrix by a vector with entries of slowly increasing
// magnitude and alternating sign:
// v_i = (-1)^{i} (1 + (i / (dim-1))), i = 0,...,dim-1.
// This improvement to Hager's algorithm above is due to Higham. It was
// added to make the algorithm more robust in certain corner cases where
// large elements in the matrix might otherwise escape detection due to
// exact cancellation (especially when op and op_adjoint correspond to a
// sequence of backsubstitutions and permutations), which could cause
// Hager's algorithm to vastly underestimate ||matrix||_1.
Scalar alternating_sign(RealScalar(1));
for (Index i = 0; i < n; ++i) {
// The static_cast is needed when Scalar is a complex and RealScalar implements expression templates
v[i] = alternating_sign * static_cast<RealScalar>(RealScalar(1) + (RealScalar(i) / (RealScalar(n - 1))));
alternating_sign = -alternating_sign;
}
v = dec.solve(v);
const RealScalar alternate_lower_bound = (2 * v.template lpNorm<1>()) / (3 * RealScalar(n));
return numext::maxi(lower_bound, alternate_lower_bound);
}
/** \brief Reciprocal condition number estimator.
*
* Computing a decomposition of a dense matrix takes O(n^3) operations, while
* this method estimates the condition number quickly and reliably in O(n^2)
* operations.
*
* \returns an estimate of the reciprocal condition number
* (1 / (||matrix||_1 * ||inv(matrix)||_1)) of matrix, given ||matrix||_1 and
* its decomposition. Supports the following decompositions: FullPivLU,
* PartialPivLU, LDLT, and LLT.
*
* \sa FullPivLU, PartialPivLU, LDLT, LLT.
*/
template <typename Decomposition>
typename Decomposition::RealScalar rcond_estimate_helper(typename Decomposition::RealScalar matrix_norm,
const Decomposition& dec) {
typedef typename Decomposition::RealScalar RealScalar;
eigen_assert(dec.rows() == dec.cols());
if (dec.rows() == 0) return NumTraits<RealScalar>::infinity();
if (numext::is_exactly_zero(matrix_norm)) return RealScalar(0);
if (dec.rows() == 1) return RealScalar(1);
const RealScalar inverse_matrix_norm = rcond_invmatrix_L1_norm_estimate(dec);
return (numext::is_exactly_zero(inverse_matrix_norm) ? RealScalar(0)
: (RealScalar(1) / inverse_matrix_norm) / matrix_norm);
}
} // namespace internal
} // namespace Eigen
#endif

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_COREITERATORS_H
#define EIGEN_COREITERATORS_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
/* This file contains the respective InnerIterator definition of the expressions defined in Eigen/Core
*/
namespace internal {
template <typename XprType, typename EvaluatorKind>
class inner_iterator_selector;
}
/** \class InnerIterator
* \brief An InnerIterator allows to loop over the element of any matrix expression.
*
* \warning To be used with care because an evaluator is constructed every time an InnerIterator iterator is
* constructed.
*
* TODO: add a usage example
*/
template <typename XprType>
class InnerIterator {
protected:
typedef internal::inner_iterator_selector<XprType, typename internal::evaluator_traits<XprType>::Kind> IteratorType;
typedef internal::evaluator<XprType> EvaluatorType;
typedef typename internal::traits<XprType>::Scalar Scalar;
public:
/** Construct an iterator over the \a outerId -th row or column of \a xpr */
InnerIterator(const XprType &xpr, const Index &outerId) : m_eval(xpr), m_iter(m_eval, outerId, xpr.innerSize()) {}
/// \returns the value of the current coefficient.
EIGEN_STRONG_INLINE Scalar value() const { return m_iter.value(); }
/** Increment the iterator \c *this to the next non-zero coefficient.
* Explicit zeros are not skipped over. To skip explicit zeros, see class SparseView
*/
EIGEN_STRONG_INLINE InnerIterator &operator++() {
m_iter.operator++();
return *this;
}
EIGEN_STRONG_INLINE InnerIterator &operator+=(Index i) {
m_iter.operator+=(i);
return *this;
}
EIGEN_STRONG_INLINE InnerIterator operator+(Index i) {
InnerIterator result(*this);
result += i;
return result;
}
/// \returns the column or row index of the current coefficient.
EIGEN_STRONG_INLINE Index index() const { return m_iter.index(); }
/// \returns the row index of the current coefficient.
EIGEN_STRONG_INLINE Index row() const { return m_iter.row(); }
/// \returns the column index of the current coefficient.
EIGEN_STRONG_INLINE Index col() const { return m_iter.col(); }
/// \returns \c true if the iterator \c *this still references a valid coefficient.
EIGEN_STRONG_INLINE operator bool() const { return m_iter; }
protected:
EvaluatorType m_eval;
IteratorType m_iter;
private:
// If you get here, then you're not using the right InnerIterator type, e.g.:
// SparseMatrix<double,RowMajor> A;
// SparseMatrix<double>::InnerIterator it(A,0);
template <typename T>
InnerIterator(const EigenBase<T> &, Index outer);
};
namespace internal {
// Generic inner iterator implementation for dense objects
template <typename XprType>
class inner_iterator_selector<XprType, IndexBased> {
protected:
typedef evaluator<XprType> EvaluatorType;
typedef typename traits<XprType>::Scalar Scalar;
enum { IsRowMajor = (XprType::Flags & RowMajorBit) == RowMajorBit };
public:
EIGEN_STRONG_INLINE inner_iterator_selector(const EvaluatorType &eval, const Index &outerId, const Index &innerSize)
: m_eval(eval), m_inner(0), m_outer(outerId), m_end(innerSize) {}
EIGEN_STRONG_INLINE Scalar value() const {
return (IsRowMajor) ? m_eval.coeff(m_outer, m_inner) : m_eval.coeff(m_inner, m_outer);
}
EIGEN_STRONG_INLINE inner_iterator_selector &operator++() {
m_inner++;
return *this;
}
EIGEN_STRONG_INLINE Index index() const { return m_inner; }
inline Index row() const { return IsRowMajor ? m_outer : index(); }
inline Index col() const { return IsRowMajor ? index() : m_outer; }
EIGEN_STRONG_INLINE operator bool() const { return m_inner < m_end && m_inner >= 0; }
protected:
const EvaluatorType &m_eval;
Index m_inner;
const Index m_outer;
const Index m_end;
};
// For iterator-based evaluator, inner-iterator is already implemented as
// evaluator<>::InnerIterator
template <typename XprType>
class inner_iterator_selector<XprType, IteratorBased> : public evaluator<XprType>::InnerIterator {
protected:
typedef typename evaluator<XprType>::InnerIterator Base;
typedef evaluator<XprType> EvaluatorType;
public:
EIGEN_STRONG_INLINE inner_iterator_selector(const EvaluatorType &eval, const Index &outerId,
const Index & /*innerSize*/)
: Base(eval, outerId) {}
};
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_COREITERATORS_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_CWISE_BINARY_OP_H
#define EIGEN_CWISE_BINARY_OP_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
template <typename BinaryOp, typename Lhs, typename Rhs>
struct traits<CwiseBinaryOp<BinaryOp, Lhs, Rhs>> {
// we must not inherit from traits<Lhs> since it has
// the potential to cause problems with MSVC
typedef remove_all_t<Lhs> Ancestor;
typedef typename traits<Ancestor>::XprKind XprKind;
enum {
RowsAtCompileTime = traits<Ancestor>::RowsAtCompileTime,
ColsAtCompileTime = traits<Ancestor>::ColsAtCompileTime,
MaxRowsAtCompileTime = traits<Ancestor>::MaxRowsAtCompileTime,
MaxColsAtCompileTime = traits<Ancestor>::MaxColsAtCompileTime
};
// even though we require Lhs and Rhs to have the same scalar type (see CwiseBinaryOp constructor),
// we still want to handle the case when the result type is different.
typedef typename result_of<BinaryOp(const typename Lhs::Scalar&, const typename Rhs::Scalar&)>::type Scalar;
typedef typename cwise_promote_storage_type<typename traits<Lhs>::StorageKind, typename traits<Rhs>::StorageKind,
BinaryOp>::ret StorageKind;
typedef typename promote_index_type<typename traits<Lhs>::StorageIndex, typename traits<Rhs>::StorageIndex>::type
StorageIndex;
typedef typename Lhs::Nested LhsNested;
typedef typename Rhs::Nested RhsNested;
typedef std::remove_reference_t<LhsNested> LhsNested_;
typedef std::remove_reference_t<RhsNested> RhsNested_;
enum {
Flags = cwise_promote_storage_order<typename traits<Lhs>::StorageKind, typename traits<Rhs>::StorageKind,
LhsNested_::Flags & RowMajorBit, RhsNested_::Flags & RowMajorBit>::value
};
};
} // end namespace internal
template <typename BinaryOp, typename Lhs, typename Rhs, typename StorageKind>
class CwiseBinaryOpImpl;
/** \class CwiseBinaryOp
* \ingroup Core_Module
*
* \brief Generic expression where a coefficient-wise binary operator is applied to two expressions
*
* \tparam BinaryOp template functor implementing the operator
* \tparam LhsType the type of the left-hand side
* \tparam RhsType the type of the right-hand side
*
* This class represents an expression where a coefficient-wise binary operator is applied to two expressions.
* It is the return type of binary operators, by which we mean only those binary operators where
* both the left-hand side and the right-hand side are Eigen expressions.
* For example, the return type of matrix1+matrix2 is a CwiseBinaryOp.
*
* Most of the time, this is the only way that it is used, so you typically don't have to name
* CwiseBinaryOp types explicitly.
*
* \sa MatrixBase::binaryExpr(const MatrixBase<OtherDerived> &,const CustomBinaryOp &) const, class CwiseUnaryOp, class
* CwiseNullaryOp
*/
template <typename BinaryOp, typename LhsType, typename RhsType>
class CwiseBinaryOp : public CwiseBinaryOpImpl<BinaryOp, LhsType, RhsType,
typename internal::cwise_promote_storage_type<
typename internal::traits<LhsType>::StorageKind,
typename internal::traits<RhsType>::StorageKind, BinaryOp>::ret>,
internal::no_assignment_operator {
public:
typedef internal::remove_all_t<BinaryOp> Functor;
typedef internal::remove_all_t<LhsType> Lhs;
typedef internal::remove_all_t<RhsType> Rhs;
typedef typename CwiseBinaryOpImpl<
BinaryOp, LhsType, RhsType,
typename internal::cwise_promote_storage_type<typename internal::traits<LhsType>::StorageKind,
typename internal::traits<Rhs>::StorageKind, BinaryOp>::ret>::Base
Base;
EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseBinaryOp)
EIGEN_CHECK_BINARY_COMPATIBILIY(BinaryOp, typename Lhs::Scalar, typename Rhs::Scalar)
EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Lhs, Rhs)
typedef typename internal::ref_selector<LhsType>::type LhsNested;
typedef typename internal::ref_selector<RhsType>::type RhsNested;
typedef std::remove_reference_t<LhsNested> LhsNested_;
typedef std::remove_reference_t<RhsNested> RhsNested_;
#if EIGEN_COMP_MSVC
// Required for Visual Studio or the Copy constructor will probably not get inlined!
EIGEN_STRONG_INLINE CwiseBinaryOp(const CwiseBinaryOp<BinaryOp, LhsType, RhsType>&) = default;
#endif
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CwiseBinaryOp(const Lhs& aLhs, const Rhs& aRhs,
const BinaryOp& func = BinaryOp())
: m_lhs(aLhs), m_rhs(aRhs), m_functor(func) {
eigen_assert(aLhs.rows() == aRhs.rows() && aLhs.cols() == aRhs.cols());
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index rows() const noexcept {
// return the fixed size type if available to enable compile time optimizations
return internal::traits<internal::remove_all_t<LhsNested>>::RowsAtCompileTime == Dynamic ? m_rhs.rows()
: m_lhs.rows();
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index cols() const noexcept {
// return the fixed size type if available to enable compile time optimizations
return internal::traits<internal::remove_all_t<LhsNested>>::ColsAtCompileTime == Dynamic ? m_rhs.cols()
: m_lhs.cols();
}
/** \returns the left hand side nested expression */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const LhsNested_& lhs() const { return m_lhs; }
/** \returns the right hand side nested expression */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const RhsNested_& rhs() const { return m_rhs; }
/** \returns the functor representing the binary operation */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const BinaryOp& functor() const { return m_functor; }
protected:
LhsNested m_lhs;
RhsNested m_rhs;
const BinaryOp m_functor;
};
// Generic API dispatcher
template <typename BinaryOp, typename Lhs, typename Rhs, typename StorageKind>
class CwiseBinaryOpImpl : public internal::generic_xpr_base<CwiseBinaryOp<BinaryOp, Lhs, Rhs>>::type {
public:
typedef typename internal::generic_xpr_base<CwiseBinaryOp<BinaryOp, Lhs, Rhs>>::type Base;
};
/** replaces \c *this by \c *this - \a other.
*
* \returns a reference to \c *this
*/
template <typename Derived>
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator-=(const MatrixBase<OtherDerived>& other) {
call_assignment(derived(), other.derived(), internal::sub_assign_op<Scalar, typename OtherDerived::Scalar>());
return derived();
}
/** replaces \c *this by \c *this + \a other.
*
* \returns a reference to \c *this
*/
template <typename Derived>
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator+=(const MatrixBase<OtherDerived>& other) {
call_assignment(derived(), other.derived(), internal::add_assign_op<Scalar, typename OtherDerived::Scalar>());
return derived();
}
} // end namespace Eigen
#endif // EIGEN_CWISE_BINARY_OP_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_CWISE_NULLARY_OP_H
#define EIGEN_CWISE_NULLARY_OP_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
template <typename NullaryOp, typename PlainObjectType>
struct traits<CwiseNullaryOp<NullaryOp, PlainObjectType> > : traits<PlainObjectType> {
enum { Flags = traits<PlainObjectType>::Flags & RowMajorBit };
};
} // namespace internal
/** \class CwiseNullaryOp
* \ingroup Core_Module
*
* \brief Generic expression of a matrix where all coefficients are defined by a functor
*
* \tparam NullaryOp template functor implementing the operator
* \tparam PlainObjectType the underlying plain matrix/array type
*
* This class represents an expression of a generic nullary operator.
* It is the return type of the Ones(), Zero(), Constant(), Identity() and Random() methods,
* and most of the time this is the only way it is used.
*
* However, if you want to write a function returning such an expression, you
* will need to use this class.
*
* The functor NullaryOp must expose one of the following method:
<table class="manual">
<tr ><td>\c operator()() </td><td>if the procedural generation does not depend on the coefficient entries
(e.g., random numbers)</td></tr> <tr class="alt"><td>\c operator()(Index i)</td><td>if the procedural generation makes
sense for vectors only and that it depends on the coefficient index \c i (e.g., linspace) </td></tr> <tr ><td>\c
operator()(Index i,Index j)</td><td>if the procedural generation depends on the matrix coordinates \c i, \c j (e.g.,
to generate a checkerboard with 0 and 1)</td></tr>
</table>
* It is also possible to expose the last two operators if the generation makes sense for matrices but can be optimized
for vectors.
*
* See DenseBase::NullaryExpr(Index,const CustomNullaryOp&) for an example binding
* C++11 random number generators.
*
* A nullary expression can also be used to implement custom sophisticated matrix manipulations
* that cannot be covered by the existing set of natively supported matrix manipulations.
* See this \ref TopicCustomizing_NullaryExpr "page" for some examples and additional explanations
* on the behavior of CwiseNullaryOp.
*
* \sa class CwiseUnaryOp, class CwiseBinaryOp, DenseBase::NullaryExpr
*/
template <typename NullaryOp, typename PlainObjectType>
class CwiseNullaryOp : public internal::dense_xpr_base<CwiseNullaryOp<NullaryOp, PlainObjectType> >::type,
internal::no_assignment_operator {
public:
typedef typename internal::dense_xpr_base<CwiseNullaryOp>::type Base;
EIGEN_DENSE_PUBLIC_INTERFACE(CwiseNullaryOp)
EIGEN_DEVICE_FUNC CwiseNullaryOp(Index rows, Index cols, const NullaryOp& func = NullaryOp())
: m_rows(rows), m_cols(cols), m_functor(func) {
eigen_assert(rows >= 0 && (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows) && cols >= 0 &&
(ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols));
}
EIGEN_DEVICE_FUNC CwiseNullaryOp(Index size, const NullaryOp& func = NullaryOp())
: CwiseNullaryOp(RowsAtCompileTime == 1 ? 1 : size, RowsAtCompileTime == 1 ? size : 1, func) {
EIGEN_STATIC_ASSERT(CwiseNullaryOp::IsVectorAtCompileTime, YOU_TRIED_CALLING_A_VECTOR_METHOD_ON_A_MATRIX);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index rows() const { return m_rows.value(); }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index cols() const { return m_cols.value(); }
/** \returns the functor representing the nullary operation */
EIGEN_DEVICE_FUNC const NullaryOp& functor() const { return m_functor; }
protected:
const internal::variable_if_dynamic<Index, RowsAtCompileTime> m_rows;
const internal::variable_if_dynamic<Index, ColsAtCompileTime> m_cols;
const NullaryOp m_functor;
};
/** \returns an expression of a matrix defined by a custom functor \a func
*
* The parameters \a rows and \a cols are the number of rows and of columns of
* the returned matrix. Must be compatible with this MatrixBase type.
*
* This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
* it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used
* instead.
*
* The template parameter \a CustomNullaryOp is the type of the functor.
*
* \sa class CwiseNullaryOp
*/
template <typename Derived>
template <typename CustomNullaryOp>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
#ifndef EIGEN_PARSED_BY_DOXYGEN
const CwiseNullaryOp<CustomNullaryOp, typename DenseBase<Derived>::PlainObject>
#else
const CwiseNullaryOp<CustomNullaryOp, PlainObject>
#endif
DenseBase<Derived>::NullaryExpr(Index rows, Index cols, const CustomNullaryOp& func) {
return CwiseNullaryOp<CustomNullaryOp, PlainObject>(rows, cols, func);
}
/** \returns an expression of a matrix defined by a custom functor \a func
*
* The parameter \a size is the size of the returned vector.
* Must be compatible with this MatrixBase type.
*
* \only_for_vectors
*
* This variant is meant to be used for dynamic-size vector types. For fixed-size types,
* it is redundant to pass \a size as argument, so Zero() should be used
* instead.
*
* The template parameter \a CustomNullaryOp is the type of the functor.
*
* Here is an example with C++11 random generators: \include random_cpp11.cpp
* Output: \verbinclude random_cpp11.out
*
* \sa class CwiseNullaryOp
*/
template <typename Derived>
template <typename CustomNullaryOp>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
#ifndef EIGEN_PARSED_BY_DOXYGEN
const CwiseNullaryOp<CustomNullaryOp, typename DenseBase<Derived>::PlainObject>
#else
const CwiseNullaryOp<CustomNullaryOp, PlainObject>
#endif
DenseBase<Derived>::NullaryExpr(Index size, const CustomNullaryOp& func) {
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
if (RowsAtCompileTime == 1)
return CwiseNullaryOp<CustomNullaryOp, PlainObject>(1, size, func);
else
return CwiseNullaryOp<CustomNullaryOp, PlainObject>(size, 1, func);
}
/** \returns an expression of a matrix defined by a custom functor \a func
*
* This variant is only for fixed-size DenseBase types. For dynamic-size types, you
* need to use the variants taking size arguments.
*
* The template parameter \a CustomNullaryOp is the type of the functor.
*
* \sa class CwiseNullaryOp
*/
template <typename Derived>
template <typename CustomNullaryOp>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
#ifndef EIGEN_PARSED_BY_DOXYGEN
const CwiseNullaryOp<CustomNullaryOp, typename DenseBase<Derived>::PlainObject>
#else
const CwiseNullaryOp<CustomNullaryOp, PlainObject>
#endif
DenseBase<Derived>::NullaryExpr(const CustomNullaryOp& func) {
return CwiseNullaryOp<CustomNullaryOp, PlainObject>(RowsAtCompileTime, ColsAtCompileTime, func);
}
/** \returns an expression of a constant matrix of value \a value
*
* The parameters \a rows and \a cols are the number of rows and of columns of
* the returned matrix. Must be compatible with this DenseBase type.
*
* This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
* it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used
* instead.
*
* The template parameter \a CustomNullaryOp is the type of the functor.
*
* \sa class CwiseNullaryOp
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
DenseBase<Derived>::Constant(Index rows, Index cols, const Scalar& value) {
return DenseBase<Derived>::NullaryExpr(rows, cols, internal::scalar_constant_op<Scalar>(value));
}
/** \returns an expression of a constant matrix of value \a value
*
* The parameter \a size is the size of the returned vector.
* Must be compatible with this DenseBase type.
*
* \only_for_vectors
*
* This variant is meant to be used for dynamic-size vector types. For fixed-size types,
* it is redundant to pass \a size as argument, so Zero() should be used
* instead.
*
* The template parameter \a CustomNullaryOp is the type of the functor.
*
* \sa class CwiseNullaryOp
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
DenseBase<Derived>::Constant(Index size, const Scalar& value) {
return DenseBase<Derived>::NullaryExpr(size, internal::scalar_constant_op<Scalar>(value));
}
/** \returns an expression of a constant matrix of value \a value
*
* This variant is only for fixed-size DenseBase types. For dynamic-size types, you
* need to use the variants taking size arguments.
*
* The template parameter \a CustomNullaryOp is the type of the functor.
*
* \sa class CwiseNullaryOp
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
DenseBase<Derived>::Constant(const Scalar& value) {
EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
return DenseBase<Derived>::NullaryExpr(RowsAtCompileTime, ColsAtCompileTime,
internal::scalar_constant_op<Scalar>(value));
}
/** \deprecated because of accuracy loss. In Eigen 3.3, it is an alias for LinSpaced(Index,const Scalar&,const Scalar&)
*
* \only_for_vectors
*
* Example: \include DenseBase_LinSpaced_seq_deprecated.cpp
* Output: \verbinclude DenseBase_LinSpaced_seq_deprecated.out
*
* \sa LinSpaced(Index,const Scalar&, const Scalar&), setLinSpaced(Index,const Scalar&,const Scalar&)
*/
template <typename Derived>
EIGEN_DEPRECATED EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<
Derived>::RandomAccessLinSpacedReturnType
DenseBase<Derived>::LinSpaced(Sequential_t, Index size, const Scalar& low, const Scalar& high) {
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
return DenseBase<Derived>::NullaryExpr(size, internal::linspaced_op<Scalar>(low, high, size));
}
/** \deprecated because of accuracy loss. In Eigen 3.3, it is an alias for LinSpaced(const Scalar&,const Scalar&)
*
* \sa LinSpaced(const Scalar&, const Scalar&)
*/
template <typename Derived>
EIGEN_DEPRECATED EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<
Derived>::RandomAccessLinSpacedReturnType
DenseBase<Derived>::LinSpaced(Sequential_t, const Scalar& low, const Scalar& high) {
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
return DenseBase<Derived>::NullaryExpr(Derived::SizeAtCompileTime,
internal::linspaced_op<Scalar>(low, high, Derived::SizeAtCompileTime));
}
/**
* \brief Sets a linearly spaced vector.
*
* The function generates 'size' equally spaced values in the closed interval [low,high].
* When size is set to 1, a vector of length 1 containing 'high' is returned.
*
* \only_for_vectors
*
* Example: \include DenseBase_LinSpaced.cpp
* Output: \verbinclude DenseBase_LinSpaced.out
*
* For integer scalar types, an even spacing is possible if and only if the length of the range,
* i.e., \c high-low is a scalar multiple of \c size-1, or if \c size is a scalar multiple of the
* number of values \c high-low+1 (meaning each value can be repeated the same number of time).
* If one of these two considions is not satisfied, then \c high is lowered to the largest value
* satisfying one of this constraint.
* Here are some examples:
*
* Example: \include DenseBase_LinSpacedInt.cpp
* Output: \verbinclude DenseBase_LinSpacedInt.out
*
* \sa setLinSpaced(Index,const Scalar&,const Scalar&), CwiseNullaryOp
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType
DenseBase<Derived>::LinSpaced(Index size, const Scalar& low, const Scalar& high) {
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
return DenseBase<Derived>::NullaryExpr(size, internal::linspaced_op<Scalar>(low, high, size));
}
/**
* \copydoc DenseBase::LinSpaced(Index, const DenseBase::Scalar&, const DenseBase::Scalar&)
* Special version for fixed size types which does not require the size parameter.
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType
DenseBase<Derived>::LinSpaced(const Scalar& low, const Scalar& high) {
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
return DenseBase<Derived>::NullaryExpr(Derived::SizeAtCompileTime,
internal::linspaced_op<Scalar>(low, high, Derived::SizeAtCompileTime));
}
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessEqualSpacedReturnType
DenseBase<Derived>::EqualSpaced(Index size, const Scalar& low, const Scalar& step) {
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
return DenseBase<Derived>::NullaryExpr(size, internal::equalspaced_op<Scalar>(low, step));
}
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessEqualSpacedReturnType
DenseBase<Derived>::EqualSpaced(const Scalar& low, const Scalar& step) {
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
return DenseBase<Derived>::NullaryExpr(Derived::SizeAtCompileTime, internal::equalspaced_op<Scalar>(low, step));
}
/** \returns true if all coefficients in this matrix are approximately equal to \a val, to within precision \a prec */
template <typename Derived>
EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isApproxToConstant(const Scalar& val, const RealScalar& prec) const {
typename internal::nested_eval<Derived, 1>::type self(derived());
for (Index j = 0; j < cols(); ++j)
for (Index i = 0; i < rows(); ++i)
if (!internal::isApprox(self.coeff(i, j), val, prec)) return false;
return true;
}
/** This is just an alias for isApproxToConstant().
*
* \returns true if all coefficients in this matrix are approximately equal to \a value, to within precision \a prec */
template <typename Derived>
EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isConstant(const Scalar& val, const RealScalar& prec) const {
return isApproxToConstant(val, prec);
}
/** Alias for setConstant(): sets all coefficients in this expression to \a val.
*
* \sa setConstant(), Constant(), class CwiseNullaryOp
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void DenseBase<Derived>::fill(const Scalar& val) {
setConstant(val);
}
/** Sets all coefficients in this expression to value \a val.
*
* \sa fill(), setConstant(Index,const Scalar&), setConstant(Index,Index,const Scalar&), setZero(), setOnes(),
* Constant(), class CwiseNullaryOp, setZero(), setOnes()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setConstant(const Scalar& val) {
internal::eigen_fill_impl<Derived>::run(derived(), val);
return derived();
}
/** Resizes to the given \a size, and sets all coefficients in this expression to the given value \a val.
*
* \only_for_vectors
*
* Example: \include Matrix_setConstant_int.cpp
* Output: \verbinclude Matrix_setConstant_int.out
*
* \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,Index,const Scalar&), class CwiseNullaryOp,
* MatrixBase::Constant(const Scalar&)
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setConstant(Index size, const Scalar& val) {
resize(size);
return setConstant(val);
}
/** Resizes to the given size, and sets all coefficients in this expression to the given value \a val.
*
* \param rows the new number of rows
* \param cols the new number of columns
* \param val the value to which all coefficients are set
*
* Example: \include Matrix_setConstant_int_int.cpp
* Output: \verbinclude Matrix_setConstant_int_int.out
*
* \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,const Scalar&), class CwiseNullaryOp,
* MatrixBase::Constant(const Scalar&)
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setConstant(Index rows, Index cols,
const Scalar& val) {
resize(rows, cols);
return setConstant(val);
}
/** Resizes to the given size, changing only the number of columns, and sets all
* coefficients in this expression to the given value \a val. For the parameter
* of type NoChange_t, just pass the special value \c NoChange.
*
* \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,const Scalar&), class CwiseNullaryOp,
* MatrixBase::Constant(const Scalar&)
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setConstant(NoChange_t, Index cols,
const Scalar& val) {
return setConstant(rows(), cols, val);
}
/** Resizes to the given size, changing only the number of rows, and sets all
* coefficients in this expression to the given value \a val. For the parameter
* of type NoChange_t, just pass the special value \c NoChange.
*
* \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,const Scalar&), class CwiseNullaryOp,
* MatrixBase::Constant(const Scalar&)
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setConstant(Index rows, NoChange_t,
const Scalar& val) {
return setConstant(rows, cols(), val);
}
/**
* \brief Sets a linearly spaced vector.
*
* The function generates 'size' equally spaced values in the closed interval [low,high].
* When size is set to 1, a vector of length 1 containing 'high' is returned.
*
* \only_for_vectors
*
* Example: \include DenseBase_setLinSpaced.cpp
* Output: \verbinclude DenseBase_setLinSpaced.out
*
* For integer scalar types, do not miss the explanations on the definition
* of \link LinSpaced(Index,const Scalar&,const Scalar&) even spacing \endlink.
*
* \sa LinSpaced(Index,const Scalar&,const Scalar&), CwiseNullaryOp
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setLinSpaced(Index newSize, const Scalar& low,
const Scalar& high) {
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
return derived() = Derived::NullaryExpr(newSize, internal::linspaced_op<Scalar>(low, high, newSize));
}
/**
* \brief Sets a linearly spaced vector.
*
* The function fills \c *this with equally spaced values in the closed interval [low,high].
* When size is set to 1, a vector of length 1 containing 'high' is returned.
*
* \only_for_vectors
*
* For integer scalar types, do not miss the explanations on the definition
* of \link LinSpaced(Index,const Scalar&,const Scalar&) even spacing \endlink.
*
* \sa LinSpaced(Index,const Scalar&,const Scalar&), setLinSpaced(Index, const Scalar&, const Scalar&), CwiseNullaryOp
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setLinSpaced(const Scalar& low, const Scalar& high) {
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
return setLinSpaced(size(), low, high);
}
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setEqualSpaced(Index newSize, const Scalar& low,
const Scalar& step) {
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
return derived() = Derived::NullaryExpr(newSize, internal::equalspaced_op<Scalar>(low, step));
}
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setEqualSpaced(const Scalar& low,
const Scalar& step) {
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
return setEqualSpaced(size(), low, step);
}
// zero:
/** \returns an expression of a zero matrix.
*
* The parameters \a rows and \a cols are the number of rows and of columns of
* the returned matrix. Must be compatible with this MatrixBase type.
*
* This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
* it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used
* instead.
*
* Example: \include MatrixBase_zero_int_int.cpp
* Output: \verbinclude MatrixBase_zero_int_int.out
*
* \sa Zero(), Zero(Index)
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ZeroReturnType DenseBase<Derived>::Zero(
Index rows, Index cols) {
return ZeroReturnType(rows, cols);
}
/** \returns an expression of a zero vector.
*
* The parameter \a size is the size of the returned vector.
* Must be compatible with this MatrixBase type.
*
* \only_for_vectors
*
* This variant is meant to be used for dynamic-size vector types. For fixed-size types,
* it is redundant to pass \a size as argument, so Zero() should be used
* instead.
*
* Example: \include MatrixBase_zero_int.cpp
* Output: \verbinclude MatrixBase_zero_int.out
*
* \sa Zero(), Zero(Index,Index)
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ZeroReturnType DenseBase<Derived>::Zero(
Index size) {
return ZeroReturnType(size);
}
/** \returns an expression of a fixed-size zero matrix or vector.
*
* This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
* need to use the variants taking size arguments.
*
* Example: \include MatrixBase_zero.cpp
* Output: \verbinclude MatrixBase_zero.out
*
* \sa Zero(Index), Zero(Index,Index)
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ZeroReturnType DenseBase<Derived>::Zero() {
return ZeroReturnType(RowsAtCompileTime, ColsAtCompileTime);
}
/** \returns true if *this is approximately equal to the zero matrix,
* within the precision given by \a prec.
*
* Example: \include MatrixBase_isZero.cpp
* Output: \verbinclude MatrixBase_isZero.out
*
* \sa class CwiseNullaryOp, Zero()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isZero(const RealScalar& prec) const {
typename internal::nested_eval<Derived, 1>::type self(derived());
for (Index j = 0; j < cols(); ++j)
for (Index i = 0; i < rows(); ++i)
if (!internal::isMuchSmallerThan(self.coeff(i, j), static_cast<Scalar>(1), prec)) return false;
return true;
}
/** Sets all coefficients in this expression to zero.
*
* Example: \include MatrixBase_setZero.cpp
* Output: \verbinclude MatrixBase_setZero.out
*
* \sa class CwiseNullaryOp, Zero()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setZero() {
internal::eigen_zero_impl<Derived>::run(derived());
return derived();
}
/** Resizes to the given \a size, and sets all coefficients in this expression to zero.
*
* \only_for_vectors
*
* Example: \include Matrix_setZero_int.cpp
* Output: \verbinclude Matrix_setZero_int.out
*
* \sa DenseBase::setZero(), setZero(Index,Index), class CwiseNullaryOp, DenseBase::Zero()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setZero(Index newSize) {
resize(newSize);
return setZero();
}
/** Resizes to the given size, and sets all coefficients in this expression to zero.
*
* \param rows the new number of rows
* \param cols the new number of columns
*
* Example: \include Matrix_setZero_int_int.cpp
* Output: \verbinclude Matrix_setZero_int_int.out
*
* \sa DenseBase::setZero(), setZero(Index), class CwiseNullaryOp, DenseBase::Zero()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setZero(Index rows, Index cols) {
resize(rows, cols);
return setZero();
}
/** Resizes to the given size, changing only the number of columns, and sets all
* coefficients in this expression to zero. For the parameter of type NoChange_t,
* just pass the special value \c NoChange.
*
* \sa DenseBase::setZero(), setZero(Index), setZero(Index, Index), setZero(Index, NoChange_t), class CwiseNullaryOp,
* DenseBase::Zero()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setZero(NoChange_t, Index cols) {
return setZero(rows(), cols);
}
/** Resizes to the given size, changing only the number of rows, and sets all
* coefficients in this expression to zero. For the parameter of type NoChange_t,
* just pass the special value \c NoChange.
*
* \sa DenseBase::setZero(), setZero(Index), setZero(Index, Index), setZero(NoChange_t, Index), class CwiseNullaryOp,
* DenseBase::Zero()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setZero(Index rows, NoChange_t) {
return setZero(rows, cols());
}
// ones:
/** \returns an expression of a matrix where all coefficients equal one.
*
* The parameters \a rows and \a cols are the number of rows and of columns of
* the returned matrix. Must be compatible with this MatrixBase type.
*
* This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
* it is redundant to pass \a rows and \a cols as arguments, so Ones() should be used
* instead.
*
* Example: \include MatrixBase_ones_int_int.cpp
* Output: \verbinclude MatrixBase_ones_int_int.out
*
* \sa Ones(), Ones(Index), isOnes(), class Ones
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType DenseBase<Derived>::Ones(
Index rows, Index cols) {
return Constant(rows, cols, Scalar(1));
}
/** \returns an expression of a vector where all coefficients equal one.
*
* The parameter \a newSize is the size of the returned vector.
* Must be compatible with this MatrixBase type.
*
* \only_for_vectors
*
* This variant is meant to be used for dynamic-size vector types. For fixed-size types,
* it is redundant to pass \a size as argument, so Ones() should be used
* instead.
*
* Example: \include MatrixBase_ones_int.cpp
* Output: \verbinclude MatrixBase_ones_int.out
*
* \sa Ones(), Ones(Index,Index), isOnes(), class Ones
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType DenseBase<Derived>::Ones(
Index newSize) {
return Constant(newSize, Scalar(1));
}
/** \returns an expression of a fixed-size matrix or vector where all coefficients equal one.
*
* This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
* need to use the variants taking size arguments.
*
* Example: \include MatrixBase_ones.cpp
* Output: \verbinclude MatrixBase_ones.out
*
* \sa Ones(Index), Ones(Index,Index), isOnes(), class Ones
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType DenseBase<Derived>::Ones() {
return Constant(Scalar(1));
}
/** \returns true if *this is approximately equal to the matrix where all coefficients
* are equal to 1, within the precision given by \a prec.
*
* Example: \include MatrixBase_isOnes.cpp
* Output: \verbinclude MatrixBase_isOnes.out
*
* \sa class CwiseNullaryOp, Ones()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isOnes(const RealScalar& prec) const {
return isApproxToConstant(Scalar(1), prec);
}
/** Sets all coefficients in this expression to one.
*
* Example: \include MatrixBase_setOnes.cpp
* Output: \verbinclude MatrixBase_setOnes.out
*
* \sa class CwiseNullaryOp, Ones()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setOnes() {
return setConstant(Scalar(1));
}
/** Resizes to the given \a newSize, and sets all coefficients in this expression to one.
*
* \only_for_vectors
*
* Example: \include Matrix_setOnes_int.cpp
* Output: \verbinclude Matrix_setOnes_int.out
*
* \sa MatrixBase::setOnes(), setOnes(Index,Index), class CwiseNullaryOp, MatrixBase::Ones()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setOnes(Index newSize) {
resize(newSize);
return setConstant(Scalar(1));
}
/** Resizes to the given size, and sets all coefficients in this expression to one.
*
* \param rows the new number of rows
* \param cols the new number of columns
*
* Example: \include Matrix_setOnes_int_int.cpp
* Output: \verbinclude Matrix_setOnes_int_int.out
*
* \sa MatrixBase::setOnes(), setOnes(Index), class CwiseNullaryOp, MatrixBase::Ones()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setOnes(Index rows, Index cols) {
resize(rows, cols);
return setConstant(Scalar(1));
}
/** Resizes to the given size, changing only the number of rows, and sets all
* coefficients in this expression to one. For the parameter of type NoChange_t,
* just pass the special value \c NoChange.
*
* \sa MatrixBase::setOnes(), setOnes(Index), setOnes(Index, Index), setOnes(NoChange_t, Index), class CwiseNullaryOp,
* MatrixBase::Ones()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setOnes(Index rows, NoChange_t) {
return setOnes(rows, cols());
}
/** Resizes to the given size, changing only the number of columns, and sets all
* coefficients in this expression to one. For the parameter of type NoChange_t,
* just pass the special value \c NoChange.
*
* \sa MatrixBase::setOnes(), setOnes(Index), setOnes(Index, Index), setOnes(Index, NoChange_t) class CwiseNullaryOp,
* MatrixBase::Ones()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setOnes(NoChange_t, Index cols) {
return setOnes(rows(), cols);
}
// Identity:
/** \returns an expression of the identity matrix (not necessarily square).
*
* The parameters \a rows and \a cols are the number of rows and of columns of
* the returned matrix. Must be compatible with this MatrixBase type.
*
* This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
* it is redundant to pass \a rows and \a cols as arguments, so Identity() should be used
* instead.
*
* Example: \include MatrixBase_identity_int_int.cpp
* Output: \verbinclude MatrixBase_identity_int_int.out
*
* \sa Identity(), setIdentity(), isIdentity()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::IdentityReturnType
MatrixBase<Derived>::Identity(Index rows, Index cols) {
return DenseBase<Derived>::NullaryExpr(rows, cols, internal::scalar_identity_op<Scalar>());
}
/** \returns an expression of the identity matrix (not necessarily square).
*
* This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
* need to use the variant taking size arguments.
*
* Example: \include MatrixBase_identity.cpp
* Output: \verbinclude MatrixBase_identity.out
*
* \sa Identity(Index,Index), setIdentity(), isIdentity()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::IdentityReturnType
MatrixBase<Derived>::Identity() {
EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
return MatrixBase<Derived>::NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, internal::scalar_identity_op<Scalar>());
}
/** \returns true if *this is approximately equal to the identity matrix
* (not necessarily square),
* within the precision given by \a prec.
*
* Example: \include MatrixBase_isIdentity.cpp
* Output: \verbinclude MatrixBase_isIdentity.out
*
* \sa class CwiseNullaryOp, Identity(), Identity(Index,Index), setIdentity()
*/
template <typename Derived>
bool MatrixBase<Derived>::isIdentity(const RealScalar& prec) const {
typename internal::nested_eval<Derived, 1>::type self(derived());
for (Index j = 0; j < cols(); ++j) {
for (Index i = 0; i < rows(); ++i) {
if (i == j) {
if (!internal::isApprox(self.coeff(i, j), static_cast<Scalar>(1), prec)) return false;
} else {
if (!internal::isMuchSmallerThan(self.coeff(i, j), static_cast<RealScalar>(1), prec)) return false;
}
}
}
return true;
}
namespace internal {
template <typename Derived, bool Big = (Derived::SizeAtCompileTime >= 16)>
struct setIdentity_impl {
EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Derived& run(Derived& m) {
return m = Derived::Identity(m.rows(), m.cols());
}
};
template <typename Derived>
struct setIdentity_impl<Derived, true> {
EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Derived& run(Derived& m) {
m.setZero();
const Index size = numext::mini(m.rows(), m.cols());
for (Index i = 0; i < size; ++i) m.coeffRef(i, i) = typename Derived::Scalar(1);
return m;
}
};
} // end namespace internal
/** Writes the identity expression (not necessarily square) into *this.
*
* Example: \include MatrixBase_setIdentity.cpp
* Output: \verbinclude MatrixBase_setIdentity.out
*
* \sa class CwiseNullaryOp, Identity(), Identity(Index,Index), isIdentity()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setIdentity() {
return internal::setIdentity_impl<Derived>::run(derived());
}
/** \brief Resizes to the given size, and writes the identity expression (not necessarily square) into *this.
*
* \param rows the new number of rows
* \param cols the new number of columns
*
* Example: \include Matrix_setIdentity_int_int.cpp
* Output: \verbinclude Matrix_setIdentity_int_int.out
*
* \sa MatrixBase::setIdentity(), class CwiseNullaryOp, MatrixBase::Identity()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setIdentity(Index rows, Index cols) {
derived().resize(rows, cols);
return setIdentity();
}
/** \returns an expression of the i-th unit (basis) vector.
*
* \only_for_vectors
*
* \sa MatrixBase::Unit(Index), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::Unit(
Index newSize, Index i) {
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
return BasisReturnType(SquareMatrixType::Identity(newSize, newSize), i);
}
/** \returns an expression of the i-th unit (basis) vector.
*
* \only_for_vectors
*
* This variant is for fixed-size vector only.
*
* \sa MatrixBase::Unit(Index,Index), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::Unit(
Index i) {
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
return BasisReturnType(SquareMatrixType::Identity(), i);
}
/** \returns an expression of the X axis unit vector (1{,0}^*)
*
* \only_for_vectors
*
* \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(),
* MatrixBase::UnitW()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitX() {
return Derived::Unit(0);
}
/** \returns an expression of the Y axis unit vector (0,1{,0}^*)
*
* \only_for_vectors
*
* \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(),
* MatrixBase::UnitW()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitY() {
return Derived::Unit(1);
}
/** \returns an expression of the Z axis unit vector (0,0,1{,0}^*)
*
* \only_for_vectors
*
* \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(),
* MatrixBase::UnitW()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitZ() {
return Derived::Unit(2);
}
/** \returns an expression of the W axis unit vector (0,0,0,1)
*
* \only_for_vectors
*
* \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(),
* MatrixBase::UnitW()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitW() {
return Derived::Unit(3);
}
/** \brief Set the coefficients of \c *this to the i-th unit (basis) vector
*
* \param i index of the unique coefficient to be set to 1
*
* \only_for_vectors
*
* \sa MatrixBase::setIdentity(), class CwiseNullaryOp, MatrixBase::Unit(Index,Index)
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setUnit(Index i) {
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
eigen_assert(i < size());
derived().setZero();
derived().coeffRef(i) = Scalar(1);
return derived();
}
/** \brief Resizes to the given \a newSize, and writes the i-th unit (basis) vector into *this.
*
* \param newSize the new size of the vector
* \param i index of the unique coefficient to be set to 1
*
* \only_for_vectors
*
* \sa MatrixBase::setIdentity(), class CwiseNullaryOp, MatrixBase::Unit(Index,Index)
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setUnit(Index newSize, Index i) {
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
eigen_assert(i < newSize);
derived().resize(newSize);
return setUnit(i);
}
} // end namespace Eigen
#endif // EIGEN_CWISE_NULLARY_OP_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2016 Eugene Brevdo <ebrevdo@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_CWISE_TERNARY_OP_H
#define EIGEN_CWISE_TERNARY_OP_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
template <typename TernaryOp, typename Arg1, typename Arg2, typename Arg3>
struct traits<CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3>> {
// we must not inherit from traits<Arg1> since it has
// the potential to cause problems with MSVC
typedef remove_all_t<Arg1> Ancestor;
typedef typename traits<Ancestor>::XprKind XprKind;
enum {
RowsAtCompileTime = traits<Ancestor>::RowsAtCompileTime,
ColsAtCompileTime = traits<Ancestor>::ColsAtCompileTime,
MaxRowsAtCompileTime = traits<Ancestor>::MaxRowsAtCompileTime,
MaxColsAtCompileTime = traits<Ancestor>::MaxColsAtCompileTime
};
// even though we require Arg1, Arg2, and Arg3 to have the same scalar type
// (see CwiseTernaryOp constructor),
// we still want to handle the case when the result type is different.
typedef typename result_of<TernaryOp(const typename Arg1::Scalar&, const typename Arg2::Scalar&,
const typename Arg3::Scalar&)>::type Scalar;
typedef typename internal::traits<Arg1>::StorageKind StorageKind;
typedef typename internal::traits<Arg1>::StorageIndex StorageIndex;
typedef typename Arg1::Nested Arg1Nested;
typedef typename Arg2::Nested Arg2Nested;
typedef typename Arg3::Nested Arg3Nested;
typedef std::remove_reference_t<Arg1Nested> Arg1Nested_;
typedef std::remove_reference_t<Arg2Nested> Arg2Nested_;
typedef std::remove_reference_t<Arg3Nested> Arg3Nested_;
enum { Flags = Arg1Nested_::Flags & RowMajorBit };
};
} // end namespace internal
template <typename TernaryOp, typename Arg1, typename Arg2, typename Arg3, typename StorageKind>
class CwiseTernaryOpImpl;
/** \class CwiseTernaryOp
* \ingroup Core_Module
*
* \brief Generic expression where a coefficient-wise ternary operator is
* applied to two expressions
*
* \tparam TernaryOp template functor implementing the operator
* \tparam Arg1Type the type of the first argument
* \tparam Arg2Type the type of the second argument
* \tparam Arg3Type the type of the third argument
*
* This class represents an expression where a coefficient-wise ternary
* operator is applied to three expressions.
* It is the return type of ternary operators, by which we mean only those
* ternary operators where
* all three arguments are Eigen expressions.
* For example, the return type of betainc(matrix1, matrix2, matrix3) is a
* CwiseTernaryOp.
*
* Most of the time, this is the only way that it is used, so you typically
* don't have to name
* CwiseTernaryOp types explicitly.
*
* \sa MatrixBase::ternaryExpr(const MatrixBase<Argument2> &, const
* MatrixBase<Argument3> &, const CustomTernaryOp &) const, class CwiseBinaryOp,
* class CwiseUnaryOp, class CwiseNullaryOp
*/
template <typename TernaryOp, typename Arg1Type, typename Arg2Type, typename Arg3Type>
class CwiseTernaryOp : public CwiseTernaryOpImpl<TernaryOp, Arg1Type, Arg2Type, Arg3Type,
typename internal::traits<Arg1Type>::StorageKind>,
internal::no_assignment_operator {
public:
typedef internal::remove_all_t<Arg1Type> Arg1;
typedef internal::remove_all_t<Arg2Type> Arg2;
typedef internal::remove_all_t<Arg3Type> Arg3;
// require the sizes to match
EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Arg1, Arg2)
EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Arg1, Arg3)
// The index types should match
EIGEN_STATIC_ASSERT((internal::is_same<typename internal::traits<Arg1Type>::StorageKind,
typename internal::traits<Arg2Type>::StorageKind>::value),
STORAGE_KIND_MUST_MATCH)
EIGEN_STATIC_ASSERT((internal::is_same<typename internal::traits<Arg1Type>::StorageKind,
typename internal::traits<Arg3Type>::StorageKind>::value),
STORAGE_KIND_MUST_MATCH)
typedef typename CwiseTernaryOpImpl<TernaryOp, Arg1Type, Arg2Type, Arg3Type,
typename internal::traits<Arg1Type>::StorageKind>::Base Base;
EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseTernaryOp)
typedef typename internal::ref_selector<Arg1Type>::type Arg1Nested;
typedef typename internal::ref_selector<Arg2Type>::type Arg2Nested;
typedef typename internal::ref_selector<Arg3Type>::type Arg3Nested;
typedef std::remove_reference_t<Arg1Nested> Arg1Nested_;
typedef std::remove_reference_t<Arg2Nested> Arg2Nested_;
typedef std::remove_reference_t<Arg3Nested> Arg3Nested_;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CwiseTernaryOp(const Arg1& a1, const Arg2& a2, const Arg3& a3,
const TernaryOp& func = TernaryOp())
: m_arg1(a1), m_arg2(a2), m_arg3(a3), m_functor(func) {
eigen_assert(a1.rows() == a2.rows() && a1.cols() == a2.cols() && a1.rows() == a3.rows() && a1.cols() == a3.cols());
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index rows() const {
// return the fixed size type if available to enable compile time
// optimizations
if (internal::traits<internal::remove_all_t<Arg1Nested>>::RowsAtCompileTime == Dynamic &&
internal::traits<internal::remove_all_t<Arg2Nested>>::RowsAtCompileTime == Dynamic)
return m_arg3.rows();
else if (internal::traits<internal::remove_all_t<Arg1Nested>>::RowsAtCompileTime == Dynamic &&
internal::traits<internal::remove_all_t<Arg3Nested>>::RowsAtCompileTime == Dynamic)
return m_arg2.rows();
else
return m_arg1.rows();
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index cols() const {
// return the fixed size type if available to enable compile time
// optimizations
if (internal::traits<internal::remove_all_t<Arg1Nested>>::ColsAtCompileTime == Dynamic &&
internal::traits<internal::remove_all_t<Arg2Nested>>::ColsAtCompileTime == Dynamic)
return m_arg3.cols();
else if (internal::traits<internal::remove_all_t<Arg1Nested>>::ColsAtCompileTime == Dynamic &&
internal::traits<internal::remove_all_t<Arg3Nested>>::ColsAtCompileTime == Dynamic)
return m_arg2.cols();
else
return m_arg1.cols();
}
/** \returns the first argument nested expression */
EIGEN_DEVICE_FUNC const Arg1Nested_& arg1() const { return m_arg1; }
/** \returns the first argument nested expression */
EIGEN_DEVICE_FUNC const Arg2Nested_& arg2() const { return m_arg2; }
/** \returns the third argument nested expression */
EIGEN_DEVICE_FUNC const Arg3Nested_& arg3() const { return m_arg3; }
/** \returns the functor representing the ternary operation */
EIGEN_DEVICE_FUNC const TernaryOp& functor() const { return m_functor; }
protected:
Arg1Nested m_arg1;
Arg2Nested m_arg2;
Arg3Nested m_arg3;
const TernaryOp m_functor;
};
// Generic API dispatcher
template <typename TernaryOp, typename Arg1, typename Arg2, typename Arg3, typename StorageKind>
class CwiseTernaryOpImpl : public internal::generic_xpr_base<CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3>>::type {
public:
typedef typename internal::generic_xpr_base<CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3>>::type Base;
};
} // end namespace Eigen
#endif // EIGEN_CWISE_TERNARY_OP_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_CWISE_UNARY_OP_H
#define EIGEN_CWISE_UNARY_OP_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
template <typename UnaryOp, typename XprType>
struct traits<CwiseUnaryOp<UnaryOp, XprType> > : traits<XprType> {
typedef typename result_of<UnaryOp(const typename XprType::Scalar&)>::type Scalar;
typedef typename XprType::Nested XprTypeNested;
typedef std::remove_reference_t<XprTypeNested> XprTypeNested_;
enum { Flags = XprTypeNested_::Flags & RowMajorBit };
};
} // namespace internal
template <typename UnaryOp, typename XprType, typename StorageKind>
class CwiseUnaryOpImpl;
/** \class CwiseUnaryOp
* \ingroup Core_Module
*
* \brief Generic expression where a coefficient-wise unary operator is applied to an expression
*
* \tparam UnaryOp template functor implementing the operator
* \tparam XprType the type of the expression to which we are applying the unary operator
*
* This class represents an expression where a unary operator is applied to an expression.
* It is the return type of all operations taking exactly 1 input expression, regardless of the
* presence of other inputs such as scalars. For example, the operator* in the expression 3*matrix
* is considered unary, because only the right-hand side is an expression, and its
* return type is a specialization of CwiseUnaryOp.
*
* Most of the time, this is the only way that it is used, so you typically don't have to name
* CwiseUnaryOp types explicitly.
*
* \sa MatrixBase::unaryExpr(const CustomUnaryOp &) const, class CwiseBinaryOp, class CwiseNullaryOp
*/
template <typename UnaryOp, typename XprType>
class CwiseUnaryOp : public CwiseUnaryOpImpl<UnaryOp, XprType, typename internal::traits<XprType>::StorageKind>,
internal::no_assignment_operator {
public:
typedef typename CwiseUnaryOpImpl<UnaryOp, XprType, typename internal::traits<XprType>::StorageKind>::Base Base;
EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseUnaryOp)
typedef typename internal::ref_selector<XprType>::type XprTypeNested;
typedef internal::remove_all_t<XprType> NestedExpression;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit CwiseUnaryOp(const XprType& xpr, const UnaryOp& func = UnaryOp())
: m_xpr(xpr), m_functor(func) {}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index rows() const noexcept { return m_xpr.rows(); }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index cols() const noexcept { return m_xpr.cols(); }
/** \returns the functor representing the unary operation */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const UnaryOp& functor() const { return m_functor; }
/** \returns the nested expression */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const internal::remove_all_t<XprTypeNested>& nestedExpression() const {
return m_xpr;
}
/** \returns the nested expression */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE internal::remove_all_t<XprTypeNested>& nestedExpression() { return m_xpr; }
protected:
XprTypeNested m_xpr;
const UnaryOp m_functor;
};
// Generic API dispatcher
template <typename UnaryOp, typename XprType, typename StorageKind>
class CwiseUnaryOpImpl : public internal::generic_xpr_base<CwiseUnaryOp<UnaryOp, XprType> >::type {
public:
typedef typename internal::generic_xpr_base<CwiseUnaryOp<UnaryOp, XprType> >::type Base;
};
} // end namespace Eigen
#endif // EIGEN_CWISE_UNARY_OP_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_CWISE_UNARY_VIEW_H
#define EIGEN_CWISE_UNARY_VIEW_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
template <typename ViewOp, typename MatrixType, typename StrideType>
struct traits<CwiseUnaryView<ViewOp, MatrixType, StrideType> > : traits<MatrixType> {
typedef typename result_of<ViewOp(typename traits<MatrixType>::Scalar&)>::type1 ScalarRef;
static_assert(std::is_reference<ScalarRef>::value, "Views must return a reference type.");
typedef remove_all_t<ScalarRef> Scalar;
typedef typename MatrixType::Nested MatrixTypeNested;
typedef remove_all_t<MatrixTypeNested> MatrixTypeNested_;
enum {
FlagsLvalueBit = is_lvalue<MatrixType>::value ? LvalueBit : 0,
Flags =
traits<MatrixTypeNested_>::Flags &
(RowMajorBit | FlagsLvalueBit | DirectAccessBit), // FIXME DirectAccessBit should not be handled by expressions
MatrixTypeInnerStride = inner_stride_at_compile_time<MatrixType>::ret,
// need to cast the sizeof's from size_t to int explicitly, otherwise:
// "error: no integral type can represent all of the enumerator values
InnerStrideAtCompileTime =
StrideType::InnerStrideAtCompileTime == 0
? (MatrixTypeInnerStride == Dynamic
? int(Dynamic)
: int(MatrixTypeInnerStride) * int(sizeof(typename traits<MatrixType>::Scalar) / sizeof(Scalar)))
: int(StrideType::InnerStrideAtCompileTime),
OuterStrideAtCompileTime = StrideType::OuterStrideAtCompileTime == 0
? (outer_stride_at_compile_time<MatrixType>::ret == Dynamic
? int(Dynamic)
: outer_stride_at_compile_time<MatrixType>::ret *
int(sizeof(typename traits<MatrixType>::Scalar) / sizeof(Scalar)))
: int(StrideType::OuterStrideAtCompileTime)
};
};
// Generic API dispatcher
template <typename ViewOp, typename XprType, typename StrideType, typename StorageKind,
bool Mutable = !std::is_const<XprType>::value>
class CwiseUnaryViewImpl : public generic_xpr_base<CwiseUnaryView<ViewOp, XprType, StrideType> >::type {
public:
typedef typename generic_xpr_base<CwiseUnaryView<ViewOp, XprType, StrideType> >::type Base;
};
template <typename ViewOp, typename MatrixType, typename StrideType>
class CwiseUnaryViewImpl<ViewOp, MatrixType, StrideType, Dense, false>
: public dense_xpr_base<CwiseUnaryView<ViewOp, MatrixType, StrideType> >::type {
public:
typedef CwiseUnaryView<ViewOp, MatrixType, StrideType> Derived;
typedef typename dense_xpr_base<CwiseUnaryView<ViewOp, MatrixType, StrideType> >::type Base;
EIGEN_DENSE_PUBLIC_INTERFACE(Derived)
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(CwiseUnaryViewImpl)
EIGEN_DEVICE_FUNC inline const Scalar* data() const { return &(this->coeffRef(0)); }
EIGEN_DEVICE_FUNC constexpr Index innerStride() const {
return StrideType::InnerStrideAtCompileTime != 0 ? int(StrideType::InnerStrideAtCompileTime)
: derived().nestedExpression().innerStride() *
sizeof(typename traits<MatrixType>::Scalar) / sizeof(Scalar);
}
EIGEN_DEVICE_FUNC constexpr Index outerStride() const {
return StrideType::OuterStrideAtCompileTime != 0 ? int(StrideType::OuterStrideAtCompileTime)
: derived().nestedExpression().outerStride() *
sizeof(typename traits<MatrixType>::Scalar) / sizeof(Scalar);
}
protected:
EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(CwiseUnaryViewImpl)
// Allow const access to coeffRef for the case of direct access being enabled.
EIGEN_DEVICE_FUNC inline const Scalar& coeffRef(Index index) const {
return internal::evaluator<Derived>(derived()).coeffRef(index);
}
EIGEN_DEVICE_FUNC inline const Scalar& coeffRef(Index row, Index col) const {
return internal::evaluator<Derived>(derived()).coeffRef(row, col);
}
};
template <typename ViewOp, typename MatrixType, typename StrideType>
class CwiseUnaryViewImpl<ViewOp, MatrixType, StrideType, Dense, true>
: public CwiseUnaryViewImpl<ViewOp, MatrixType, StrideType, Dense, false> {
public:
typedef CwiseUnaryViewImpl<ViewOp, MatrixType, StrideType, Dense, false> Base;
typedef CwiseUnaryView<ViewOp, MatrixType, StrideType> Derived;
EIGEN_DENSE_PUBLIC_INTERFACE(Derived)
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(CwiseUnaryViewImpl)
using Base::data;
EIGEN_DEVICE_FUNC inline Scalar* data() { return &(this->coeffRef(0)); }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index row, Index col) {
return internal::evaluator<Derived>(derived()).coeffRef(row, col);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index index) {
return internal::evaluator<Derived>(derived()).coeffRef(index);
}
protected:
EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(CwiseUnaryViewImpl)
};
} // namespace internal
/** \class CwiseUnaryView
* \ingroup Core_Module
*
* \brief Generic lvalue expression of a coefficient-wise unary operator of a matrix or a vector
*
* \tparam ViewOp template functor implementing the view
* \tparam MatrixType the type of the matrix we are applying the unary operator
*
* This class represents a lvalue expression of a generic unary view operator of a matrix or a vector.
* It is the return type of real() and imag(), and most of the time this is the only way it is used.
*
* \sa MatrixBase::unaryViewExpr(const CustomUnaryOp &) const, class CwiseUnaryOp
*/
template <typename ViewOp, typename MatrixType, typename StrideType>
class CwiseUnaryView : public internal::CwiseUnaryViewImpl<ViewOp, MatrixType, StrideType,
typename internal::traits<MatrixType>::StorageKind> {
public:
typedef typename internal::CwiseUnaryViewImpl<ViewOp, MatrixType, StrideType,
typename internal::traits<MatrixType>::StorageKind>::Base Base;
EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseUnaryView)
typedef typename internal::ref_selector<MatrixType>::non_const_type MatrixTypeNested;
typedef internal::remove_all_t<MatrixType> NestedExpression;
explicit EIGEN_DEVICE_FUNC inline CwiseUnaryView(MatrixType& mat, const ViewOp& func = ViewOp())
: m_matrix(mat), m_functor(func) {}
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(CwiseUnaryView)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index rows() const noexcept { return m_matrix.rows(); }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index cols() const noexcept { return m_matrix.cols(); }
/** \returns the functor representing unary operation */
EIGEN_DEVICE_FUNC const ViewOp& functor() const { return m_functor; }
/** \returns the nested expression */
EIGEN_DEVICE_FUNC const internal::remove_all_t<MatrixTypeNested>& nestedExpression() const { return m_matrix; }
/** \returns the nested expression */
EIGEN_DEVICE_FUNC std::remove_reference_t<MatrixTypeNested>& nestedExpression() { return m_matrix; }
protected:
MatrixTypeNested m_matrix;
ViewOp m_functor;
};
} // namespace Eigen
#endif // EIGEN_CWISE_UNARY_VIEW_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2007-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_DENSEBASE_H
#define EIGEN_DENSEBASE_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
// The index type defined by EIGEN_DEFAULT_DENSE_INDEX_TYPE must be a signed type.
EIGEN_STATIC_ASSERT(NumTraits<DenseIndex>::IsSigned, THE_INDEX_TYPE_MUST_BE_A_SIGNED_TYPE)
/** \class DenseBase
* \ingroup Core_Module
*
* \brief Base class for all dense matrices, vectors, and arrays
*
* This class is the base that is inherited by all dense objects (matrix, vector, arrays,
* and related expression types). The common Eigen API for dense objects is contained in this class.
*
* \tparam Derived is the derived type, e.g., a matrix type or an expression.
*
* This class can be extended with the help of the plugin mechanism described on the page
* \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_DENSEBASE_PLUGIN.
*
* \sa \blank \ref TopicClassHierarchy
*/
template <typename Derived>
class DenseBase
#ifndef EIGEN_PARSED_BY_DOXYGEN
: public DenseCoeffsBase<Derived, internal::accessors_level<Derived>::value>
#else
: public DenseCoeffsBase<Derived, DirectWriteAccessors>
#endif // not EIGEN_PARSED_BY_DOXYGEN
{
public:
/** Inner iterator type to iterate over the coefficients of a row or column.
* \sa class InnerIterator
*/
typedef Eigen::InnerIterator<Derived> InnerIterator;
typedef typename internal::traits<Derived>::StorageKind StorageKind;
/**
* \brief The type used to store indices
* \details This typedef is relevant for types that store multiple indices such as
* PermutationMatrix or Transpositions, otherwise it defaults to Eigen::Index
* \sa \blank \ref TopicPreprocessorDirectives, Eigen::Index, SparseMatrixBase.
*/
typedef typename internal::traits<Derived>::StorageIndex StorageIndex;
/** The numeric type of the expression' coefficients, e.g. float, double, int or std::complex<float>, etc. */
typedef typename internal::traits<Derived>::Scalar Scalar;
/** The numeric type of the expression' coefficients, e.g. float, double, int or std::complex<float>, etc.
*
* It is an alias for the Scalar type */
typedef Scalar value_type;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef DenseCoeffsBase<Derived, internal::accessors_level<Derived>::value> Base;
using Base::coeff;
using Base::coeffByOuterInner;
using Base::colIndexByOuterInner;
using Base::cols;
using Base::const_cast_derived;
using Base::derived;
using Base::rowIndexByOuterInner;
using Base::rows;
using Base::size;
using Base::operator();
using Base::operator[];
using Base::colStride;
using Base::innerStride;
using Base::outerStride;
using Base::rowStride;
using Base::stride;
using Base::w;
using Base::x;
using Base::y;
using Base::z;
typedef typename Base::CoeffReturnType CoeffReturnType;
enum {
RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
/**< The number of rows at compile-time. This is just a copy of the value provided
* by the \a Derived type. If a value is not known at compile-time,
* it is set to the \a Dynamic constant.
* \sa MatrixBase::rows(), MatrixBase::cols(), ColsAtCompileTime, SizeAtCompileTime */
ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
/**< The number of columns at compile-time. This is just a copy of the value provided
* by the \a Derived type. If a value is not known at compile-time,
* it is set to the \a Dynamic constant.
* \sa MatrixBase::rows(), MatrixBase::cols(), RowsAtCompileTime, SizeAtCompileTime */
SizeAtCompileTime = (internal::size_of_xpr_at_compile_time<Derived>::ret),
/**< This is equal to the number of coefficients, i.e. the number of
* rows times the number of columns, or to \a Dynamic if this is not
* known at compile-time. \sa RowsAtCompileTime, ColsAtCompileTime */
MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime,
/**< This value is equal to the maximum possible number of rows that this expression
* might have. If this expression might have an arbitrarily high number of rows,
* this value is set to \a Dynamic.
*
* This value is useful to know when evaluating an expression, in order to determine
* whether it is possible to avoid doing a dynamic memory allocation.
*
* \sa RowsAtCompileTime, MaxColsAtCompileTime, MaxSizeAtCompileTime
*/
MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime,
/**< This value is equal to the maximum possible number of columns that this expression
* might have. If this expression might have an arbitrarily high number of columns,
* this value is set to \a Dynamic.
*
* This value is useful to know when evaluating an expression, in order to determine
* whether it is possible to avoid doing a dynamic memory allocation.
*
* \sa ColsAtCompileTime, MaxRowsAtCompileTime, MaxSizeAtCompileTime
*/
MaxSizeAtCompileTime = internal::size_at_compile_time(internal::traits<Derived>::MaxRowsAtCompileTime,
internal::traits<Derived>::MaxColsAtCompileTime),
/**< This value is equal to the maximum possible number of coefficients that this expression
* might have. If this expression might have an arbitrarily high number of coefficients,
* this value is set to \a Dynamic.
*
* This value is useful to know when evaluating an expression, in order to determine
* whether it is possible to avoid doing a dynamic memory allocation.
*
* \sa SizeAtCompileTime, MaxRowsAtCompileTime, MaxColsAtCompileTime
*/
IsVectorAtCompileTime =
internal::traits<Derived>::RowsAtCompileTime == 1 || internal::traits<Derived>::ColsAtCompileTime == 1,
/**< This is set to true if either the number of rows or the number of
* columns is known at compile-time to be equal to 1. Indeed, in that case,
* we are dealing with a column-vector (if there is only one column) or with
* a row-vector (if there is only one row). */
NumDimensions = int(MaxSizeAtCompileTime) == 1 ? 0
: bool(IsVectorAtCompileTime) ? 1
: 2,
/**< This value is equal to Tensor::NumDimensions, i.e. 0 for scalars, 1 for vectors,
* and 2 for matrices.
*/
Flags = internal::traits<Derived>::Flags,
/**< This stores expression \ref flags flags which may or may not be inherited by new expressions
* constructed from this one. See the \ref flags "list of flags".
*/
IsRowMajor = int(Flags) & RowMajorBit, /**< True if this expression has row-major storage order. */
InnerSizeAtCompileTime = int(IsVectorAtCompileTime) ? int(SizeAtCompileTime)
: int(IsRowMajor) ? int(ColsAtCompileTime)
: int(RowsAtCompileTime),
InnerStrideAtCompileTime = internal::inner_stride_at_compile_time<Derived>::ret,
OuterStrideAtCompileTime = internal::outer_stride_at_compile_time<Derived>::ret
};
typedef typename internal::find_best_packet<Scalar, SizeAtCompileTime>::type PacketScalar;
enum { IsPlainObjectBase = 0 };
/** The plain matrix type corresponding to this expression.
* \sa PlainObject */
typedef Matrix<typename internal::traits<Derived>::Scalar, internal::traits<Derived>::RowsAtCompileTime,
internal::traits<Derived>::ColsAtCompileTime,
AutoAlign | (internal::traits<Derived>::Flags & RowMajorBit ? RowMajor : ColMajor),
internal::traits<Derived>::MaxRowsAtCompileTime, internal::traits<Derived>::MaxColsAtCompileTime>
PlainMatrix;
/** The plain array type corresponding to this expression.
* \sa PlainObject */
typedef Array<typename internal::traits<Derived>::Scalar, internal::traits<Derived>::RowsAtCompileTime,
internal::traits<Derived>::ColsAtCompileTime,
AutoAlign | (internal::traits<Derived>::Flags & RowMajorBit ? RowMajor : ColMajor),
internal::traits<Derived>::MaxRowsAtCompileTime, internal::traits<Derived>::MaxColsAtCompileTime>
PlainArray;
/** \brief The plain matrix or array type corresponding to this expression.
*
* This is not necessarily exactly the return type of eval(). In the case of plain matrices,
* the return type of eval() is a const reference to a matrix, not a matrix! It is however guaranteed
* that the return type of eval() is either PlainObject or const PlainObject&.
*/
typedef std::conditional_t<internal::is_same<typename internal::traits<Derived>::XprKind, MatrixXpr>::value,
PlainMatrix, PlainArray>
PlainObject;
/** \returns the outer size.
*
* \note For a vector, this returns just 1. For a matrix (non-vector), this is the major dimension
* with respect to the \ref TopicStorageOrders "storage order", i.e., the number of columns for a
* column-major matrix, and the number of rows for a row-major matrix. */
EIGEN_DEVICE_FUNC constexpr Index outerSize() const {
return IsVectorAtCompileTime ? 1 : int(IsRowMajor) ? this->rows() : this->cols();
}
/** \returns the inner size.
*
* \note For a vector, this is just the size. For a matrix (non-vector), this is the minor dimension
* with respect to the \ref TopicStorageOrders "storage order", i.e., the number of rows for a
* column-major matrix, and the number of columns for a row-major matrix. */
EIGEN_DEVICE_FUNC constexpr Index innerSize() const {
return IsVectorAtCompileTime ? this->size() : int(IsRowMajor) ? this->cols() : this->rows();
}
/** Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are
* Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and
* does nothing else.
*/
EIGEN_DEVICE_FUNC void resize(Index newSize) {
EIGEN_ONLY_USED_FOR_DEBUG(newSize);
eigen_assert(newSize == this->size() && "DenseBase::resize() does not actually allow to resize.");
}
/** Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are
* Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and
* does nothing else.
*/
EIGEN_DEVICE_FUNC void resize(Index rows, Index cols) {
EIGEN_ONLY_USED_FOR_DEBUG(rows);
EIGEN_ONLY_USED_FOR_DEBUG(cols);
eigen_assert(rows == this->rows() && cols == this->cols() &&
"DenseBase::resize() does not actually allow to resize.");
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** \internal Represents a matrix with all coefficients equal to one another*/
typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject> ConstantReturnType;
/** \internal Represents a matrix with all coefficients equal to zero*/
typedef CwiseNullaryOp<internal::scalar_zero_op<Scalar>, PlainObject> ZeroReturnType;
/** \internal \deprecated Represents a vector with linearly spaced coefficients that allows sequential access only. */
EIGEN_DEPRECATED typedef CwiseNullaryOp<internal::linspaced_op<Scalar>, PlainObject> SequentialLinSpacedReturnType;
/** \internal Represents a vector with linearly spaced coefficients that allows random access. */
typedef CwiseNullaryOp<internal::linspaced_op<Scalar>, PlainObject> RandomAccessLinSpacedReturnType;
/** \internal Represents a vector with equally spaced coefficients that allows random access. */
typedef CwiseNullaryOp<internal::equalspaced_op<Scalar>, PlainObject> RandomAccessEqualSpacedReturnType;
/** \internal the return type of MatrixBase::eigenvalues() */
typedef Matrix<typename NumTraits<typename internal::traits<Derived>::Scalar>::Real,
internal::traits<Derived>::ColsAtCompileTime, 1>
EigenvaluesReturnType;
#endif // not EIGEN_PARSED_BY_DOXYGEN
/** Copies \a other into *this. \returns a reference to *this. */
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const DenseBase<OtherDerived>& other);
/** Special case of the template operator=, in order to prevent the compiler
* from generating a default operator= (issue hit with g++ 4.1)
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const DenseBase& other);
template <typename OtherDerived>
EIGEN_DEVICE_FUNC Derived& operator=(const EigenBase<OtherDerived>& other);
template <typename OtherDerived>
EIGEN_DEVICE_FUNC Derived& operator+=(const EigenBase<OtherDerived>& other);
template <typename OtherDerived>
EIGEN_DEVICE_FUNC Derived& operator-=(const EigenBase<OtherDerived>& other);
template <typename OtherDerived>
EIGEN_DEVICE_FUNC Derived& operator=(const ReturnByValue<OtherDerived>& func);
/** \internal
* Copies \a other into *this without evaluating other. \returns a reference to *this. */
template <typename OtherDerived>
/** \deprecated */
EIGEN_DEPRECATED EIGEN_DEVICE_FUNC Derived& lazyAssign(const DenseBase<OtherDerived>& other);
EIGEN_DEVICE_FUNC CommaInitializer<Derived> operator<<(const Scalar& s);
template <unsigned int Added, unsigned int Removed>
/** \deprecated it now returns \c *this */
EIGEN_DEPRECATED const Derived& flagged() const {
return derived();
}
template <typename OtherDerived>
EIGEN_DEVICE_FUNC CommaInitializer<Derived> operator<<(const DenseBase<OtherDerived>& other);
typedef Transpose<Derived> TransposeReturnType;
EIGEN_DEVICE_FUNC TransposeReturnType transpose();
typedef Transpose<const Derived> ConstTransposeReturnType;
EIGEN_DEVICE_FUNC const ConstTransposeReturnType transpose() const;
EIGEN_DEVICE_FUNC void transposeInPlace();
EIGEN_DEVICE_FUNC static const ConstantReturnType Constant(Index rows, Index cols, const Scalar& value);
EIGEN_DEVICE_FUNC static const ConstantReturnType Constant(Index size, const Scalar& value);
EIGEN_DEVICE_FUNC static const ConstantReturnType Constant(const Scalar& value);
EIGEN_DEPRECATED EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType LinSpaced(Sequential_t, Index size,
const Scalar& low,
const Scalar& high);
EIGEN_DEPRECATED EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType LinSpaced(Sequential_t,
const Scalar& low,
const Scalar& high);
EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType LinSpaced(Index size, const Scalar& low,
const Scalar& high);
EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType LinSpaced(const Scalar& low, const Scalar& high);
EIGEN_DEVICE_FUNC static const RandomAccessEqualSpacedReturnType EqualSpaced(Index size, const Scalar& low,
const Scalar& step);
EIGEN_DEVICE_FUNC static const RandomAccessEqualSpacedReturnType EqualSpaced(const Scalar& low, const Scalar& step);
template <typename CustomNullaryOp>
EIGEN_DEVICE_FUNC static const CwiseNullaryOp<CustomNullaryOp, PlainObject> NullaryExpr(Index rows, Index cols,
const CustomNullaryOp& func);
template <typename CustomNullaryOp>
EIGEN_DEVICE_FUNC static const CwiseNullaryOp<CustomNullaryOp, PlainObject> NullaryExpr(Index size,
const CustomNullaryOp& func);
template <typename CustomNullaryOp>
EIGEN_DEVICE_FUNC static const CwiseNullaryOp<CustomNullaryOp, PlainObject> NullaryExpr(const CustomNullaryOp& func);
EIGEN_DEVICE_FUNC static const ZeroReturnType Zero(Index rows, Index cols);
EIGEN_DEVICE_FUNC static const ZeroReturnType Zero(Index size);
EIGEN_DEVICE_FUNC static const ZeroReturnType Zero();
EIGEN_DEVICE_FUNC static const ConstantReturnType Ones(Index rows, Index cols);
EIGEN_DEVICE_FUNC static const ConstantReturnType Ones(Index size);
EIGEN_DEVICE_FUNC static const ConstantReturnType Ones();
EIGEN_DEVICE_FUNC void fill(const Scalar& value);
EIGEN_DEVICE_FUNC Derived& setConstant(const Scalar& value);
EIGEN_DEVICE_FUNC Derived& setLinSpaced(Index size, const Scalar& low, const Scalar& high);
EIGEN_DEVICE_FUNC Derived& setLinSpaced(const Scalar& low, const Scalar& high);
EIGEN_DEVICE_FUNC Derived& setEqualSpaced(Index size, const Scalar& low, const Scalar& step);
EIGEN_DEVICE_FUNC Derived& setEqualSpaced(const Scalar& low, const Scalar& step);
EIGEN_DEVICE_FUNC Derived& setZero();
EIGEN_DEVICE_FUNC Derived& setOnes();
EIGEN_DEVICE_FUNC Derived& setRandom();
template <typename OtherDerived>
EIGEN_DEVICE_FUNC bool isApprox(const DenseBase<OtherDerived>& other,
const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
EIGEN_DEVICE_FUNC bool isMuchSmallerThan(const RealScalar& other,
const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
template <typename OtherDerived>
EIGEN_DEVICE_FUNC bool isMuchSmallerThan(const DenseBase<OtherDerived>& other,
const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
EIGEN_DEVICE_FUNC bool isApproxToConstant(const Scalar& value,
const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
EIGEN_DEVICE_FUNC bool isConstant(const Scalar& value,
const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
EIGEN_DEVICE_FUNC bool isZero(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
EIGEN_DEVICE_FUNC bool isOnes(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
EIGEN_DEVICE_FUNC inline bool hasNaN() const;
EIGEN_DEVICE_FUNC inline bool allFinite() const;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator*=(const Scalar& other);
template <bool Enable = !internal::is_same<Scalar, RealScalar>::value, typename = std::enable_if_t<Enable>>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator*=(const RealScalar& other);
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator/=(const Scalar& other);
template <bool Enable = !internal::is_same<Scalar, RealScalar>::value, typename = std::enable_if_t<Enable>>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator/=(const RealScalar& other);
typedef internal::add_const_on_value_type_t<typename internal::eval<Derived>::type> EvalReturnType;
/** \returns the matrix or vector obtained by evaluating this expression.
*
* Notice that in the case of a plain matrix or vector (not an expression) this function just returns
* a const reference, in order to avoid a useless copy.
*
* \warning Be careful with eval() and the auto C++ keyword, as detailed in this \link TopicPitfalls_auto_keyword page
* \endlink.
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EvalReturnType eval() const {
// Even though MSVC does not honor strong inlining when the return type
// is a dynamic matrix, we desperately need strong inlining for fixed
// size types on MSVC.
return typename internal::eval<Derived>::type(derived());
}
/** swaps *this with the expression \a other.
*
*/
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void swap(const DenseBase<OtherDerived>& other) {
EIGEN_STATIC_ASSERT(!OtherDerived::IsPlainObjectBase, THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY);
eigen_assert(rows() == other.rows() && cols() == other.cols());
call_assignment(derived(), other.const_cast_derived(), internal::swap_assign_op<Scalar>());
}
/** swaps *this with the matrix or array \a other.
*
*/
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void swap(PlainObjectBase<OtherDerived>& other) {
eigen_assert(rows() == other.rows() && cols() == other.cols());
call_assignment(derived(), other.derived(), internal::swap_assign_op<Scalar>());
}
EIGEN_DEVICE_FUNC inline const NestByValue<Derived> nestByValue() const;
EIGEN_DEVICE_FUNC inline const ForceAlignedAccess<Derived> forceAlignedAccess() const;
EIGEN_DEVICE_FUNC inline ForceAlignedAccess<Derived> forceAlignedAccess();
template <bool Enable>
EIGEN_DEVICE_FUNC inline const std::conditional_t<Enable, ForceAlignedAccess<Derived>, Derived&>
forceAlignedAccessIf() const;
template <bool Enable>
EIGEN_DEVICE_FUNC inline std::conditional_t<Enable, ForceAlignedAccess<Derived>, Derived&> forceAlignedAccessIf();
EIGEN_DEVICE_FUNC Scalar sum() const;
EIGEN_DEVICE_FUNC Scalar mean() const;
EIGEN_DEVICE_FUNC Scalar trace() const;
EIGEN_DEVICE_FUNC Scalar prod() const;
template <int NaNPropagation>
EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar minCoeff() const;
template <int NaNPropagation>
EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar maxCoeff() const;
// By default, the fastest version with undefined NaN propagation semantics is
// used.
// TODO(rmlarsen): Replace with default template argument when we move to
// c++11 or beyond.
EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Scalar minCoeff() const {
return minCoeff<PropagateFast>();
}
EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Scalar maxCoeff() const {
return maxCoeff<PropagateFast>();
}
template <int NaNPropagation, typename IndexType>
EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar minCoeff(IndexType* row, IndexType* col) const;
template <int NaNPropagation, typename IndexType>
EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar maxCoeff(IndexType* row, IndexType* col) const;
template <int NaNPropagation, typename IndexType>
EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar minCoeff(IndexType* index) const;
template <int NaNPropagation, typename IndexType>
EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar maxCoeff(IndexType* index) const;
// TODO(rmlarsen): Replace these methods with a default template argument.
template <typename IndexType>
EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Scalar minCoeff(IndexType* row, IndexType* col) const {
return minCoeff<PropagateFast>(row, col);
}
template <typename IndexType>
EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Scalar maxCoeff(IndexType* row, IndexType* col) const {
return maxCoeff<PropagateFast>(row, col);
}
template <typename IndexType>
EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Scalar minCoeff(IndexType* index) const {
return minCoeff<PropagateFast>(index);
}
template <typename IndexType>
EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Scalar maxCoeff(IndexType* index) const {
return maxCoeff<PropagateFast>(index);
}
template <typename BinaryOp>
EIGEN_DEVICE_FUNC Scalar redux(const BinaryOp& func) const;
template <typename Visitor>
EIGEN_DEVICE_FUNC void visit(Visitor& func) const;
/** \returns a WithFormat proxy object allowing to print a matrix the with given
* format \a fmt.
*
* See class IOFormat for some examples.
*
* \sa class IOFormat, class WithFormat
*/
inline const WithFormat<Derived> format(const IOFormat& fmt) const { return WithFormat<Derived>(derived(), fmt); }
/** \returns the unique coefficient of a 1x1 expression */
EIGEN_DEVICE_FUNC CoeffReturnType value() const {
EIGEN_STATIC_ASSERT_SIZE_1x1(Derived) eigen_assert(this->rows() == 1 && this->cols() == 1);
return derived().coeff(0, 0);
}
EIGEN_DEVICE_FUNC bool all() const;
EIGEN_DEVICE_FUNC bool any() const;
EIGEN_DEVICE_FUNC Index count() const;
typedef VectorwiseOp<Derived, Horizontal> RowwiseReturnType;
typedef const VectorwiseOp<const Derived, Horizontal> ConstRowwiseReturnType;
typedef VectorwiseOp<Derived, Vertical> ColwiseReturnType;
typedef const VectorwiseOp<const Derived, Vertical> ConstColwiseReturnType;
/** \returns a VectorwiseOp wrapper of *this for broadcasting and partial reductions
*
* Example: \include MatrixBase_rowwise.cpp
* Output: \verbinclude MatrixBase_rowwise.out
*
* \sa colwise(), class VectorwiseOp, \ref TutorialReductionsVisitorsBroadcasting
*/
// Code moved here due to a CUDA compiler bug
EIGEN_DEVICE_FUNC inline ConstRowwiseReturnType rowwise() const { return ConstRowwiseReturnType(derived()); }
EIGEN_DEVICE_FUNC RowwiseReturnType rowwise();
/** \returns a VectorwiseOp wrapper of *this broadcasting and partial reductions
*
* Example: \include MatrixBase_colwise.cpp
* Output: \verbinclude MatrixBase_colwise.out
*
* \sa rowwise(), class VectorwiseOp, \ref TutorialReductionsVisitorsBroadcasting
*/
EIGEN_DEVICE_FUNC inline ConstColwiseReturnType colwise() const { return ConstColwiseReturnType(derived()); }
EIGEN_DEVICE_FUNC ColwiseReturnType colwise();
typedef CwiseNullaryOp<internal::scalar_random_op<Scalar>, PlainObject> RandomReturnType;
static const RandomReturnType Random(Index rows, Index cols);
static const RandomReturnType Random(Index size);
static const RandomReturnType Random();
template <typename ThenDerived, typename ElseDerived>
inline EIGEN_DEVICE_FUNC
CwiseTernaryOp<internal::scalar_boolean_select_op<typename DenseBase<ThenDerived>::Scalar,
typename DenseBase<ElseDerived>::Scalar, Scalar>,
ThenDerived, ElseDerived, Derived>
select(const DenseBase<ThenDerived>& thenMatrix, const DenseBase<ElseDerived>& elseMatrix) const;
template <typename ThenDerived>
inline EIGEN_DEVICE_FUNC
CwiseTernaryOp<internal::scalar_boolean_select_op<typename DenseBase<ThenDerived>::Scalar,
typename DenseBase<ThenDerived>::Scalar, Scalar>,
ThenDerived, typename DenseBase<ThenDerived>::ConstantReturnType, Derived>
select(const DenseBase<ThenDerived>& thenMatrix, const typename DenseBase<ThenDerived>::Scalar& elseScalar) const;
template <typename ElseDerived>
inline EIGEN_DEVICE_FUNC
CwiseTernaryOp<internal::scalar_boolean_select_op<typename DenseBase<ElseDerived>::Scalar,
typename DenseBase<ElseDerived>::Scalar, Scalar>,
typename DenseBase<ElseDerived>::ConstantReturnType, ElseDerived, Derived>
select(const typename DenseBase<ElseDerived>::Scalar& thenScalar, const DenseBase<ElseDerived>& elseMatrix) const;
template <int p>
RealScalar lpNorm() const;
template <int RowFactor, int ColFactor>
EIGEN_DEVICE_FUNC const Replicate<Derived, RowFactor, ColFactor> replicate() const;
/**
* \return an expression of the replication of \c *this
*
* Example: \include MatrixBase_replicate_int_int.cpp
* Output: \verbinclude MatrixBase_replicate_int_int.out
*
* \sa VectorwiseOp::replicate(), DenseBase::replicate<int,int>(), class Replicate
*/
// Code moved here due to a CUDA compiler bug
EIGEN_DEVICE_FUNC const Replicate<Derived, Dynamic, Dynamic> replicate(Index rowFactor, Index colFactor) const {
return Replicate<Derived, Dynamic, Dynamic>(derived(), rowFactor, colFactor);
}
typedef Reverse<Derived, BothDirections> ReverseReturnType;
typedef const Reverse<const Derived, BothDirections> ConstReverseReturnType;
EIGEN_DEVICE_FUNC ReverseReturnType reverse();
/** This is the const version of reverse(). */
// Code moved here due to a CUDA compiler bug
EIGEN_DEVICE_FUNC ConstReverseReturnType reverse() const { return ConstReverseReturnType(derived()); }
EIGEN_DEVICE_FUNC void reverseInPlace();
#ifdef EIGEN_PARSED_BY_DOXYGEN
/** STL-like <a href="https://en.cppreference.com/w/cpp/named_req/RandomAccessIterator">RandomAccessIterator</a>
* iterator type as returned by the begin() and end() methods.
*/
typedef random_access_iterator_type iterator;
/** This is the const version of iterator (aka read-only) */
typedef random_access_iterator_type const_iterator;
#else
typedef std::conditional_t<(Flags & DirectAccessBit) == DirectAccessBit,
internal::pointer_based_stl_iterator<Derived>,
internal::generic_randaccess_stl_iterator<Derived> >
iterator_type;
typedef std::conditional_t<(Flags & DirectAccessBit) == DirectAccessBit,
internal::pointer_based_stl_iterator<const Derived>,
internal::generic_randaccess_stl_iterator<const Derived> >
const_iterator_type;
// Stl-style iterators are supported only for vectors.
typedef std::conditional_t<IsVectorAtCompileTime, iterator_type, void> iterator;
typedef std::conditional_t<IsVectorAtCompileTime, const_iterator_type, void> const_iterator;
#endif
inline iterator begin();
inline const_iterator begin() const;
inline const_iterator cbegin() const;
inline iterator end();
inline const_iterator end() const;
inline const_iterator cend() const;
using RealViewReturnType = std::conditional_t<NumTraits<Scalar>::IsComplex, RealView<Derived>, Derived&>;
using ConstRealViewReturnType =
std::conditional_t<NumTraits<Scalar>::IsComplex, RealView<const Derived>, const Derived&>;
EIGEN_DEVICE_FUNC RealViewReturnType realView();
EIGEN_DEVICE_FUNC ConstRealViewReturnType realView() const;
#define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::DenseBase
#define EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL
#define EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(COND)
#define EIGEN_DOC_UNARY_ADDONS(X, Y)
#include "../plugins/CommonCwiseUnaryOps.inc"
#include "../plugins/BlockMethods.inc"
#include "../plugins/IndexedViewMethods.inc"
#include "../plugins/ReshapedMethods.inc"
#ifdef EIGEN_DENSEBASE_PLUGIN
#include EIGEN_DENSEBASE_PLUGIN
#endif
#undef EIGEN_CURRENT_STORAGE_BASE_CLASS
#undef EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL
#undef EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF
#undef EIGEN_DOC_UNARY_ADDONS
// disable the use of evalTo for dense objects with a nice compilation error
template <typename Dest>
EIGEN_DEVICE_FUNC inline void evalTo(Dest&) const {
EIGEN_STATIC_ASSERT((internal::is_same<Dest, void>::value),
THE_EVAL_EVALTO_FUNCTION_SHOULD_NEVER_BE_CALLED_FOR_DENSE_OBJECTS);
}
protected:
EIGEN_DEFAULT_COPY_CONSTRUCTOR(DenseBase)
/** Default constructor. Do nothing. */
#ifdef EIGEN_INTERNAL_DEBUGGING
EIGEN_DEVICE_FUNC constexpr DenseBase() {
/* Just checks for self-consistency of the flags.
* Only do it when debugging Eigen, as this borders on paranoia and could slow compilation down
*/
EIGEN_STATIC_ASSERT(
(internal::check_implication(MaxRowsAtCompileTime == 1 && MaxColsAtCompileTime != 1, int(IsRowMajor)) &&
internal::check_implication(MaxColsAtCompileTime == 1 && MaxRowsAtCompileTime != 1, int(!IsRowMajor))),
INVALID_STORAGE_ORDER_FOR_THIS_VECTOR_EXPRESSION)
}
#else
EIGEN_DEVICE_FUNC constexpr DenseBase() = default;
#endif
private:
EIGEN_DEVICE_FUNC explicit DenseBase(int);
EIGEN_DEVICE_FUNC DenseBase(int, int);
template <typename OtherDerived>
EIGEN_DEVICE_FUNC explicit DenseBase(const DenseBase<OtherDerived>&);
};
/** Free-function swap.
*/
template <typename DerivedA, typename DerivedB>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
// Use forwarding references to capture all combinations of cv-qualified l+r-value cases.
std::enable_if_t<std::is_base_of<DenseBase<std::decay_t<DerivedA>>, std::decay_t<DerivedA>>::value &&
std::is_base_of<DenseBase<std::decay_t<DerivedB>>, std::decay_t<DerivedB>>::value,
void>
swap(DerivedA&& a, DerivedB&& b) {
a.swap(b);
}
} // end namespace Eigen
#endif // EIGEN_DENSEBASE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_DENSECOEFFSBASE_H
#define EIGEN_DENSECOEFFSBASE_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
template <typename T>
struct add_const_on_value_type_if_arithmetic {
typedef std::conditional_t<is_arithmetic<T>::value, T, add_const_on_value_type_t<T>> type;
};
} // namespace internal
/** \brief Base class providing read-only coefficient access to matrices and arrays.
* \ingroup Core_Module
* \tparam Derived Type of the derived class
*
* \note #ReadOnlyAccessors Constant indicating read-only access
*
* This class defines the \c operator() \c const function and friends, which can be used to read specific
* entries of a matrix or array.
*
* \sa DenseCoeffsBase<Derived, WriteAccessors>, DenseCoeffsBase<Derived, DirectAccessors>,
* \ref TopicClassHierarchy
*/
template <typename Derived>
class DenseCoeffsBase<Derived, ReadOnlyAccessors> : public EigenBase<Derived> {
public:
typedef typename internal::traits<Derived>::StorageKind StorageKind;
typedef typename internal::traits<Derived>::Scalar Scalar;
typedef typename internal::packet_traits<Scalar>::type PacketScalar;
// Explanation for this CoeffReturnType typedef.
// - This is the return type of the coeff() method.
// - The LvalueBit means exactly that we can offer a coeffRef() method, which means exactly that we can get references
// to coeffs, which means exactly that we can have coeff() return a const reference (as opposed to returning a value).
// - The DirectAccessBit means exactly that the underlying data of coefficients can be directly accessed as a plain
// strided array, which means exactly that the underlying data of coefficients does exist in memory, which means
// exactly that the coefficients is const-referencable, which means exactly that we can have coeff() return a const
// reference. For example, Map<const Matrix> have DirectAccessBit but not LvalueBit, so that Map<const Matrix>.coeff()
// does points to a const Scalar& which exists in memory, while does not allow coeffRef() as it would not provide a
// lvalue. Notice that DirectAccessBit and LvalueBit are mutually orthogonal.
// - The is_arithmetic check is required since "const int", "const double", etc. will cause warnings on some systems
// while the declaration of "const T", where T is a non arithmetic type does not. Always returning "const Scalar&" is
// not possible, since the underlying expressions might not offer a valid address the reference could be referring to.
typedef std::conditional_t<bool(internal::traits<Derived>::Flags&(LvalueBit | DirectAccessBit)), const Scalar&,
std::conditional_t<internal::is_arithmetic<Scalar>::value, Scalar, const Scalar>>
CoeffReturnType;
typedef typename internal::add_const_on_value_type_if_arithmetic<typename internal::packet_traits<Scalar>::type>::type
PacketReturnType;
typedef EigenBase<Derived> Base;
using Base::cols;
using Base::derived;
using Base::rows;
using Base::size;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index rowIndexByOuterInner(Index outer, Index inner) const {
return int(Derived::RowsAtCompileTime) == 1 ? 0
: int(Derived::ColsAtCompileTime) == 1 ? inner
: int(Derived::Flags) & RowMajorBit ? outer
: inner;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index colIndexByOuterInner(Index outer, Index inner) const {
return int(Derived::ColsAtCompileTime) == 1 ? 0
: int(Derived::RowsAtCompileTime) == 1 ? inner
: int(Derived::Flags) & RowMajorBit ? inner
: outer;
}
/** Short version: don't use this function, use
* \link operator()(Index,Index) const \endlink instead.
*
* Long version: this function is similar to
* \link operator()(Index,Index) const \endlink, but without the assertion.
* Use this for limiting the performance cost of debugging code when doing
* repeated coefficient access. Only use this when it is guaranteed that the
* parameters \a row and \a col are in range.
*
* If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this
* function equivalent to \link operator()(Index,Index) const \endlink.
*
* \sa operator()(Index,Index) const, coeffRef(Index,Index), coeff(Index) const
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr CoeffReturnType coeff(Index row, Index col) const {
eigen_internal_assert(row >= 0 && row < rows() && col >= 0 && col < cols());
return internal::evaluator<Derived>(derived()).coeff(row, col);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr CoeffReturnType coeffByOuterInner(Index outer, Index inner) const {
return coeff(rowIndexByOuterInner(outer, inner), colIndexByOuterInner(outer, inner));
}
/** \returns the coefficient at given the given row and column.
*
* \sa operator()(Index,Index), operator[](Index)
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr CoeffReturnType operator()(Index row, Index col) const {
eigen_assert(row >= 0 && row < rows() && col >= 0 && col < cols());
return coeff(row, col);
}
/** Short version: don't use this function, use
* \link operator[](Index) const \endlink instead.
*
* Long version: this function is similar to
* \link operator[](Index) const \endlink, but without the assertion.
* Use this for limiting the performance cost of debugging code when doing
* repeated coefficient access. Only use this when it is guaranteed that the
* parameter \a index is in range.
*
* If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this
* function equivalent to \link operator[](Index) const \endlink.
*
* \sa operator[](Index) const, coeffRef(Index), coeff(Index,Index) const
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr CoeffReturnType coeff(Index index) const {
EIGEN_STATIC_ASSERT(internal::evaluator<Derived>::Flags & LinearAccessBit,
THIS_COEFFICIENT_ACCESSOR_TAKING_ONE_ACCESS_IS_ONLY_FOR_EXPRESSIONS_ALLOWING_LINEAR_ACCESS)
eigen_internal_assert(index >= 0 && index < size());
return internal::evaluator<Derived>(derived()).coeff(index);
}
/** \returns the coefficient at given index.
*
* This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
*
* \sa operator[](Index), operator()(Index,Index) const, x() const, y() const,
* z() const, w() const
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr CoeffReturnType operator[](Index index) const {
EIGEN_STATIC_ASSERT(Derived::IsVectorAtCompileTime,
THE_BRACKET_OPERATOR_IS_ONLY_FOR_VECTORS__USE_THE_PARENTHESIS_OPERATOR_INSTEAD)
eigen_assert(index >= 0 && index < size());
return coeff(index);
}
/** \returns the coefficient at given index.
*
* This is synonymous to operator[](Index) const.
*
* This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
*
* \sa operator[](Index), operator()(Index,Index) const, x() const, y() const,
* z() const, w() const
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr CoeffReturnType operator()(Index index) const {
eigen_assert(index >= 0 && index < size());
return coeff(index);
}
/** equivalent to operator[](0). */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr CoeffReturnType x() const { return (*this)[0]; }
/** equivalent to operator[](1). */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr CoeffReturnType y() const {
EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime == -1 || Derived::SizeAtCompileTime >= 2, OUT_OF_RANGE_ACCESS);
return (*this)[1];
}
/** equivalent to operator[](2). */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr CoeffReturnType z() const {
EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime == -1 || Derived::SizeAtCompileTime >= 3, OUT_OF_RANGE_ACCESS);
return (*this)[2];
}
/** equivalent to operator[](3). */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr CoeffReturnType w() const {
EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime == -1 || Derived::SizeAtCompileTime >= 4, OUT_OF_RANGE_ACCESS);
return (*this)[3];
}
/** \internal
* \returns the packet of coefficients starting at the given row and column. It is your responsibility
* to ensure that a packet really starts there. This method is only available on expressions having the
* PacketAccessBit.
*
* The \a LoadMode parameter may have the value \a #Aligned or \a #Unaligned. Its effect is to select
* the appropriate vectorization instruction. Aligned access is faster, but is only possible for packets
* starting at an address which is a multiple of the packet size.
*/
template <int LoadMode>
EIGEN_STRONG_INLINE PacketReturnType packet(Index row, Index col) const {
typedef typename internal::packet_traits<Scalar>::type DefaultPacketType;
eigen_internal_assert(row >= 0 && row < rows() && col >= 0 && col < cols());
return internal::evaluator<Derived>(derived()).template packet<LoadMode, DefaultPacketType>(row, col);
}
/** \internal */
template <int LoadMode>
EIGEN_STRONG_INLINE PacketReturnType packetByOuterInner(Index outer, Index inner) const {
return packet<LoadMode>(rowIndexByOuterInner(outer, inner), colIndexByOuterInner(outer, inner));
}
/** \internal
* \returns the packet of coefficients starting at the given index. It is your responsibility
* to ensure that a packet really starts there. This method is only available on expressions having the
* PacketAccessBit and the LinearAccessBit.
*
* The \a LoadMode parameter may have the value \a #Aligned or \a #Unaligned. Its effect is to select
* the appropriate vectorization instruction. Aligned access is faster, but is only possible for packets
* starting at an address which is a multiple of the packet size.
*/
template <int LoadMode>
EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const {
EIGEN_STATIC_ASSERT(internal::evaluator<Derived>::Flags & LinearAccessBit,
THIS_COEFFICIENT_ACCESSOR_TAKING_ONE_ACCESS_IS_ONLY_FOR_EXPRESSIONS_ALLOWING_LINEAR_ACCESS)
typedef typename internal::packet_traits<Scalar>::type DefaultPacketType;
eigen_internal_assert(index >= 0 && index < size());
return internal::evaluator<Derived>(derived()).template packet<LoadMode, DefaultPacketType>(index);
}
protected:
// explanation: DenseBase is doing "using ..." on the methods from DenseCoeffsBase.
// But some methods are only available in the DirectAccess case.
// So we add dummy methods here with these names, so that "using... " doesn't fail.
// It's not private so that the child class DenseBase can access them, and it's not public
// either since it's an implementation detail, so has to be protected.
void coeffRef();
void coeffRefByOuterInner();
void writePacket();
void writePacketByOuterInner();
void copyCoeff();
void copyCoeffByOuterInner();
void copyPacket();
void copyPacketByOuterInner();
void stride();
void innerStride();
void outerStride();
void rowStride();
void colStride();
};
/** \brief Base class providing read/write coefficient access to matrices and arrays.
* \ingroup Core_Module
* \tparam Derived Type of the derived class
*
* \note #WriteAccessors Constant indicating read/write access
*
* This class defines the non-const \c operator() function and friends, which can be used to write specific
* entries of a matrix or array. This class inherits DenseCoeffsBase<Derived, ReadOnlyAccessors> which
* defines the const variant for reading specific entries.
*
* \sa DenseCoeffsBase<Derived, DirectAccessors>, \ref TopicClassHierarchy
*/
template <typename Derived>
class DenseCoeffsBase<Derived, WriteAccessors> : public DenseCoeffsBase<Derived, ReadOnlyAccessors> {
public:
typedef DenseCoeffsBase<Derived, ReadOnlyAccessors> Base;
typedef typename internal::traits<Derived>::StorageKind StorageKind;
typedef typename internal::traits<Derived>::Scalar Scalar;
typedef typename internal::packet_traits<Scalar>::type PacketScalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
using Base::coeff;
using Base::colIndexByOuterInner;
using Base::cols;
using Base::derived;
using Base::rowIndexByOuterInner;
using Base::rows;
using Base::size;
using Base::operator[];
using Base::operator();
using Base::w;
using Base::x;
using Base::y;
using Base::z;
/** Short version: don't use this function, use
* \link operator()(Index,Index) \endlink instead.
*
* Long version: this function is similar to
* \link operator()(Index,Index) \endlink, but without the assertion.
* Use this for limiting the performance cost of debugging code when doing
* repeated coefficient access. Only use this when it is guaranteed that the
* parameters \a row and \a col are in range.
*
* If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this
* function equivalent to \link operator()(Index,Index) \endlink.
*
* \sa operator()(Index,Index), coeff(Index, Index) const, coeffRef(Index)
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Scalar& coeffRef(Index row, Index col) {
eigen_internal_assert(row >= 0 && row < rows() && col >= 0 && col < cols());
return internal::evaluator<Derived>(derived()).coeffRef(row, col);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRefByOuterInner(Index outer, Index inner) {
return coeffRef(rowIndexByOuterInner(outer, inner), colIndexByOuterInner(outer, inner));
}
/** \returns a reference to the coefficient at given the given row and column.
*
* \sa operator[](Index)
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Scalar& operator()(Index row, Index col) {
eigen_assert(row >= 0 && row < rows() && col >= 0 && col < cols());
return coeffRef(row, col);
}
/** Short version: don't use this function, use
* \link operator[](Index) \endlink instead.
*
* Long version: this function is similar to
* \link operator[](Index) \endlink, but without the assertion.
* Use this for limiting the performance cost of debugging code when doing
* repeated coefficient access. Only use this when it is guaranteed that the
* parameters \a row and \a col are in range.
*
* If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this
* function equivalent to \link operator[](Index) \endlink.
*
* \sa operator[](Index), coeff(Index) const, coeffRef(Index,Index)
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Scalar& coeffRef(Index index) {
EIGEN_STATIC_ASSERT(internal::evaluator<Derived>::Flags & LinearAccessBit,
THIS_COEFFICIENT_ACCESSOR_TAKING_ONE_ACCESS_IS_ONLY_FOR_EXPRESSIONS_ALLOWING_LINEAR_ACCESS)
eigen_internal_assert(index >= 0 && index < size());
return internal::evaluator<Derived>(derived()).coeffRef(index);
}
/** \returns a reference to the coefficient at given index.
*
* This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
*
* \sa operator[](Index) const, operator()(Index,Index), x(), y(), z(), w()
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Scalar& operator[](Index index) {
EIGEN_STATIC_ASSERT(Derived::IsVectorAtCompileTime,
THE_BRACKET_OPERATOR_IS_ONLY_FOR_VECTORS__USE_THE_PARENTHESIS_OPERATOR_INSTEAD)
eigen_assert(index >= 0 && index < size());
return coeffRef(index);
}
/** \returns a reference to the coefficient at given index.
*
* This is synonymous to operator[](Index).
*
* This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
*
* \sa operator[](Index) const, operator()(Index,Index), x(), y(), z(), w()
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Scalar& operator()(Index index) {
eigen_assert(index >= 0 && index < size());
return coeffRef(index);
}
/** equivalent to operator[](0). */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Scalar& x() { return (*this)[0]; }
/** equivalent to operator[](1). */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Scalar& y() {
EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime == -1 || Derived::SizeAtCompileTime >= 2, OUT_OF_RANGE_ACCESS);
return (*this)[1];
}
/** equivalent to operator[](2). */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Scalar& z() {
EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime == -1 || Derived::SizeAtCompileTime >= 3, OUT_OF_RANGE_ACCESS);
return (*this)[2];
}
/** equivalent to operator[](3). */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Scalar& w() {
EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime == -1 || Derived::SizeAtCompileTime >= 4, OUT_OF_RANGE_ACCESS);
return (*this)[3];
}
};
/** \brief Base class providing direct read-only coefficient access to matrices and arrays.
* \ingroup Core_Module
* \tparam Derived Type of the derived class
*
* \note #DirectAccessors Constant indicating direct access
*
* This class defines functions to work with strides which can be used to access entries directly. This class
* inherits DenseCoeffsBase<Derived, ReadOnlyAccessors> which defines functions to access entries read-only using
* \c operator() .
*
* \sa \blank \ref TopicClassHierarchy
*/
template <typename Derived>
class DenseCoeffsBase<Derived, DirectAccessors> : public DenseCoeffsBase<Derived, ReadOnlyAccessors> {
public:
typedef DenseCoeffsBase<Derived, ReadOnlyAccessors> Base;
typedef typename internal::traits<Derived>::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
using Base::cols;
using Base::derived;
using Base::rows;
using Base::size;
/** \returns the pointer increment between two consecutive elements within a slice in the inner direction.
*
* \sa outerStride(), rowStride(), colStride()
*/
EIGEN_DEVICE_FUNC constexpr Index innerStride() const { return derived().innerStride(); }
/** \returns the pointer increment between two consecutive inner slices (for example, between two consecutive columns
* in a column-major matrix).
*
* \sa innerStride(), rowStride(), colStride()
*/
EIGEN_DEVICE_FUNC constexpr Index outerStride() const { return derived().outerStride(); }
// FIXME shall we remove it ?
constexpr Index stride() const { return Derived::IsVectorAtCompileTime ? innerStride() : outerStride(); }
/** \returns the pointer increment between two consecutive rows.
*
* \sa innerStride(), outerStride(), colStride()
*/
EIGEN_DEVICE_FUNC constexpr Index rowStride() const { return Derived::IsRowMajor ? outerStride() : innerStride(); }
/** \returns the pointer increment between two consecutive columns.
*
* \sa innerStride(), outerStride(), rowStride()
*/
EIGEN_DEVICE_FUNC constexpr Index colStride() const { return Derived::IsRowMajor ? innerStride() : outerStride(); }
};
/** \brief Base class providing direct read/write coefficient access to matrices and arrays.
* \ingroup Core_Module
* \tparam Derived Type of the derived class
*
* \note #DirectWriteAccessors Constant indicating direct access
*
* This class defines functions to work with strides which can be used to access entries directly. This class
* inherits DenseCoeffsBase<Derived, WriteAccessors> which defines functions to access entries read/write using
* \c operator().
*
* \sa \blank \ref TopicClassHierarchy
*/
template <typename Derived>
class DenseCoeffsBase<Derived, DirectWriteAccessors> : public DenseCoeffsBase<Derived, WriteAccessors> {
public:
typedef DenseCoeffsBase<Derived, WriteAccessors> Base;
typedef typename internal::traits<Derived>::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
using Base::cols;
using Base::derived;
using Base::rows;
using Base::size;
/** \returns the pointer increment between two consecutive elements within a slice in the inner direction.
*
* \sa outerStride(), rowStride(), colStride()
*/
EIGEN_DEVICE_FUNC constexpr Index innerStride() const noexcept { return derived().innerStride(); }
/** \returns the pointer increment between two consecutive inner slices (for example, between two consecutive columns
* in a column-major matrix).
*
* \sa innerStride(), rowStride(), colStride()
*/
EIGEN_DEVICE_FUNC constexpr Index outerStride() const noexcept { return derived().outerStride(); }
// FIXME shall we remove it ?
constexpr Index stride() const noexcept { return Derived::IsVectorAtCompileTime ? innerStride() : outerStride(); }
/** \returns the pointer increment between two consecutive rows.
*
* \sa innerStride(), outerStride(), colStride()
*/
EIGEN_DEVICE_FUNC constexpr Index rowStride() const noexcept {
return Derived::IsRowMajor ? outerStride() : innerStride();
}
/** \returns the pointer increment between two consecutive columns.
*
* \sa innerStride(), outerStride(), rowStride()
*/
EIGEN_DEVICE_FUNC constexpr Index colStride() const noexcept {
return Derived::IsRowMajor ? innerStride() : outerStride();
}
};
namespace internal {
template <int Alignment, typename Derived, bool JustReturnZero>
struct first_aligned_impl {
static constexpr Index run(const Derived&) noexcept { return 0; }
};
template <int Alignment, typename Derived>
struct first_aligned_impl<Alignment, Derived, false> {
static inline Index run(const Derived& m) { return internal::first_aligned<Alignment>(m.data(), m.size()); }
};
/** \internal \returns the index of the first element of the array stored by \a m that is properly aligned with respect
* to \a Alignment for vectorization.
*
* \tparam Alignment requested alignment in Bytes.
*
* There is also the variant first_aligned(const Scalar*, Integer) defined in Memory.h. See it for more
* documentation.
*/
template <int Alignment, typename Derived>
static inline Index first_aligned(const DenseBase<Derived>& m) {
enum { ReturnZero = (int(evaluator<Derived>::Alignment) >= Alignment) || !(Derived::Flags & DirectAccessBit) };
return first_aligned_impl<Alignment, Derived, ReturnZero>::run(m.derived());
}
template <typename Derived>
static inline Index first_default_aligned(const DenseBase<Derived>& m) {
typedef typename Derived::Scalar Scalar;
typedef typename packet_traits<Scalar>::type DefaultPacketType;
return internal::first_aligned<int(unpacket_traits<DefaultPacketType>::alignment), Derived>(m);
}
template <typename Derived, bool HasDirectAccess = has_direct_access<Derived>::ret>
struct inner_stride_at_compile_time {
enum { ret = traits<Derived>::InnerStrideAtCompileTime };
};
template <typename Derived>
struct inner_stride_at_compile_time<Derived, false> {
enum { ret = 0 };
};
template <typename Derived, bool HasDirectAccess = has_direct_access<Derived>::ret>
struct outer_stride_at_compile_time {
enum { ret = traits<Derived>::OuterStrideAtCompileTime };
};
template <typename Derived>
struct outer_stride_at_compile_time<Derived, false> {
enum { ret = 0 };
};
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_DENSECOEFFSBASE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2006-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2010-2013 Hauke Heibel <hauke.heibel@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_MATRIXSTORAGE_H
#define EIGEN_MATRIXSTORAGE_H
#ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
#define EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(X) \
X; \
EIGEN_DENSE_STORAGE_CTOR_PLUGIN;
#else
#define EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(X)
#endif
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
#if defined(EIGEN_DISABLE_UNALIGNED_ARRAY_ASSERT)
#define EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(Alignment)
#else
#define EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(Alignment) \
eigen_assert((is_constant_evaluated() || (std::uintptr_t(array) % Alignment == 0)) && \
"this assertion is explained here: " \
"http://eigen.tuxfamily.org/dox-devel/group__TopicUnalignedArrayAssert.html" \
" **** READ THIS WEB PAGE !!! ****");
#endif
#if EIGEN_STACK_ALLOCATION_LIMIT
#define EIGEN_MAKE_STACK_ALLOCATION_ASSERT(X) \
EIGEN_STATIC_ASSERT(X <= EIGEN_STACK_ALLOCATION_LIMIT, OBJECT_ALLOCATED_ON_STACK_IS_TOO_BIG)
#else
#define EIGEN_MAKE_STACK_ALLOCATION_ASSERT(X)
#endif
/** \internal
* Static array. If the MatrixOrArrayOptions require auto-alignment, the array will be automatically aligned:
* to 16 bytes boundary if the total size is a multiple of 16 bytes.
*/
template <typename T, int Size, int MatrixOrArrayOptions,
int Alignment = (MatrixOrArrayOptions & DontAlign) ? 0 : compute_default_alignment<T, Size>::value>
struct plain_array {
EIGEN_ALIGN_TO_BOUNDARY(Alignment) T array[Size];
#if defined(EIGEN_NO_DEBUG) || defined(EIGEN_TESTING_PLAINOBJECT_CTOR)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr plain_array() = default;
#else
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr plain_array() {
EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(Alignment)
EIGEN_MAKE_STACK_ALLOCATION_ASSERT(Size * sizeof(T))
}
#endif
};
template <typename T, int Size, int MatrixOrArrayOptions>
struct plain_array<T, Size, MatrixOrArrayOptions, 0> {
T array[Size];
#if defined(EIGEN_NO_DEBUG) || defined(EIGEN_TESTING_PLAINOBJECT_CTOR)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr plain_array() = default;
#else
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr plain_array() { EIGEN_MAKE_STACK_ALLOCATION_ASSERT(Size * sizeof(T)) }
#endif
};
template <typename T, int MatrixOrArrayOptions, int Alignment>
struct plain_array<T, 0, MatrixOrArrayOptions, Alignment> {
T array[1];
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr plain_array() = default;
};
template <typename T, int Size, int Options, int Alignment>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void swap_plain_array(plain_array<T, Size, Options, Alignment>& a,
plain_array<T, Size, Options, Alignment>& b,
Index a_size, Index b_size) {
Index common_size = numext::mini(a_size, b_size);
std::swap_ranges(a.array, a.array + common_size, b.array);
if (a_size > b_size)
smart_copy(a.array + common_size, a.array + a_size, b.array + common_size);
else if (b_size > a_size)
smart_copy(b.array + common_size, b.array + b_size, a.array + common_size);
}
template <typename T, int Size, int Rows, int Cols, int Options>
class DenseStorage_impl {
plain_array<T, Size, Options> m_data;
public:
#ifndef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl() = default;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl(const DenseStorage_impl&) = default;
#else
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl() {
EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(Index size = Size)
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl(const DenseStorage_impl& other) {
EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(Index size = Size)
smart_copy(other.m_data.array, other.m_data.array + Size, m_data.array);
}
#endif
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl(Index /*size*/, Index /*rows*/, Index /*cols*/) {}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl& operator=(const DenseStorage_impl&) = default;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void swap(DenseStorage_impl& other) {
numext::swap(m_data, other.m_data);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void conservativeResize(Index /*size*/, Index /*rows*/,
Index /*cols*/) {}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void resize(Index /*size*/, Index /*rows*/, Index /*cols*/) {}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index rows() const { return Rows; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index cols() const { return Cols; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index size() const { return Rows * Cols; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr T* data() { return m_data.array; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr const T* data() const { return m_data.array; }
};
template <typename T, int Size, int Cols, int Options>
class DenseStorage_impl<T, Size, Dynamic, Cols, Options> {
plain_array<T, Size, Options> m_data;
Index m_rows = 0;
public:
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl() = default;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl(const DenseStorage_impl& other)
: m_rows(other.m_rows) {
EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(Index size = other.size())
smart_copy(other.m_data.array, other.m_data.array + other.size(), m_data.array);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl(Index size, Index rows, Index /*cols*/)
: m_rows(rows) {
EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({})
EIGEN_UNUSED_VARIABLE(size)
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl& operator=(const DenseStorage_impl& other) {
smart_copy(other.m_data.array, other.m_data.array + other.size(), m_data.array);
m_rows = other.m_rows;
return *this;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void swap(DenseStorage_impl& other) {
swap_plain_array(m_data, other.m_data, size(), other.size());
numext::swap(m_rows, other.m_rows);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void conservativeResize(Index /*size*/, Index rows, Index /*cols*/) {
m_rows = rows;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void resize(Index /*size*/, Index rows, Index /*cols*/) {
m_rows = rows;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index rows() const { return m_rows; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index cols() const { return Cols; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index size() const { return m_rows * Cols; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr T* data() { return m_data.array; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr const T* data() const { return m_data.array; }
};
template <typename T, int Size, int Rows, int Options>
class DenseStorage_impl<T, Size, Rows, Dynamic, Options> {
plain_array<T, Size, Options> m_data;
Index m_cols = 0;
public:
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl() = default;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl(const DenseStorage_impl& other)
: m_cols(other.m_cols) {
EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(Index size = other.size())
smart_copy(other.m_data.array, other.m_data.array + other.size(), m_data.array);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl(Index size, Index /*rows*/, Index cols)
: m_cols(cols) {
EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({})
EIGEN_UNUSED_VARIABLE(size)
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl& operator=(const DenseStorage_impl& other) {
smart_copy(other.m_data.array, other.m_data.array + other.size(), m_data.array);
m_cols = other.m_cols;
return *this;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void swap(DenseStorage_impl& other) {
swap_plain_array(m_data, other.m_data, size(), other.size());
numext::swap(m_cols, other.m_cols);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void conservativeResize(Index /*size*/, Index /*rows*/, Index cols) {
m_cols = cols;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void resize(Index /*size*/, Index /*rows*/, Index cols) {
m_cols = cols;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index rows() const { return Rows; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index cols() const { return m_cols; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index size() const { return Rows * m_cols; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr T* data() { return m_data.array; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr const T* data() const { return m_data.array; }
};
template <typename T, int Size, int Options>
class DenseStorage_impl<T, Size, Dynamic, Dynamic, Options> {
plain_array<T, Size, Options> m_data;
Index m_rows = 0;
Index m_cols = 0;
public:
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl() = default;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl(const DenseStorage_impl& other)
: m_rows(other.m_rows), m_cols(other.m_cols) {
EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(Index size = other.size())
smart_copy(other.m_data.array, other.m_data.array + other.size(), m_data.array);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl(Index size, Index rows, Index cols)
: m_rows(rows), m_cols(cols) {
EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({})
EIGEN_UNUSED_VARIABLE(size)
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl& operator=(const DenseStorage_impl& other) {
smart_copy(other.m_data.array, other.m_data.array + other.size(), m_data.array);
m_rows = other.m_rows;
m_cols = other.m_cols;
return *this;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void swap(DenseStorage_impl& other) {
swap_plain_array(m_data, other.m_data, size(), other.size());
numext::swap(m_rows, other.m_rows);
numext::swap(m_cols, other.m_cols);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void conservativeResize(Index /*size*/, Index rows, Index cols) {
m_rows = rows;
m_cols = cols;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void resize(Index /*size*/, Index rows, Index cols) {
m_rows = rows;
m_cols = cols;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index rows() const { return m_rows; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index cols() const { return m_cols; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index size() const { return m_rows * m_cols; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr T* data() { return m_data.array; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr const T* data() const { return m_data.array; }
};
// null matrix variants
template <typename T, int Rows, int Cols, int Options>
class DenseStorage_impl<T, 0, Rows, Cols, Options> {
public:
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl() = default;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl(const DenseStorage_impl&) = default;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl(Index /*size*/, Index /*rows*/, Index /*cols*/) {}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl& operator=(const DenseStorage_impl&) = default;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void swap(DenseStorage_impl&) {}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void conservativeResize(Index /*size*/, Index /*rows*/,
Index /*cols*/) {}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void resize(Index /*size*/, Index /*rows*/, Index /*cols*/) {}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index rows() const { return Rows; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index cols() const { return Cols; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index size() const { return Rows * Cols; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr T* data() { return nullptr; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr const T* data() const { return nullptr; }
};
template <typename T, int Cols, int Options>
class DenseStorage_impl<T, 0, Dynamic, Cols, Options> {
Index m_rows = 0;
public:
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl() = default;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl(const DenseStorage_impl&) = default;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl(Index /*size*/, Index rows, Index /*cols*/)
: m_rows(rows) {}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl& operator=(const DenseStorage_impl&) = default;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void swap(DenseStorage_impl& other) noexcept {
numext::swap(m_rows, other.m_rows);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void conservativeResize(Index /*size*/, Index rows, Index /*cols*/) {
m_rows = rows;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void resize(Index /*size*/, Index rows, Index /*cols*/) {
m_rows = rows;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index rows() const { return m_rows; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index cols() const { return Cols; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index size() const { return m_rows * Cols; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr T* data() { return nullptr; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr const T* data() const { return nullptr; }
};
template <typename T, int Rows, int Options>
class DenseStorage_impl<T, 0, Rows, Dynamic, Options> {
Index m_cols = 0;
public:
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl() = default;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl(const DenseStorage_impl&) = default;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl(Index /*size*/, Index /*rows*/, Index cols)
: m_cols(cols) {}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl& operator=(const DenseStorage_impl&) = default;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void swap(DenseStorage_impl& other) noexcept {
numext::swap(m_cols, other.m_cols);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void conservativeResize(Index /*size*/, Index /*rows*/, Index cols) {
m_cols = cols;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void resize(Index /*size*/, Index /*rows*/, Index cols) {
m_cols = cols;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index rows() const { return Rows; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index cols() const { return m_cols; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index size() const { return Rows * m_cols; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr T* data() { return nullptr; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr const T* data() const { return nullptr; }
};
template <typename T, int Options>
class DenseStorage_impl<T, 0, Dynamic, Dynamic, Options> {
Index m_rows = 0;
Index m_cols = 0;
public:
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl() = default;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl(const DenseStorage_impl&) = default;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl(Index /*size*/, Index rows, Index cols)
: m_rows(rows), m_cols(cols) {}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl& operator=(const DenseStorage_impl&) = default;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void swap(DenseStorage_impl& other) noexcept {
numext::swap(m_rows, other.m_rows);
numext::swap(m_cols, other.m_cols);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void conservativeResize(Index /*size*/, Index rows, Index cols) {
m_rows = rows;
m_cols = cols;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void resize(Index /*size*/, Index rows, Index cols) {
m_rows = rows;
m_cols = cols;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index rows() const { return m_rows; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index cols() const { return m_cols; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index size() const { return m_rows * m_cols; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr T* data() { return nullptr; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr const T* data() const { return nullptr; }
};
// fixed-size matrix with dynamic memory allocation not currently supported
template <typename T, int Rows, int Cols, int Options>
class DenseStorage_impl<T, Dynamic, Rows, Cols, Options> {};
// dynamic-sized variants
template <typename T, int Cols, int Options>
class DenseStorage_impl<T, Dynamic, Dynamic, Cols, Options> {
static constexpr bool Align = (Options & DontAlign) == 0;
T* m_data = nullptr;
Index m_rows = 0;
public:
static constexpr int Size = Dynamic;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl() = default;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl(const DenseStorage_impl& other)
: m_data(conditional_aligned_new_auto<T, Align>(other.size())), m_rows(other.m_rows) {
EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(Index size = other.size())
smart_copy(other.m_data, other.m_data + other.size(), m_data);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl(Index size, Index rows, Index /*cols*/)
: m_data(conditional_aligned_new_auto<T, Align>(size)), m_rows(rows) {
EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({})
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl(DenseStorage_impl&& other) noexcept
: m_data(other.m_data), m_rows(other.m_rows) {
other.m_data = nullptr;
other.m_rows = 0;
}
EIGEN_DEVICE_FUNC ~DenseStorage_impl() { conditional_aligned_delete_auto<T, Align>(m_data, size()); }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl& operator=(const DenseStorage_impl& other) {
resize(other.size(), other.rows(), other.cols());
smart_copy(other.m_data, other.m_data + other.size(), m_data);
return *this;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl& operator=(DenseStorage_impl&& other) noexcept {
this->swap(other);
return *this;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void swap(DenseStorage_impl& other) noexcept {
numext::swap(m_data, other.m_data);
numext::swap(m_rows, other.m_rows);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void conservativeResize(Index size, Index rows, Index /*cols*/) {
m_data = conditional_aligned_realloc_new_auto<T, Align>(m_data, size, this->size());
m_rows = rows;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void resize(Index size, Index rows, Index /*cols*/) {
Index oldSize = this->size();
if (oldSize != size) {
conditional_aligned_delete_auto<T, Align>(m_data, oldSize);
m_data = conditional_aligned_new_auto<T, Align>(size);
EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({})
}
m_rows = rows;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index rows() const { return m_rows; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index cols() const { return Cols; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index size() const { return m_rows * Cols; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr T* data() { return m_data; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr const T* data() const { return m_data; }
};
template <typename T, int Rows, int Options>
class DenseStorage_impl<T, Dynamic, Rows, Dynamic, Options> {
static constexpr bool Align = (Options & DontAlign) == 0;
T* m_data = nullptr;
Index m_cols = 0;
public:
static constexpr int Size = Dynamic;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl() = default;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl(const DenseStorage_impl& other)
: m_data(conditional_aligned_new_auto<T, Align>(other.size())), m_cols(other.m_cols) {
EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(Index size = other.size())
smart_copy(other.m_data, other.m_data + other.size(), m_data);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl(Index size, Index /*rows*/, Index cols)
: m_data(conditional_aligned_new_auto<T, Align>(size)), m_cols(cols) {
EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({})
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl(DenseStorage_impl&& other) noexcept
: m_data(other.m_data), m_cols(other.m_cols) {
other.m_data = nullptr;
other.m_cols = 0;
}
EIGEN_DEVICE_FUNC ~DenseStorage_impl() { conditional_aligned_delete_auto<T, Align>(m_data, size()); }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl& operator=(const DenseStorage_impl& other) {
resize(other.size(), other.rows(), other.cols());
smart_copy(other.m_data, other.m_data + other.size(), m_data);
return *this;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl& operator=(DenseStorage_impl&& other) noexcept {
this->swap(other);
return *this;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void swap(DenseStorage_impl& other) noexcept {
numext::swap(m_data, other.m_data);
numext::swap(m_cols, other.m_cols);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void conservativeResize(Index size, Index /*rows*/, Index cols) {
m_data = conditional_aligned_realloc_new_auto<T, Align>(m_data, size, this->size());
m_cols = cols;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void resize(Index size, Index /*rows*/, Index cols) {
Index oldSize = this->size();
if (oldSize != size) {
conditional_aligned_delete_auto<T, Align>(m_data, oldSize);
m_data = conditional_aligned_new_auto<T, Align>(size);
EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({})
}
m_cols = cols;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index rows() const { return Rows; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index cols() const { return m_cols; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index size() const { return Rows * m_cols; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr T* data() { return m_data; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr const T* data() const { return m_data; }
};
template <typename T, int Options>
class DenseStorage_impl<T, Dynamic, Dynamic, Dynamic, Options> {
static constexpr bool Align = (Options & DontAlign) == 0;
T* m_data = nullptr;
Index m_rows = 0;
Index m_cols = 0;
public:
static constexpr int Size = Dynamic;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl() = default;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl(const DenseStorage_impl& other)
: m_data(conditional_aligned_new_auto<T, Align>(other.size())), m_rows(other.m_rows), m_cols(other.m_cols) {
EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(Index size = other.size())
smart_copy(other.m_data, other.m_data + other.size(), m_data);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl(Index size, Index rows, Index cols)
: m_data(conditional_aligned_new_auto<T, Align>(size)), m_rows(rows), m_cols(cols) {
EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({})
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl(DenseStorage_impl&& other) noexcept
: m_data(other.m_data), m_rows(other.m_rows), m_cols(other.m_cols) {
other.m_data = nullptr;
other.m_rows = 0;
other.m_cols = 0;
}
EIGEN_DEVICE_FUNC ~DenseStorage_impl() { conditional_aligned_delete_auto<T, Align>(m_data, size()); }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl& operator=(const DenseStorage_impl& other) {
resize(other.size(), other.rows(), other.cols());
smart_copy(other.m_data, other.m_data + other.size(), m_data);
return *this;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage_impl& operator=(DenseStorage_impl&& other) noexcept {
this->swap(other);
return *this;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void swap(DenseStorage_impl& other) noexcept {
numext::swap(m_data, other.m_data);
numext::swap(m_rows, other.m_rows);
numext::swap(m_cols, other.m_cols);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void conservativeResize(Index size, Index rows, Index cols) {
m_data = conditional_aligned_realloc_new_auto<T, Align>(m_data, size, this->size());
m_rows = rows;
m_cols = cols;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void resize(Index size, Index rows, Index cols) {
Index oldSize = this->size();
if (oldSize != size) {
conditional_aligned_delete_auto<T, Align>(m_data, oldSize);
m_data = conditional_aligned_new_auto<T, Align>(size);
EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({})
}
m_rows = rows;
m_cols = cols;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index rows() const { return m_rows; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index cols() const { return m_cols; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index size() const { return m_rows * m_cols; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr T* data() { return m_data; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr const T* data() const { return m_data; }
};
template <typename T, int Size, int Rows, int Cols>
struct use_default_move {
static constexpr bool DynamicObject = Size == Dynamic;
static constexpr bool TrivialObject =
(!NumTraits<T>::RequireInitialization) && (Rows >= 0) && (Cols >= 0) && (Size == Rows * Cols);
static constexpr bool value = DynamicObject || TrivialObject;
};
} // end namespace internal
/** \internal
*
* \class DenseStorage_impl
* \ingroup Core_Module
*
* \brief Stores the data of a matrix
*
* This class stores the data of fixed-size, dynamic-size or mixed matrices
* in a way as compact as possible.
*
* \sa Matrix
*/
template <typename T, int Size, int Rows, int Cols, int Options,
bool Trivial = internal::use_default_move<T, Size, Rows, Cols>::value>
class DenseStorage : public internal::DenseStorage_impl<T, Size, Rows, Cols, Options> {
using Base = internal::DenseStorage_impl<T, Size, Rows, Cols, Options>;
public:
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage() = default;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage(const DenseStorage&) = default;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage(Index size, Index rows, Index cols)
: Base(size, rows, cols) {}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage& operator=(const DenseStorage&) = default;
// if DenseStorage meets the requirements of use_default_move, then use the move construction and move assignment
// operation defined in DenseStorage_impl, or the compiler-generated version if none is defined
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage(DenseStorage&&) = default;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage& operator=(DenseStorage&&) = default;
};
template <typename T, int Size, int Rows, int Cols, int Options>
class DenseStorage<T, Size, Rows, Cols, Options, false>
: public internal::DenseStorage_impl<T, Size, Rows, Cols, Options> {
using Base = internal::DenseStorage_impl<T, Size, Rows, Cols, Options>;
public:
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage() = default;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage(const DenseStorage&) = default;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage(Index size, Index rows, Index cols)
: Base(size, rows, cols) {}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage& operator=(const DenseStorage&) = default;
// if DenseStorage does not meet the requirements of use_default_move, then defer to the copy construction and copy
// assignment behavior
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage(DenseStorage&& other)
: DenseStorage(static_cast<const DenseStorage&>(other)) {}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr DenseStorage& operator=(DenseStorage&& other) {
*this = other;
return *this;
}
};
} // end namespace Eigen
#endif // EIGEN_MATRIX_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2023 Charlie Schlosser <cs.schlosser@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_DEVICEWRAPPER_H
#define EIGEN_DEVICEWRAPPER_H
namespace Eigen {
template <typename Derived, typename Device>
struct DeviceWrapper {
using Base = EigenBase<internal::remove_all_t<Derived>>;
using Scalar = typename Derived::Scalar;
EIGEN_DEVICE_FUNC DeviceWrapper(Base& xpr, Device& device) : m_xpr(xpr.derived()), m_device(device) {}
EIGEN_DEVICE_FUNC DeviceWrapper(const Base& xpr, Device& device) : m_xpr(xpr.derived()), m_device(device) {}
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const EigenBase<OtherDerived>& other) {
using AssignOp = internal::assign_op<Scalar, typename OtherDerived::Scalar>;
internal::call_assignment(*this, other.derived(), AssignOp());
return m_xpr;
}
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator+=(const EigenBase<OtherDerived>& other) {
using AddAssignOp = internal::add_assign_op<Scalar, typename OtherDerived::Scalar>;
internal::call_assignment(*this, other.derived(), AddAssignOp());
return m_xpr;
}
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator-=(const EigenBase<OtherDerived>& other) {
using SubAssignOp = internal::sub_assign_op<Scalar, typename OtherDerived::Scalar>;
internal::call_assignment(*this, other.derived(), SubAssignOp());
return m_xpr;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& derived() { return m_xpr; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Device& device() { return m_device; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE NoAlias<DeviceWrapper, EigenBase> noalias() {
return NoAlias<DeviceWrapper, EigenBase>(*this);
}
Derived& m_xpr;
Device& m_device;
};
namespace internal {
// this is where we differentiate between lazy assignment and specialized kernels (e.g. matrix products)
template <typename DstXprType, typename SrcXprType, typename Functor, typename Device,
typename Kind = typename AssignmentKind<typename evaluator_traits<DstXprType>::Shape,
typename evaluator_traits<SrcXprType>::Shape>::Kind,
typename EnableIf = void>
struct AssignmentWithDevice;
// unless otherwise specified, use the default product implementation
template <typename DstXprType, typename Lhs, typename Rhs, int Options, typename Functor, typename Device,
typename Weak>
struct AssignmentWithDevice<DstXprType, Product<Lhs, Rhs, Options>, Functor, Device, Dense2Dense, Weak> {
using SrcXprType = Product<Lhs, Rhs, Options>;
using Base = Assignment<DstXprType, SrcXprType, Functor>;
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(DstXprType& dst, const SrcXprType& src, const Functor& func,
Device&) {
Base::run(dst, src, func);
}
};
// specialization for coeffcient-wise assignment
template <typename DstXprType, typename SrcXprType, typename Functor, typename Device, typename Weak>
struct AssignmentWithDevice<DstXprType, SrcXprType, Functor, Device, Dense2Dense, Weak> {
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(DstXprType& dst, const SrcXprType& src, const Functor& func,
Device& device) {
#ifndef EIGEN_NO_DEBUG
internal::check_for_aliasing(dst, src);
#endif
call_dense_assignment_loop(dst, src, func, device);
}
};
// this allows us to use the default evaluation scheme if it is not specialized for the device
template <typename Kernel, typename Device, int Traversal = Kernel::AssignmentTraits::Traversal,
int Unrolling = Kernel::AssignmentTraits::Unrolling>
struct dense_assignment_loop_with_device {
using Base = dense_assignment_loop<Kernel, Traversal, Unrolling>;
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void run(Kernel& kernel, Device&) { Base::run(kernel); }
};
// entry point for a generic expression with device
template <typename Dst, typename Src, typename Func, typename Device>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void call_assignment_no_alias(DeviceWrapper<Dst, Device> dst,
const Src& src, const Func& func) {
enum {
NeedToTranspose = ((int(Dst::RowsAtCompileTime) == 1 && int(Src::ColsAtCompileTime) == 1) ||
(int(Dst::ColsAtCompileTime) == 1 && int(Src::RowsAtCompileTime) == 1)) &&
int(Dst::SizeAtCompileTime) != 1
};
using ActualDstTypeCleaned = std::conditional_t<NeedToTranspose, Transpose<Dst>, Dst>;
using ActualDstType = std::conditional_t<NeedToTranspose, Transpose<Dst>, Dst&>;
ActualDstType actualDst(dst.derived());
// TODO check whether this is the right place to perform these checks:
EIGEN_STATIC_ASSERT_LVALUE(Dst)
EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(ActualDstTypeCleaned, Src)
EIGEN_CHECK_BINARY_COMPATIBILIY(Func, typename ActualDstTypeCleaned::Scalar, typename Src::Scalar);
// this provides a mechanism for specializing simple assignments, matrix products, etc
AssignmentWithDevice<ActualDstTypeCleaned, Src, Func, Device>::run(actualDst, src, func, dst.device());
}
// copy and pasted from AssignEvaluator except forward device to kernel
template <typename DstXprType, typename SrcXprType, typename Functor, typename Device>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void call_dense_assignment_loop(DstXprType& dst, const SrcXprType& src,
const Functor& func, Device& device) {
using DstEvaluatorType = evaluator<DstXprType>;
using SrcEvaluatorType = evaluator<SrcXprType>;
SrcEvaluatorType srcEvaluator(src);
// NOTE To properly handle A = (A*A.transpose())/s with A rectangular,
// we need to resize the destination after the source evaluator has been created.
resize_if_allowed(dst, src, func);
DstEvaluatorType dstEvaluator(dst);
using Kernel = generic_dense_assignment_kernel<DstEvaluatorType, SrcEvaluatorType, Functor>;
Kernel kernel(dstEvaluator, srcEvaluator, func, dst.const_cast_derived());
dense_assignment_loop_with_device<Kernel, Device>::run(kernel, device);
}
} // namespace internal
template <typename Derived>
template <typename Device>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DeviceWrapper<Derived, Device> EigenBase<Derived>::device(Device& device) {
return DeviceWrapper<Derived, Device>(derived(), device);
}
template <typename Derived>
template <typename Device>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DeviceWrapper<const Derived, Device> EigenBase<Derived>::device(
Device& device) const {
return DeviceWrapper<const Derived, Device>(derived(), device);
}
} // namespace Eigen
#endif

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_DIAGONAL_H
#define EIGEN_DIAGONAL_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
/** \class Diagonal
* \ingroup Core_Module
*
* \brief Expression of a diagonal/subdiagonal/superdiagonal in a matrix
*
* \tparam MatrixType the type of the object in which we are taking a sub/main/super diagonal
* \tparam DiagIndex the index of the sub/super diagonal. The default is 0 and it means the main diagonal.
* A positive value means a superdiagonal, a negative value means a subdiagonal.
* You can also use DynamicIndex so the index can be set at runtime.
*
* The matrix is not required to be square.
*
* This class represents an expression of the main diagonal, or any sub/super diagonal
* of a square matrix. It is the return type of MatrixBase::diagonal() and MatrixBase::diagonal(Index) and most of the
* time this is the only way it is used.
*
* \sa MatrixBase::diagonal(), MatrixBase::diagonal(Index)
*/
namespace internal {
template <typename MatrixType, int DiagIndex>
struct traits<Diagonal<MatrixType, DiagIndex> > : traits<MatrixType> {
typedef typename ref_selector<MatrixType>::type MatrixTypeNested;
typedef std::remove_reference_t<MatrixTypeNested> MatrixTypeNested_;
typedef typename MatrixType::StorageKind StorageKind;
enum {
RowsAtCompileTime = (int(DiagIndex) == DynamicIndex || int(MatrixType::SizeAtCompileTime) == Dynamic)
? Dynamic
: (plain_enum_min(MatrixType::RowsAtCompileTime - plain_enum_max(-DiagIndex, 0),
MatrixType::ColsAtCompileTime - plain_enum_max(DiagIndex, 0))),
ColsAtCompileTime = 1,
MaxRowsAtCompileTime =
int(MatrixType::MaxSizeAtCompileTime) == Dynamic ? Dynamic
: DiagIndex == DynamicIndex
? min_size_prefer_fixed(MatrixType::MaxRowsAtCompileTime, MatrixType::MaxColsAtCompileTime)
: (plain_enum_min(MatrixType::MaxRowsAtCompileTime - plain_enum_max(-DiagIndex, 0),
MatrixType::MaxColsAtCompileTime - plain_enum_max(DiagIndex, 0))),
MaxColsAtCompileTime = 1,
MaskLvalueBit = is_lvalue<MatrixType>::value ? LvalueBit : 0,
Flags = (unsigned int)MatrixTypeNested_::Flags & (RowMajorBit | MaskLvalueBit | DirectAccessBit) &
~RowMajorBit, // FIXME DirectAccessBit should not be handled by expressions
MatrixTypeOuterStride = outer_stride_at_compile_time<MatrixType>::ret,
InnerStrideAtCompileTime = MatrixTypeOuterStride == Dynamic ? Dynamic : MatrixTypeOuterStride + 1,
OuterStrideAtCompileTime = 0
};
};
} // namespace internal
template <typename MatrixType, int DiagIndex_>
class Diagonal : public internal::dense_xpr_base<Diagonal<MatrixType, DiagIndex_> >::type {
public:
enum { DiagIndex = DiagIndex_ };
typedef typename internal::dense_xpr_base<Diagonal>::type Base;
EIGEN_DENSE_PUBLIC_INTERFACE(Diagonal)
EIGEN_DEVICE_FUNC explicit inline Diagonal(MatrixType& matrix, Index a_index = DiagIndex)
: m_matrix(matrix), m_index(a_index) {
eigen_assert(a_index <= m_matrix.cols() && -a_index <= m_matrix.rows());
}
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Diagonal)
EIGEN_DEVICE_FUNC inline Index rows() const {
return m_index.value() < 0 ? numext::mini<Index>(m_matrix.cols(), m_matrix.rows() + m_index.value())
: numext::mini<Index>(m_matrix.rows(), m_matrix.cols() - m_index.value());
}
EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return 1; }
EIGEN_DEVICE_FUNC constexpr Index innerStride() const noexcept { return m_matrix.outerStride() + 1; }
EIGEN_DEVICE_FUNC constexpr Index outerStride() const noexcept { return 0; }
typedef std::conditional_t<internal::is_lvalue<MatrixType>::value, Scalar, const Scalar> ScalarWithConstIfNotLvalue;
EIGEN_DEVICE_FUNC inline ScalarWithConstIfNotLvalue* data() { return &(m_matrix.coeffRef(rowOffset(), colOffset())); }
EIGEN_DEVICE_FUNC inline const Scalar* data() const { return &(m_matrix.coeffRef(rowOffset(), colOffset())); }
EIGEN_DEVICE_FUNC inline Scalar& coeffRef(Index row, Index) {
EIGEN_STATIC_ASSERT_LVALUE(MatrixType)
return m_matrix.coeffRef(row + rowOffset(), row + colOffset());
}
EIGEN_DEVICE_FUNC inline const Scalar& coeffRef(Index row, Index) const {
return m_matrix.coeffRef(row + rowOffset(), row + colOffset());
}
EIGEN_DEVICE_FUNC inline CoeffReturnType coeff(Index row, Index) const {
return m_matrix.coeff(row + rowOffset(), row + colOffset());
}
EIGEN_DEVICE_FUNC inline Scalar& coeffRef(Index idx) {
EIGEN_STATIC_ASSERT_LVALUE(MatrixType)
return m_matrix.coeffRef(idx + rowOffset(), idx + colOffset());
}
EIGEN_DEVICE_FUNC inline const Scalar& coeffRef(Index idx) const {
return m_matrix.coeffRef(idx + rowOffset(), idx + colOffset());
}
EIGEN_DEVICE_FUNC inline CoeffReturnType coeff(Index idx) const {
return m_matrix.coeff(idx + rowOffset(), idx + colOffset());
}
EIGEN_DEVICE_FUNC inline const internal::remove_all_t<typename MatrixType::Nested>& nestedExpression() const {
return m_matrix;
}
EIGEN_DEVICE_FUNC inline Index index() const { return m_index.value(); }
protected:
typename internal::ref_selector<MatrixType>::non_const_type m_matrix;
const internal::variable_if_dynamicindex<Index, DiagIndex> m_index;
private:
// some compilers may fail to optimize std::max etc in case of compile-time constants...
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index absDiagIndex() const noexcept {
return m_index.value() > 0 ? m_index.value() : -m_index.value();
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index rowOffset() const noexcept {
return m_index.value() > 0 ? 0 : -m_index.value();
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index colOffset() const noexcept {
return m_index.value() > 0 ? m_index.value() : 0;
}
// trigger a compile-time error if someone try to call packet
template <int LoadMode>
typename MatrixType::PacketReturnType packet(Index) const;
template <int LoadMode>
typename MatrixType::PacketReturnType packet(Index, Index) const;
};
/** \returns an expression of the main diagonal of the matrix \c *this
*
* \c *this is not required to be square.
*
* Example: \include MatrixBase_diagonal.cpp
* Output: \verbinclude MatrixBase_diagonal.out
*
* \sa class Diagonal */
template <typename Derived>
EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::DiagonalReturnType MatrixBase<Derived>::diagonal() {
return DiagonalReturnType(derived());
}
/** This is the const version of diagonal(). */
template <typename Derived>
EIGEN_DEVICE_FUNC inline const typename MatrixBase<Derived>::ConstDiagonalReturnType MatrixBase<Derived>::diagonal()
const {
return ConstDiagonalReturnType(derived());
}
/** \returns an expression of the \a DiagIndex-th sub or super diagonal of the matrix \c *this
*
* \c *this is not required to be square.
*
* The template parameter \a DiagIndex represent a super diagonal if \a DiagIndex > 0
* and a sub diagonal otherwise. \a DiagIndex == 0 is equivalent to the main diagonal.
*
* Example: \include MatrixBase_diagonal_int.cpp
* Output: \verbinclude MatrixBase_diagonal_int.out
*
* \sa MatrixBase::diagonal(), class Diagonal */
template <typename Derived>
EIGEN_DEVICE_FUNC inline Diagonal<Derived, DynamicIndex> MatrixBase<Derived>::diagonal(Index index) {
return Diagonal<Derived, DynamicIndex>(derived(), index);
}
/** This is the const version of diagonal(Index). */
template <typename Derived>
EIGEN_DEVICE_FUNC inline const Diagonal<const Derived, DynamicIndex> MatrixBase<Derived>::diagonal(Index index) const {
return Diagonal<const Derived, DynamicIndex>(derived(), index);
}
/** \returns an expression of the \a DiagIndex-th sub or super diagonal of the matrix \c *this
*
* \c *this is not required to be square.
*
* The template parameter \a DiagIndex represent a super diagonal if \a DiagIndex > 0
* and a sub diagonal otherwise. \a DiagIndex == 0 is equivalent to the main diagonal.
*
* Example: \include MatrixBase_diagonal_template_int.cpp
* Output: \verbinclude MatrixBase_diagonal_template_int.out
*
* \sa MatrixBase::diagonal(), class Diagonal */
template <typename Derived>
template <int Index_>
EIGEN_DEVICE_FUNC inline Diagonal<Derived, Index_> MatrixBase<Derived>::diagonal() {
return Diagonal<Derived, Index_>(derived());
}
/** This is the const version of diagonal<int>(). */
template <typename Derived>
template <int Index_>
EIGEN_DEVICE_FUNC inline const Diagonal<const Derived, Index_> MatrixBase<Derived>::diagonal() const {
return Diagonal<const Derived, Index_>(derived());
}
} // end namespace Eigen
#endif // EIGEN_DIAGONAL_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_DIAGONALMATRIX_H
#define EIGEN_DIAGONALMATRIX_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
/** \class DiagonalBase
* \ingroup Core_Module
*
* \brief Base class for diagonal matrices and expressions
*
* This is the base class that is inherited by diagonal matrix and related expression
* types, which internally use a vector for storing the diagonal entries. Diagonal
* types always represent square matrices.
*
* \tparam Derived is the derived type, a DiagonalMatrix or DiagonalWrapper.
*
* \sa class DiagonalMatrix, class DiagonalWrapper
*/
template <typename Derived>
class DiagonalBase : public EigenBase<Derived> {
public:
typedef typename internal::traits<Derived>::DiagonalVectorType DiagonalVectorType;
typedef typename DiagonalVectorType::Scalar Scalar;
typedef typename DiagonalVectorType::RealScalar RealScalar;
typedef typename internal::traits<Derived>::StorageKind StorageKind;
typedef typename internal::traits<Derived>::StorageIndex StorageIndex;
enum {
RowsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
ColsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
MaxRowsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
MaxColsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
IsVectorAtCompileTime = 0,
Flags = NoPreferredStorageOrderBit
};
typedef Matrix<Scalar, RowsAtCompileTime, ColsAtCompileTime, 0, MaxRowsAtCompileTime, MaxColsAtCompileTime>
DenseMatrixType;
typedef DenseMatrixType DenseType;
typedef DiagonalMatrix<Scalar, DiagonalVectorType::SizeAtCompileTime, DiagonalVectorType::MaxSizeAtCompileTime>
PlainObject;
/** \returns a reference to the derived object. */
EIGEN_DEVICE_FUNC inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
/** \returns a const reference to the derived object. */
EIGEN_DEVICE_FUNC inline Derived& derived() { return *static_cast<Derived*>(this); }
/**
* Constructs a dense matrix from \c *this. Note, this directly returns a dense matrix type,
* not an expression.
* \returns A dense matrix, with its diagonal entries set from the the derived object. */
EIGEN_DEVICE_FUNC DenseMatrixType toDenseMatrix() const { return derived(); }
/** \returns a reference to the derived object's vector of diagonal coefficients. */
EIGEN_DEVICE_FUNC inline const DiagonalVectorType& diagonal() const { return derived().diagonal(); }
/** \returns a const reference to the derived object's vector of diagonal coefficients. */
EIGEN_DEVICE_FUNC inline DiagonalVectorType& diagonal() { return derived().diagonal(); }
/** \returns the value of the coefficient as if \c *this was a dense matrix. */
EIGEN_DEVICE_FUNC inline Scalar coeff(Index row, Index col) const {
eigen_assert(row >= 0 && col >= 0 && row < rows() && col <= cols());
return row == col ? diagonal().coeff(row) : Scalar(0);
}
/** \returns the number of rows. */
EIGEN_DEVICE_FUNC constexpr Index rows() const { return diagonal().size(); }
/** \returns the number of columns. */
EIGEN_DEVICE_FUNC constexpr Index cols() const { return diagonal().size(); }
/** \returns the diagonal matrix product of \c *this by the dense matrix, \a matrix */
template <typename MatrixDerived>
EIGEN_DEVICE_FUNC const Product<Derived, MatrixDerived, LazyProduct> operator*(
const MatrixBase<MatrixDerived>& matrix) const {
return Product<Derived, MatrixDerived, LazyProduct>(derived(), matrix.derived());
}
template <typename OtherDerived>
using DiagonalProductReturnType = DiagonalWrapper<const EIGEN_CWISE_BINARY_RETURN_TYPE(
DiagonalVectorType, typename OtherDerived::DiagonalVectorType, product)>;
/** \returns the diagonal matrix product of \c *this by the diagonal matrix \a other */
template <typename OtherDerived>
EIGEN_DEVICE_FUNC const DiagonalProductReturnType<OtherDerived> operator*(
const DiagonalBase<OtherDerived>& other) const {
return diagonal().cwiseProduct(other.diagonal()).asDiagonal();
}
using DiagonalInverseReturnType =
DiagonalWrapper<const CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const DiagonalVectorType>>;
/** \returns the inverse \c *this. Computed as the coefficient-wise inverse of the diagonal. */
EIGEN_DEVICE_FUNC inline const DiagonalInverseReturnType inverse() const {
return diagonal().cwiseInverse().asDiagonal();
}
using DiagonalScaleReturnType =
DiagonalWrapper<const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DiagonalVectorType, Scalar, product)>;
/** \returns the product of \c *this by the scalar \a scalar */
EIGEN_DEVICE_FUNC inline const DiagonalScaleReturnType operator*(const Scalar& scalar) const {
return (diagonal() * scalar).asDiagonal();
}
using ScaleDiagonalReturnType =
DiagonalWrapper<const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar, DiagonalVectorType, product)>;
/** \returns the product of a scalar and the diagonal matrix \a other */
EIGEN_DEVICE_FUNC friend inline const ScaleDiagonalReturnType operator*(const Scalar& scalar,
const DiagonalBase& other) {
return (scalar * other.diagonal()).asDiagonal();
}
template <typename OtherDerived>
using DiagonalSumReturnType = DiagonalWrapper<const EIGEN_CWISE_BINARY_RETURN_TYPE(
DiagonalVectorType, typename OtherDerived::DiagonalVectorType, sum)>;
/** \returns the sum of \c *this and the diagonal matrix \a other */
template <typename OtherDerived>
EIGEN_DEVICE_FUNC inline const DiagonalSumReturnType<OtherDerived> operator+(
const DiagonalBase<OtherDerived>& other) const {
return (diagonal() + other.diagonal()).asDiagonal();
}
template <typename OtherDerived>
using DiagonalDifferenceReturnType = DiagonalWrapper<const EIGEN_CWISE_BINARY_RETURN_TYPE(
DiagonalVectorType, typename OtherDerived::DiagonalVectorType, difference)>;
/** \returns the difference of \c *this and the diagonal matrix \a other */
template <typename OtherDerived>
EIGEN_DEVICE_FUNC inline const DiagonalDifferenceReturnType<OtherDerived> operator-(
const DiagonalBase<OtherDerived>& other) const {
return (diagonal() - other.diagonal()).asDiagonal();
}
};
/** \class DiagonalMatrix
* \ingroup Core_Module
*
* \brief Represents a diagonal matrix with its storage
*
* \tparam Scalar_ the type of coefficients
* \tparam SizeAtCompileTime the dimension of the matrix, or Dynamic
* \tparam MaxSizeAtCompileTime the dimension of the matrix, or Dynamic. This parameter is optional and defaults
* to SizeAtCompileTime. Most of the time, you do not need to specify it.
*
* \sa class DiagonalBase, class DiagonalWrapper
*/
namespace internal {
template <typename Scalar_, int SizeAtCompileTime, int MaxSizeAtCompileTime>
struct traits<DiagonalMatrix<Scalar_, SizeAtCompileTime, MaxSizeAtCompileTime>>
: traits<Matrix<Scalar_, SizeAtCompileTime, SizeAtCompileTime, 0, MaxSizeAtCompileTime, MaxSizeAtCompileTime>> {
typedef Matrix<Scalar_, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1> DiagonalVectorType;
typedef DiagonalShape StorageKind;
enum { Flags = LvalueBit | NoPreferredStorageOrderBit | NestByRefBit };
};
} // namespace internal
template <typename Scalar_, int SizeAtCompileTime, int MaxSizeAtCompileTime>
class DiagonalMatrix : public DiagonalBase<DiagonalMatrix<Scalar_, SizeAtCompileTime, MaxSizeAtCompileTime>> {
public:
#ifndef EIGEN_PARSED_BY_DOXYGEN
typedef typename internal::traits<DiagonalMatrix>::DiagonalVectorType DiagonalVectorType;
typedef const DiagonalMatrix& Nested;
typedef Scalar_ Scalar;
typedef typename internal::traits<DiagonalMatrix>::StorageKind StorageKind;
typedef typename internal::traits<DiagonalMatrix>::StorageIndex StorageIndex;
#endif
protected:
DiagonalVectorType m_diagonal;
public:
/** const version of diagonal(). */
EIGEN_DEVICE_FUNC inline const DiagonalVectorType& diagonal() const { return m_diagonal; }
/** \returns a reference to the stored vector of diagonal coefficients. */
EIGEN_DEVICE_FUNC inline DiagonalVectorType& diagonal() { return m_diagonal; }
/** Default constructor without initialization */
EIGEN_DEVICE_FUNC inline DiagonalMatrix() {}
/** Constructs a diagonal matrix with given dimension */
EIGEN_DEVICE_FUNC explicit inline DiagonalMatrix(Index dim) : m_diagonal(dim) {}
/** 2D constructor. */
EIGEN_DEVICE_FUNC inline DiagonalMatrix(const Scalar& x, const Scalar& y) : m_diagonal(x, y) {}
/** 3D constructor. */
EIGEN_DEVICE_FUNC inline DiagonalMatrix(const Scalar& x, const Scalar& y, const Scalar& z) : m_diagonal(x, y, z) {}
/** \brief Construct a diagonal matrix with fixed size from an arbitrary number of coefficients.
*
* \warning To construct a diagonal matrix of fixed size, the number of values passed to this
* constructor must match the fixed dimension of \c *this.
*
* \sa DiagonalMatrix(const Scalar&, const Scalar&)
* \sa DiagonalMatrix(const Scalar&, const Scalar&, const Scalar&)
*/
template <typename... ArgTypes>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DiagonalMatrix(const Scalar& a0, const Scalar& a1, const Scalar& a2,
const ArgTypes&... args)
: m_diagonal(a0, a1, a2, args...) {}
/** \brief Constructs a DiagonalMatrix and initializes it by elements given by an initializer list of initializer
* lists \cpp11
*/
EIGEN_DEVICE_FUNC explicit EIGEN_STRONG_INLINE DiagonalMatrix(
const std::initializer_list<std::initializer_list<Scalar>>& list)
: m_diagonal(list) {}
/** \brief Constructs a DiagonalMatrix from an r-value diagonal vector type */
EIGEN_DEVICE_FUNC explicit inline DiagonalMatrix(DiagonalVectorType&& diag) : m_diagonal(std::move(diag)) {}
/** Copy constructor. */
template <typename OtherDerived>
EIGEN_DEVICE_FUNC inline DiagonalMatrix(const DiagonalBase<OtherDerived>& other) : m_diagonal(other.diagonal()) {}
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** copy constructor. prevent a default copy constructor from hiding the other templated constructor */
inline DiagonalMatrix(const DiagonalMatrix& other) : m_diagonal(other.diagonal()) {}
#endif
/** generic constructor from expression of the diagonal coefficients */
template <typename OtherDerived>
EIGEN_DEVICE_FUNC explicit inline DiagonalMatrix(const MatrixBase<OtherDerived>& other) : m_diagonal(other) {}
/** Copy operator. */
template <typename OtherDerived>
EIGEN_DEVICE_FUNC DiagonalMatrix& operator=(const DiagonalBase<OtherDerived>& other) {
m_diagonal = other.diagonal();
return *this;
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** This is a special case of the templated operator=. Its purpose is to
* prevent a default operator= from hiding the templated operator=.
*/
EIGEN_DEVICE_FUNC DiagonalMatrix& operator=(const DiagonalMatrix& other) {
m_diagonal = other.diagonal();
return *this;
}
#endif
typedef DiagonalWrapper<const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, DiagonalVectorType>>
InitializeReturnType;
typedef DiagonalWrapper<const CwiseNullaryOp<internal::scalar_zero_op<Scalar>, DiagonalVectorType>>
ZeroInitializeReturnType;
/** Initializes a diagonal matrix of size SizeAtCompileTime with coefficients set to zero */
EIGEN_DEVICE_FUNC static const ZeroInitializeReturnType Zero() { return DiagonalVectorType::Zero().asDiagonal(); }
/** Initializes a diagonal matrix of size dim with coefficients set to zero */
EIGEN_DEVICE_FUNC static const ZeroInitializeReturnType Zero(Index size) {
return DiagonalVectorType::Zero(size).asDiagonal();
}
/** Initializes a identity matrix of size SizeAtCompileTime */
EIGEN_DEVICE_FUNC static const InitializeReturnType Identity() { return DiagonalVectorType::Ones().asDiagonal(); }
/** Initializes a identity matrix of size dim */
EIGEN_DEVICE_FUNC static const InitializeReturnType Identity(Index size) {
return DiagonalVectorType::Ones(size).asDiagonal();
}
/** Resizes to given size. */
EIGEN_DEVICE_FUNC inline void resize(Index size) { m_diagonal.resize(size); }
/** Sets all coefficients to zero. */
EIGEN_DEVICE_FUNC inline void setZero() { m_diagonal.setZero(); }
/** Resizes and sets all coefficients to zero. */
EIGEN_DEVICE_FUNC inline void setZero(Index size) { m_diagonal.setZero(size); }
/** Sets this matrix to be the identity matrix of the current size. */
EIGEN_DEVICE_FUNC inline void setIdentity() { m_diagonal.setOnes(); }
/** Sets this matrix to be the identity matrix of the given size. */
EIGEN_DEVICE_FUNC inline void setIdentity(Index size) { m_diagonal.setOnes(size); }
};
/** \class DiagonalWrapper
* \ingroup Core_Module
*
* \brief Expression of a diagonal matrix
*
* \tparam DiagonalVectorType_ the type of the vector of diagonal coefficients
*
* This class is an expression of a diagonal matrix, but not storing its own vector of diagonal coefficients,
* instead wrapping an existing vector expression. It is the return type of MatrixBase::asDiagonal()
* and most of the time this is the only way that it is used.
*
* \sa class DiagonalMatrix, class DiagonalBase, MatrixBase::asDiagonal()
*/
namespace internal {
template <typename DiagonalVectorType_>
struct traits<DiagonalWrapper<DiagonalVectorType_>> {
typedef DiagonalVectorType_ DiagonalVectorType;
typedef typename DiagonalVectorType::Scalar Scalar;
typedef typename DiagonalVectorType::StorageIndex StorageIndex;
typedef DiagonalShape StorageKind;
typedef typename traits<DiagonalVectorType>::XprKind XprKind;
enum {
RowsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
ColsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
MaxRowsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
MaxColsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
Flags = (traits<DiagonalVectorType>::Flags & LvalueBit) | NoPreferredStorageOrderBit
};
};
} // namespace internal
template <typename DiagonalVectorType_>
class DiagonalWrapper : public DiagonalBase<DiagonalWrapper<DiagonalVectorType_>>, internal::no_assignment_operator {
public:
#ifndef EIGEN_PARSED_BY_DOXYGEN
typedef DiagonalVectorType_ DiagonalVectorType;
typedef DiagonalWrapper Nested;
#endif
/** Constructor from expression of diagonal coefficients to wrap. */
EIGEN_DEVICE_FUNC explicit inline DiagonalWrapper(DiagonalVectorType& a_diagonal) : m_diagonal(a_diagonal) {}
/** \returns a const reference to the wrapped expression of diagonal coefficients. */
EIGEN_DEVICE_FUNC const DiagonalVectorType& diagonal() const { return m_diagonal; }
protected:
typename DiagonalVectorType::Nested m_diagonal;
};
/** \returns a pseudo-expression of a diagonal matrix with *this as vector of diagonal coefficients
*
* \only_for_vectors
*
* Example: \include MatrixBase_asDiagonal.cpp
* Output: \verbinclude MatrixBase_asDiagonal.out
*
* \sa class DiagonalWrapper, class DiagonalMatrix, diagonal(), isDiagonal()
**/
template <typename Derived>
EIGEN_DEVICE_FUNC inline const DiagonalWrapper<const Derived> MatrixBase<Derived>::asDiagonal() const {
return DiagonalWrapper<const Derived>(derived());
}
/** \returns true if *this is approximately equal to a diagonal matrix,
* within the precision given by \a prec.
*
* Example: \include MatrixBase_isDiagonal.cpp
* Output: \verbinclude MatrixBase_isDiagonal.out
*
* \sa asDiagonal()
*/
template <typename Derived>
bool MatrixBase<Derived>::isDiagonal(const RealScalar& prec) const {
if (cols() != rows()) return false;
RealScalar maxAbsOnDiagonal = static_cast<RealScalar>(-1);
for (Index j = 0; j < cols(); ++j) {
RealScalar absOnDiagonal = numext::abs(coeff(j, j));
if (absOnDiagonal > maxAbsOnDiagonal) maxAbsOnDiagonal = absOnDiagonal;
}
for (Index j = 0; j < cols(); ++j)
for (Index i = 0; i < j; ++i) {
if (!internal::isMuchSmallerThan(coeff(i, j), maxAbsOnDiagonal, prec)) return false;
if (!internal::isMuchSmallerThan(coeff(j, i), maxAbsOnDiagonal, prec)) return false;
}
return true;
}
namespace internal {
template <>
struct storage_kind_to_shape<DiagonalShape> {
typedef DiagonalShape Shape;
};
struct Diagonal2Dense {};
template <>
struct AssignmentKind<DenseShape, DiagonalShape> {
typedef Diagonal2Dense Kind;
};
// Diagonal matrix to Dense assignment
template <typename DstXprType, typename SrcXprType, typename Functor>
struct Assignment<DstXprType, SrcXprType, Functor, Diagonal2Dense> {
static EIGEN_DEVICE_FUNC void run(
DstXprType& dst, const SrcXprType& src,
const internal::assign_op<typename DstXprType::Scalar, typename SrcXprType::Scalar>& /*func*/) {
Index dstRows = src.rows();
Index dstCols = src.cols();
if ((dst.rows() != dstRows) || (dst.cols() != dstCols)) dst.resize(dstRows, dstCols);
dst.setZero();
dst.diagonal() = src.diagonal();
}
static EIGEN_DEVICE_FUNC void run(
DstXprType& dst, const SrcXprType& src,
const internal::add_assign_op<typename DstXprType::Scalar, typename SrcXprType::Scalar>& /*func*/) {
dst.diagonal() += src.diagonal();
}
static EIGEN_DEVICE_FUNC void run(
DstXprType& dst, const SrcXprType& src,
const internal::sub_assign_op<typename DstXprType::Scalar, typename SrcXprType::Scalar>& /*func*/) {
dst.diagonal() -= src.diagonal();
}
};
} // namespace internal
} // end namespace Eigen
#endif // EIGEN_DIAGONALMATRIX_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_DIAGONALPRODUCT_H
#define EIGEN_DIAGONALPRODUCT_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
/** \returns the diagonal matrix product of \c *this by the diagonal matrix \a diagonal.
*/
template <typename Derived>
template <typename DiagonalDerived>
EIGEN_DEVICE_FUNC inline const Product<Derived, DiagonalDerived, LazyProduct> MatrixBase<Derived>::operator*(
const DiagonalBase<DiagonalDerived> &a_diagonal) const {
return Product<Derived, DiagonalDerived, LazyProduct>(derived(), a_diagonal.derived());
}
} // end namespace Eigen
#endif // EIGEN_DIAGONALPRODUCT_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2008, 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_DOT_H
#define EIGEN_DOT_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
template <typename Derived, typename Scalar = typename traits<Derived>::Scalar>
struct squared_norm_impl {
using Real = typename NumTraits<Scalar>::Real;
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Real run(const Derived& a) {
Scalar result = a.unaryExpr(squared_norm_functor<Scalar>()).sum();
return numext::real(result) + numext::imag(result);
}
};
template <typename Derived>
struct squared_norm_impl<Derived, bool> {
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool run(const Derived& a) { return a.any(); }
};
} // end namespace internal
/** \fn MatrixBase::dot
* \returns the dot product of *this with other.
*
* \only_for_vectors
*
* \note If the scalar type is complex numbers, then this function returns the hermitian
* (sesquilinear) dot product, conjugate-linear in the first variable and linear in the
* second variable.
*
* \sa squaredNorm(), norm()
*/
template <typename Derived>
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,
typename internal::traits<OtherDerived>::Scalar>::ReturnType
MatrixBase<Derived>::dot(const MatrixBase<OtherDerived>& other) const {
return internal::dot_impl<Derived, OtherDerived>::run(derived(), other.derived());
}
//---------- implementation of L2 norm and related functions ----------
/** \returns, for vectors, the squared \em l2 norm of \c *this, and for matrices the squared Frobenius norm.
* In both cases, it consists in the sum of the square of all the matrix entries.
* For vectors, this is also equals to the dot product of \c *this with itself.
*
* \sa dot(), norm(), lpNorm()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
MatrixBase<Derived>::squaredNorm() const {
return internal::squared_norm_impl<Derived>::run(derived());
}
/** \returns, for vectors, the \em l2 norm of \c *this, and for matrices the Frobenius norm.
* In both cases, it consists in the square root of the sum of the square of all the matrix entries.
* For vectors, this is also equals to the square root of the dot product of \c *this with itself.
*
* \sa lpNorm(), dot(), squaredNorm()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
MatrixBase<Derived>::norm() const {
return numext::sqrt(squaredNorm());
}
/** \returns an expression of the quotient of \c *this by its own norm.
*
* \warning If the input vector is too small (i.e., this->norm()==0),
* then this function returns a copy of the input.
*
* \only_for_vectors
*
* \sa norm(), normalize()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::PlainObject MatrixBase<Derived>::normalized()
const {
typedef typename internal::nested_eval<Derived, 2>::type Nested_;
Nested_ n(derived());
RealScalar z = n.squaredNorm();
// NOTE: after extensive benchmarking, this conditional does not impact performance, at least on recent x86 CPU
if (z > RealScalar(0))
return n / numext::sqrt(z);
else
return n;
}
/** Normalizes the vector, i.e. divides it by its own norm.
*
* \only_for_vectors
*
* \warning If the input vector is too small (i.e., this->norm()==0), then \c *this is left unchanged.
*
* \sa norm(), normalized()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void MatrixBase<Derived>::normalize() {
RealScalar z = squaredNorm();
// NOTE: after extensive benchmarking, this conditional does not impact performance, at least on recent x86 CPU
if (z > RealScalar(0)) derived() /= numext::sqrt(z);
}
/** \returns an expression of the quotient of \c *this by its own norm while avoiding underflow and overflow.
*
* \only_for_vectors
*
* This method is analogue to the normalized() method, but it reduces the risk of
* underflow and overflow when computing the norm.
*
* \warning If the input vector is too small (i.e., this->norm()==0),
* then this function returns a copy of the input.
*
* \sa stableNorm(), stableNormalize(), normalized()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::PlainObject
MatrixBase<Derived>::stableNormalized() const {
typedef typename internal::nested_eval<Derived, 3>::type Nested_;
Nested_ n(derived());
RealScalar w = n.cwiseAbs().maxCoeff();
RealScalar z = (n / w).squaredNorm();
if (z > RealScalar(0))
return n / (numext::sqrt(z) * w);
else
return n;
}
/** Normalizes the vector while avoid underflow and overflow
*
* \only_for_vectors
*
* This method is analogue to the normalize() method, but it reduces the risk of
* underflow and overflow when computing the norm.
*
* \warning If the input vector is too small (i.e., this->norm()==0), then \c *this is left unchanged.
*
* \sa stableNorm(), stableNormalized(), normalize()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void MatrixBase<Derived>::stableNormalize() {
RealScalar w = cwiseAbs().maxCoeff();
RealScalar z = (derived() / w).squaredNorm();
if (z > RealScalar(0)) derived() /= numext::sqrt(z) * w;
}
//---------- implementation of other norms ----------
namespace internal {
template <typename Derived, int p>
struct lpNorm_selector {
typedef typename NumTraits<typename traits<Derived>::Scalar>::Real RealScalar;
EIGEN_DEVICE_FUNC static inline RealScalar run(const MatrixBase<Derived>& m) {
EIGEN_USING_STD(pow)
return pow(m.cwiseAbs().array().pow(p).sum(), RealScalar(1) / p);
}
};
template <typename Derived>
struct lpNorm_selector<Derived, 1> {
EIGEN_DEVICE_FUNC static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(
const MatrixBase<Derived>& m) {
return m.cwiseAbs().sum();
}
};
template <typename Derived>
struct lpNorm_selector<Derived, 2> {
EIGEN_DEVICE_FUNC static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(
const MatrixBase<Derived>& m) {
return m.norm();
}
};
template <typename Derived>
struct lpNorm_selector<Derived, Infinity> {
typedef typename NumTraits<typename traits<Derived>::Scalar>::Real RealScalar;
EIGEN_DEVICE_FUNC static inline RealScalar run(const MatrixBase<Derived>& m) {
if (Derived::SizeAtCompileTime == 0 || (Derived::SizeAtCompileTime == Dynamic && m.size() == 0))
return RealScalar(0);
return m.cwiseAbs().maxCoeff();
}
};
} // end namespace internal
/** \returns the \b coefficient-wise \f$ \ell^p \f$ norm of \c *this, that is, returns the p-th root of the sum of the
* p-th powers of the absolute values of the coefficients of \c *this. If \a p is the special value \a Eigen::Infinity,
* this function returns the \f$ \ell^\infty \f$ norm, that is the maximum of the absolute values of the coefficients of
* \c *this.
*
* In all cases, if \c *this is empty, then the value 0 is returned.
*
* \note For matrices, this function does not compute the <a
* href="https://en.wikipedia.org/wiki/Operator_norm">operator-norm</a>. That is, if \c *this is a matrix, then its
* coefficients are interpreted as a 1D vector. Nonetheless, you can easily compute the 1-norm and \f$\infty\f$-norm
* matrix operator norms using \link TutorialReductionsVisitorsBroadcastingReductionsNorm partial reductions \endlink.
*
* \sa norm()
*/
template <typename Derived>
template <int p>
#ifndef EIGEN_PARSED_BY_DOXYGEN
EIGEN_DEVICE_FUNC inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
#else
EIGEN_DEVICE_FUNC MatrixBase<Derived>::RealScalar
#endif
MatrixBase<Derived>::lpNorm() const {
return internal::lpNorm_selector<Derived, p>::run(*this);
}
//---------- implementation of isOrthogonal / isUnitary ----------
/** \returns true if *this is approximately orthogonal to \a other,
* within the precision given by \a prec.
*
* Example: \include MatrixBase_isOrthogonal.cpp
* Output: \verbinclude MatrixBase_isOrthogonal.out
*/
template <typename Derived>
template <typename OtherDerived>
bool MatrixBase<Derived>::isOrthogonal(const MatrixBase<OtherDerived>& other, const RealScalar& prec) const {
typename internal::nested_eval<Derived, 2>::type nested(derived());
typename internal::nested_eval<OtherDerived, 2>::type otherNested(other.derived());
return numext::abs2(nested.dot(otherNested)) <= prec * prec * nested.squaredNorm() * otherNested.squaredNorm();
}
/** \returns true if *this is approximately an unitary matrix,
* within the precision given by \a prec. In the case where the \a Scalar
* type is real numbers, a unitary matrix is an orthogonal matrix, whence the name.
*
* \note This can be used to check whether a family of vectors forms an orthonormal basis.
* Indeed, \c m.isUnitary() returns true if and only if the columns (equivalently, the rows) of m form an
* orthonormal basis.
*
* Example: \include MatrixBase_isUnitary.cpp
* Output: \verbinclude MatrixBase_isUnitary.out
*/
template <typename Derived>
bool MatrixBase<Derived>::isUnitary(const RealScalar& prec) const {
typename internal::nested_eval<Derived, 1>::type self(derived());
for (Index i = 0; i < cols(); ++i) {
if (!internal::isApprox(self.col(i).squaredNorm(), static_cast<RealScalar>(1), prec)) return false;
for (Index j = 0; j < i; ++j)
if (!internal::isMuchSmallerThan(self.col(i).dot(self.col(j)), static_cast<Scalar>(1), prec)) return false;
}
return true;
}
} // end namespace Eigen
#endif // EIGEN_DOT_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_EIGENBASE_H
#define EIGEN_EIGENBASE_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
/** \class EigenBase
* \ingroup Core_Module
*
* Common base class for all classes T such that MatrixBase has an operator=(T) and a constructor MatrixBase(T).
*
* In other words, an EigenBase object is an object that can be copied into a MatrixBase.
*
* Besides MatrixBase-derived classes, this also includes special matrix classes such as diagonal matrices, etc.
*
* Notice that this class is trivial, it is only used to disambiguate overloaded functions.
*
* \sa \blank \ref TopicClassHierarchy
*/
template <typename Derived>
struct EigenBase {
// typedef typename internal::plain_matrix_type<Derived>::type PlainObject;
/** \brief The interface type of indices
* \details To change this, \c \#define the preprocessor symbol \c EIGEN_DEFAULT_DENSE_INDEX_TYPE.
* \sa StorageIndex, \ref TopicPreprocessorDirectives.
* DEPRECATED: Since Eigen 3.3, its usage is deprecated. Use Eigen::Index instead.
* Deprecation is not marked with a doxygen comment because there are too many existing usages to add the deprecation
* attribute.
*/
typedef Eigen::Index Index;
// FIXME is it needed?
typedef typename internal::traits<Derived>::StorageKind StorageKind;
/** \returns a reference to the derived object */
EIGEN_DEVICE_FUNC constexpr Derived& derived() { return *static_cast<Derived*>(this); }
/** \returns a const reference to the derived object */
EIGEN_DEVICE_FUNC constexpr const Derived& derived() const { return *static_cast<const Derived*>(this); }
EIGEN_DEVICE_FUNC inline constexpr Derived& const_cast_derived() const {
return *static_cast<Derived*>(const_cast<EigenBase*>(this));
}
EIGEN_DEVICE_FUNC inline const Derived& const_derived() const { return *static_cast<const Derived*>(this); }
/** \returns the number of rows. \sa cols(), RowsAtCompileTime */
EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return derived().rows(); }
/** \returns the number of columns. \sa rows(), ColsAtCompileTime*/
EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return derived().cols(); }
/** \returns the number of coefficients, which is rows()*cols().
* \sa rows(), cols(), SizeAtCompileTime. */
EIGEN_DEVICE_FUNC constexpr Index size() const noexcept { return rows() * cols(); }
/** \internal Don't use it, but do the equivalent: \code dst = *this; \endcode */
template <typename Dest>
EIGEN_DEVICE_FUNC inline void evalTo(Dest& dst) const {
derived().evalTo(dst);
}
/** \internal Don't use it, but do the equivalent: \code dst += *this; \endcode */
template <typename Dest>
EIGEN_DEVICE_FUNC inline void addTo(Dest& dst) const {
// This is the default implementation,
// derived class can reimplement it in a more optimized way.
typename Dest::PlainObject res(rows(), cols());
evalTo(res);
dst += res;
}
/** \internal Don't use it, but do the equivalent: \code dst -= *this; \endcode */
template <typename Dest>
EIGEN_DEVICE_FUNC inline void subTo(Dest& dst) const {
// This is the default implementation,
// derived class can reimplement it in a more optimized way.
typename Dest::PlainObject res(rows(), cols());
evalTo(res);
dst -= res;
}
/** \internal Don't use it, but do the equivalent: \code dst.applyOnTheRight(*this); \endcode */
template <typename Dest>
EIGEN_DEVICE_FUNC inline void applyThisOnTheRight(Dest& dst) const {
// This is the default implementation,
// derived class can reimplement it in a more optimized way.
dst = dst * this->derived();
}
/** \internal Don't use it, but do the equivalent: \code dst.applyOnTheLeft(*this); \endcode */
template <typename Dest>
EIGEN_DEVICE_FUNC inline void applyThisOnTheLeft(Dest& dst) const {
// This is the default implementation,
// derived class can reimplement it in a more optimized way.
dst = this->derived() * dst;
}
template <typename Device>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DeviceWrapper<Derived, Device> device(Device& device);
template <typename Device>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DeviceWrapper<const Derived, Device> device(Device& device) const;
};
/***************************************************************************
* Implementation of matrix base methods
***************************************************************************/
/** \brief Copies the generic expression \a other into *this.
*
* \details The expression must provide a (templated) evalTo(Derived& dst) const
* function which does the actual job. In practice, this allows any user to write
* its own special matrix without having to modify MatrixBase
*
* \returns a reference to *this.
*/
template <typename Derived>
template <typename OtherDerived>
EIGEN_DEVICE_FUNC Derived& DenseBase<Derived>::operator=(const EigenBase<OtherDerived>& other) {
call_assignment(derived(), other.derived());
return derived();
}
template <typename Derived>
template <typename OtherDerived>
EIGEN_DEVICE_FUNC Derived& DenseBase<Derived>::operator+=(const EigenBase<OtherDerived>& other) {
call_assignment(derived(), other.derived(), internal::add_assign_op<Scalar, typename OtherDerived::Scalar>());
return derived();
}
template <typename Derived>
template <typename OtherDerived>
EIGEN_DEVICE_FUNC Derived& DenseBase<Derived>::operator-=(const EigenBase<OtherDerived>& other) {
call_assignment(derived(), other.derived(), internal::sub_assign_op<Scalar, typename OtherDerived::Scalar>());
return derived();
}
} // end namespace Eigen
#endif // EIGEN_EIGENBASE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2024 Charles Schlosser <cs.schlosser@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_FILL_H
#define EIGEN_FILL_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
template <typename Xpr>
struct eigen_fill_helper : std::false_type {};
template <typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
struct eigen_fill_helper<Matrix<Scalar, Rows, Cols, Options, MaxRows, MaxCols>> : std::true_type {};
template <typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
struct eigen_fill_helper<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols>> : std::true_type {};
template <typename Xpr, int BlockRows, int BlockCols>
struct eigen_fill_helper<Block<Xpr, BlockRows, BlockCols, /*InnerPanel*/ true>> : eigen_fill_helper<Xpr> {};
template <typename Xpr, int BlockRows, int BlockCols>
struct eigen_fill_helper<Block<Xpr, BlockRows, BlockCols, /*InnerPanel*/ false>>
: std::integral_constant<bool, eigen_fill_helper<Xpr>::value &&
(Xpr::IsRowMajor ? (BlockRows == 1) : (BlockCols == 1))> {};
template <typename Xpr, int Options>
struct eigen_fill_helper<Map<Xpr, Options, Stride<0, 0>>> : eigen_fill_helper<Xpr> {};
template <typename Xpr, int Options, int OuterStride_>
struct eigen_fill_helper<Map<Xpr, Options, Stride<OuterStride_, 0>>>
: std::integral_constant<bool, eigen_fill_helper<Xpr>::value &&
enum_eq_not_dynamic(OuterStride_, Xpr::InnerSizeAtCompileTime)> {};
template <typename Xpr, int Options, int OuterStride_>
struct eigen_fill_helper<Map<Xpr, Options, Stride<OuterStride_, 1>>>
: eigen_fill_helper<Map<Xpr, Options, Stride<OuterStride_, 0>>> {};
template <typename Xpr, int Options, int InnerStride_>
struct eigen_fill_helper<Map<Xpr, Options, InnerStride<InnerStride_>>>
: eigen_fill_helper<Map<Xpr, Options, Stride<0, InnerStride_>>> {};
template <typename Xpr, int Options, int OuterStride_>
struct eigen_fill_helper<Map<Xpr, Options, OuterStride<OuterStride_>>>
: eigen_fill_helper<Map<Xpr, Options, Stride<OuterStride_, 0>>> {};
template <typename Xpr>
struct eigen_fill_impl<Xpr, /*use_fill*/ false> {
using Scalar = typename Xpr::Scalar;
using Func = scalar_constant_op<Scalar>;
using PlainObject = typename Xpr::PlainObject;
using Constant = typename PlainObject::ConstantReturnType;
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void run(Xpr& dst, const Scalar& val) {
const Constant src(dst.rows(), dst.cols(), val);
run(dst, src);
}
template <typename SrcXpr>
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void run(Xpr& dst, const SrcXpr& src) {
call_dense_assignment_loop(dst, src, assign_op<Scalar, Scalar>());
}
};
#if EIGEN_COMP_MSVC || defined(EIGEN_GPU_COMPILE_PHASE)
template <typename Xpr>
struct eigen_fill_impl<Xpr, /*use_fill*/ true> : eigen_fill_impl<Xpr, /*use_fill*/ false> {};
#else
template <typename Xpr>
struct eigen_fill_impl<Xpr, /*use_fill*/ true> {
using Scalar = typename Xpr::Scalar;
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Xpr& dst, const Scalar& val) {
const Scalar val_copy = val;
using std::fill_n;
fill_n(dst.data(), dst.size(), val_copy);
}
template <typename SrcXpr>
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Xpr& dst, const SrcXpr& src) {
resize_if_allowed(dst, src, assign_op<Scalar, Scalar>());
const Scalar& val = src.functor()();
run(dst, val);
}
};
#endif
template <typename Xpr>
struct eigen_memset_helper {
static constexpr bool value =
std::is_trivially_copyable<typename Xpr::Scalar>::value && eigen_fill_helper<Xpr>::value;
};
template <typename Xpr>
struct eigen_zero_impl<Xpr, /*use_memset*/ false> {
using Scalar = typename Xpr::Scalar;
using PlainObject = typename Xpr::PlainObject;
using Zero = typename PlainObject::ZeroReturnType;
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void run(Xpr& dst) {
const Zero src(dst.rows(), dst.cols());
run(dst, src);
}
template <typename SrcXpr>
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void run(Xpr& dst, const SrcXpr& src) {
call_dense_assignment_loop(dst, src, assign_op<Scalar, Scalar>());
}
};
template <typename Xpr>
struct eigen_zero_impl<Xpr, /*use_memset*/ true> {
using Scalar = typename Xpr::Scalar;
static constexpr size_t max_bytes = (std::numeric_limits<std::ptrdiff_t>::max)();
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Xpr& dst) {
const size_t num_bytes = dst.size() * sizeof(Scalar);
if (num_bytes == 0) return;
void* dst_ptr = static_cast<void*>(dst.data());
#ifndef EIGEN_NO_DEBUG
if (num_bytes > max_bytes) throw_std_bad_alloc();
eigen_assert((dst_ptr != nullptr) && "null pointer dereference error!");
#endif
EIGEN_USING_STD(memset);
memset(dst_ptr, 0, num_bytes);
}
template <typename SrcXpr>
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Xpr& dst, const SrcXpr& src) {
resize_if_allowed(dst, src, assign_op<Scalar, Scalar>());
run(dst);
}
};
} // namespace internal
} // namespace Eigen
#endif // EIGEN_FILL_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2025 Charlie Schlosser <cs.schlosser@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_FIND_COEFF_H
#define EIGEN_FIND_COEFF_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
template <typename Scalar, int NaNPropagation, bool IsInteger = NumTraits<Scalar>::IsInteger>
struct max_coeff_functor {
EIGEN_DEVICE_FUNC inline bool compareCoeff(const Scalar& incumbent, const Scalar& candidate) const {
return candidate > incumbent;
}
template <typename Packet>
EIGEN_DEVICE_FUNC inline Packet comparePacket(const Packet& incumbent, const Packet& candidate) const {
return pcmp_lt(incumbent, candidate);
}
template <typename Packet>
EIGEN_DEVICE_FUNC inline Scalar predux(const Packet& a) const {
return predux_max(a);
}
};
template <typename Scalar>
struct max_coeff_functor<Scalar, PropagateNaN, false> {
EIGEN_DEVICE_FUNC inline Scalar compareCoeff(const Scalar& incumbent, const Scalar& candidate) {
return (candidate > incumbent) || ((candidate != candidate) && (incumbent == incumbent));
}
template <typename Packet>
EIGEN_DEVICE_FUNC inline Packet comparePacket(const Packet& incumbent, const Packet& candidate) {
return pandnot(pcmp_lt_or_nan(incumbent, candidate), pisnan(incumbent));
}
template <typename Packet>
EIGEN_DEVICE_FUNC inline Scalar predux(const Packet& a) const {
return predux_max<PropagateNaN>(a);
}
};
template <typename Scalar>
struct max_coeff_functor<Scalar, PropagateNumbers, false> {
EIGEN_DEVICE_FUNC inline bool compareCoeff(const Scalar& incumbent, const Scalar& candidate) const {
return (candidate > incumbent) || ((candidate == candidate) && (incumbent != incumbent));
}
template <typename Packet>
EIGEN_DEVICE_FUNC inline Packet comparePacket(const Packet& incumbent, const Packet& candidate) const {
return pandnot(pcmp_lt_or_nan(incumbent, candidate), pisnan(candidate));
}
template <typename Packet>
EIGEN_DEVICE_FUNC inline Scalar predux(const Packet& a) const {
return predux_max<PropagateNumbers>(a);
}
};
template <typename Scalar, int NaNPropagation, bool IsInteger = NumTraits<Scalar>::IsInteger>
struct min_coeff_functor {
EIGEN_DEVICE_FUNC inline bool compareCoeff(const Scalar& incumbent, const Scalar& candidate) const {
return candidate < incumbent;
}
template <typename Packet>
EIGEN_DEVICE_FUNC inline Packet comparePacket(const Packet& incumbent, const Packet& candidate) const {
return pcmp_lt(candidate, incumbent);
}
template <typename Packet>
EIGEN_DEVICE_FUNC inline Scalar predux(const Packet& a) const {
return predux_min(a);
}
};
template <typename Scalar>
struct min_coeff_functor<Scalar, PropagateNaN, false> {
EIGEN_DEVICE_FUNC inline Scalar compareCoeff(const Scalar& incumbent, const Scalar& candidate) {
return (candidate < incumbent) || ((candidate != candidate) && (incumbent == incumbent));
}
template <typename Packet>
EIGEN_DEVICE_FUNC inline Packet comparePacket(const Packet& incumbent, const Packet& candidate) {
return pandnot(pcmp_lt_or_nan(candidate, incumbent), pisnan(incumbent));
}
template <typename Packet>
EIGEN_DEVICE_FUNC inline Scalar predux(const Packet& a) const {
return predux_min<PropagateNaN>(a);
}
};
template <typename Scalar>
struct min_coeff_functor<Scalar, PropagateNumbers, false> {
EIGEN_DEVICE_FUNC inline bool compareCoeff(const Scalar& incumbent, const Scalar& candidate) const {
return (candidate < incumbent) || ((candidate == candidate) && (incumbent != incumbent));
}
template <typename Packet>
EIGEN_DEVICE_FUNC inline Packet comparePacket(const Packet& incumbent, const Packet& candidate) const {
return pandnot(pcmp_lt_or_nan(candidate, incumbent), pisnan(candidate));
}
template <typename Packet>
EIGEN_DEVICE_FUNC inline Scalar predux(const Packet& a) const {
return predux_min<PropagateNumbers>(a);
}
};
template <typename Scalar>
struct min_max_traits {
static constexpr bool PacketAccess = packet_traits<Scalar>::Vectorizable;
};
template <typename Scalar, int NaNPropagation>
struct functor_traits<max_coeff_functor<Scalar, NaNPropagation>> : min_max_traits<Scalar> {};
template <typename Scalar, int NaNPropagation>
struct functor_traits<min_coeff_functor<Scalar, NaNPropagation>> : min_max_traits<Scalar> {};
template <typename Evaluator, typename Func, bool Linear, bool Vectorize>
struct find_coeff_loop;
template <typename Evaluator, typename Func>
struct find_coeff_loop<Evaluator, Func, /*Linear*/ false, /*Vectorize*/ false> {
using Scalar = typename Evaluator::Scalar;
static EIGEN_DEVICE_FUNC inline void run(const Evaluator& eval, Func& func, Scalar& res, Index& outer, Index& inner) {
Index outerSize = eval.outerSize();
Index innerSize = eval.innerSize();
/* initialization performed in calling function */
/* result = eval.coeff(0, 0); */
/* outer = 0; */
/* inner = 0; */
for (Index j = 0; j < outerSize; j++) {
for (Index i = 0; i < innerSize; i++) {
Scalar xprCoeff = eval.coeffByOuterInner(j, i);
bool newRes = func.compareCoeff(res, xprCoeff);
if (newRes) {
outer = j;
inner = i;
res = xprCoeff;
}
}
}
}
};
template <typename Evaluator, typename Func>
struct find_coeff_loop<Evaluator, Func, /*Linear*/ true, /*Vectorize*/ false> {
using Scalar = typename Evaluator::Scalar;
static EIGEN_DEVICE_FUNC inline void run(const Evaluator& eval, Func& func, Scalar& res, Index& index) {
Index size = eval.size();
/* initialization performed in calling function */
/* result = eval.coeff(0); */
/* index = 0; */
for (Index k = 0; k < size; k++) {
Scalar xprCoeff = eval.coeff(k);
bool newRes = func.compareCoeff(res, xprCoeff);
if (newRes) {
index = k;
res = xprCoeff;
}
}
}
};
template <typename Evaluator, typename Func>
struct find_coeff_loop<Evaluator, Func, /*Linear*/ false, /*Vectorize*/ true> {
using ScalarImpl = find_coeff_loop<Evaluator, Func, false, false>;
using Scalar = typename Evaluator::Scalar;
using Packet = typename Evaluator::Packet;
static constexpr int PacketSize = unpacket_traits<Packet>::size;
static EIGEN_DEVICE_FUNC inline void run(const Evaluator& eval, Func& func, Scalar& result, Index& outer,
Index& inner) {
Index outerSize = eval.outerSize();
Index innerSize = eval.innerSize();
Index packetEnd = numext::round_down(innerSize, PacketSize);
/* initialization performed in calling function */
/* result = eval.coeff(0, 0); */
/* outer = 0; */
/* inner = 0; */
bool checkPacket = false;
for (Index j = 0; j < outerSize; j++) {
Packet resultPacket = pset1<Packet>(result);
for (Index i = 0; i < packetEnd; i += PacketSize) {
Packet xprPacket = eval.template packetByOuterInner<Unaligned, Packet>(j, i);
if (predux_any(func.comparePacket(resultPacket, xprPacket))) {
outer = j;
inner = i;
result = func.predux(xprPacket);
resultPacket = pset1<Packet>(result);
checkPacket = true;
}
}
for (Index i = packetEnd; i < innerSize; i++) {
Scalar xprCoeff = eval.coeffByOuterInner(j, i);
if (func.compareCoeff(result, xprCoeff)) {
outer = j;
inner = i;
result = xprCoeff;
checkPacket = false;
}
}
}
if (checkPacket) {
result = eval.coeffByOuterInner(outer, inner);
Index i_end = inner + PacketSize;
for (Index i = inner; i < i_end; i++) {
Scalar xprCoeff = eval.coeffByOuterInner(outer, i);
if (func.compareCoeff(result, xprCoeff)) {
inner = i;
result = xprCoeff;
}
}
}
}
};
template <typename Evaluator, typename Func>
struct find_coeff_loop<Evaluator, Func, /*Linear*/ true, /*Vectorize*/ true> {
using ScalarImpl = find_coeff_loop<Evaluator, Func, true, false>;
using Scalar = typename Evaluator::Scalar;
using Packet = typename Evaluator::Packet;
static constexpr int PacketSize = unpacket_traits<Packet>::size;
static constexpr int Alignment = Evaluator::Alignment;
static EIGEN_DEVICE_FUNC inline void run(const Evaluator& eval, Func& func, Scalar& result, Index& index) {
Index size = eval.size();
Index packetEnd = numext::round_down(size, PacketSize);
/* initialization performed in calling function */
/* result = eval.coeff(0); */
/* index = 0; */
Packet resultPacket = pset1<Packet>(result);
bool checkPacket = false;
for (Index k = 0; k < packetEnd; k += PacketSize) {
Packet xprPacket = eval.template packet<Alignment, Packet>(k);
if (predux_any(func.comparePacket(resultPacket, xprPacket))) {
index = k;
result = func.predux(xprPacket);
resultPacket = pset1<Packet>(result);
checkPacket = true;
}
}
for (Index k = packetEnd; k < size; k++) {
Scalar xprCoeff = eval.coeff(k);
if (func.compareCoeff(result, xprCoeff)) {
index = k;
result = xprCoeff;
checkPacket = false;
}
}
if (checkPacket) {
result = eval.coeff(index);
Index k_end = index + PacketSize;
for (Index k = index; k < k_end; k++) {
Scalar xprCoeff = eval.coeff(k);
if (func.compareCoeff(result, xprCoeff)) {
index = k;
result = xprCoeff;
}
}
}
}
};
template <typename Derived>
struct find_coeff_evaluator : public evaluator<Derived> {
using Base = evaluator<Derived>;
using Scalar = typename Derived::Scalar;
using Packet = typename packet_traits<Scalar>::type;
static constexpr int Flags = Base::Flags;
static constexpr bool IsRowMajor = bool(Flags & RowMajorBit);
EIGEN_DEVICE_FUNC inline find_coeff_evaluator(const Derived& xpr) : Base(xpr), m_xpr(xpr) {}
EIGEN_DEVICE_FUNC inline Scalar coeffByOuterInner(Index outer, Index inner) const {
Index row = IsRowMajor ? outer : inner;
Index col = IsRowMajor ? inner : outer;
return Base::coeff(row, col);
}
template <int LoadMode, typename PacketType>
EIGEN_DEVICE_FUNC inline PacketType packetByOuterInner(Index outer, Index inner) const {
Index row = IsRowMajor ? outer : inner;
Index col = IsRowMajor ? inner : outer;
return Base::template packet<LoadMode, PacketType>(row, col);
}
EIGEN_DEVICE_FUNC inline Index innerSize() const { return m_xpr.innerSize(); }
EIGEN_DEVICE_FUNC inline Index outerSize() const { return m_xpr.outerSize(); }
EIGEN_DEVICE_FUNC inline Index size() const { return m_xpr.size(); }
const Derived& m_xpr;
};
template <typename Derived, typename Func>
struct find_coeff_impl {
using Evaluator = find_coeff_evaluator<Derived>;
static constexpr int Flags = Evaluator::Flags;
static constexpr int Alignment = Evaluator::Alignment;
static constexpr bool IsRowMajor = Derived::IsRowMajor;
static constexpr int MaxInnerSizeAtCompileTime =
IsRowMajor ? Derived::MaxColsAtCompileTime : Derived::MaxRowsAtCompileTime;
static constexpr int MaxSizeAtCompileTime = Derived::MaxSizeAtCompileTime;
using Scalar = typename Derived::Scalar;
using Packet = typename Evaluator::Packet;
static constexpr int PacketSize = unpacket_traits<Packet>::size;
static constexpr bool Linearize = bool(Flags & LinearAccessBit);
static constexpr bool DontVectorize =
enum_lt_not_dynamic(Linearize ? MaxSizeAtCompileTime : MaxInnerSizeAtCompileTime, PacketSize);
static constexpr bool Vectorize =
!DontVectorize && bool(Flags & PacketAccessBit) && functor_traits<Func>::PacketAccess;
using Loop = find_coeff_loop<Evaluator, Func, Linearize, Vectorize>;
template <bool ForwardLinearAccess = Linearize, std::enable_if_t<!ForwardLinearAccess, bool> = true>
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(const Derived& xpr, Func& func, Scalar& res, Index& outer,
Index& inner) {
Evaluator eval(xpr);
Loop::run(eval, func, res, outer, inner);
}
template <bool ForwardLinearAccess = Linearize, std::enable_if_t<ForwardLinearAccess, bool> = true>
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(const Derived& xpr, Func& func, Scalar& res, Index& outer,
Index& inner) {
// where possible, use the linear loop and back-calculate the outer and inner indices
Index index = 0;
run(xpr, func, res, index);
outer = index / xpr.innerSize();
inner = index % xpr.innerSize();
}
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(const Derived& xpr, Func& func, Scalar& res, Index& index) {
Evaluator eval(xpr);
Loop::run(eval, func, res, index);
}
};
template <typename Derived, typename IndexType, typename Func>
EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar findCoeff(const DenseBase<Derived>& mat, Func& func,
IndexType* rowPtr, IndexType* colPtr) {
eigen_assert(mat.rows() > 0 && mat.cols() > 0 && "you are using an empty matrix");
using Scalar = typename DenseBase<Derived>::Scalar;
using FindCoeffImpl = internal::find_coeff_impl<Derived, Func>;
Index outer = 0;
Index inner = 0;
Scalar res = mat.coeff(0, 0);
FindCoeffImpl::run(mat.derived(), func, res, outer, inner);
*rowPtr = internal::convert_index<IndexType>(Derived::IsRowMajor ? outer : inner);
if (colPtr) *colPtr = internal::convert_index<IndexType>(Derived::IsRowMajor ? inner : outer);
return res;
}
template <typename Derived, typename IndexType, typename Func>
EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar findCoeff(const DenseBase<Derived>& mat, Func& func,
IndexType* indexPtr) {
eigen_assert(mat.size() > 0 && "you are using an empty matrix");
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
using Scalar = typename DenseBase<Derived>::Scalar;
using FindCoeffImpl = internal::find_coeff_impl<Derived, Func>;
Index index = 0;
Scalar res = mat.coeff(0);
FindCoeffImpl::run(mat.derived(), func, res, index);
*indexPtr = internal::convert_index<IndexType>(index);
return res;
}
} // namespace internal
/** \fn DenseBase<Derived>::minCoeff(IndexType* rowId, IndexType* colId) const
* \returns the minimum of all coefficients of *this and puts in *row and *col its location.
*
* If there are multiple coefficients with the same extreme value, the location of the first instance is returned.
*
* In case \c *this contains NaN, NaNPropagation determines the behavior:
* NaNPropagation == PropagateFast : undefined
* NaNPropagation == PropagateNaN : result is NaN
* NaNPropagation == PropagateNumbers : result is maximum of elements that are not NaN
* \warning the matrix must be not empty, otherwise an assertion is triggered.
*
* \sa DenseBase::minCoeff(Index*), DenseBase::maxCoeff(Index*,Index*), DenseBase::visit(), DenseBase::minCoeff()
*/
template <typename Derived>
template <int NaNPropagation, typename IndexType>
EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar DenseBase<Derived>::minCoeff(IndexType* rowPtr,
IndexType* colPtr) const {
using Func = internal::min_coeff_functor<Scalar, NaNPropagation>;
Func func;
return internal::findCoeff(derived(), func, rowPtr, colPtr);
}
/** \returns the minimum of all coefficients of *this and puts in *index its location.
*
* If there are multiple coefficients with the same extreme value, the location of the first instance is returned.
*
* In case \c *this contains NaN, NaNPropagation determines the behavior:
* NaNPropagation == PropagateFast : undefined
* NaNPropagation == PropagateNaN : result is NaN
* NaNPropagation == PropagateNumbers : result is maximum of elements that are not NaN
* \warning the matrix must be not empty, otherwise an assertion is triggered.
*
* \sa DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::maxCoeff(IndexType*,IndexType*), DenseBase::visit(),
* DenseBase::minCoeff()
*/
template <typename Derived>
template <int NaNPropagation, typename IndexType>
EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar DenseBase<Derived>::minCoeff(IndexType* indexPtr) const {
using Func = internal::min_coeff_functor<Scalar, NaNPropagation>;
Func func;
return internal::findCoeff(derived(), func, indexPtr);
}
/** \fn DenseBase<Derived>::maxCoeff(IndexType* rowId, IndexType* colId) const
* \returns the maximum of all coefficients of *this and puts in *row and *col its location.
*
* If there are multiple coefficients with the same extreme value, the location of the first instance is returned.
*
* In case \c *this contains NaN, NaNPropagation determines the behavior:
* NaNPropagation == PropagateFast : undefined
* NaNPropagation == PropagateNaN : result is NaN
* NaNPropagation == PropagateNumbers : result is maximum of elements that are not NaN
* \warning the matrix must be not empty, otherwise an assertion is triggered.
*
* \sa DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::visit(), DenseBase::maxCoeff()
*/
template <typename Derived>
template <int NaNPropagation, typename IndexType>
EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar DenseBase<Derived>::maxCoeff(IndexType* rowPtr,
IndexType* colPtr) const {
using Func = internal::max_coeff_functor<Scalar, NaNPropagation>;
Func func;
return internal::findCoeff(derived(), func, rowPtr, colPtr);
}
/** \returns the maximum of all coefficients of *this and puts in *index its location.
*
* If there are multiple coefficients with the same extreme value, the location of the first instance is returned.
*
* In case \c *this contains NaN, NaNPropagation determines the behavior:
* NaNPropagation == PropagateFast : undefined
* NaNPropagation == PropagateNaN : result is NaN
* NaNPropagation == PropagateNumbers : result is maximum of elements that are not NaN
* \warning the matrix must be not empty, otherwise an assertion is triggered.
*
* \sa DenseBase::maxCoeff(IndexType*,IndexType*), DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::visitor(),
* DenseBase::maxCoeff()
*/
template <typename Derived>
template <int NaNPropagation, typename IndexType>
EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar DenseBase<Derived>::maxCoeff(IndexType* indexPtr) const {
using Func = internal::max_coeff_functor<Scalar, NaNPropagation>;
Func func;
return internal::findCoeff(derived(), func, indexPtr);
}
} // namespace Eigen
#endif // EIGEN_FIND_COEFF_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_FORCEALIGNEDACCESS_H
#define EIGEN_FORCEALIGNEDACCESS_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
/** \class ForceAlignedAccess
* \ingroup Core_Module
*
* \brief Enforce aligned packet loads and stores regardless of what is requested
*
* \param ExpressionType the type of the object of which we are forcing aligned packet access
*
* This class is the return type of MatrixBase::forceAlignedAccess()
* and most of the time this is the only way it is used.
*
* \sa MatrixBase::forceAlignedAccess()
*/
namespace internal {
template <typename ExpressionType>
struct traits<ForceAlignedAccess<ExpressionType>> : public traits<ExpressionType> {};
} // namespace internal
template <typename ExpressionType>
class ForceAlignedAccess : public internal::dense_xpr_base<ForceAlignedAccess<ExpressionType>>::type {
public:
typedef typename internal::dense_xpr_base<ForceAlignedAccess>::type Base;
EIGEN_DENSE_PUBLIC_INTERFACE(ForceAlignedAccess)
EIGEN_DEVICE_FUNC explicit inline ForceAlignedAccess(const ExpressionType& matrix) : m_expression(matrix) {}
EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return m_expression.rows(); }
EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return m_expression.cols(); }
EIGEN_DEVICE_FUNC constexpr Index outerStride() const noexcept { return m_expression.outerStride(); }
EIGEN_DEVICE_FUNC constexpr Index innerStride() const noexcept { return m_expression.innerStride(); }
EIGEN_DEVICE_FUNC inline const CoeffReturnType coeff(Index row, Index col) const {
return m_expression.coeff(row, col);
}
EIGEN_DEVICE_FUNC inline Scalar& coeffRef(Index row, Index col) {
return m_expression.const_cast_derived().coeffRef(row, col);
}
EIGEN_DEVICE_FUNC inline const CoeffReturnType coeff(Index index) const { return m_expression.coeff(index); }
EIGEN_DEVICE_FUNC inline Scalar& coeffRef(Index index) { return m_expression.const_cast_derived().coeffRef(index); }
template <int LoadMode>
inline const PacketScalar packet(Index row, Index col) const {
return m_expression.template packet<Aligned>(row, col);
}
template <int LoadMode>
inline void writePacket(Index row, Index col, const PacketScalar& x) {
m_expression.const_cast_derived().template writePacket<Aligned>(row, col, x);
}
template <int LoadMode>
inline const PacketScalar packet(Index index) const {
return m_expression.template packet<Aligned>(index);
}
template <int LoadMode>
inline void writePacket(Index index, const PacketScalar& x) {
m_expression.const_cast_derived().template writePacket<Aligned>(index, x);
}
EIGEN_DEVICE_FUNC operator const ExpressionType&() const { return m_expression; }
protected:
const ExpressionType& m_expression;
private:
ForceAlignedAccess& operator=(const ForceAlignedAccess&);
};
/** \returns an expression of *this with forced aligned access
* \sa forceAlignedAccessIf(),class ForceAlignedAccess
*/
template <typename Derived>
inline const ForceAlignedAccess<Derived> MatrixBase<Derived>::forceAlignedAccess() const {
return ForceAlignedAccess<Derived>(derived());
}
/** \returns an expression of *this with forced aligned access
* \sa forceAlignedAccessIf(), class ForceAlignedAccess
*/
template <typename Derived>
inline ForceAlignedAccess<Derived> MatrixBase<Derived>::forceAlignedAccess() {
return ForceAlignedAccess<Derived>(derived());
}
/** \returns an expression of *this with forced aligned access if \a Enable is true.
* \sa forceAlignedAccess(), class ForceAlignedAccess
*/
template <typename Derived>
template <bool Enable>
inline add_const_on_value_type_t<std::conditional_t<Enable, ForceAlignedAccess<Derived>, Derived&>>
MatrixBase<Derived>::forceAlignedAccessIf() const {
return derived(); // FIXME This should not work but apparently is never used
}
/** \returns an expression of *this with forced aligned access if \a Enable is true.
* \sa forceAlignedAccess(), class ForceAlignedAccess
*/
template <typename Derived>
template <bool Enable>
inline std::conditional_t<Enable, ForceAlignedAccess<Derived>, Derived&> MatrixBase<Derived>::forceAlignedAccessIf() {
return derived(); // FIXME This should not work but apparently is never used
}
} // end namespace Eigen
#endif // EIGEN_FORCEALIGNEDACCESS_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_FUZZY_H
#define EIGEN_FUZZY_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
template <typename Derived, typename OtherDerived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>
struct isApprox_selector {
EIGEN_DEVICE_FUNC static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar& prec) {
typename internal::nested_eval<Derived, 2>::type nested(x);
typename internal::nested_eval<OtherDerived, 2>::type otherNested(y);
return (nested.matrix() - otherNested.matrix()).cwiseAbs2().sum() <=
prec * prec * numext::mini(nested.cwiseAbs2().sum(), otherNested.cwiseAbs2().sum());
}
};
template <typename Derived, typename OtherDerived>
struct isApprox_selector<Derived, OtherDerived, true> {
EIGEN_DEVICE_FUNC static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar&) {
return x.matrix() == y.matrix();
}
};
template <typename Derived, typename OtherDerived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>
struct isMuchSmallerThan_object_selector {
EIGEN_DEVICE_FUNC static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar& prec) {
return x.cwiseAbs2().sum() <= numext::abs2(prec) * y.cwiseAbs2().sum();
}
};
template <typename Derived, typename OtherDerived>
struct isMuchSmallerThan_object_selector<Derived, OtherDerived, true> {
EIGEN_DEVICE_FUNC static bool run(const Derived& x, const OtherDerived&, const typename Derived::RealScalar&) {
return x.matrix() == Derived::Zero(x.rows(), x.cols()).matrix();
}
};
template <typename Derived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>
struct isMuchSmallerThan_scalar_selector {
EIGEN_DEVICE_FUNC static bool run(const Derived& x, const typename Derived::RealScalar& y,
const typename Derived::RealScalar& prec) {
return x.cwiseAbs2().sum() <= numext::abs2(prec * y);
}
};
template <typename Derived>
struct isMuchSmallerThan_scalar_selector<Derived, true> {
EIGEN_DEVICE_FUNC static bool run(const Derived& x, const typename Derived::RealScalar&,
const typename Derived::RealScalar&) {
return x.matrix() == Derived::Zero(x.rows(), x.cols()).matrix();
}
};
} // end namespace internal
/** \returns \c true if \c *this is approximately equal to \a other, within the precision
* determined by \a prec.
*
* \note The fuzzy compares are done multiplicatively. Two vectors \f$ v \f$ and \f$ w \f$
* are considered to be approximately equal within precision \f$ p \f$ if
* \f[ \Vert v - w \Vert \leqslant p\,\min(\Vert v\Vert, \Vert w\Vert). \f]
* For matrices, the comparison is done using the Hilbert-Schmidt norm (aka Frobenius norm
* L2 norm).
*
* \note Because of the multiplicativeness of this comparison, one can't use this function
* to check whether \c *this is approximately equal to the zero matrix or vector.
* Indeed, \c isApprox(zero) returns false unless \c *this itself is exactly the zero matrix
* or vector. If you want to test whether \c *this is zero, use internal::isMuchSmallerThan(const
* RealScalar&, RealScalar) instead.
*
* \sa internal::isMuchSmallerThan(const RealScalar&, RealScalar) const
*/
template <typename Derived>
template <typename OtherDerived>
EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isApprox(const DenseBase<OtherDerived>& other,
const RealScalar& prec) const {
return internal::isApprox_selector<Derived, OtherDerived>::run(derived(), other.derived(), prec);
}
/** \returns \c true if the norm of \c *this is much smaller than \a other,
* within the precision determined by \a prec.
*
* \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is
* considered to be much smaller than \f$ x \f$ within precision \f$ p \f$ if
* \f[ \Vert v \Vert \leqslant p\,\vert x\vert. \f]
*
* For matrices, the comparison is done using the Hilbert-Schmidt norm. For this reason,
* the value of the reference scalar \a other should come from the Hilbert-Schmidt norm
* of a reference matrix of same dimensions.
*
* \sa isApprox(), isMuchSmallerThan(const DenseBase<OtherDerived>&, RealScalar) const
*/
template <typename Derived>
EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isMuchSmallerThan(const typename NumTraits<Scalar>::Real& other,
const RealScalar& prec) const {
return internal::isMuchSmallerThan_scalar_selector<Derived>::run(derived(), other, prec);
}
/** \returns \c true if the norm of \c *this is much smaller than the norm of \a other,
* within the precision determined by \a prec.
*
* \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is
* considered to be much smaller than a vector \f$ w \f$ within precision \f$ p \f$ if
* \f[ \Vert v \Vert \leqslant p\,\Vert w\Vert. \f]
* For matrices, the comparison is done using the Hilbert-Schmidt norm.
*
* \sa isApprox(), isMuchSmallerThan(const RealScalar&, RealScalar) const
*/
template <typename Derived>
template <typename OtherDerived>
EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isMuchSmallerThan(const DenseBase<OtherDerived>& other,
const RealScalar& prec) const {
return internal::isMuchSmallerThan_object_selector<Derived, OtherDerived>::run(derived(), other.derived(), prec);
}
} // end namespace Eigen
#endif // EIGEN_FUZZY_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_GENERAL_PRODUCT_H
#define EIGEN_GENERAL_PRODUCT_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
enum { Large = 2, Small = 3 };
// Define the threshold value to fallback from the generic matrix-matrix product
// implementation (heavy) to the lightweight coeff-based product one.
// See generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,GemmProduct>
// in products/GeneralMatrixMatrix.h for more details.
// TODO This threshold should also be used in the compile-time selector below.
#ifndef EIGEN_GEMM_TO_COEFFBASED_THRESHOLD
// This default value has been obtained on a Haswell architecture.
#define EIGEN_GEMM_TO_COEFFBASED_THRESHOLD 20
#endif
namespace internal {
template <int Rows, int Cols, int Depth>
struct product_type_selector;
template <int Size, int MaxSize>
struct product_size_category {
enum {
#ifndef EIGEN_GPU_COMPILE_PHASE
is_large = MaxSize == Dynamic || Size >= EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD ||
(Size == Dynamic && MaxSize >= EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD),
#else
is_large = 0,
#endif
value = is_large ? Large
: Size == 1 ? 1
: Small
};
};
template <typename Lhs, typename Rhs>
struct product_type {
typedef remove_all_t<Lhs> Lhs_;
typedef remove_all_t<Rhs> Rhs_;
enum {
MaxRows = traits<Lhs_>::MaxRowsAtCompileTime,
Rows = traits<Lhs_>::RowsAtCompileTime,
MaxCols = traits<Rhs_>::MaxColsAtCompileTime,
Cols = traits<Rhs_>::ColsAtCompileTime,
MaxDepth = min_size_prefer_fixed(traits<Lhs_>::MaxColsAtCompileTime, traits<Rhs_>::MaxRowsAtCompileTime),
Depth = min_size_prefer_fixed(traits<Lhs_>::ColsAtCompileTime, traits<Rhs_>::RowsAtCompileTime)
};
// the splitting into different lines of code here, introducing the _select enums and the typedef below,
// is to work around an internal compiler error with gcc 4.1 and 4.2.
private:
enum {
rows_select = product_size_category<Rows, MaxRows>::value,
cols_select = product_size_category<Cols, MaxCols>::value,
depth_select = product_size_category<Depth, MaxDepth>::value
};
typedef product_type_selector<rows_select, cols_select, depth_select> selector;
public:
enum { value = selector::ret, ret = selector::ret };
#ifdef EIGEN_DEBUG_PRODUCT
static void debug() {
EIGEN_DEBUG_VAR(Rows);
EIGEN_DEBUG_VAR(Cols);
EIGEN_DEBUG_VAR(Depth);
EIGEN_DEBUG_VAR(rows_select);
EIGEN_DEBUG_VAR(cols_select);
EIGEN_DEBUG_VAR(depth_select);
EIGEN_DEBUG_VAR(value);
}
#endif
};
/* The following allows to select the kind of product at compile time
* based on the three dimensions of the product.
* This is a compile time mapping from {1,Small,Large}^3 -> {product types} */
// FIXME I'm not sure the current mapping is the ideal one.
template <int M, int N>
struct product_type_selector<M, N, 1> {
enum { ret = OuterProduct };
};
template <int M>
struct product_type_selector<M, 1, 1> {
enum { ret = LazyCoeffBasedProductMode };
};
template <int N>
struct product_type_selector<1, N, 1> {
enum { ret = LazyCoeffBasedProductMode };
};
template <int Depth>
struct product_type_selector<1, 1, Depth> {
enum { ret = InnerProduct };
};
template <>
struct product_type_selector<1, 1, 1> {
enum { ret = InnerProduct };
};
template <>
struct product_type_selector<Small, 1, Small> {
enum { ret = CoeffBasedProductMode };
};
template <>
struct product_type_selector<1, Small, Small> {
enum { ret = CoeffBasedProductMode };
};
template <>
struct product_type_selector<Small, Small, Small> {
enum { ret = CoeffBasedProductMode };
};
template <>
struct product_type_selector<Small, Small, 1> {
enum { ret = LazyCoeffBasedProductMode };
};
template <>
struct product_type_selector<Small, Large, 1> {
enum { ret = LazyCoeffBasedProductMode };
};
template <>
struct product_type_selector<Large, Small, 1> {
enum { ret = LazyCoeffBasedProductMode };
};
template <>
struct product_type_selector<1, Large, Small> {
enum { ret = CoeffBasedProductMode };
};
template <>
struct product_type_selector<1, Large, Large> {
enum { ret = GemvProduct };
};
template <>
struct product_type_selector<1, Small, Large> {
enum { ret = CoeffBasedProductMode };
};
template <>
struct product_type_selector<Large, 1, Small> {
enum { ret = CoeffBasedProductMode };
};
template <>
struct product_type_selector<Large, 1, Large> {
enum { ret = GemvProduct };
};
template <>
struct product_type_selector<Small, 1, Large> {
enum { ret = CoeffBasedProductMode };
};
template <>
struct product_type_selector<Small, Small, Large> {
enum { ret = GemmProduct };
};
template <>
struct product_type_selector<Large, Small, Large> {
enum { ret = GemmProduct };
};
template <>
struct product_type_selector<Small, Large, Large> {
enum { ret = GemmProduct };
};
template <>
struct product_type_selector<Large, Large, Large> {
enum { ret = GemmProduct };
};
template <>
struct product_type_selector<Large, Small, Small> {
enum { ret = CoeffBasedProductMode };
};
template <>
struct product_type_selector<Small, Large, Small> {
enum { ret = CoeffBasedProductMode };
};
template <>
struct product_type_selector<Large, Large, Small> {
enum { ret = GemmProduct };
};
} // end namespace internal
/***********************************************************************
* Implementation of Inner Vector Vector Product
***********************************************************************/
// FIXME : maybe the "inner product" could return a Scalar
// instead of a 1x1 matrix ??
// Pro: more natural for the user
// Cons: this could be a problem if in a meta unrolled algorithm a matrix-matrix
// product ends up to a row-vector times col-vector product... To tackle this use
// case, we could have a specialization for Block<MatrixType,1,1> with: operator=(Scalar x);
/***********************************************************************
* Implementation of Outer Vector Vector Product
***********************************************************************/
/***********************************************************************
* Implementation of General Matrix Vector Product
***********************************************************************/
/* According to the shape/flags of the matrix we have to distinghish 3 different cases:
* 1 - the matrix is col-major, BLAS compatible and M is large => call fast BLAS-like colmajor routine
* 2 - the matrix is row-major, BLAS compatible and N is large => call fast BLAS-like rowmajor routine
* 3 - all other cases are handled using a simple loop along the outer-storage direction.
* Therefore we need a lower level meta selector.
* Furthermore, if the matrix is the rhs, then the product has to be transposed.
*/
namespace internal {
template <int Side, int StorageOrder, bool BlasCompatible>
struct gemv_dense_selector;
} // end namespace internal
namespace internal {
template <typename Scalar, int Size, int MaxSize, bool Cond>
struct gemv_static_vector_if;
template <typename Scalar, int Size, int MaxSize>
struct gemv_static_vector_if<Scalar, Size, MaxSize, false> {
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC constexpr Scalar* data() {
eigen_internal_assert(false && "should never be called");
return 0;
}
};
template <typename Scalar, int Size>
struct gemv_static_vector_if<Scalar, Size, Dynamic, true> {
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC constexpr Scalar* data() { return 0; }
};
template <typename Scalar, int Size, int MaxSize>
struct gemv_static_vector_if<Scalar, Size, MaxSize, true> {
#if EIGEN_MAX_STATIC_ALIGN_BYTES != 0
internal::plain_array<Scalar, internal::min_size_prefer_fixed(Size, MaxSize), 0, AlignedMax> m_data;
EIGEN_STRONG_INLINE constexpr Scalar* data() { return m_data.array; }
#else
// Some architectures cannot align on the stack,
// => let's manually enforce alignment by allocating more data and return the address of the first aligned element.
internal::plain_array<Scalar, internal::min_size_prefer_fixed(Size, MaxSize) + EIGEN_MAX_ALIGN_BYTES, 0> m_data;
EIGEN_STRONG_INLINE constexpr Scalar* data() {
return reinterpret_cast<Scalar*>((std::uintptr_t(m_data.array) & ~(std::size_t(EIGEN_MAX_ALIGN_BYTES - 1))) +
EIGEN_MAX_ALIGN_BYTES);
}
#endif
};
// The vector is on the left => transposition
template <int StorageOrder, bool BlasCompatible>
struct gemv_dense_selector<OnTheLeft, StorageOrder, BlasCompatible> {
template <typename Lhs, typename Rhs, typename Dest>
static void run(const Lhs& lhs, const Rhs& rhs, Dest& dest, const typename Dest::Scalar& alpha) {
Transpose<Dest> destT(dest);
enum { OtherStorageOrder = StorageOrder == RowMajor ? ColMajor : RowMajor };
gemv_dense_selector<OnTheRight, OtherStorageOrder, BlasCompatible>::run(rhs.transpose(), lhs.transpose(), destT,
alpha);
}
};
template <>
struct gemv_dense_selector<OnTheRight, ColMajor, true> {
template <typename Lhs, typename Rhs, typename Dest>
static inline void run(const Lhs& lhs, const Rhs& rhs, Dest& dest, const typename Dest::Scalar& alpha) {
typedef typename Lhs::Scalar LhsScalar;
typedef typename Rhs::Scalar RhsScalar;
typedef typename Dest::Scalar ResScalar;
typedef internal::blas_traits<Lhs> LhsBlasTraits;
typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
typedef internal::blas_traits<Rhs> RhsBlasTraits;
typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
typedef Map<Matrix<ResScalar, Dynamic, 1>, plain_enum_min(AlignedMax, internal::packet_traits<ResScalar>::size)>
MappedDest;
ActualLhsType actualLhs = LhsBlasTraits::extract(lhs);
ActualRhsType actualRhs = RhsBlasTraits::extract(rhs);
ResScalar actualAlpha = combine_scalar_factors(alpha, lhs, rhs);
// make sure Dest is a compile-time vector type (bug 1166)
typedef std::conditional_t<Dest::IsVectorAtCompileTime, Dest, typename Dest::ColXpr> ActualDest;
enum {
// FIXME find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1
// on, the other hand it is good for the cache to pack the vector anyways...
EvalToDestAtCompileTime = (ActualDest::InnerStrideAtCompileTime == 1),
ComplexByReal = (NumTraits<LhsScalar>::IsComplex) && (!NumTraits<RhsScalar>::IsComplex),
MightCannotUseDest = ((!EvalToDestAtCompileTime) || ComplexByReal) && (ActualDest::MaxSizeAtCompileTime != 0)
};
typedef const_blas_data_mapper<LhsScalar, Index, ColMajor> LhsMapper;
typedef const_blas_data_mapper<RhsScalar, Index, RowMajor> RhsMapper;
RhsScalar compatibleAlpha = get_factor<ResScalar, RhsScalar>::run(actualAlpha);
if (!MightCannotUseDest) {
// shortcut if we are sure to be able to use dest directly,
// this ease the compiler to generate cleaner and more optimzized code for most common cases
general_matrix_vector_product<Index, LhsScalar, LhsMapper, ColMajor, LhsBlasTraits::NeedToConjugate, RhsScalar,
RhsMapper, RhsBlasTraits::NeedToConjugate>::run(actualLhs.rows(), actualLhs.cols(),
LhsMapper(actualLhs.data(),
actualLhs.outerStride()),
RhsMapper(actualRhs.data(),
actualRhs.innerStride()),
dest.data(), 1, compatibleAlpha);
} else {
gemv_static_vector_if<ResScalar, ActualDest::SizeAtCompileTime, ActualDest::MaxSizeAtCompileTime,
MightCannotUseDest>
static_dest;
const bool alphaIsCompatible = (!ComplexByReal) || (numext::is_exactly_zero(numext::imag(actualAlpha)));
const bool evalToDest = EvalToDestAtCompileTime && alphaIsCompatible;
ei_declare_aligned_stack_constructed_variable(ResScalar, actualDestPtr, dest.size(),
evalToDest ? dest.data() : static_dest.data());
if (!evalToDest) {
#ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
constexpr int Size = Dest::SizeAtCompileTime;
Index size = dest.size();
EIGEN_DENSE_STORAGE_CTOR_PLUGIN
#endif
if (!alphaIsCompatible) {
MappedDest(actualDestPtr, dest.size()).setZero();
compatibleAlpha = RhsScalar(1);
} else
MappedDest(actualDestPtr, dest.size()) = dest;
}
general_matrix_vector_product<Index, LhsScalar, LhsMapper, ColMajor, LhsBlasTraits::NeedToConjugate, RhsScalar,
RhsMapper, RhsBlasTraits::NeedToConjugate>::run(actualLhs.rows(), actualLhs.cols(),
LhsMapper(actualLhs.data(),
actualLhs.outerStride()),
RhsMapper(actualRhs.data(),
actualRhs.innerStride()),
actualDestPtr, 1, compatibleAlpha);
if (!evalToDest) {
if (!alphaIsCompatible)
dest.matrix() += actualAlpha * MappedDest(actualDestPtr, dest.size());
else
dest = MappedDest(actualDestPtr, dest.size());
}
}
}
};
template <>
struct gemv_dense_selector<OnTheRight, RowMajor, true> {
template <typename Lhs, typename Rhs, typename Dest>
static void run(const Lhs& lhs, const Rhs& rhs, Dest& dest, const typename Dest::Scalar& alpha) {
typedef typename Lhs::Scalar LhsScalar;
typedef typename Rhs::Scalar RhsScalar;
typedef typename Dest::Scalar ResScalar;
typedef internal::blas_traits<Lhs> LhsBlasTraits;
typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
typedef internal::blas_traits<Rhs> RhsBlasTraits;
typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
typedef internal::remove_all_t<ActualRhsType> ActualRhsTypeCleaned;
std::add_const_t<ActualLhsType> actualLhs = LhsBlasTraits::extract(lhs);
std::add_const_t<ActualRhsType> actualRhs = RhsBlasTraits::extract(rhs);
ResScalar actualAlpha = combine_scalar_factors(alpha, lhs, rhs);
enum {
// FIXME find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1
// on, the other hand it is good for the cache to pack the vector anyways...
DirectlyUseRhs =
ActualRhsTypeCleaned::InnerStrideAtCompileTime == 1 || ActualRhsTypeCleaned::MaxSizeAtCompileTime == 0
};
gemv_static_vector_if<RhsScalar, ActualRhsTypeCleaned::SizeAtCompileTime,
ActualRhsTypeCleaned::MaxSizeAtCompileTime, !DirectlyUseRhs>
static_rhs;
ei_declare_aligned_stack_constructed_variable(
RhsScalar, actualRhsPtr, actualRhs.size(),
DirectlyUseRhs ? const_cast<RhsScalar*>(actualRhs.data()) : static_rhs.data());
if (!DirectlyUseRhs) {
#ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
constexpr int Size = ActualRhsTypeCleaned::SizeAtCompileTime;
Index size = actualRhs.size();
EIGEN_DENSE_STORAGE_CTOR_PLUGIN
#endif
Map<typename ActualRhsTypeCleaned::PlainObject>(actualRhsPtr, actualRhs.size()) = actualRhs;
}
typedef const_blas_data_mapper<LhsScalar, Index, RowMajor> LhsMapper;
typedef const_blas_data_mapper<RhsScalar, Index, ColMajor> RhsMapper;
general_matrix_vector_product<Index, LhsScalar, LhsMapper, RowMajor, LhsBlasTraits::NeedToConjugate, RhsScalar,
RhsMapper, RhsBlasTraits::NeedToConjugate>::
run(actualLhs.rows(), actualLhs.cols(), LhsMapper(actualLhs.data(), actualLhs.outerStride()),
RhsMapper(actualRhsPtr, 1), dest.data(),
dest.col(0).innerStride(), // NOTE if dest is not a vector at compile-time, then dest.innerStride() might
// be wrong. (bug 1166)
actualAlpha);
}
};
template <>
struct gemv_dense_selector<OnTheRight, ColMajor, false> {
template <typename Lhs, typename Rhs, typename Dest>
static void run(const Lhs& lhs, const Rhs& rhs, Dest& dest, const typename Dest::Scalar& alpha) {
EIGEN_STATIC_ASSERT((!nested_eval<Lhs, 1>::Evaluate),
EIGEN_INTERNAL_COMPILATION_ERROR_OR_YOU_MADE_A_PROGRAMMING_MISTAKE);
// TODO if rhs is large enough it might be beneficial to make sure that dest is sequentially stored in memory,
// otherwise use a temp
typename nested_eval<Rhs, 1>::type actual_rhs(rhs);
const Index size = rhs.rows();
for (Index k = 0; k < size; ++k) dest += (alpha * actual_rhs.coeff(k)) * lhs.col(k);
}
};
template <>
struct gemv_dense_selector<OnTheRight, RowMajor, false> {
template <typename Lhs, typename Rhs, typename Dest>
static void run(const Lhs& lhs, const Rhs& rhs, Dest& dest, const typename Dest::Scalar& alpha) {
EIGEN_STATIC_ASSERT((!nested_eval<Lhs, 1>::Evaluate),
EIGEN_INTERNAL_COMPILATION_ERROR_OR_YOU_MADE_A_PROGRAMMING_MISTAKE);
typename nested_eval<Rhs, Lhs::RowsAtCompileTime>::type actual_rhs(rhs);
const Index rows = dest.rows();
for (Index i = 0; i < rows; ++i)
dest.coeffRef(i) += alpha * (lhs.row(i).cwiseProduct(actual_rhs.transpose())).sum();
}
};
} // end namespace internal
/***************************************************************************
* Implementation of matrix base methods
***************************************************************************/
/** \returns the matrix product of \c *this and \a other.
*
* \note If instead of the matrix product you want the coefficient-wise product, see Cwise::operator*().
*
* \sa lazyProduct(), operator*=(const MatrixBase&), Cwise::operator*()
*/
template <typename Derived>
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Product<Derived, OtherDerived> MatrixBase<Derived>::operator*(
const MatrixBase<OtherDerived>& other) const {
// A note regarding the function declaration: In MSVC, this function will sometimes
// not be inlined since DenseStorage is an unwindable object for dynamic
// matrices and product types are holding a member to store the result.
// Thus it does not help tagging this function with EIGEN_STRONG_INLINE.
enum {
ProductIsValid = Derived::ColsAtCompileTime == Dynamic || OtherDerived::RowsAtCompileTime == Dynamic ||
int(Derived::ColsAtCompileTime) == int(OtherDerived::RowsAtCompileTime),
AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,
SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived, OtherDerived)
};
// note to the lost user:
// * for a dot product use: v1.dot(v2)
// * for a coeff-wise product use: v1.cwiseProduct(v2)
EIGEN_STATIC_ASSERT(
ProductIsValid || !(AreVectors && SameSizes),
INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
#ifdef EIGEN_DEBUG_PRODUCT
internal::product_type<Derived, OtherDerived>::debug();
#endif
return Product<Derived, OtherDerived>(derived(), other.derived());
}
/** \returns an expression of the matrix product of \c *this and \a other without implicit evaluation.
*
* The returned product will behave like any other expressions: the coefficients of the product will be
* computed once at a time as requested. This might be useful in some extremely rare cases when only
* a small and no coherent fraction of the result's coefficients have to be computed.
*
* \warning This version of the matrix product can be much much slower. So use it only if you know
* what you are doing and that you measured a true speed improvement.
*
* \sa operator*(const MatrixBase&)
*/
template <typename Derived>
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Product<Derived, OtherDerived, LazyProduct>
MatrixBase<Derived>::lazyProduct(const MatrixBase<OtherDerived>& other) const {
enum {
ProductIsValid = Derived::ColsAtCompileTime == Dynamic || OtherDerived::RowsAtCompileTime == Dynamic ||
int(Derived::ColsAtCompileTime) == int(OtherDerived::RowsAtCompileTime),
AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,
SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived, OtherDerived)
};
// note to the lost user:
// * for a dot product use: v1.dot(v2)
// * for a coeff-wise product use: v1.cwiseProduct(v2)
EIGEN_STATIC_ASSERT(
ProductIsValid || !(AreVectors && SameSizes),
INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
return Product<Derived, OtherDerived, LazyProduct>(derived(), other.derived());
}
} // end namespace Eigen
#endif // EIGEN_PRODUCT_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2010-2016 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_GLOBAL_FUNCTIONS_H
#define EIGEN_GLOBAL_FUNCTIONS_H
#ifdef EIGEN_PARSED_BY_DOXYGEN
#define EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(NAME, FUNCTOR, DOC_OP, DOC_DETAILS) \
/** \returns an expression of the coefficient-wise DOC_OP of \a x \
\ \
DOC_DETAILS \
\ \
\sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_##NAME">Math functions</a>, class CwiseUnaryOp \
*/ \
template <typename Derived> \
inline const Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived> NAME( \
const Eigen::ArrayBase<Derived>& x);
#else
#define EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(NAME, FUNCTOR, DOC_OP, DOC_DETAILS) \
template <typename Derived> \
inline const Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived>(NAME)( \
const Eigen::ArrayBase<Derived>& x) { \
return Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived>(x.derived()); \
}
#endif // EIGEN_PARSED_BY_DOXYGEN
#define EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(NAME, FUNCTOR) \
\
template <typename Derived> \
struct NAME##_retval<ArrayBase<Derived> > { \
typedef const Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived> type; \
}; \
template <typename Derived> \
struct NAME##_impl<ArrayBase<Derived> > { \
static inline typename NAME##_retval<ArrayBase<Derived> >::type run(const Eigen::ArrayBase<Derived>& x) { \
return typename NAME##_retval<ArrayBase<Derived> >::type(x.derived()); \
} \
};
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(real, scalar_real_op, real part,\sa ArrayBase::real)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(imag, scalar_imag_op, imaginary part,\sa ArrayBase::imag)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(conj, scalar_conjugate_op, complex conjugate,\sa ArrayBase::conjugate)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(inverse, scalar_inverse_op, inverse,\sa ArrayBase::inverse)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sin, scalar_sin_op, sine,\sa ArrayBase::sin)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cos, scalar_cos_op, cosine,\sa ArrayBase::cos)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(tan, scalar_tan_op, tangent,\sa ArrayBase::tan)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(atan, scalar_atan_op, arc - tangent,\sa ArrayBase::atan)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(asin, scalar_asin_op, arc - sine,\sa ArrayBase::asin)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(acos, scalar_acos_op, arc - consine,\sa ArrayBase::acos)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sinh, scalar_sinh_op, hyperbolic sine,\sa ArrayBase::sinh)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cosh, scalar_cosh_op, hyperbolic cosine,\sa ArrayBase::cosh)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(tanh, scalar_tanh_op, hyperbolic tangent,\sa ArrayBase::tanh)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(asinh, scalar_asinh_op, inverse hyperbolic sine,\sa ArrayBase::asinh)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(acosh, scalar_acosh_op, inverse hyperbolic cosine,\sa ArrayBase::acosh)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(atanh, scalar_atanh_op, inverse hyperbolic tangent,\sa ArrayBase::atanh)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(logistic, scalar_logistic_op, logistic function,\sa ArrayBase::logistic)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(lgamma, scalar_lgamma_op,
natural logarithm of the gamma function,\sa ArrayBase::lgamma)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(digamma, scalar_digamma_op, derivative of lgamma,\sa ArrayBase::digamma)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(erf, scalar_erf_op, error function,\sa ArrayBase::erf)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(erfc, scalar_erfc_op, complement error function,\sa ArrayBase::erfc)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(ndtri, scalar_ndtri_op, inverse normal distribution function,\sa ArrayBase::ndtri)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(exp, scalar_exp_op, exponential,\sa ArrayBase::exp)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(exp2, scalar_exp2_op, exponential,\sa ArrayBase::exp2)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(expm1, scalar_expm1_op, exponential of a value minus 1,\sa ArrayBase::expm1)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log, scalar_log_op, natural logarithm,\sa Eigen::log10 DOXCOMMA ArrayBase::log)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log1p, scalar_log1p_op, natural logarithm of 1 plus the value,\sa ArrayBase::log1p)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log10, scalar_log10_op, base 10 logarithm,\sa Eigen::log DOXCOMMA ArrayBase::log10)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log2, scalar_log2_op, base 2 logarithm,\sa Eigen::log DOXCOMMA ArrayBase::log2)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(abs, scalar_abs_op, absolute value,\sa ArrayBase::abs DOXCOMMA MatrixBase::cwiseAbs)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(abs2, scalar_abs2_op,
squared absolute value,\sa ArrayBase::abs2 DOXCOMMA MatrixBase::cwiseAbs2)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(arg, scalar_arg_op, complex argument,\sa ArrayBase::arg DOXCOMMA MatrixBase::cwiseArg)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(carg, scalar_carg_op,
complex argument, \sa ArrayBase::carg DOXCOMMA MatrixBase::cwiseCArg)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sqrt, scalar_sqrt_op, square root,\sa ArrayBase::sqrt DOXCOMMA MatrixBase::cwiseSqrt)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cbrt, scalar_cbrt_op, cube root,\sa ArrayBase::cbrt DOXCOMMA MatrixBase::cwiseCbrt)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(rsqrt, scalar_rsqrt_op, reciprocal square root,\sa ArrayBase::rsqrt)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(square, scalar_square_op,
square(power 2),\sa Eigen::abs2 DOXCOMMA Eigen::pow DOXCOMMA ArrayBase::square)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cube, scalar_cube_op, cube(power 3),\sa Eigen::pow DOXCOMMA ArrayBase::cube)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(rint, scalar_rint_op,
nearest integer,\sa Eigen::floor DOXCOMMA Eigen::ceil DOXCOMMA ArrayBase::round)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(round, scalar_round_op,
nearest integer,\sa Eigen::floor DOXCOMMA Eigen::ceil DOXCOMMA ArrayBase::round)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(
floor, scalar_floor_op, nearest integer not greater than the given value,\sa Eigen::ceil DOXCOMMA ArrayBase::floor)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(
ceil, scalar_ceil_op, nearest integer not less than the given value,\sa Eigen::floor DOXCOMMA ArrayBase::ceil)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(trunc, scalar_trunc_op,
nearest integer not greater in magnitude than the given value,\sa Eigen::trunc DOXCOMMA
ArrayBase::trunc)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(
isnan, scalar_isnan_op, not -a - number test,\sa Eigen::isinf DOXCOMMA Eigen::isfinite DOXCOMMA ArrayBase::isnan)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(
isinf, scalar_isinf_op, infinite value test,\sa Eigen::isnan DOXCOMMA Eigen::isfinite DOXCOMMA ArrayBase::isinf)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(isfinite, scalar_isfinite_op,
finite value test,\sa Eigen::isinf DOXCOMMA Eigen::isnan DOXCOMMA ArrayBase::isfinite)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sign, scalar_sign_op, sign(or 0),\sa ArrayBase::sign)
template <typename Derived, typename ScalarExponent>
using GlobalUnaryPowReturnType = std::enable_if_t<
!internal::is_arithmetic<typename NumTraits<Derived>::Real>::value &&
internal::is_arithmetic<typename NumTraits<ScalarExponent>::Real>::value,
CwiseUnaryOp<internal::scalar_unary_pow_op<typename Derived::Scalar, ScalarExponent>, const Derived> >;
/** \returns an expression of the coefficient-wise power of \a x to the given constant \a exponent.
*
* \tparam ScalarExponent is the scalar type of \a exponent. It must be compatible with the scalar type of the given
* expression (\c Derived::Scalar).
*
* \sa ArrayBase::pow()
*
* \relates ArrayBase
*/
#ifdef EIGEN_PARSED_BY_DOXYGEN
template <typename Derived, typename ScalarExponent>
EIGEN_DEVICE_FUNC inline const GlobalUnaryPowReturnType<Derived, ScalarExponent> pow(const Eigen::ArrayBase<Derived>& x,
const ScalarExponent& exponent);
#else
template <typename Derived, typename ScalarExponent>
EIGEN_DEVICE_FUNC inline const GlobalUnaryPowReturnType<Derived, ScalarExponent> pow(const Eigen::ArrayBase<Derived>& x,
const ScalarExponent& exponent) {
return GlobalUnaryPowReturnType<Derived, ScalarExponent>(
x.derived(), internal::scalar_unary_pow_op<typename Derived::Scalar, ScalarExponent>(exponent));
}
#endif
/** \returns an expression of the coefficient-wise power of \a x to the given array of \a exponents.
*
* This function computes the coefficient-wise power.
*
* Example: \include Cwise_array_power_array.cpp
* Output: \verbinclude Cwise_array_power_array.out
*
* \sa ArrayBase::pow()
*
* \relates ArrayBase
*/
template <typename Derived, typename ExponentDerived>
inline const Eigen::CwiseBinaryOp<
Eigen::internal::scalar_pow_op<typename Derived::Scalar, typename ExponentDerived::Scalar>, const Derived,
const ExponentDerived>
pow(const Eigen::ArrayBase<Derived>& x, const Eigen::ArrayBase<ExponentDerived>& exponents) {
return Eigen::CwiseBinaryOp<
Eigen::internal::scalar_pow_op<typename Derived::Scalar, typename ExponentDerived::Scalar>, const Derived,
const ExponentDerived>(x.derived(), exponents.derived());
}
/** \returns an expression of the coefficient-wise power of the scalar \a x to the given array of \a exponents.
*
* This function computes the coefficient-wise power between a scalar and an array of exponents.
*
* \tparam Scalar is the scalar type of \a x. It must be compatible with the scalar type of the given array expression
* (\c Derived::Scalar).
*
* Example: \include Cwise_scalar_power_array.cpp
* Output: \verbinclude Cwise_scalar_power_array.out
*
* \sa ArrayBase::pow()
*
* \relates ArrayBase
*/
#ifdef EIGEN_PARSED_BY_DOXYGEN
template <typename Scalar, typename Derived>
inline const CwiseBinaryOp<internal::scalar_pow_op<Scalar, Derived::Scalar>, Constant<Scalar>, Derived> pow(
const Scalar& x, const Eigen::ArrayBase<Derived>& x);
#else
template <typename Scalar, typename Derived>
EIGEN_DEVICE_FUNC inline const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(
typename internal::promote_scalar_arg<typename Derived::Scalar EIGEN_COMMA Scalar EIGEN_COMMA
EIGEN_SCALAR_BINARY_SUPPORTED(pow, Scalar,
typename Derived::Scalar)>::type,
Derived, pow) pow(const Scalar& x, const Eigen::ArrayBase<Derived>& exponents) {
typedef
typename internal::promote_scalar_arg<typename Derived::Scalar, Scalar,
EIGEN_SCALAR_BINARY_SUPPORTED(pow, Scalar, typename Derived::Scalar)>::type
PromotedScalar;
return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(PromotedScalar, Derived, pow)(
typename internal::plain_constant_type<Derived, PromotedScalar>::type(
exponents.derived().rows(), exponents.derived().cols(), internal::scalar_constant_op<PromotedScalar>(x)),
exponents.derived());
}
#endif
/** \returns an expression of the coefficient-wise atan2(\a x, \a y). \a x and \a y must be of the same type.
*
* This function computes the coefficient-wise atan2().
*
* \sa ArrayBase::atan2()
*
* \relates ArrayBase
*/
template <typename LhsDerived, typename RhsDerived>
inline const std::enable_if_t<
std::is_same<typename LhsDerived::Scalar, typename RhsDerived::Scalar>::value,
Eigen::CwiseBinaryOp<Eigen::internal::scalar_atan2_op<typename LhsDerived::Scalar, typename RhsDerived::Scalar>,
const LhsDerived, const RhsDerived> >
atan2(const Eigen::ArrayBase<LhsDerived>& x, const Eigen::ArrayBase<RhsDerived>& exponents) {
return Eigen::CwiseBinaryOp<
Eigen::internal::scalar_atan2_op<typename LhsDerived::Scalar, typename RhsDerived::Scalar>, const LhsDerived,
const RhsDerived>(x.derived(), exponents.derived());
}
namespace internal {
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(real, scalar_real_op)
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(imag, scalar_imag_op)
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(abs2, scalar_abs2_op)
} // namespace internal
} // namespace Eigen
// TODO: cleanly disable those functions that are not supported on Array (numext::real_ref, internal::random,
// internal::isApprox...)
#endif // EIGEN_GLOBAL_FUNCTIONS_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_IO_H
#define EIGEN_IO_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
enum { DontAlignCols = 1 };
enum { StreamPrecision = -1, FullPrecision = -2 };
namespace internal {
template <typename Derived>
std::ostream& print_matrix(std::ostream& s, const Derived& _m, const IOFormat& fmt);
}
/** \class IOFormat
* \ingroup Core_Module
*
* \brief Stores a set of parameters controlling the way matrices are printed
*
* List of available parameters:
* - \b precision number of digits for floating point values, or one of the special constants \c StreamPrecision and \c
* FullPrecision. The default is the special value \c StreamPrecision which means to use the stream's own precision
* setting, as set for instance using \c cout.precision(3). The other special value \c FullPrecision means that the
* number of digits will be computed to match the full precision of each floating-point type.
* - \b flags an OR-ed combination of flags, the default value is 0, the only currently available flag is \c
* DontAlignCols which allows to disable the alignment of columns, resulting in faster code.
* - \b coeffSeparator string printed between two coefficients of the same row
* - \b rowSeparator string printed between two rows
* - \b rowPrefix string printed at the beginning of each row
* - \b rowSuffix string printed at the end of each row
* - \b matPrefix string printed at the beginning of the matrix
* - \b matSuffix string printed at the end of the matrix
* - \b fill character printed to fill the empty space in aligned columns
*
* Example: \include IOFormat.cpp
* Output: \verbinclude IOFormat.out
*
* \sa DenseBase::format(), class WithFormat
*/
struct IOFormat {
/** Default constructor, see class IOFormat for the meaning of the parameters */
IOFormat(int _precision = StreamPrecision, int _flags = 0, const std::string& _coeffSeparator = " ",
const std::string& _rowSeparator = "\n", const std::string& _rowPrefix = "",
const std::string& _rowSuffix = "", const std::string& _matPrefix = "", const std::string& _matSuffix = "",
const char _fill = ' ')
: matPrefix(_matPrefix),
matSuffix(_matSuffix),
rowPrefix(_rowPrefix),
rowSuffix(_rowSuffix),
rowSeparator(_rowSeparator),
rowSpacer(""),
coeffSeparator(_coeffSeparator),
fill(_fill),
precision(_precision),
flags(_flags) {
// TODO check if rowPrefix, rowSuffix or rowSeparator contains a newline
// don't add rowSpacer if columns are not to be aligned
if ((flags & DontAlignCols)) return;
int i = int(matPrefix.length()) - 1;
while (i >= 0 && matPrefix[i] != '\n') {
rowSpacer += ' ';
i--;
}
}
std::string matPrefix, matSuffix;
std::string rowPrefix, rowSuffix, rowSeparator, rowSpacer;
std::string coeffSeparator;
char fill;
int precision;
int flags;
};
/** \class WithFormat
* \ingroup Core_Module
*
* \brief Pseudo expression providing matrix output with given format
*
* \tparam ExpressionType the type of the object on which IO stream operations are performed
*
* This class represents an expression with stream operators controlled by a given IOFormat.
* It is the return type of DenseBase::format()
* and most of the time this is the only way it is used.
*
* See class IOFormat for some examples.
*
* \sa DenseBase::format(), class IOFormat
*/
template <typename ExpressionType>
class WithFormat {
public:
WithFormat(const ExpressionType& matrix, const IOFormat& format) : m_matrix(matrix), m_format(format) {}
friend std::ostream& operator<<(std::ostream& s, const WithFormat& wf) {
return internal::print_matrix(s, wf.m_matrix.eval(), wf.m_format);
}
protected:
typename ExpressionType::Nested m_matrix;
IOFormat m_format;
};
namespace internal {
// NOTE: This helper is kept for backward compatibility with previous code specializing
// this internal::significant_decimals_impl structure. In the future we should directly
// call max_digits10().
template <typename Scalar>
struct significant_decimals_impl {
static inline int run() { return NumTraits<Scalar>::max_digits10(); }
};
/** \internal
* print the matrix \a _m to the output stream \a s using the output format \a fmt */
template <typename Derived>
std::ostream& print_matrix(std::ostream& s, const Derived& _m, const IOFormat& fmt) {
using internal::is_same;
if (_m.size() == 0) {
s << fmt.matPrefix << fmt.matSuffix;
return s;
}
typename Derived::Nested m = _m;
typedef typename Derived::Scalar Scalar;
typedef std::conditional_t<is_same<Scalar, char>::value || is_same<Scalar, unsigned char>::value ||
is_same<Scalar, numext::int8_t>::value || is_same<Scalar, numext::uint8_t>::value,
int,
std::conditional_t<is_same<Scalar, std::complex<char> >::value ||
is_same<Scalar, std::complex<unsigned char> >::value ||
is_same<Scalar, std::complex<numext::int8_t> >::value ||
is_same<Scalar, std::complex<numext::uint8_t> >::value,
std::complex<int>, const Scalar&> >
PrintType;
Index width = 0;
std::streamsize explicit_precision;
if (fmt.precision == StreamPrecision) {
explicit_precision = 0;
} else if (fmt.precision == FullPrecision) {
if (NumTraits<Scalar>::IsInteger) {
explicit_precision = 0;
} else {
explicit_precision = significant_decimals_impl<Scalar>::run();
}
} else {
explicit_precision = fmt.precision;
}
std::streamsize old_precision = 0;
if (explicit_precision) old_precision = s.precision(explicit_precision);
bool align_cols = !(fmt.flags & DontAlignCols);
if (align_cols) {
// compute the largest width
for (Index j = 0; j < m.cols(); ++j)
for (Index i = 0; i < m.rows(); ++i) {
std::stringstream sstr;
sstr.copyfmt(s);
sstr << static_cast<PrintType>(m.coeff(i, j));
width = std::max<Index>(width, Index(sstr.str().length()));
}
}
std::streamsize old_width = s.width();
char old_fill_character = s.fill();
s << fmt.matPrefix;
for (Index i = 0; i < m.rows(); ++i) {
if (i) s << fmt.rowSpacer;
s << fmt.rowPrefix;
if (width) {
s.fill(fmt.fill);
s.width(width);
}
s << static_cast<PrintType>(m.coeff(i, 0));
for (Index j = 1; j < m.cols(); ++j) {
s << fmt.coeffSeparator;
if (width) {
s.fill(fmt.fill);
s.width(width);
}
s << static_cast<PrintType>(m.coeff(i, j));
}
s << fmt.rowSuffix;
if (i < m.rows() - 1) s << fmt.rowSeparator;
}
s << fmt.matSuffix;
if (explicit_precision) s.precision(old_precision);
if (width) {
s.fill(old_fill_character);
s.width(old_width);
}
return s;
}
} // end namespace internal
/** \relates DenseBase
*
* Outputs the matrix, to the given stream.
*
* If you wish to print the matrix with a format different than the default, use DenseBase::format().
*
* It is also possible to change the default format by defining EIGEN_DEFAULT_IO_FORMAT before including Eigen headers.
* If not defined, this will automatically be defined to Eigen::IOFormat(), that is the Eigen::IOFormat with default
* parameters.
*
* \sa DenseBase::format()
*/
template <typename Derived>
std::ostream& operator<<(std::ostream& s, const DenseBase<Derived>& m) {
return internal::print_matrix(s, m.eval(), EIGEN_DEFAULT_IO_FORMAT);
}
template <typename Derived>
std::ostream& operator<<(std::ostream& s, const DiagonalBase<Derived>& m) {
return internal::print_matrix(s, m.derived(), EIGEN_DEFAULT_IO_FORMAT);
}
} // end namespace Eigen
#endif // EIGEN_IO_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2017 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_INDEXED_VIEW_H
#define EIGEN_INDEXED_VIEW_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
template <typename XprType, typename RowIndices, typename ColIndices>
struct traits<IndexedView<XprType, RowIndices, ColIndices>> : traits<XprType> {
enum {
RowsAtCompileTime = int(IndexedViewHelper<RowIndices>::SizeAtCompileTime),
ColsAtCompileTime = int(IndexedViewHelper<ColIndices>::SizeAtCompileTime),
MaxRowsAtCompileTime = RowsAtCompileTime,
MaxColsAtCompileTime = ColsAtCompileTime,
XprTypeIsRowMajor = (int(traits<XprType>::Flags) & RowMajorBit) != 0,
IsRowMajor = (MaxRowsAtCompileTime == 1 && MaxColsAtCompileTime != 1) ? 1
: (MaxColsAtCompileTime == 1 && MaxRowsAtCompileTime != 1) ? 0
: XprTypeIsRowMajor,
RowIncr = int(IndexedViewHelper<RowIndices>::IncrAtCompileTime),
ColIncr = int(IndexedViewHelper<ColIndices>::IncrAtCompileTime),
InnerIncr = IsRowMajor ? ColIncr : RowIncr,
OuterIncr = IsRowMajor ? RowIncr : ColIncr,
HasSameStorageOrderAsXprType = (IsRowMajor == XprTypeIsRowMajor),
XprInnerStride = HasSameStorageOrderAsXprType ? int(inner_stride_at_compile_time<XprType>::ret)
: int(outer_stride_at_compile_time<XprType>::ret),
XprOuterstride = HasSameStorageOrderAsXprType ? int(outer_stride_at_compile_time<XprType>::ret)
: int(inner_stride_at_compile_time<XprType>::ret),
InnerSize = XprTypeIsRowMajor ? ColsAtCompileTime : RowsAtCompileTime,
IsBlockAlike = InnerIncr == 1 && OuterIncr == 1,
IsInnerPannel = HasSameStorageOrderAsXprType &&
is_same<AllRange<InnerSize>, std::conditional_t<XprTypeIsRowMajor, ColIndices, RowIndices>>::value,
InnerStrideAtCompileTime =
InnerIncr < 0 || InnerIncr == DynamicIndex || XprInnerStride == Dynamic || InnerIncr == Undefined
? Dynamic
: XprInnerStride * InnerIncr,
OuterStrideAtCompileTime =
OuterIncr < 0 || OuterIncr == DynamicIndex || XprOuterstride == Dynamic || OuterIncr == Undefined
? Dynamic
: XprOuterstride * OuterIncr,
ReturnAsScalar = is_single_range<RowIndices>::value && is_single_range<ColIndices>::value,
ReturnAsBlock = (!ReturnAsScalar) && IsBlockAlike,
ReturnAsIndexedView = (!ReturnAsScalar) && (!ReturnAsBlock),
// FIXME we deal with compile-time strides if and only if we have DirectAccessBit flag,
// but this is too strict regarding negative strides...
DirectAccessMask = (int(InnerIncr) != Undefined && int(OuterIncr) != Undefined && InnerIncr >= 0 && OuterIncr >= 0)
? DirectAccessBit
: 0,
FlagsRowMajorBit = IsRowMajor ? RowMajorBit : 0,
FlagsLvalueBit = is_lvalue<XprType>::value ? LvalueBit : 0,
FlagsLinearAccessBit = (RowsAtCompileTime == 1 || ColsAtCompileTime == 1) ? LinearAccessBit : 0,
Flags = (traits<XprType>::Flags & (HereditaryBits | DirectAccessMask)) | FlagsLvalueBit | FlagsRowMajorBit |
FlagsLinearAccessBit
};
typedef Block<XprType, RowsAtCompileTime, ColsAtCompileTime, IsInnerPannel> BlockType;
};
template <typename XprType, typename RowIndices, typename ColIndices, typename StorageKind, bool DirectAccess>
class IndexedViewImpl;
} // namespace internal
/** \class IndexedView
* \ingroup Core_Module
*
* \brief Expression of a non-sequential sub-matrix defined by arbitrary sequences of row and column indices
*
* \tparam XprType the type of the expression in which we are taking the intersections of sub-rows and sub-columns
* \tparam RowIndices the type of the object defining the sequence of row indices
* \tparam ColIndices the type of the object defining the sequence of column indices
*
* This class represents an expression of a sub-matrix (or sub-vector) defined as the intersection
* of sub-sets of rows and columns, that are themself defined by generic sequences of row indices \f$
* \{r_0,r_1,..r_{m-1}\} \f$ and column indices \f$ \{c_0,c_1,..c_{n-1} \}\f$. Let \f$ A \f$ be the nested matrix, then
* the resulting matrix \f$ B \f$ has \c m rows and \c n columns, and its entries are given by: \f$ B(i,j) = A(r_i,c_j)
* \f$.
*
* The \c RowIndices and \c ColIndices types must be compatible with the following API:
* \code
* <integral type> operator[](Index) const;
* Index size() const;
* \endcode
*
* Typical supported types thus include:
* - std::vector<int>
* - std::valarray<int>
* - std::array<int>
* - Eigen::ArrayXi
* - decltype(ArrayXi::LinSpaced(...))
* - Any view/expressions of the previous types
* - Eigen::ArithmeticSequence
* - Eigen::internal::AllRange (helper for Eigen::placeholders::all)
* - Eigen::internal::SingleRange (helper for single index)
* - etc.
*
* In typical usages of %Eigen, this class should never be used directly. It is the return type of
* DenseBase::operator()(const RowIndices&, const ColIndices&).
*
* \sa class Block
*/
template <typename XprType, typename RowIndices, typename ColIndices>
class IndexedView
: public internal::IndexedViewImpl<XprType, RowIndices, ColIndices, typename internal::traits<XprType>::StorageKind,
(internal::traits<IndexedView<XprType, RowIndices, ColIndices>>::Flags &
DirectAccessBit) != 0> {
public:
typedef typename internal::IndexedViewImpl<
XprType, RowIndices, ColIndices, typename internal::traits<XprType>::StorageKind,
(internal::traits<IndexedView<XprType, RowIndices, ColIndices>>::Flags & DirectAccessBit) != 0>
Base;
EIGEN_GENERIC_PUBLIC_INTERFACE(IndexedView)
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(IndexedView)
template <typename T0, typename T1>
IndexedView(XprType& xpr, const T0& rowIndices, const T1& colIndices) : Base(xpr, rowIndices, colIndices) {}
};
namespace internal {
// Generic API dispatcher
template <typename XprType, typename RowIndices, typename ColIndices, typename StorageKind, bool DirectAccess>
class IndexedViewImpl : public internal::generic_xpr_base<IndexedView<XprType, RowIndices, ColIndices>>::type {
public:
typedef typename internal::generic_xpr_base<IndexedView<XprType, RowIndices, ColIndices>>::type Base;
typedef typename internal::ref_selector<XprType>::non_const_type MatrixTypeNested;
typedef internal::remove_all_t<XprType> NestedExpression;
typedef typename XprType::Scalar Scalar;
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(IndexedViewImpl)
template <typename T0, typename T1>
IndexedViewImpl(XprType& xpr, const T0& rowIndices, const T1& colIndices)
: m_xpr(xpr), m_rowIndices(rowIndices), m_colIndices(colIndices) {}
/** \returns number of rows */
Index rows() const { return IndexedViewHelper<RowIndices>::size(m_rowIndices); }
/** \returns number of columns */
Index cols() const { return IndexedViewHelper<ColIndices>::size(m_colIndices); }
/** \returns the nested expression */
const internal::remove_all_t<XprType>& nestedExpression() const { return m_xpr; }
/** \returns the nested expression */
std::remove_reference_t<XprType>& nestedExpression() { return m_xpr; }
/** \returns a const reference to the object storing/generating the row indices */
const RowIndices& rowIndices() const { return m_rowIndices; }
/** \returns a const reference to the object storing/generating the column indices */
const ColIndices& colIndices() const { return m_colIndices; }
constexpr Scalar& coeffRef(Index rowId, Index colId) {
return nestedExpression().coeffRef(m_rowIndices[rowId], m_colIndices[colId]);
}
constexpr const Scalar& coeffRef(Index rowId, Index colId) const {
return nestedExpression().coeffRef(m_rowIndices[rowId], m_colIndices[colId]);
}
protected:
MatrixTypeNested m_xpr;
RowIndices m_rowIndices;
ColIndices m_colIndices;
};
template <typename XprType, typename RowIndices, typename ColIndices, typename StorageKind>
class IndexedViewImpl<XprType, RowIndices, ColIndices, StorageKind, true>
: public IndexedViewImpl<XprType, RowIndices, ColIndices, StorageKind, false> {
public:
using Base = internal::IndexedViewImpl<XprType, RowIndices, ColIndices,
typename internal::traits<XprType>::StorageKind, false>;
using Derived = IndexedView<XprType, RowIndices, ColIndices>;
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(IndexedViewImpl)
template <typename T0, typename T1>
IndexedViewImpl(XprType& xpr, const T0& rowIndices, const T1& colIndices) : Base(xpr, rowIndices, colIndices) {}
Index rowIncrement() const {
if (traits<Derived>::RowIncr != DynamicIndex && traits<Derived>::RowIncr != Undefined) {
return traits<Derived>::RowIncr;
}
return IndexedViewHelper<RowIndices>::incr(this->rowIndices());
}
Index colIncrement() const {
if (traits<Derived>::ColIncr != DynamicIndex && traits<Derived>::ColIncr != Undefined) {
return traits<Derived>::ColIncr;
}
return IndexedViewHelper<ColIndices>::incr(this->colIndices());
}
Index innerIncrement() const { return traits<Derived>::IsRowMajor ? colIncrement() : rowIncrement(); }
Index outerIncrement() const { return traits<Derived>::IsRowMajor ? rowIncrement() : colIncrement(); }
std::decay_t<typename XprType::Scalar>* data() {
Index row_offset = this->rowIndices()[0] * this->nestedExpression().rowStride();
Index col_offset = this->colIndices()[0] * this->nestedExpression().colStride();
return this->nestedExpression().data() + row_offset + col_offset;
}
const std::decay_t<typename XprType::Scalar>* data() const {
Index row_offset = this->rowIndices()[0] * this->nestedExpression().rowStride();
Index col_offset = this->colIndices()[0] * this->nestedExpression().colStride();
return this->nestedExpression().data() + row_offset + col_offset;
}
EIGEN_DEVICE_FUNC constexpr Index innerStride() const noexcept {
if (traits<Derived>::InnerStrideAtCompileTime != Dynamic) {
return traits<Derived>::InnerStrideAtCompileTime;
}
return innerIncrement() * this->nestedExpression().innerStride();
}
EIGEN_DEVICE_FUNC constexpr Index outerStride() const noexcept {
if (traits<Derived>::OuterStrideAtCompileTime != Dynamic) {
return traits<Derived>::OuterStrideAtCompileTime;
}
return outerIncrement() * this->nestedExpression().outerStride();
}
};
template <typename ArgType, typename RowIndices, typename ColIndices>
struct unary_evaluator<IndexedView<ArgType, RowIndices, ColIndices>, IndexBased>
: evaluator_base<IndexedView<ArgType, RowIndices, ColIndices>> {
typedef IndexedView<ArgType, RowIndices, ColIndices> XprType;
enum {
CoeffReadCost = evaluator<ArgType>::CoeffReadCost /* TODO + cost of row/col index */,
FlagsLinearAccessBit =
(traits<XprType>::RowsAtCompileTime == 1 || traits<XprType>::ColsAtCompileTime == 1) ? LinearAccessBit : 0,
FlagsRowMajorBit = traits<XprType>::FlagsRowMajorBit,
Flags = (evaluator<ArgType>::Flags & (HereditaryBits & ~RowMajorBit /*| LinearAccessBit | DirectAccessBit*/)) |
FlagsLinearAccessBit | FlagsRowMajorBit,
Alignment = 0
};
EIGEN_DEVICE_FUNC explicit unary_evaluator(const XprType& xpr) : m_argImpl(xpr.nestedExpression()), m_xpr(xpr) {
EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
}
typedef typename XprType::Scalar Scalar;
typedef typename XprType::CoeffReturnType CoeffReturnType;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index row, Index col) const {
eigen_assert(m_xpr.rowIndices()[row] >= 0 && m_xpr.rowIndices()[row] < m_xpr.nestedExpression().rows() &&
m_xpr.colIndices()[col] >= 0 && m_xpr.colIndices()[col] < m_xpr.nestedExpression().cols());
return m_argImpl.coeff(m_xpr.rowIndices()[row], m_xpr.colIndices()[col]);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index row, Index col) {
eigen_assert(m_xpr.rowIndices()[row] >= 0 && m_xpr.rowIndices()[row] < m_xpr.nestedExpression().rows() &&
m_xpr.colIndices()[col] >= 0 && m_xpr.colIndices()[col] < m_xpr.nestedExpression().cols());
return m_argImpl.coeffRef(m_xpr.rowIndices()[row], m_xpr.colIndices()[col]);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index index) {
EIGEN_STATIC_ASSERT_LVALUE(XprType)
Index row = XprType::RowsAtCompileTime == 1 ? 0 : index;
Index col = XprType::RowsAtCompileTime == 1 ? index : 0;
eigen_assert(m_xpr.rowIndices()[row] >= 0 && m_xpr.rowIndices()[row] < m_xpr.nestedExpression().rows() &&
m_xpr.colIndices()[col] >= 0 && m_xpr.colIndices()[col] < m_xpr.nestedExpression().cols());
return m_argImpl.coeffRef(m_xpr.rowIndices()[row], m_xpr.colIndices()[col]);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& coeffRef(Index index) const {
Index row = XprType::RowsAtCompileTime == 1 ? 0 : index;
Index col = XprType::RowsAtCompileTime == 1 ? index : 0;
eigen_assert(m_xpr.rowIndices()[row] >= 0 && m_xpr.rowIndices()[row] < m_xpr.nestedExpression().rows() &&
m_xpr.colIndices()[col] >= 0 && m_xpr.colIndices()[col] < m_xpr.nestedExpression().cols());
return m_argImpl.coeffRef(m_xpr.rowIndices()[row], m_xpr.colIndices()[col]);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CoeffReturnType coeff(Index index) const {
Index row = XprType::RowsAtCompileTime == 1 ? 0 : index;
Index col = XprType::RowsAtCompileTime == 1 ? index : 0;
eigen_assert(m_xpr.rowIndices()[row] >= 0 && m_xpr.rowIndices()[row] < m_xpr.nestedExpression().rows() &&
m_xpr.colIndices()[col] >= 0 && m_xpr.colIndices()[col] < m_xpr.nestedExpression().cols());
return m_argImpl.coeff(m_xpr.rowIndices()[row], m_xpr.colIndices()[col]);
}
protected:
evaluator<ArgType> m_argImpl;
const XprType& m_xpr;
};
// Catch assignments to an IndexedView.
template <typename ArgType, typename RowIndices, typename ColIndices>
struct evaluator_assume_aliasing<IndexedView<ArgType, RowIndices, ColIndices>> {
static const bool value = true;
};
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_INDEXED_VIEW_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2024 Charlie Schlosser <cs.schlosser@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_INNER_PRODUCT_EVAL_H
#define EIGEN_INNER_PRODUCT_EVAL_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
// recursively searches for the largest simd type that does not exceed Size, or the smallest if no such type exists
template <typename Scalar, int Size, typename Packet = typename packet_traits<Scalar>::type,
bool Stop =
(unpacket_traits<Packet>::size <= Size) || is_same<Packet, typename unpacket_traits<Packet>::half>::value>
struct find_inner_product_packet_helper;
template <typename Scalar, int Size, typename Packet>
struct find_inner_product_packet_helper<Scalar, Size, Packet, false> {
using type = typename find_inner_product_packet_helper<Scalar, Size, typename unpacket_traits<Packet>::half>::type;
};
template <typename Scalar, int Size, typename Packet>
struct find_inner_product_packet_helper<Scalar, Size, Packet, true> {
using type = Packet;
};
template <typename Scalar, int Size>
struct find_inner_product_packet : find_inner_product_packet_helper<Scalar, Size> {};
template <typename Scalar>
struct find_inner_product_packet<Scalar, Dynamic> {
using type = typename packet_traits<Scalar>::type;
};
template <typename Lhs, typename Rhs>
struct inner_product_assert {
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Lhs)
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Rhs)
EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Lhs, Rhs)
#ifndef EIGEN_NO_DEBUG
static EIGEN_DEVICE_FUNC void run(const Lhs& lhs, const Rhs& rhs) {
eigen_assert((lhs.size() == rhs.size()) && "Inner product: lhs and rhs vectors must have same size");
}
#else
static EIGEN_DEVICE_FUNC void run(const Lhs&, const Rhs&) {}
#endif
};
template <typename Func, typename Lhs, typename Rhs>
struct inner_product_evaluator {
static constexpr int LhsFlags = evaluator<Lhs>::Flags;
static constexpr int RhsFlags = evaluator<Rhs>::Flags;
static constexpr int SizeAtCompileTime = size_prefer_fixed(Lhs::SizeAtCompileTime, Rhs::SizeAtCompileTime);
static constexpr int MaxSizeAtCompileTime =
min_size_prefer_fixed(Lhs::MaxSizeAtCompileTime, Rhs::MaxSizeAtCompileTime);
static constexpr int LhsAlignment = evaluator<Lhs>::Alignment;
static constexpr int RhsAlignment = evaluator<Rhs>::Alignment;
using Scalar = typename Func::result_type;
using Packet = typename find_inner_product_packet<Scalar, SizeAtCompileTime>::type;
static constexpr bool Vectorize =
bool(LhsFlags & RhsFlags & PacketAccessBit) && Func::PacketAccess &&
((MaxSizeAtCompileTime == Dynamic) || (unpacket_traits<Packet>::size <= MaxSizeAtCompileTime));
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit inner_product_evaluator(const Lhs& lhs, const Rhs& rhs,
Func func = Func())
: m_func(func), m_lhs(lhs), m_rhs(rhs), m_size(lhs.size()) {
inner_product_assert<Lhs, Rhs>::run(lhs, rhs);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index size() const { return m_size.value(); }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(Index index) const {
return m_func.coeff(m_lhs.coeff(index), m_rhs.coeff(index));
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(const Scalar& value, Index index) const {
return m_func.coeff(value, m_lhs.coeff(index), m_rhs.coeff(index));
}
template <typename PacketType, int LhsMode = LhsAlignment, int RhsMode = RhsAlignment>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(Index index) const {
return m_func.packet(m_lhs.template packet<LhsMode, PacketType>(index),
m_rhs.template packet<RhsMode, PacketType>(index));
}
template <typename PacketType, int LhsMode = LhsAlignment, int RhsMode = RhsAlignment>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(const PacketType& value, Index index) const {
return m_func.packet(value, m_lhs.template packet<LhsMode, PacketType>(index),
m_rhs.template packet<RhsMode, PacketType>(index));
}
const Func m_func;
const evaluator<Lhs> m_lhs;
const evaluator<Rhs> m_rhs;
const variable_if_dynamic<Index, SizeAtCompileTime> m_size;
};
template <typename Evaluator, bool Vectorize = Evaluator::Vectorize>
struct inner_product_impl;
// scalar loop
template <typename Evaluator>
struct inner_product_impl<Evaluator, false> {
using Scalar = typename Evaluator::Scalar;
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar run(const Evaluator& eval) {
const Index size = eval.size();
if (size == 0) return Scalar(0);
Scalar result = eval.coeff(0);
for (Index k = 1; k < size; k++) {
result = eval.coeff(result, k);
}
return result;
}
};
// vector loop
template <typename Evaluator>
struct inner_product_impl<Evaluator, true> {
using UnsignedIndex = std::make_unsigned_t<Index>;
using Scalar = typename Evaluator::Scalar;
using Packet = typename Evaluator::Packet;
static constexpr int PacketSize = unpacket_traits<Packet>::size;
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar run(const Evaluator& eval) {
const UnsignedIndex size = static_cast<UnsignedIndex>(eval.size());
if (size < PacketSize) return inner_product_impl<Evaluator, false>::run(eval);
const UnsignedIndex packetEnd = numext::round_down(size, PacketSize);
const UnsignedIndex quadEnd = numext::round_down(size, 4 * PacketSize);
const UnsignedIndex numPackets = size / PacketSize;
const UnsignedIndex numRemPackets = (packetEnd - quadEnd) / PacketSize;
Packet presult0, presult1, presult2, presult3;
presult0 = eval.template packet<Packet>(0 * PacketSize);
if (numPackets >= 2) presult1 = eval.template packet<Packet>(1 * PacketSize);
if (numPackets >= 3) presult2 = eval.template packet<Packet>(2 * PacketSize);
if (numPackets >= 4) {
presult3 = eval.template packet<Packet>(3 * PacketSize);
for (UnsignedIndex k = 4 * PacketSize; k < quadEnd; k += 4 * PacketSize) {
presult0 = eval.packet(presult0, k + 0 * PacketSize);
presult1 = eval.packet(presult1, k + 1 * PacketSize);
presult2 = eval.packet(presult2, k + 2 * PacketSize);
presult3 = eval.packet(presult3, k + 3 * PacketSize);
}
if (numRemPackets >= 1) presult0 = eval.packet(presult0, quadEnd + 0 * PacketSize);
if (numRemPackets >= 2) presult1 = eval.packet(presult1, quadEnd + 1 * PacketSize);
if (numRemPackets == 3) presult2 = eval.packet(presult2, quadEnd + 2 * PacketSize);
presult2 = padd(presult2, presult3);
}
if (numPackets >= 3) presult1 = padd(presult1, presult2);
if (numPackets >= 2) presult0 = padd(presult0, presult1);
Scalar result = predux(presult0);
for (UnsignedIndex k = packetEnd; k < size; k++) {
result = eval.coeff(result, k);
}
return result;
}
};
template <typename Scalar, bool Conj>
struct conditional_conj;
template <typename Scalar>
struct conditional_conj<Scalar, true> {
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(const Scalar& a) { return numext::conj(a); }
template <typename Packet>
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packet(const Packet& a) {
return pconj(a);
}
};
template <typename Scalar>
struct conditional_conj<Scalar, false> {
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(const Scalar& a) { return a; }
template <typename Packet>
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packet(const Packet& a) {
return a;
}
};
template <typename LhsScalar, typename RhsScalar, bool Conj>
struct scalar_inner_product_op {
using result_type = typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType;
using conj_helper = conditional_conj<LhsScalar, Conj>;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type coeff(const LhsScalar& a, const RhsScalar& b) const {
return (conj_helper::coeff(a) * b);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type coeff(const result_type& accum, const LhsScalar& a,
const RhsScalar& b) const {
return (conj_helper::coeff(a) * b) + accum;
}
static constexpr bool PacketAccess = false;
};
template <typename Scalar, bool Conj>
struct scalar_inner_product_op<Scalar, Scalar, Conj> {
using result_type = Scalar;
using conj_helper = conditional_conj<Scalar, Conj>;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(const Scalar& a, const Scalar& b) const {
return pmul(conj_helper::coeff(a), b);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(const Scalar& accum, const Scalar& a, const Scalar& b) const {
return pmadd(conj_helper::coeff(a), b, accum);
}
template <typename Packet>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packet(const Packet& a, const Packet& b) const {
return pmul(conj_helper::packet(a), b);
}
template <typename Packet>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packet(const Packet& accum, const Packet& a, const Packet& b) const {
return pmadd(conj_helper::packet(a), b, accum);
}
static constexpr bool PacketAccess = packet_traits<Scalar>::HasMul && packet_traits<Scalar>::HasAdd;
};
template <typename Lhs, typename Rhs, bool Conj>
struct default_inner_product_impl {
using LhsScalar = typename traits<Lhs>::Scalar;
using RhsScalar = typename traits<Rhs>::Scalar;
using Op = scalar_inner_product_op<LhsScalar, RhsScalar, Conj>;
using Evaluator = inner_product_evaluator<Op, Lhs, Rhs>;
using result_type = typename Evaluator::Scalar;
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type run(const MatrixBase<Lhs>& a, const MatrixBase<Rhs>& b) {
Evaluator eval(a.derived(), b.derived(), Op());
return inner_product_impl<Evaluator>::run(eval);
}
};
template <typename Lhs, typename Rhs>
struct dot_impl : default_inner_product_impl<Lhs, Rhs, true> {};
} // namespace internal
} // namespace Eigen
#endif // EIGEN_INNER_PRODUCT_EVAL_H

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#ifndef EIGEN_CORE_MODULE_H
#error "Please include Eigen/Core instead of including headers inside the src directory directly."
#endif

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2014-2019 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_INVERSE_H
#define EIGEN_INVERSE_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
template <typename XprType, typename StorageKind>
class InverseImpl;
namespace internal {
template <typename XprType>
struct traits<Inverse<XprType> > : traits<typename XprType::PlainObject> {
typedef typename XprType::PlainObject PlainObject;
typedef traits<PlainObject> BaseTraits;
enum { Flags = BaseTraits::Flags & RowMajorBit };
};
} // end namespace internal
/** \class Inverse
*
* \brief Expression of the inverse of another expression
*
* \tparam XprType the type of the expression we are taking the inverse
*
* This class represents an abstract expression of A.inverse()
* and most of the time this is the only way it is used.
*
*/
template <typename XprType>
class Inverse : public InverseImpl<XprType, typename internal::traits<XprType>::StorageKind> {
public:
typedef typename XprType::StorageIndex StorageIndex;
typedef typename XprType::Scalar Scalar;
typedef typename internal::ref_selector<XprType>::type XprTypeNested;
typedef internal::remove_all_t<XprTypeNested> XprTypeNestedCleaned;
typedef typename internal::ref_selector<Inverse>::type Nested;
typedef internal::remove_all_t<XprType> NestedExpression;
explicit EIGEN_DEVICE_FUNC Inverse(const XprType& xpr) : m_xpr(xpr) {}
EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return m_xpr.cols(); }
EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return m_xpr.rows(); }
EIGEN_DEVICE_FUNC const XprTypeNestedCleaned& nestedExpression() const { return m_xpr; }
protected:
XprTypeNested m_xpr;
};
// Generic API dispatcher
template <typename XprType, typename StorageKind>
class InverseImpl : public internal::generic_xpr_base<Inverse<XprType> >::type {
public:
typedef typename internal::generic_xpr_base<Inverse<XprType> >::type Base;
typedef typename XprType::Scalar Scalar;
private:
Scalar coeff(Index row, Index col) const;
Scalar coeff(Index i) const;
};
namespace internal {
/** \internal
* \brief Default evaluator for Inverse expression.
*
* This default evaluator for Inverse expression simply evaluate the inverse into a temporary
* by a call to internal::call_assignment_no_alias.
* Therefore, inverse implementers only have to specialize Assignment<Dst,Inverse<...>, ...> for
* there own nested expression.
*
* \sa class Inverse
*/
template <typename ArgType>
struct unary_evaluator<Inverse<ArgType> > : public evaluator<typename Inverse<ArgType>::PlainObject> {
typedef Inverse<ArgType> InverseType;
typedef typename InverseType::PlainObject PlainObject;
typedef evaluator<PlainObject> Base;
enum { Flags = Base::Flags | EvalBeforeNestingBit };
EIGEN_DEVICE_FUNC unary_evaluator(const InverseType& inv_xpr) : m_result(inv_xpr.rows(), inv_xpr.cols()) {
internal::construct_at<Base>(this, m_result);
internal::call_assignment_no_alias(m_result, inv_xpr);
}
protected:
PlainObject m_result;
};
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_INVERSE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2007-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_MAP_H
#define EIGEN_MAP_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
template <typename PlainObjectType, int MapOptions, typename StrideType>
struct traits<Map<PlainObjectType, MapOptions, StrideType> > : public traits<PlainObjectType> {
typedef traits<PlainObjectType> TraitsBase;
enum {
PlainObjectTypeInnerSize = ((traits<PlainObjectType>::Flags & RowMajorBit) == RowMajorBit)
? PlainObjectType::ColsAtCompileTime
: PlainObjectType::RowsAtCompileTime,
InnerStrideAtCompileTime = StrideType::InnerStrideAtCompileTime == 0
? int(PlainObjectType::InnerStrideAtCompileTime)
: int(StrideType::InnerStrideAtCompileTime),
OuterStrideAtCompileTime = StrideType::OuterStrideAtCompileTime == 0
? (InnerStrideAtCompileTime == Dynamic || PlainObjectTypeInnerSize == Dynamic
? Dynamic
: int(InnerStrideAtCompileTime) * int(PlainObjectTypeInnerSize))
: int(StrideType::OuterStrideAtCompileTime),
Alignment = int(MapOptions) & int(AlignedMask),
Flags0 = TraitsBase::Flags & (~NestByRefBit),
Flags = is_lvalue<PlainObjectType>::value ? int(Flags0) : (int(Flags0) & ~LvalueBit)
};
private:
enum { Options }; // Expressions don't have Options
};
} // namespace internal
/** \class Map
* \ingroup Core_Module
*
* \brief A matrix or vector expression mapping an existing array of data.
*
* \tparam PlainObjectType the equivalent matrix type of the mapped data
* \tparam MapOptions specifies the pointer alignment in bytes. It can be: \c #Aligned128, \c #Aligned64, \c #Aligned32,
* \c #Aligned16, \c #Aligned8 or \c #Unaligned. The default is \c #Unaligned. \tparam StrideType optionally specifies
* strides. By default, Map assumes the memory layout of an ordinary, contiguous array. This can be overridden by
* specifying strides. The type passed here must be a specialization of the Stride template, see examples below.
*
* This class represents a matrix or vector expression mapping an existing array of data.
* It can be used to let Eigen interface without any overhead with non-Eigen data structures,
* such as plain C arrays or structures from other libraries. By default, it assumes that the
* data is laid out contiguously in memory. You can however override this by explicitly specifying
* inner and outer strides.
*
* Here's an example of simply mapping a contiguous array as a \ref TopicStorageOrders "column-major" matrix:
* \include Map_simple.cpp
* Output: \verbinclude Map_simple.out
*
* If you need to map non-contiguous arrays, you can do so by specifying strides:
*
* Here's an example of mapping an array as a vector, specifying an inner stride, that is, the pointer
* increment between two consecutive coefficients. Here, we're specifying the inner stride as a compile-time
* fixed value.
* \include Map_inner_stride.cpp
* Output: \verbinclude Map_inner_stride.out
*
* Here's an example of mapping an array while specifying an outer stride. Here, since we're mapping
* as a column-major matrix, 'outer stride' means the pointer increment between two consecutive columns.
* Here, we're specifying the outer stride as a runtime parameter. Note that here \c OuterStride<> is
* a short version of \c OuterStride<Dynamic> because the default template parameter of OuterStride
* is \c Dynamic
* \include Map_outer_stride.cpp
* Output: \verbinclude Map_outer_stride.out
*
* For more details and for an example of specifying both an inner and an outer stride, see class Stride.
*
* \b Tip: to change the array of data mapped by a Map object, you can use the C++
* placement new syntax:
*
* Example: \include Map_placement_new.cpp
* Output: \verbinclude Map_placement_new.out
*
* This class is the return type of PlainObjectBase::Map() but can also be used directly.
*
* \sa PlainObjectBase::Map(), \ref TopicStorageOrders
*/
template <typename PlainObjectType, int MapOptions, typename StrideType>
class Map : public MapBase<Map<PlainObjectType, MapOptions, StrideType> > {
public:
typedef MapBase<Map> Base;
EIGEN_DENSE_PUBLIC_INTERFACE(Map)
typedef typename Base::PointerType PointerType;
typedef PointerType PointerArgType;
EIGEN_DEVICE_FUNC inline PointerType cast_to_pointer_type(PointerArgType ptr) { return ptr; }
EIGEN_DEVICE_FUNC constexpr Index innerStride() const {
return StrideType::InnerStrideAtCompileTime != 0 ? m_stride.inner() : 1;
}
EIGEN_DEVICE_FUNC constexpr Index outerStride() const {
return StrideType::OuterStrideAtCompileTime != 0 ? m_stride.outer()
: internal::traits<Map>::OuterStrideAtCompileTime != Dynamic
? Index(internal::traits<Map>::OuterStrideAtCompileTime)
: IsVectorAtCompileTime ? (this->size() * innerStride())
: int(Flags) & RowMajorBit ? (this->cols() * innerStride())
: (this->rows() * innerStride());
}
/** Constructor in the fixed-size case.
*
* \param dataPtr pointer to the array to map
* \param stride optional Stride object, passing the strides.
*/
EIGEN_DEVICE_FUNC explicit inline Map(PointerArgType dataPtr, const StrideType& stride = StrideType())
: Base(cast_to_pointer_type(dataPtr)), m_stride(stride) {}
/** Constructor in the dynamic-size vector case.
*
* \param dataPtr pointer to the array to map
* \param size the size of the vector expression
* \param stride optional Stride object, passing the strides.
*/
EIGEN_DEVICE_FUNC inline Map(PointerArgType dataPtr, Index size, const StrideType& stride = StrideType())
: Base(cast_to_pointer_type(dataPtr), size), m_stride(stride) {}
/** Constructor in the dynamic-size matrix case.
*
* \param dataPtr pointer to the array to map
* \param rows the number of rows of the matrix expression
* \param cols the number of columns of the matrix expression
* \param stride optional Stride object, passing the strides.
*/
EIGEN_DEVICE_FUNC inline Map(PointerArgType dataPtr, Index rows, Index cols, const StrideType& stride = StrideType())
: Base(cast_to_pointer_type(dataPtr), rows, cols), m_stride(stride) {}
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Map)
protected:
StrideType m_stride;
};
} // end namespace Eigen
#endif // EIGEN_MAP_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2007-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_MAPBASE_H
#define EIGEN_MAPBASE_H
#define EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived) \
EIGEN_STATIC_ASSERT((int(internal::evaluator<Derived>::Flags) & LinearAccessBit) || Derived::IsVectorAtCompileTime, \
YOU_ARE_TRYING_TO_USE_AN_INDEX_BASED_ACCESSOR_ON_AN_EXPRESSION_THAT_DOES_NOT_SUPPORT_THAT)
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
/** \ingroup Core_Module
*
* \brief Base class for dense Map and Block expression with direct access
*
* This base class provides the const low-level accessors (e.g. coeff, coeffRef) of dense
* Map and Block objects with direct access.
* Typical users do not have to directly deal with this class.
*
* This class can be extended by through the macro plugin \c EIGEN_MAPBASE_PLUGIN.
* See \link TopicCustomizing_Plugins customizing Eigen \endlink for details.
*
* The \c Derived class has to provide the following two methods describing the memory layout:
* \code Index innerStride() const; \endcode
* \code Index outerStride() const; \endcode
*
* \sa class Map, class Block
*/
template <typename Derived>
class MapBase<Derived, ReadOnlyAccessors> : public internal::dense_xpr_base<Derived>::type {
public:
typedef typename internal::dense_xpr_base<Derived>::type Base;
enum {
RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
InnerStrideAtCompileTime = internal::traits<Derived>::InnerStrideAtCompileTime,
SizeAtCompileTime = Base::SizeAtCompileTime
};
typedef typename internal::traits<Derived>::StorageKind StorageKind;
typedef typename internal::traits<Derived>::Scalar Scalar;
typedef typename internal::packet_traits<Scalar>::type PacketScalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef std::conditional_t<bool(internal::is_lvalue<Derived>::value), Scalar*, const Scalar*> PointerType;
using Base::derived;
// using Base::RowsAtCompileTime;
// using Base::ColsAtCompileTime;
// using Base::SizeAtCompileTime;
using Base::Flags;
using Base::IsRowMajor;
using Base::IsVectorAtCompileTime;
using Base::MaxColsAtCompileTime;
using Base::MaxRowsAtCompileTime;
using Base::MaxSizeAtCompileTime;
using Base::coeff;
using Base::coeffRef;
using Base::cols;
using Base::eval;
using Base::lazyAssign;
using Base::rows;
using Base::size;
using Base::colStride;
using Base::innerStride;
using Base::outerStride;
using Base::rowStride;
// bug 217 - compile error on ICC 11.1
using Base::operator=;
typedef typename Base::CoeffReturnType CoeffReturnType;
/** \copydoc DenseBase::rows() */
EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return m_rows.value(); }
/** \copydoc DenseBase::cols() */
EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return m_cols.value(); }
/** Returns a pointer to the first coefficient of the matrix or vector.
*
* \note When addressing this data, make sure to honor the strides returned by innerStride() and outerStride().
*
* \sa innerStride(), outerStride()
*/
EIGEN_DEVICE_FUNC constexpr const Scalar* data() const { return m_data; }
/** \copydoc PlainObjectBase::coeff(Index,Index) const */
EIGEN_DEVICE_FUNC inline const Scalar& coeff(Index rowId, Index colId) const {
return m_data[colId * colStride() + rowId * rowStride()];
}
/** \copydoc PlainObjectBase::coeff(Index) const */
EIGEN_DEVICE_FUNC inline const Scalar& coeff(Index index) const {
EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
return m_data[index * innerStride()];
}
/** \copydoc PlainObjectBase::coeffRef(Index,Index) const */
EIGEN_DEVICE_FUNC inline const Scalar& coeffRef(Index rowId, Index colId) const {
return this->m_data[colId * colStride() + rowId * rowStride()];
}
/** \copydoc PlainObjectBase::coeffRef(Index) const */
EIGEN_DEVICE_FUNC inline const Scalar& coeffRef(Index index) const {
EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
return this->m_data[index * innerStride()];
}
/** \internal */
template <int LoadMode>
inline PacketScalar packet(Index rowId, Index colId) const {
return internal::ploadt<PacketScalar, LoadMode>(m_data + (colId * colStride() + rowId * rowStride()));
}
/** \internal */
template <int LoadMode>
inline PacketScalar packet(Index index) const {
EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
return internal::ploadt<PacketScalar, LoadMode>(m_data + index * innerStride());
}
/** \internal Constructor for fixed size matrices or vectors */
EIGEN_DEVICE_FUNC explicit inline MapBase(PointerType dataPtr)
: m_data(dataPtr), m_rows(RowsAtCompileTime), m_cols(ColsAtCompileTime) {
EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
checkSanity<Derived>();
}
/** \internal Constructor for dynamically sized vectors */
EIGEN_DEVICE_FUNC inline MapBase(PointerType dataPtr, Index vecSize)
: m_data(dataPtr),
m_rows(RowsAtCompileTime == Dynamic ? vecSize : Index(RowsAtCompileTime)),
m_cols(ColsAtCompileTime == Dynamic ? vecSize : Index(ColsAtCompileTime)) {
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
eigen_assert(vecSize >= 0);
eigen_assert(dataPtr == 0 || SizeAtCompileTime == Dynamic || SizeAtCompileTime == vecSize);
checkSanity<Derived>();
}
/** \internal Constructor for dynamically sized matrices */
EIGEN_DEVICE_FUNC inline MapBase(PointerType dataPtr, Index rows, Index cols)
: m_data(dataPtr), m_rows(rows), m_cols(cols) {
eigen_assert((dataPtr == 0) || (rows >= 0 && (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows) &&
cols >= 0 && (ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols)));
checkSanity<Derived>();
}
#ifdef EIGEN_MAPBASE_PLUGIN
#include EIGEN_MAPBASE_PLUGIN
#endif
protected:
EIGEN_DEFAULT_COPY_CONSTRUCTOR(MapBase)
EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(MapBase)
template <typename T>
EIGEN_DEVICE_FUNC void checkSanity(std::enable_if_t<(internal::traits<T>::Alignment > 0), void*> = 0) const {
// Temporary macro to allow scalars to not be properly aligned. This is while we sort out failures
// in TensorFlow Lite that are currently relying on this UB.
#ifndef EIGEN_ALLOW_UNALIGNED_SCALARS
// Pointer must be aligned to the Scalar type, otherwise we get UB.
eigen_assert((std::uintptr_t(m_data) % alignof(Scalar) == 0) && "data is not scalar-aligned");
#endif
#if EIGEN_MAX_ALIGN_BYTES > 0
// innerStride() is not set yet when this function is called, so we optimistically assume the lowest plausible
// value:
const Index minInnerStride = InnerStrideAtCompileTime == Dynamic ? 1 : Index(InnerStrideAtCompileTime);
EIGEN_ONLY_USED_FOR_DEBUG(minInnerStride);
eigen_assert((((std::uintptr_t(m_data) % internal::traits<Derived>::Alignment) == 0) ||
(cols() * rows() * minInnerStride * sizeof(Scalar)) < internal::traits<Derived>::Alignment) &&
"data is not aligned");
#endif
}
template <typename T>
EIGEN_DEVICE_FUNC void checkSanity(std::enable_if_t<internal::traits<T>::Alignment == 0, void*> = 0) const {
#ifndef EIGEN_ALLOW_UNALIGNED_SCALARS
// Pointer must be aligned to the Scalar type, otherwise we get UB.
eigen_assert((std::uintptr_t(m_data) % alignof(Scalar) == 0) && "data is not scalar-aligned");
#endif
}
PointerType m_data;
const internal::variable_if_dynamic<Index, RowsAtCompileTime> m_rows;
const internal::variable_if_dynamic<Index, ColsAtCompileTime> m_cols;
};
/** \ingroup Core_Module
*
* \brief Base class for non-const dense Map and Block expression with direct access
*
* This base class provides the non-const low-level accessors (e.g. coeff and coeffRef) of
* dense Map and Block objects with direct access.
* It inherits MapBase<Derived, ReadOnlyAccessors> which defines the const variant for reading specific entries.
*
* \sa class Map, class Block
*/
template <typename Derived>
class MapBase<Derived, WriteAccessors> : public MapBase<Derived, ReadOnlyAccessors> {
typedef MapBase<Derived, ReadOnlyAccessors> ReadOnlyMapBase;
public:
typedef MapBase<Derived, ReadOnlyAccessors> Base;
typedef typename Base::Scalar Scalar;
typedef typename Base::PacketScalar PacketScalar;
typedef typename Base::StorageIndex StorageIndex;
typedef typename Base::PointerType PointerType;
using Base::coeff;
using Base::coeffRef;
using Base::cols;
using Base::derived;
using Base::rows;
using Base::size;
using Base::colStride;
using Base::innerStride;
using Base::outerStride;
using Base::rowStride;
typedef std::conditional_t<internal::is_lvalue<Derived>::value, Scalar, const Scalar> ScalarWithConstIfNotLvalue;
EIGEN_DEVICE_FUNC constexpr const Scalar* data() const { return this->m_data; }
EIGEN_DEVICE_FUNC constexpr ScalarWithConstIfNotLvalue* data() {
return this->m_data;
} // no const-cast here so non-const-correct code will give a compile error
EIGEN_DEVICE_FUNC inline ScalarWithConstIfNotLvalue& coeffRef(Index row, Index col) {
return this->m_data[col * colStride() + row * rowStride()];
}
EIGEN_DEVICE_FUNC inline ScalarWithConstIfNotLvalue& coeffRef(Index index) {
EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
return this->m_data[index * innerStride()];
}
template <int StoreMode>
inline void writePacket(Index row, Index col, const PacketScalar& val) {
internal::pstoret<Scalar, PacketScalar, StoreMode>(this->m_data + (col * colStride() + row * rowStride()), val);
}
template <int StoreMode>
inline void writePacket(Index index, const PacketScalar& val) {
EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
internal::pstoret<Scalar, PacketScalar, StoreMode>(this->m_data + index * innerStride(), val);
}
EIGEN_DEVICE_FUNC explicit inline MapBase(PointerType dataPtr) : Base(dataPtr) {}
EIGEN_DEVICE_FUNC inline MapBase(PointerType dataPtr, Index vecSize) : Base(dataPtr, vecSize) {}
EIGEN_DEVICE_FUNC inline MapBase(PointerType dataPtr, Index rows, Index cols) : Base(dataPtr, rows, cols) {}
EIGEN_DEVICE_FUNC Derived& operator=(const MapBase& other) {
ReadOnlyMapBase::Base::operator=(other);
return derived();
}
// In theory we could simply refer to Base:Base::operator=, but MSVC does not like Base::Base,
// see bugs 821 and 920.
using ReadOnlyMapBase::Base::operator=;
protected:
EIGEN_DEFAULT_COPY_CONSTRUCTOR(MapBase)
EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(MapBase)
};
#undef EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS
} // end namespace Eigen
#endif // EIGEN_MAPBASE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2014 Pedro Gonnet (pedro.gonnet@gmail.com)
// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_MATHFUNCTIONSIMPL_H
#define EIGEN_MATHFUNCTIONSIMPL_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
/** \internal Fast reciprocal using Newton-Raphson's method.
Preconditions:
1. The starting guess provided in approx_a_recip must have at least half
the leading mantissa bits in the correct result, such that a single
Newton-Raphson step is sufficient to get within 1-2 ulps of the correct
result.
2. If a is zero, approx_a_recip must be infinite with the same sign as a.
3. If a is infinite, approx_a_recip must be zero with the same sign as a.
If the preconditions are satisfied, which they are for the _*_rcp_ps
instructions on x86, the result has a maximum relative error of 2 ulps,
and correctly handles reciprocals of zero, infinity, and NaN.
*/
template <typename Packet, int Steps>
struct generic_reciprocal_newton_step {
static_assert(Steps > 0, "Steps must be at least 1.");
EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Packet run(const Packet& a, const Packet& approx_a_recip) {
using Scalar = typename unpacket_traits<Packet>::type;
const Packet two = pset1<Packet>(Scalar(2));
// Refine the approximation using one Newton-Raphson step:
// x_{i} = x_{i-1} * (2 - a * x_{i-1})
const Packet x = generic_reciprocal_newton_step<Packet, Steps - 1>::run(a, approx_a_recip);
const Packet tmp = pnmadd(a, x, two);
// If tmp is NaN, it means that a is either +/-0 or +/-Inf.
// In this case return the approximation directly.
const Packet is_not_nan = pcmp_eq(tmp, tmp);
return pselect(is_not_nan, pmul(x, tmp), x);
}
};
template <typename Packet>
struct generic_reciprocal_newton_step<Packet, 0> {
EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Packet run(const Packet& /*unused*/, const Packet& approx_rsqrt) {
return approx_rsqrt;
}
};
/** \internal Fast reciprocal sqrt using Newton-Raphson's method.
Preconditions:
1. The starting guess provided in approx_a_recip must have at least half
the leading mantissa bits in the correct result, such that a single
Newton-Raphson step is sufficient to get within 1-2 ulps of the correct
result.
2. If a is zero, approx_a_recip must be infinite with the same sign as a.
3. If a is infinite, approx_a_recip must be zero with the same sign as a.
If the preconditions are satisfied, which they are for the _*_rcp_ps
instructions on x86, the result has a maximum relative error of 2 ulps,
and correctly handles zero, infinity, and NaN. Positive denormals are
treated as zero.
*/
template <typename Packet, int Steps>
struct generic_rsqrt_newton_step {
static_assert(Steps > 0, "Steps must be at least 1.");
using Scalar = typename unpacket_traits<Packet>::type;
EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Packet run(const Packet& a, const Packet& approx_rsqrt) {
const Scalar kMinusHalf = Scalar(-1) / Scalar(2);
const Packet cst_minus_half = pset1<Packet>(kMinusHalf);
const Packet cst_minus_one = pset1<Packet>(Scalar(-1));
Packet inv_sqrt = approx_rsqrt;
for (int step = 0; step < Steps; ++step) {
// Refine the approximation using one Newton-Raphson step:
// h_n = (x * inv_sqrt) * inv_sqrt - 1 (so that h_n is nearly 0).
// inv_sqrt = inv_sqrt - 0.5 * inv_sqrt * h_n
Packet r2 = pmul(a, inv_sqrt);
Packet half_r = pmul(inv_sqrt, cst_minus_half);
Packet h_n = pmadd(r2, inv_sqrt, cst_minus_one);
inv_sqrt = pmadd(half_r, h_n, inv_sqrt);
}
// If x is NaN, then either:
// 1) the input is NaN
// 2) zero and infinity were multiplied
// In either of these cases, return approx_rsqrt
return pselect(pisnan(inv_sqrt), approx_rsqrt, inv_sqrt);
}
};
template <typename Packet>
struct generic_rsqrt_newton_step<Packet, 0> {
EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Packet run(const Packet& /*unused*/, const Packet& approx_rsqrt) {
return approx_rsqrt;
}
};
/** \internal Fast sqrt using Newton-Raphson's method.
Preconditions:
1. The starting guess for the reciprocal sqrt provided in approx_rsqrt must
have at least half the leading mantissa bits in the correct result, such
that a single Newton-Raphson step is sufficient to get within 1-2 ulps of
the correct result.
2. If a is zero, approx_rsqrt must be infinite.
3. If a is infinite, approx_rsqrt must be zero.
If the preconditions are satisfied, which they are for the _*_rsqrt_ps
instructions on x86, the result has a maximum relative error of 2 ulps,
and correctly handles zero and infinity, and NaN. Positive denormal inputs
are treated as zero.
*/
template <typename Packet, int Steps = 1>
struct generic_sqrt_newton_step {
static_assert(Steps > 0, "Steps must be at least 1.");
EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Packet run(const Packet& a, const Packet& approx_rsqrt) {
using Scalar = typename unpacket_traits<Packet>::type;
const Packet one_point_five = pset1<Packet>(Scalar(1.5));
const Packet minus_half = pset1<Packet>(Scalar(-0.5));
// If a is inf or zero, return a directly.
const Packet inf_mask = pcmp_eq(a, pset1<Packet>(NumTraits<Scalar>::infinity()));
const Packet return_a = por(pcmp_eq(a, pzero(a)), inf_mask);
// Do a single step of Newton's iteration for reciprocal square root:
// x_{n+1} = x_n * (1.5 + (-0.5 * x_n) * (a * x_n))).
// The Newton's step is computed this way to avoid over/under-flows.
Packet rsqrt = pmul(approx_rsqrt, pmadd(pmul(minus_half, approx_rsqrt), pmul(a, approx_rsqrt), one_point_five));
for (int step = 1; step < Steps; ++step) {
rsqrt = pmul(rsqrt, pmadd(pmul(minus_half, rsqrt), pmul(a, rsqrt), one_point_five));
}
// Return sqrt(x) = x * rsqrt(x) for non-zero finite positive arguments.
// Return a itself for 0 or +inf, NaN for negative arguments.
return pselect(return_a, a, pmul(a, rsqrt));
}
};
template <typename RealScalar>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE RealScalar positive_real_hypot(const RealScalar& x, const RealScalar& y) {
// IEEE IEC 6059 special cases.
if ((numext::isinf)(x) || (numext::isinf)(y)) return NumTraits<RealScalar>::infinity();
if ((numext::isnan)(x) || (numext::isnan)(y)) return NumTraits<RealScalar>::quiet_NaN();
EIGEN_USING_STD(sqrt);
RealScalar p, qp;
p = numext::maxi(x, y);
if (numext::is_exactly_zero(p)) return RealScalar(0);
qp = numext::mini(y, x) / p;
return p * sqrt(RealScalar(1) + qp * qp);
}
template <typename Scalar>
struct hypot_impl {
typedef typename NumTraits<Scalar>::Real RealScalar;
static EIGEN_DEVICE_FUNC inline RealScalar run(const Scalar& x, const Scalar& y) {
EIGEN_USING_STD(abs);
return positive_real_hypot<RealScalar>(abs(x), abs(y));
}
};
// Generic complex sqrt implementation that correctly handles corner cases
// according to https://en.cppreference.com/w/cpp/numeric/complex/sqrt
template <typename ComplexT>
EIGEN_DEVICE_FUNC ComplexT complex_sqrt(const ComplexT& z) {
// Computes the principal sqrt of the input.
//
// For a complex square root of the number x + i*y. We want to find real
// numbers u and v such that
// (u + i*v)^2 = x + i*y <=>
// u^2 - v^2 + i*2*u*v = x + i*v.
// By equating the real and imaginary parts we get:
// u^2 - v^2 = x
// 2*u*v = y.
//
// For x >= 0, this has the numerically stable solution
// u = sqrt(0.5 * (x + sqrt(x^2 + y^2)))
// v = y / (2 * u)
// and for x < 0,
// v = sign(y) * sqrt(0.5 * (-x + sqrt(x^2 + y^2)))
// u = y / (2 * v)
//
// Letting w = sqrt(0.5 * (|x| + |z|)),
// if x == 0: u = w, v = sign(y) * w
// if x > 0: u = w, v = y / (2 * w)
// if x < 0: u = |y| / (2 * w), v = sign(y) * w
using T = typename NumTraits<ComplexT>::Real;
const T x = numext::real(z);
const T y = numext::imag(z);
const T zero = T(0);
const T w = numext::sqrt(T(0.5) * (numext::abs(x) + numext::hypot(x, y)));
return (numext::isinf)(y) ? ComplexT(NumTraits<T>::infinity(), y)
: numext::is_exactly_zero(x) ? ComplexT(w, y < zero ? -w : w)
: x > zero ? ComplexT(w, y / (2 * w))
: ComplexT(numext::abs(y) / (2 * w), y < zero ? -w : w);
}
// Generic complex rsqrt implementation.
template <typename ComplexT>
EIGEN_DEVICE_FUNC ComplexT complex_rsqrt(const ComplexT& z) {
// Computes the principal reciprocal sqrt of the input.
//
// For a complex reciprocal square root of the number z = x + i*y. We want to
// find real numbers u and v such that
// (u + i*v)^2 = 1 / (x + i*y) <=>
// u^2 - v^2 + i*2*u*v = x/|z|^2 - i*v/|z|^2.
// By equating the real and imaginary parts we get:
// u^2 - v^2 = x/|z|^2
// 2*u*v = y/|z|^2.
//
// For x >= 0, this has the numerically stable solution
// u = sqrt(0.5 * (x + |z|)) / |z|
// v = -y / (2 * u * |z|)
// and for x < 0,
// v = -sign(y) * sqrt(0.5 * (-x + |z|)) / |z|
// u = -y / (2 * v * |z|)
//
// Letting w = sqrt(0.5 * (|x| + |z|)),
// if x == 0: u = w / |z|, v = -sign(y) * w / |z|
// if x > 0: u = w / |z|, v = -y / (2 * w * |z|)
// if x < 0: u = |y| / (2 * w * |z|), v = -sign(y) * w / |z|
using T = typename NumTraits<ComplexT>::Real;
const T x = numext::real(z);
const T y = numext::imag(z);
const T zero = T(0);
const T abs_z = numext::hypot(x, y);
const T w = numext::sqrt(T(0.5) * (numext::abs(x) + abs_z));
const T woz = w / abs_z;
// Corner cases consistent with 1/sqrt(z) on gcc/clang.
return numext::is_exactly_zero(abs_z) ? ComplexT(NumTraits<T>::infinity(), NumTraits<T>::quiet_NaN())
: ((numext::isinf)(x) || (numext::isinf)(y)) ? ComplexT(zero, zero)
: numext::is_exactly_zero(x) ? ComplexT(woz, y < zero ? woz : -woz)
: x > zero ? ComplexT(woz, -y / (2 * w * abs_z))
: ComplexT(numext::abs(y) / (2 * w * abs_z), y < zero ? woz : -woz);
}
template <typename ComplexT>
EIGEN_DEVICE_FUNC ComplexT complex_log(const ComplexT& z) {
// Computes complex log.
using T = typename NumTraits<ComplexT>::Real;
T a = numext::abs(z);
EIGEN_USING_STD(atan2);
T b = atan2(z.imag(), z.real());
return ComplexT(numext::log(a), b);
}
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_MATHFUNCTIONSIMPL_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_MATRIX_H
#define EIGEN_MATRIX_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
template <typename Scalar_, int Rows_, int Cols_, int Options_, int MaxRows_, int MaxCols_>
struct traits<Matrix<Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_>> {
private:
constexpr static int size = internal::size_at_compile_time(Rows_, Cols_);
typedef typename find_best_packet<Scalar_, size>::type PacketScalar;
enum {
row_major_bit = Options_ & RowMajor ? RowMajorBit : 0,
is_dynamic_size_storage = MaxRows_ == Dynamic || MaxCols_ == Dynamic,
max_size = is_dynamic_size_storage ? Dynamic : MaxRows_ * MaxCols_,
default_alignment = compute_default_alignment<Scalar_, max_size>::value,
actual_alignment = ((Options_ & DontAlign) == 0) ? default_alignment : 0,
required_alignment = unpacket_traits<PacketScalar>::alignment,
packet_access_bit = (packet_traits<Scalar_>::Vectorizable &&
(EIGEN_UNALIGNED_VECTORIZE || (int(actual_alignment) >= int(required_alignment))))
? PacketAccessBit
: 0
};
public:
typedef Scalar_ Scalar;
typedef Dense StorageKind;
typedef Eigen::Index StorageIndex;
typedef MatrixXpr XprKind;
enum {
RowsAtCompileTime = Rows_,
ColsAtCompileTime = Cols_,
MaxRowsAtCompileTime = MaxRows_,
MaxColsAtCompileTime = MaxCols_,
Flags = compute_matrix_flags(Options_),
Options = Options_,
InnerStrideAtCompileTime = 1,
OuterStrideAtCompileTime = (int(Options) & int(RowMajor)) ? ColsAtCompileTime : RowsAtCompileTime,
// FIXME, the following flag in only used to define NeedsToAlign in PlainObjectBase
EvaluatorFlags = LinearAccessBit | DirectAccessBit | packet_access_bit | row_major_bit,
Alignment = actual_alignment
};
};
} // namespace internal
/** \class Matrix
* \ingroup Core_Module
*
* \brief The matrix class, also used for vectors and row-vectors
*
* The %Matrix class is the work-horse for all \em dense (\ref dense "note") matrices and vectors within Eigen.
* Vectors are matrices with one column, and row-vectors are matrices with one row.
*
* The %Matrix class encompasses \em both fixed-size and dynamic-size objects (\ref fixedsize "note").
*
* The first three template parameters are required:
* \tparam Scalar_ Numeric type, e.g. float, double, int or std::complex<float>.
* User defined scalar types are supported as well (see \ref user_defined_scalars "here").
* \tparam Rows_ Number of rows, or \b Dynamic
* \tparam Cols_ Number of columns, or \b Dynamic
*
* The remaining template parameters are optional -- in most cases you don't have to worry about them.
* \tparam Options_ A combination of either \b #RowMajor or \b #ColMajor, and of either
* \b #AutoAlign or \b #DontAlign.
* The former controls \ref TopicStorageOrders "storage order", and defaults to column-major. The latter
* controls alignment, which is required for vectorization. It defaults to aligning matrices except for fixed sizes that
* aren't a multiple of the packet size. \tparam MaxRows_ Maximum number of rows. Defaults to \a Rows_ (\ref maxrows
* "note"). \tparam MaxCols_ Maximum number of columns. Defaults to \a Cols_ (\ref maxrows "note").
*
* Eigen provides a number of typedefs covering the usual cases. Here are some examples:
*
* \li \c Matrix2d is a 2x2 square matrix of doubles (\c Matrix<double, 2, 2>)
* \li \c Vector4f is a vector of 4 floats (\c Matrix<float, 4, 1>)
* \li \c RowVector3i is a row-vector of 3 ints (\c Matrix<int, 1, 3>)
*
* \li \c MatrixXf is a dynamic-size matrix of floats (\c Matrix<float, Dynamic, Dynamic>)
* \li \c VectorXf is a dynamic-size vector of floats (\c Matrix<float, Dynamic, 1>)
*
* \li \c Matrix2Xf is a partially fixed-size (dynamic-size) matrix of floats (\c Matrix<float, 2, Dynamic>)
* \li \c MatrixX3d is a partially dynamic-size (fixed-size) matrix of double (\c Matrix<double, Dynamic, 3>)
*
* See \link matrixtypedefs this page \endlink for a complete list of predefined \em %Matrix and \em Vector typedefs.
*
* You can access elements of vectors and matrices using normal subscripting:
*
* \code
* Eigen::VectorXd v(10);
* v[0] = 0.1;
* v[1] = 0.2;
* v(0) = 0.3;
* v(1) = 0.4;
*
* Eigen::MatrixXi m(10, 10);
* m(0, 1) = 1;
* m(0, 2) = 2;
* m(0, 3) = 3;
* \endcode
*
* This class can be extended with the help of the plugin mechanism described on the page
* \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_MATRIX_PLUGIN.
*
* <i><b>Some notes:</b></i>
*
* <dl>
* <dt><b>\anchor dense Dense versus sparse:</b></dt>
* <dd>This %Matrix class handles dense, not sparse matrices and vectors. For sparse matrices and vectors, see the
* Sparse module.
*
* Dense matrices and vectors are plain usual arrays of coefficients. All the coefficients are stored, in an ordinary
* contiguous array. This is unlike Sparse matrices and vectors where the coefficients are stored as a list of nonzero
* coefficients.</dd>
*
* <dt><b>\anchor fixedsize Fixed-size versus dynamic-size:</b></dt>
* <dd>Fixed-size means that the numbers of rows and columns are known at compile-time. In this case, Eigen allocates
* the array of coefficients as a fixed-size array, as a class member. This makes sense for very small matrices,
* typically up to 4x4, sometimes up to 16x16. Larger matrices should be declared as dynamic-size even if one happens to
* know their size at compile-time.
*
* Dynamic-size means that the numbers of rows or columns are not necessarily known at compile-time. In this case they
* are runtime variables, and the array of coefficients is allocated dynamically on the heap.
*
* Note that \em dense matrices, be they Fixed-size or Dynamic-size, <em>do not</em> expand dynamically in the sense of
* a std::map. If you want this behavior, see the Sparse module.</dd>
*
* <dt><b>\anchor maxrows MaxRows_ and MaxCols_:</b></dt>
* <dd>In most cases, one just leaves these parameters to the default values.
* These parameters mean the maximum size of rows and columns that the matrix may have. They are useful in cases
* when the exact numbers of rows and columns are not known at compile-time, but it is known at compile-time that they
* cannot exceed a certain value. This happens when taking dynamic-size blocks inside fixed-size matrices: in this case
* MaxRows_ and MaxCols_ are the dimensions of the original matrix, while Rows_ and Cols_ are Dynamic.</dd>
* </dl>
*
* <i><b>ABI and storage layout</b></i>
*
* The table below summarizes the ABI of some possible Matrix instances which is fixed thorough the lifetime of Eigen 3.
* <table class="manual">
* <tr><th>Matrix type</th><th>Equivalent C structure</th></tr>
* <tr><td>\code Matrix<T,Dynamic,Dynamic> \endcode</td><td>\code
* struct {
* T *data; // with (size_t(data)%EIGEN_MAX_ALIGN_BYTES)==0
* Eigen::Index rows, cols;
* };
* \endcode</td></tr>
* <tr class="alt"><td>\code
* Matrix<T,Dynamic,1>
* Matrix<T,1,Dynamic> \endcode</td><td>\code
* struct {
* T *data; // with (size_t(data)%EIGEN_MAX_ALIGN_BYTES)==0
* Eigen::Index size;
* };
* \endcode</td></tr>
* <tr><td>\code Matrix<T,Rows,Cols> \endcode</td><td>\code
* struct {
* T data[Rows*Cols]; // with (size_t(data)%A(Rows*Cols*sizeof(T)))==0
* };
* \endcode</td></tr>
* <tr class="alt"><td>\code Matrix<T,Dynamic,Dynamic,0,MaxRows,MaxCols> \endcode</td><td>\code
* struct {
* T data[MaxRows*MaxCols]; // with (size_t(data)%A(MaxRows*MaxCols*sizeof(T)))==0
* Eigen::Index rows, cols;
* };
* \endcode</td></tr>
* </table>
* Note that in this table Rows, Cols, MaxRows and MaxCols are all positive integers. A(S) is defined to the largest
* possible power-of-two smaller to EIGEN_MAX_STATIC_ALIGN_BYTES.
*
* \see MatrixBase for the majority of the API methods for matrices, \ref TopicClassHierarchy,
* \ref TopicStorageOrders
*/
template <typename Scalar_, int Rows_, int Cols_, int Options_, int MaxRows_, int MaxCols_>
class Matrix : public PlainObjectBase<Matrix<Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_>> {
public:
/** \brief Base class typedef.
* \sa PlainObjectBase
*/
typedef PlainObjectBase<Matrix> Base;
enum { Options = Options_ };
EIGEN_DENSE_PUBLIC_INTERFACE(Matrix)
typedef typename Base::PlainObject PlainObject;
using Base::base;
using Base::coeffRef;
/**
* \brief Assigns matrices to each other.
*
* \note This is a special case of the templated operator=. Its purpose is
* to prevent a default operator= from hiding the templated operator=.
*
* \callgraph
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Matrix& operator=(const Matrix& other) { return Base::_set(other); }
/** \internal
* \brief Copies the value of the expression \a other into \c *this with automatic resizing.
*
* *this might be resized to match the dimensions of \a other. If *this was a null matrix (not already initialized),
* it will be initialized.
*
* Note that copying a row-vector into a vector (and conversely) is allowed.
* The resizing, if any, is then done in the appropriate way so that row-vectors
* remain row-vectors and vectors remain vectors.
*/
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Matrix& operator=(const DenseBase<OtherDerived>& other) {
return Base::_set(other);
}
/**
* \brief Copies the generic expression \a other into *this.
* \copydetails DenseBase::operator=(const EigenBase<OtherDerived> &other)
*/
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Matrix& operator=(const EigenBase<OtherDerived>& other) {
return Base::operator=(other);
}
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Matrix& operator=(const ReturnByValue<OtherDerived>& func) {
return Base::operator=(func);
}
/** \brief Default constructor.
*
* For fixed-size matrices, does nothing.
*
* For dynamic-size matrices, creates an empty matrix of size 0. Does not allocate any array. Such a matrix
* is called a null matrix. This constructor is the unique way to create null matrices: resizing
* a matrix to 0 is not supported.
*
* \sa resize(Index,Index)
*/
#if defined(EIGEN_INITIALIZE_COEFFS)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Matrix() { EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED }
#else
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Matrix() = default;
#endif
/** \brief Move constructor */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Matrix(Matrix&&) = default;
/** \brief Moves the matrix into the other one.
*
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Matrix& operator=(Matrix&& other) noexcept(
std::is_nothrow_move_assignable<Scalar>::value) {
Base::operator=(std::move(other));
return *this;
}
/** \brief Construct a row of column vector with fixed size from an arbitrary number of coefficients.
*
* \only_for_vectors
*
* This constructor is for 1D array or vectors with more than 4 coefficients.
*
* \warning To construct a column (resp. row) vector of fixed length, the number of values passed to this
* constructor must match the the fixed number of rows (resp. columns) of \c *this.
*
*
* Example: \include Matrix_variadic_ctor_cxx11.cpp
* Output: \verbinclude Matrix_variadic_ctor_cxx11.out
*
* \sa Matrix(const std::initializer_list<std::initializer_list<Scalar>>&)
*/
template <typename... ArgTypes>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Matrix(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3,
const ArgTypes&... args)
: Base(a0, a1, a2, a3, args...) {}
/** \brief Constructs a Matrix and initializes it from the coefficients given as initializer-lists grouped by row.
* \cpp11
* \anchor matrix_initializer_list
*
* In the general case, the constructor takes a list of rows, each row being represented as a list of coefficients:
*
* Example: \include Matrix_initializer_list_23_cxx11.cpp
* Output: \verbinclude Matrix_initializer_list_23_cxx11.out
*
* Each of the inner initializer lists must contain the exact same number of elements, otherwise an assertion is
* triggered.
*
* In the case of a compile-time column vector, implicit transposition from a single row is allowed.
* Therefore <code>VectorXd{{1,2,3,4,5}}</code> is legal and the more verbose syntax
* <code>RowVectorXd{{1},{2},{3},{4},{5}}</code> can be avoided:
*
* Example: \include Matrix_initializer_list_vector_cxx11.cpp
* Output: \verbinclude Matrix_initializer_list_vector_cxx11.out
*
* In the case of fixed-sized matrices, the initializer list sizes must exactly match the matrix sizes,
* and implicit transposition is allowed for compile-time vectors only.
*
* \sa Matrix(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args)
*/
EIGEN_DEVICE_FUNC explicit constexpr EIGEN_STRONG_INLINE Matrix(
const std::initializer_list<std::initializer_list<Scalar>>& list)
: Base(list) {}
#ifndef EIGEN_PARSED_BY_DOXYGEN
// This constructor is for both 1x1 matrices and dynamic vectors
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit Matrix(const T& x) {
Base::template _init1<T>(x);
}
template <typename T0, typename T1>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Matrix(const T0& x, const T1& y) {
Base::template _init2<T0, T1>(x, y);
}
#else
/** \brief Constructs a fixed-sized matrix initialized with coefficients starting at \a data */
EIGEN_DEVICE_FUNC explicit Matrix(const Scalar* data);
/** \brief Constructs a vector or row-vector with given dimension. \only_for_vectors
*
* This is useful for dynamic-size vectors. For fixed-size vectors,
* it is redundant to pass these parameters, so one should use the default constructor
* Matrix() instead.
*
* \warning This constructor is disabled for fixed-size \c 1x1 matrices. For instance,
* calling Matrix<double,1,1>(1) will call the initialization constructor: Matrix(const Scalar&).
* For fixed-size \c 1x1 matrices it is therefore recommended to use the default
* constructor Matrix() instead, especially when using one of the non standard
* \c EIGEN_INITIALIZE_MATRICES_BY_{ZERO,\c NAN} macros (see \ref TopicPreprocessorDirectives).
*/
EIGEN_STRONG_INLINE explicit Matrix(Index dim);
/** \brief Constructs an initialized 1x1 matrix with the given coefficient
* \sa Matrix(const Scalar&, const Scalar&, const Scalar&, const Scalar&, const ArgTypes&...) */
Matrix(const Scalar& x);
/** \brief Constructs an uninitialized matrix with \a rows rows and \a cols columns.
*
* This is useful for dynamic-size matrices. For fixed-size matrices,
* it is redundant to pass these parameters, so one should use the default constructor
* Matrix() instead.
*
* \warning This constructor is disabled for fixed-size \c 1x2 and \c 2x1 vectors. For instance,
* calling Matrix2f(2,1) will call the initialization constructor: Matrix(const Scalar& x, const Scalar& y).
* For fixed-size \c 1x2 or \c 2x1 vectors it is therefore recommended to use the default
* constructor Matrix() instead, especially when using one of the non standard
* \c EIGEN_INITIALIZE_MATRICES_BY_{ZERO,\c NAN} macros (see \ref TopicPreprocessorDirectives).
*/
EIGEN_DEVICE_FUNC Matrix(Index rows, Index cols);
/** \brief Constructs an initialized 2D vector with given coefficients
* \sa Matrix(const Scalar&, const Scalar&, const Scalar&, const Scalar&, const ArgTypes&...) */
Matrix(const Scalar& x, const Scalar& y);
#endif // end EIGEN_PARSED_BY_DOXYGEN
/** \brief Constructs an initialized 3D vector with given coefficients
* \sa Matrix(const Scalar&, const Scalar&, const Scalar&, const Scalar&, const ArgTypes&...)
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Matrix(const Scalar& x, const Scalar& y, const Scalar& z) {
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Matrix, 3)
m_storage.data()[0] = x;
m_storage.data()[1] = y;
m_storage.data()[2] = z;
}
/** \brief Constructs an initialized 4D vector with given coefficients
* \sa Matrix(const Scalar&, const Scalar&, const Scalar&, const Scalar&, const ArgTypes&...)
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Matrix(const Scalar& x, const Scalar& y, const Scalar& z, const Scalar& w) {
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Matrix, 4)
m_storage.data()[0] = x;
m_storage.data()[1] = y;
m_storage.data()[2] = z;
m_storage.data()[3] = w;
}
/** \brief Copy constructor */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Matrix(const Matrix&) = default;
/** \brief Copy constructor for generic expressions.
* \sa MatrixBase::operator=(const EigenBase<OtherDerived>&)
*/
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Matrix(const EigenBase<OtherDerived>& other) : Base(other.derived()) {}
EIGEN_DEVICE_FUNC constexpr Index innerStride() const noexcept { return 1; }
EIGEN_DEVICE_FUNC constexpr Index outerStride() const noexcept { return this->innerSize(); }
/////////// Geometry module ///////////
template <typename OtherDerived>
EIGEN_DEVICE_FUNC explicit Matrix(const RotationBase<OtherDerived, ColsAtCompileTime>& r);
template <typename OtherDerived>
EIGEN_DEVICE_FUNC Matrix& operator=(const RotationBase<OtherDerived, ColsAtCompileTime>& r);
// allow to extend Matrix outside Eigen
#ifdef EIGEN_MATRIX_PLUGIN
#include EIGEN_MATRIX_PLUGIN
#endif
protected:
template <typename Derived, typename OtherDerived, bool IsVector>
friend struct internal::conservative_resize_like_impl;
using Base::m_storage;
};
/** \defgroup matrixtypedefs Global matrix typedefs
*
* \ingroup Core_Module
*
* %Eigen defines several typedef shortcuts for most common matrix and vector types.
*
* The general patterns are the following:
*
* \c MatrixSizeType where \c Size can be \c 2,\c 3,\c 4 for fixed size square matrices or \c X for dynamic size,
* and where \c Type can be \c i for integer, \c f for float, \c d for double, \c cf for complex float, \c cd
* for complex double.
*
* For example, \c Matrix3d is a fixed-size 3x3 matrix type of doubles, and \c MatrixXf is a dynamic-size matrix of
* floats.
*
* There are also \c VectorSizeType and \c RowVectorSizeType which are self-explanatory. For example, \c Vector4cf is
* a fixed-size vector of 4 complex floats.
*
* With \cpp11, template alias are also defined for common sizes.
* They follow the same pattern as above except that the scalar type suffix is replaced by a
* template parameter, i.e.:
* - `MatrixSize<Type>` where `Size` can be \c 2,\c 3,\c 4 for fixed size square matrices or \c X for dynamic size.
* - `MatrixXSize<Type>` and `MatrixSizeX<Type>` where `Size` can be \c 2,\c 3,\c 4 for hybrid dynamic/fixed matrices.
* - `VectorSize<Type>` and `RowVectorSize<Type>` for column and row vectors.
*
* With \cpp11, you can also use fully generic column and row vector types: `Vector<Type,Size>` and
* `RowVector<Type,Size>`.
*
* \sa class Matrix
*/
#define EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix) \
/** \ingroup matrixtypedefs */ \
/** \brief `Size`&times;`Size` matrix of type `Type`. */ \
typedef Matrix<Type, Size, Size> Matrix##SizeSuffix##TypeSuffix; \
/** \ingroup matrixtypedefs */ \
/** \brief `Size`&times;`1` vector of type `Type`. */ \
typedef Matrix<Type, Size, 1> Vector##SizeSuffix##TypeSuffix; \
/** \ingroup matrixtypedefs */ \
/** \brief `1`&times;`Size` vector of type `Type`. */ \
typedef Matrix<Type, 1, Size> RowVector##SizeSuffix##TypeSuffix;
#define EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, Size) \
/** \ingroup matrixtypedefs */ \
/** \brief `Size`&times;`Dynamic` matrix of type `Type`. */ \
typedef Matrix<Type, Size, Dynamic> Matrix##Size##X##TypeSuffix; \
/** \ingroup matrixtypedefs */ \
/** \brief `Dynamic`&times;`Size` matrix of type `Type`. */ \
typedef Matrix<Type, Dynamic, Size> Matrix##X##Size##TypeSuffix;
#define EIGEN_MAKE_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \
EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 2, 2) \
EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 3, 3) \
EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 4, 4) \
EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X) \
EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 2) \
EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 3) \
EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 4)
EIGEN_MAKE_TYPEDEFS_ALL_SIZES(int, i)
EIGEN_MAKE_TYPEDEFS_ALL_SIZES(float, f)
EIGEN_MAKE_TYPEDEFS_ALL_SIZES(double, d)
EIGEN_MAKE_TYPEDEFS_ALL_SIZES(std::complex<float>, cf)
EIGEN_MAKE_TYPEDEFS_ALL_SIZES(std::complex<double>, cd)
#undef EIGEN_MAKE_TYPEDEFS_ALL_SIZES
#undef EIGEN_MAKE_TYPEDEFS
#undef EIGEN_MAKE_FIXED_TYPEDEFS
#define EIGEN_MAKE_TYPEDEFS(Size, SizeSuffix) \
/** \ingroup matrixtypedefs */ \
/** \brief \cpp11 `Size`&times;`Size` matrix of type `Type`.*/ \
template <typename Type> \
using Matrix##SizeSuffix = Matrix<Type, Size, Size>; \
/** \ingroup matrixtypedefs */ \
/** \brief \cpp11 `Size`&times;`1` vector of type `Type`.*/ \
template <typename Type> \
using Vector##SizeSuffix = Matrix<Type, Size, 1>; \
/** \ingroup matrixtypedefs */ \
/** \brief \cpp11 `1`&times;`Size` vector of type `Type`.*/ \
template <typename Type> \
using RowVector##SizeSuffix = Matrix<Type, 1, Size>;
#define EIGEN_MAKE_FIXED_TYPEDEFS(Size) \
/** \ingroup matrixtypedefs */ \
/** \brief \cpp11 `Size`&times;`Dynamic` matrix of type `Type` */ \
template <typename Type> \
using Matrix##Size##X = Matrix<Type, Size, Dynamic>; \
/** \ingroup matrixtypedefs */ \
/** \brief \cpp11 `Dynamic`&times;`Size` matrix of type `Type`. */ \
template <typename Type> \
using Matrix##X##Size = Matrix<Type, Dynamic, Size>;
EIGEN_MAKE_TYPEDEFS(2, 2)
EIGEN_MAKE_TYPEDEFS(3, 3)
EIGEN_MAKE_TYPEDEFS(4, 4)
EIGEN_MAKE_TYPEDEFS(Dynamic, X)
EIGEN_MAKE_FIXED_TYPEDEFS(2)
EIGEN_MAKE_FIXED_TYPEDEFS(3)
EIGEN_MAKE_FIXED_TYPEDEFS(4)
/** \ingroup matrixtypedefs
* \brief \cpp11 `Size`&times;`1` vector of type `Type`. */
template <typename Type, int Size>
using Vector = Matrix<Type, Size, 1>;
/** \ingroup matrixtypedefs
* \brief \cpp11 `1`&times;`Size` vector of type `Type`. */
template <typename Type, int Size>
using RowVector = Matrix<Type, 1, Size>;
#undef EIGEN_MAKE_TYPEDEFS
#undef EIGEN_MAKE_FIXED_TYPEDEFS
} // end namespace Eigen
#endif // EIGEN_MATRIX_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_MATRIXBASE_H
#define EIGEN_MATRIXBASE_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
/** \class MatrixBase
* \ingroup Core_Module
*
* \brief Base class for all dense matrices, vectors, and expressions
*
* This class is the base that is inherited by all matrix, vector, and related expression
* types. Most of the Eigen API is contained in this class, and its base classes. Other important
* classes for the Eigen API are Matrix, and VectorwiseOp.
*
* Note that some methods are defined in other modules such as the \ref LU_Module LU module
* for all functions related to matrix inversions.
*
* \tparam Derived is the derived type, e.g. a matrix type, or an expression, etc.
*
* When writing a function taking Eigen objects as argument, if you want your function
* to take as argument any matrix, vector, or expression, just let it take a
* MatrixBase argument. As an example, here is a function printFirstRow which, given
* a matrix, vector, or expression \a x, prints the first row of \a x.
*
* \code
template<typename Derived>
void printFirstRow(const Eigen::MatrixBase<Derived>& x)
{
cout << x.row(0) << endl;
}
* \endcode
*
* This class can be extended with the help of the plugin mechanism described on the page
* \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_MATRIXBASE_PLUGIN.
*
* \sa \blank \ref TopicClassHierarchy
*/
template <typename Derived>
class MatrixBase : public DenseBase<Derived> {
public:
#ifndef EIGEN_PARSED_BY_DOXYGEN
typedef MatrixBase StorageBaseType;
typedef typename internal::traits<Derived>::StorageKind StorageKind;
typedef typename internal::traits<Derived>::StorageIndex StorageIndex;
typedef typename internal::traits<Derived>::Scalar Scalar;
typedef typename internal::packet_traits<Scalar>::type PacketScalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef DenseBase<Derived> Base;
using Base::ColsAtCompileTime;
using Base::Flags;
using Base::IsVectorAtCompileTime;
using Base::MaxColsAtCompileTime;
using Base::MaxRowsAtCompileTime;
using Base::MaxSizeAtCompileTime;
using Base::RowsAtCompileTime;
using Base::SizeAtCompileTime;
using Base::coeff;
using Base::coeffRef;
using Base::cols;
using Base::const_cast_derived;
using Base::derived;
using Base::eval;
using Base::lazyAssign;
using Base::rows;
using Base::size;
using Base::operator-;
using Base::operator+=;
using Base::operator-=;
using Base::operator*=;
using Base::operator/=;
typedef typename Base::CoeffReturnType CoeffReturnType;
typedef typename Base::ConstTransposeReturnType ConstTransposeReturnType;
typedef typename Base::RowXpr RowXpr;
typedef typename Base::ColXpr ColXpr;
#endif // not EIGEN_PARSED_BY_DOXYGEN
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** type of the equivalent square matrix */
typedef Matrix<Scalar, internal::max_size_prefer_dynamic(RowsAtCompileTime, ColsAtCompileTime),
internal::max_size_prefer_dynamic(RowsAtCompileTime, ColsAtCompileTime)>
SquareMatrixType;
#endif // not EIGEN_PARSED_BY_DOXYGEN
/** \returns the size of the main diagonal, which is min(rows(),cols()).
* \sa rows(), cols(), SizeAtCompileTime. */
EIGEN_DEVICE_FUNC inline Index diagonalSize() const { return (numext::mini)(rows(), cols()); }
typedef typename Base::PlainObject PlainObject;
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** \internal Represents a matrix with all coefficients equal to one another*/
typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject> ConstantReturnType;
/** \internal the return type of MatrixBase::adjoint() */
typedef std::conditional_t<NumTraits<Scalar>::IsComplex,
CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, ConstTransposeReturnType>,
ConstTransposeReturnType>
AdjointReturnType;
/** \internal Return type of eigenvalues() */
typedef Matrix<internal::make_complex_t<Scalar>, internal::traits<Derived>::ColsAtCompileTime, 1, ColMajor>
EigenvaluesReturnType;
/** \internal the return type of identity */
typedef CwiseNullaryOp<internal::scalar_identity_op<Scalar>, PlainObject> IdentityReturnType;
/** \internal the return type of unit vectors */
typedef Block<const CwiseNullaryOp<internal::scalar_identity_op<Scalar>, SquareMatrixType>,
internal::traits<Derived>::RowsAtCompileTime, internal::traits<Derived>::ColsAtCompileTime>
BasisReturnType;
#endif // not EIGEN_PARSED_BY_DOXYGEN
#define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::MatrixBase
#define EIGEN_DOC_UNARY_ADDONS(X, Y)
#include "../plugins/CommonCwiseBinaryOps.inc"
#include "../plugins/MatrixCwiseUnaryOps.inc"
#include "../plugins/MatrixCwiseBinaryOps.inc"
#ifdef EIGEN_MATRIXBASE_PLUGIN
#include EIGEN_MATRIXBASE_PLUGIN
#endif
#undef EIGEN_CURRENT_STORAGE_BASE_CLASS
#undef EIGEN_DOC_UNARY_ADDONS
/** Special case of the template operator=, in order to prevent the compiler
* from generating a default operator= (issue hit with g++ 4.1)
*/
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const MatrixBase& other);
// We cannot inherit here via Base::operator= since it is causing
// trouble with MSVC.
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const DenseBase<OtherDerived>& other);
template <typename OtherDerived>
EIGEN_DEVICE_FUNC Derived& operator=(const EigenBase<OtherDerived>& other);
template <typename OtherDerived>
EIGEN_DEVICE_FUNC Derived& operator=(const ReturnByValue<OtherDerived>& other);
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator+=(const MatrixBase<OtherDerived>& other);
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator-=(const MatrixBase<OtherDerived>& other);
template <typename OtherDerived>
EIGEN_DEVICE_FUNC const Product<Derived, OtherDerived> operator*(const MatrixBase<OtherDerived>& other) const;
template <typename OtherDerived>
EIGEN_DEVICE_FUNC const Product<Derived, OtherDerived, LazyProduct> lazyProduct(
const MatrixBase<OtherDerived>& other) const;
template <typename OtherDerived>
Derived& operator*=(const EigenBase<OtherDerived>& other);
template <typename OtherDerived>
void applyOnTheLeft(const EigenBase<OtherDerived>& other);
template <typename OtherDerived>
void applyOnTheRight(const EigenBase<OtherDerived>& other);
template <typename DiagonalDerived>
EIGEN_DEVICE_FUNC const Product<Derived, DiagonalDerived, LazyProduct> operator*(
const DiagonalBase<DiagonalDerived>& diagonal) const;
template <typename SkewDerived>
EIGEN_DEVICE_FUNC const Product<Derived, SkewDerived, LazyProduct> operator*(
const SkewSymmetricBase<SkewDerived>& skew) const;
template <typename OtherDerived>
EIGEN_DEVICE_FUNC typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,
typename internal::traits<OtherDerived>::Scalar>::ReturnType
dot(const MatrixBase<OtherDerived>& other) const;
EIGEN_DEVICE_FUNC RealScalar squaredNorm() const;
EIGEN_DEVICE_FUNC RealScalar norm() const;
RealScalar stableNorm() const;
RealScalar blueNorm() const;
RealScalar hypotNorm() const;
EIGEN_DEVICE_FUNC const PlainObject normalized() const;
EIGEN_DEVICE_FUNC const PlainObject stableNormalized() const;
EIGEN_DEVICE_FUNC void normalize();
EIGEN_DEVICE_FUNC void stableNormalize();
EIGEN_DEVICE_FUNC const AdjointReturnType adjoint() const;
EIGEN_DEVICE_FUNC void adjointInPlace();
typedef Diagonal<Derived> DiagonalReturnType;
EIGEN_DEVICE_FUNC DiagonalReturnType diagonal();
typedef Diagonal<const Derived> ConstDiagonalReturnType;
EIGEN_DEVICE_FUNC const ConstDiagonalReturnType diagonal() const;
template <int Index>
EIGEN_DEVICE_FUNC Diagonal<Derived, Index> diagonal();
template <int Index>
EIGEN_DEVICE_FUNC const Diagonal<const Derived, Index> diagonal() const;
EIGEN_DEVICE_FUNC Diagonal<Derived, DynamicIndex> diagonal(Index index);
EIGEN_DEVICE_FUNC const Diagonal<const Derived, DynamicIndex> diagonal(Index index) const;
template <unsigned int Mode>
struct TriangularViewReturnType {
typedef TriangularView<Derived, Mode> Type;
};
template <unsigned int Mode>
struct ConstTriangularViewReturnType {
typedef const TriangularView<const Derived, Mode> Type;
};
template <unsigned int Mode>
EIGEN_DEVICE_FUNC typename TriangularViewReturnType<Mode>::Type triangularView();
template <unsigned int Mode>
EIGEN_DEVICE_FUNC typename ConstTriangularViewReturnType<Mode>::Type triangularView() const;
template <unsigned int UpLo>
struct SelfAdjointViewReturnType {
typedef SelfAdjointView<Derived, UpLo> Type;
};
template <unsigned int UpLo>
struct ConstSelfAdjointViewReturnType {
typedef const SelfAdjointView<const Derived, UpLo> Type;
};
template <unsigned int UpLo>
EIGEN_DEVICE_FUNC typename SelfAdjointViewReturnType<UpLo>::Type selfadjointView();
template <unsigned int UpLo>
EIGEN_DEVICE_FUNC typename ConstSelfAdjointViewReturnType<UpLo>::Type selfadjointView() const;
const SparseView<Derived> sparseView(
const Scalar& m_reference = Scalar(0),
const typename NumTraits<Scalar>::Real& m_epsilon = NumTraits<Scalar>::dummy_precision()) const;
EIGEN_DEVICE_FUNC static const IdentityReturnType Identity();
EIGEN_DEVICE_FUNC static const IdentityReturnType Identity(Index rows, Index cols);
EIGEN_DEVICE_FUNC static const BasisReturnType Unit(Index size, Index i);
EIGEN_DEVICE_FUNC static const BasisReturnType Unit(Index i);
EIGEN_DEVICE_FUNC static const BasisReturnType UnitX();
EIGEN_DEVICE_FUNC static const BasisReturnType UnitY();
EIGEN_DEVICE_FUNC static const BasisReturnType UnitZ();
EIGEN_DEVICE_FUNC static const BasisReturnType UnitW();
EIGEN_DEVICE_FUNC const DiagonalWrapper<const Derived> asDiagonal() const;
const PermutationWrapper<const Derived> asPermutation() const;
EIGEN_DEVICE_FUNC const SkewSymmetricWrapper<const Derived> asSkewSymmetric() const;
EIGEN_DEVICE_FUNC Derived& setIdentity();
EIGEN_DEVICE_FUNC Derived& setIdentity(Index rows, Index cols);
EIGEN_DEVICE_FUNC Derived& setUnit(Index i);
EIGEN_DEVICE_FUNC Derived& setUnit(Index newSize, Index i);
bool isIdentity(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
bool isDiagonal(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
bool isUpperTriangular(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
bool isLowerTriangular(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
bool isSkewSymmetric(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
template <typename OtherDerived>
bool isOrthogonal(const MatrixBase<OtherDerived>& other,
const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
bool isUnitary(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
/** \returns true if each coefficients of \c *this and \a other are all exactly equal.
* \warning When using floating point scalar values you probably should rather use a
* fuzzy comparison such as isApprox()
* \sa isApprox(), operator!= */
template <typename OtherDerived>
EIGEN_DEVICE_FUNC inline bool operator==(const MatrixBase<OtherDerived>& other) const {
return (this->rows() == other.rows()) && (this->cols() == other.cols()) && cwiseEqual(other).all();
}
/** \returns true if at least one pair of coefficients of \c *this and \a other are not exactly equal to each other.
* \warning When using floating point scalar values you probably should rather use a
* fuzzy comparison such as isApprox()
* \sa isApprox(), operator== */
template <typename OtherDerived>
EIGEN_DEVICE_FUNC inline bool operator!=(const MatrixBase<OtherDerived>& other) const {
return !(*this == other);
}
NoAlias<Derived, Eigen::MatrixBase> EIGEN_DEVICE_FUNC noalias();
// TODO forceAlignedAccess is temporarily disabled
// Need to find a nicer workaround.
inline const Derived& forceAlignedAccess() const { return derived(); }
inline Derived& forceAlignedAccess() { return derived(); }
template <bool Enable>
inline const Derived& forceAlignedAccessIf() const {
return derived();
}
template <bool Enable>
inline Derived& forceAlignedAccessIf() {
return derived();
}
EIGEN_DEVICE_FUNC Scalar trace() const;
template <int p>
EIGEN_DEVICE_FUNC RealScalar lpNorm() const;
EIGEN_DEVICE_FUNC MatrixBase<Derived>& matrix() { return *this; }
EIGEN_DEVICE_FUNC const MatrixBase<Derived>& matrix() const { return *this; }
/** \returns an \link Eigen::ArrayBase Array \endlink expression of this matrix
* \sa ArrayBase::matrix() */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ArrayWrapper<Derived> array() { return ArrayWrapper<Derived>(derived()); }
/** \returns a const \link Eigen::ArrayBase Array \endlink expression of this matrix
* \sa ArrayBase::matrix() */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const ArrayWrapper<const Derived> array() const {
return ArrayWrapper<const Derived>(derived());
}
/////////// LU module ///////////
template <typename PermutationIndex = DefaultPermutationIndex>
inline const FullPivLU<PlainObject, PermutationIndex> fullPivLu() const;
template <typename PermutationIndex = DefaultPermutationIndex>
inline const PartialPivLU<PlainObject, PermutationIndex> partialPivLu() const;
template <typename PermutationIndex = DefaultPermutationIndex>
inline const PartialPivLU<PlainObject, PermutationIndex> lu() const;
EIGEN_DEVICE_FUNC inline const Inverse<Derived> inverse() const;
template <typename ResultType>
inline void computeInverseAndDetWithCheck(
ResultType& inverse, typename ResultType::Scalar& determinant, bool& invertible,
const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()) const;
template <typename ResultType>
inline void computeInverseWithCheck(
ResultType& inverse, bool& invertible,
const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()) const;
EIGEN_DEVICE_FUNC Scalar determinant() const;
/////////// Cholesky module ///////////
inline const LLT<PlainObject> llt() const;
inline const LDLT<PlainObject> ldlt() const;
/////////// QR module ///////////
inline const HouseholderQR<PlainObject> householderQr() const;
template <typename PermutationIndex = DefaultPermutationIndex>
inline const ColPivHouseholderQR<PlainObject, PermutationIndex> colPivHouseholderQr() const;
template <typename PermutationIndex = DefaultPermutationIndex>
inline const FullPivHouseholderQR<PlainObject, PermutationIndex> fullPivHouseholderQr() const;
template <typename PermutationIndex = DefaultPermutationIndex>
inline const CompleteOrthogonalDecomposition<PlainObject, PermutationIndex> completeOrthogonalDecomposition() const;
/////////// Eigenvalues module ///////////
inline EigenvaluesReturnType eigenvalues() const;
inline RealScalar operatorNorm() const;
/////////// SVD module ///////////
template <int Options = 0>
inline JacobiSVD<PlainObject, Options> jacobiSvd() const;
template <int Options = 0>
EIGEN_DEPRECATED inline JacobiSVD<PlainObject, Options> jacobiSvd(unsigned int computationOptions) const;
template <int Options = 0>
inline BDCSVD<PlainObject, Options> bdcSvd() const;
template <int Options = 0>
EIGEN_DEPRECATED inline BDCSVD<PlainObject, Options> bdcSvd(unsigned int computationOptions) const;
/////////// Geometry module ///////////
template <typename OtherDerived>
EIGEN_DEVICE_FUNC inline typename internal::cross_impl<Derived, OtherDerived>::return_type cross(
const MatrixBase<OtherDerived>& other) const;
template <typename OtherDerived>
EIGEN_DEVICE_FUNC inline PlainObject cross3(const MatrixBase<OtherDerived>& other) const;
EIGEN_DEVICE_FUNC inline PlainObject unitOrthogonal(void) const;
EIGEN_DEPRECATED EIGEN_DEVICE_FUNC inline Matrix<Scalar, 3, 1> eulerAngles(Index a0, Index a1, Index a2) const;
EIGEN_DEVICE_FUNC inline Matrix<Scalar, 3, 1> canonicalEulerAngles(Index a0, Index a1, Index a2) const;
// put this as separate enum value to work around possible GCC 4.3 bug (?)
enum {
HomogeneousReturnTypeDirection =
ColsAtCompileTime == 1 && RowsAtCompileTime == 1
? ((internal::traits<Derived>::Flags & RowMajorBit) == RowMajorBit ? Horizontal : Vertical)
: ColsAtCompileTime == 1 ? Vertical
: Horizontal
};
typedef Homogeneous<Derived, HomogeneousReturnTypeDirection> HomogeneousReturnType;
EIGEN_DEVICE_FUNC inline HomogeneousReturnType homogeneous() const;
enum { SizeMinusOne = SizeAtCompileTime == Dynamic ? Dynamic : SizeAtCompileTime - 1 };
typedef Block<const Derived, internal::traits<Derived>::ColsAtCompileTime == 1 ? SizeMinusOne : 1,
internal::traits<Derived>::ColsAtCompileTime == 1 ? 1 : SizeMinusOne>
ConstStartMinusOne;
typedef EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(ConstStartMinusOne, Scalar, quotient) HNormalizedReturnType;
EIGEN_DEVICE_FUNC inline const HNormalizedReturnType hnormalized() const;
////////// Householder module ///////////
EIGEN_DEVICE_FUNC void makeHouseholderInPlace(Scalar& tau, RealScalar& beta);
template <typename EssentialPart>
EIGEN_DEVICE_FUNC void makeHouseholder(EssentialPart& essential, Scalar& tau, RealScalar& beta) const;
template <typename EssentialPart>
EIGEN_DEVICE_FUNC void applyHouseholderOnTheLeft(const EssentialPart& essential, const Scalar& tau,
Scalar* workspace);
template <typename EssentialPart>
EIGEN_DEVICE_FUNC void applyHouseholderOnTheRight(const EssentialPart& essential, const Scalar& tau,
Scalar* workspace);
///////// Jacobi module /////////
template <typename OtherScalar>
EIGEN_DEVICE_FUNC void applyOnTheLeft(Index p, Index q, const JacobiRotation<OtherScalar>& j);
template <typename OtherScalar>
EIGEN_DEVICE_FUNC void applyOnTheRight(Index p, Index q, const JacobiRotation<OtherScalar>& j);
///////// SparseCore module /////////
template <typename OtherDerived>
EIGEN_STRONG_INLINE const typename SparseMatrixBase<OtherDerived>::template CwiseProductDenseReturnType<Derived>::Type
cwiseProduct(const SparseMatrixBase<OtherDerived>& other) const {
return other.cwiseProduct(derived());
}
///////// MatrixFunctions module /////////
typedef typename internal::stem_function<Scalar>::type StemFunction;
#define EIGEN_MATRIX_FUNCTION(ReturnType, Name, Description) \
/** \returns an expression of the matrix Description of \c *this. \brief This function requires the <a \
* href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module</a>. To compute the \
* coefficient-wise Description use ArrayBase::##Name . */ \
const ReturnType<Derived> Name() const;
#define EIGEN_MATRIX_FUNCTION_1(ReturnType, Name, Description, Argument) \
/** \returns an expression of the matrix Description of \c *this. \brief This function requires the <a \
* href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module</a>. To compute the \
* coefficient-wise Description use ArrayBase::##Name . */ \
const ReturnType<Derived> Name(Argument) const;
EIGEN_MATRIX_FUNCTION(MatrixExponentialReturnValue, exp, exponential)
/** \brief Helper function for the <a href="unsupported/group__MatrixFunctions__Module.html"> unsupported
* MatrixFunctions module</a>.*/
const MatrixFunctionReturnValue<Derived> matrixFunction(StemFunction f) const;
EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, cosh, hyperbolic cosine)
EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, sinh, hyperbolic sine)
EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, atanh, inverse hyperbolic cosine)
EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, acosh, inverse hyperbolic cosine)
EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, asinh, inverse hyperbolic sine)
EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, cos, cosine)
EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, sin, sine)
EIGEN_MATRIX_FUNCTION(MatrixSquareRootReturnValue, sqrt, square root)
EIGEN_MATRIX_FUNCTION(MatrixLogarithmReturnValue, log, logarithm)
EIGEN_MATRIX_FUNCTION_1(MatrixPowerReturnValue, pow, power to \c p, const RealScalar& p)
EIGEN_MATRIX_FUNCTION_1(MatrixComplexPowerReturnValue, pow, power to \c p, const internal::make_complex_t<Scalar>& p)
protected:
EIGEN_DEFAULT_COPY_CONSTRUCTOR(MatrixBase)
EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(MatrixBase)
private:
EIGEN_DEVICE_FUNC explicit MatrixBase(int);
EIGEN_DEVICE_FUNC MatrixBase(int, int);
template <typename OtherDerived>
EIGEN_DEVICE_FUNC explicit MatrixBase(const MatrixBase<OtherDerived>&);
protected:
// mixing arrays and matrices is not legal
template <typename OtherDerived>
Derived& operator+=(const ArrayBase<OtherDerived>&) {
EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar)) == -1,
YOU_CANNOT_MIX_ARRAYS_AND_MATRICES);
return *this;
}
// mixing arrays and matrices is not legal
template <typename OtherDerived>
Derived& operator-=(const ArrayBase<OtherDerived>&) {
EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar)) == -1,
YOU_CANNOT_MIX_ARRAYS_AND_MATRICES);
return *this;
}
};
/***************************************************************************
* Implementation of matrix base methods
***************************************************************************/
/** replaces \c *this by \c *this * \a other.
*
* \returns a reference to \c *this
*
* Example: \include MatrixBase_applyOnTheRight.cpp
* Output: \verbinclude MatrixBase_applyOnTheRight.out
*/
template <typename Derived>
template <typename OtherDerived>
inline Derived& MatrixBase<Derived>::operator*=(const EigenBase<OtherDerived>& other) {
other.derived().applyThisOnTheRight(derived());
return derived();
}
/** replaces \c *this by \c *this * \a other. It is equivalent to MatrixBase::operator*=().
*
* Example: \include MatrixBase_applyOnTheRight.cpp
* Output: \verbinclude MatrixBase_applyOnTheRight.out
*/
template <typename Derived>
template <typename OtherDerived>
inline void MatrixBase<Derived>::applyOnTheRight(const EigenBase<OtherDerived>& other) {
other.derived().applyThisOnTheRight(derived());
}
/** replaces \c *this by \a other * \c *this.
*
* Example: \include MatrixBase_applyOnTheLeft.cpp
* Output: \verbinclude MatrixBase_applyOnTheLeft.out
*/
template <typename Derived>
template <typename OtherDerived>
inline void MatrixBase<Derived>::applyOnTheLeft(const EigenBase<OtherDerived>& other) {
other.derived().applyThisOnTheLeft(derived());
}
} // end namespace Eigen
#endif // EIGEN_MATRIXBASE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_NESTBYVALUE_H
#define EIGEN_NESTBYVALUE_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
template <typename ExpressionType>
struct traits<NestByValue<ExpressionType> > : public traits<ExpressionType> {
enum { Flags = traits<ExpressionType>::Flags & ~NestByRefBit };
};
} // namespace internal
/** \class NestByValue
* \ingroup Core_Module
*
* \brief Expression which must be nested by value
*
* \tparam ExpressionType the type of the object of which we are requiring nesting-by-value
*
* This class is the return type of MatrixBase::nestByValue()
* and most of the time this is the only way it is used.
*
* \sa MatrixBase::nestByValue()
*/
template <typename ExpressionType>
class NestByValue : public internal::dense_xpr_base<NestByValue<ExpressionType> >::type {
public:
typedef typename internal::dense_xpr_base<NestByValue>::type Base;
static constexpr bool HasDirectAccess = internal::has_direct_access<ExpressionType>::ret;
EIGEN_DENSE_PUBLIC_INTERFACE(NestByValue)
EIGEN_DEVICE_FUNC explicit inline NestByValue(const ExpressionType& matrix) : m_expression(matrix) {}
EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return m_expression.rows(); }
EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return m_expression.cols(); }
EIGEN_DEVICE_FUNC operator const ExpressionType&() const { return m_expression; }
EIGEN_DEVICE_FUNC const ExpressionType& nestedExpression() const { return m_expression; }
EIGEN_DEVICE_FUNC typename std::enable_if<HasDirectAccess, const Scalar*>::type data() const {
return m_expression.data();
}
EIGEN_DEVICE_FUNC typename std::enable_if<HasDirectAccess, Index>::type innerStride() const {
return m_expression.innerStride();
}
EIGEN_DEVICE_FUNC typename std::enable_if<HasDirectAccess, Index>::type outerStride() const {
return m_expression.outerStride();
}
protected:
const ExpressionType m_expression;
};
/** \returns an expression of the temporary version of *this.
*/
template <typename Derived>
EIGEN_DEVICE_FUNC inline const NestByValue<Derived> DenseBase<Derived>::nestByValue() const {
return NestByValue<Derived>(derived());
}
namespace internal {
// Evaluator of Solve -> eval into a temporary
template <typename ArgType>
struct evaluator<NestByValue<ArgType> > : public evaluator<ArgType> {
typedef evaluator<ArgType> Base;
EIGEN_DEVICE_FUNC explicit evaluator(const NestByValue<ArgType>& xpr) : Base(xpr.nestedExpression()) {}
};
} // namespace internal
} // end namespace Eigen
#endif // EIGEN_NESTBYVALUE_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_NOALIAS_H
#define EIGEN_NOALIAS_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
/** \class NoAlias
* \ingroup Core_Module
*
* \brief Pseudo expression providing an operator = assuming no aliasing
*
* \tparam ExpressionType the type of the object on which to do the lazy assignment
*
* This class represents an expression with special assignment operators
* assuming no aliasing between the target expression and the source expression.
* More precisely it alloas to bypass the EvalBeforeAssignBit flag of the source expression.
* It is the return type of MatrixBase::noalias()
* and most of the time this is the only way it is used.
*
* \sa MatrixBase::noalias()
*/
template <typename ExpressionType, template <typename> class StorageBase>
class NoAlias {
public:
typedef typename ExpressionType::Scalar Scalar;
EIGEN_DEVICE_FUNC explicit NoAlias(ExpressionType& expression) : m_expression(expression) {}
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ExpressionType& operator=(const StorageBase<OtherDerived>& other) {
call_assignment_no_alias(m_expression, other.derived(),
internal::assign_op<Scalar, typename OtherDerived::Scalar>());
return m_expression;
}
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ExpressionType& operator+=(const StorageBase<OtherDerived>& other) {
call_assignment_no_alias(m_expression, other.derived(),
internal::add_assign_op<Scalar, typename OtherDerived::Scalar>());
return m_expression;
}
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ExpressionType& operator-=(const StorageBase<OtherDerived>& other) {
call_assignment_no_alias(m_expression, other.derived(),
internal::sub_assign_op<Scalar, typename OtherDerived::Scalar>());
return m_expression;
}
EIGEN_DEVICE_FUNC ExpressionType& expression() const { return m_expression; }
protected:
ExpressionType& m_expression;
};
/** \returns a pseudo expression of \c *this with an operator= assuming
* no aliasing between \c *this and the source expression.
*
* More precisely, noalias() allows to bypass the EvalBeforeAssignBit flag.
* Currently, even though several expressions may alias, only product
* expressions have this flag. Therefore, noalias() is only useful when
* the source expression contains a matrix product.
*
* Here are some examples where noalias is useful:
* \code
* D.noalias() = A * B;
* D.noalias() += A.transpose() * B;
* D.noalias() -= 2 * A * B.adjoint();
* \endcode
*
* On the other hand the following example will lead to a \b wrong result:
* \code
* A.noalias() = A * B;
* \endcode
* because the result matrix A is also an operand of the matrix product. Therefore,
* there is no alternative than evaluating A * B in a temporary, that is the default
* behavior when you write:
* \code
* A = A * B;
* \endcode
*
* \sa class NoAlias
*/
template <typename Derived>
NoAlias<Derived, MatrixBase> EIGEN_DEVICE_FUNC MatrixBase<Derived>::noalias() {
return NoAlias<Derived, Eigen::MatrixBase>(derived());
}
} // end namespace Eigen
#endif // EIGEN_NOALIAS_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_NUMTRAITS_H
#define EIGEN_NUMTRAITS_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
// default implementation of digits(), based on numeric_limits if specialized,
// 0 for integer types, and log2(epsilon()) otherwise.
template <typename T, bool use_numeric_limits = std::numeric_limits<T>::is_specialized,
bool is_integer = NumTraits<T>::IsInteger>
struct default_digits_impl {
EIGEN_DEVICE_FUNC constexpr static int run() { return std::numeric_limits<T>::digits; }
};
template <typename T>
struct default_digits_impl<T, false, false> // Floating point
{
EIGEN_DEVICE_FUNC constexpr static int run() {
using std::ceil;
using std::log2;
typedef typename NumTraits<T>::Real Real;
return int(ceil(-log2(NumTraits<Real>::epsilon())));
}
};
template <typename T>
struct default_digits_impl<T, false, true> // Integer
{
EIGEN_DEVICE_FUNC constexpr static int run() { return 0; }
};
// default implementation of digits10(), based on numeric_limits if specialized,
// 0 for integer types, and floor((digits()-1)*log10(2)) otherwise.
template <typename T, bool use_numeric_limits = std::numeric_limits<T>::is_specialized,
bool is_integer = NumTraits<T>::IsInteger>
struct default_digits10_impl {
EIGEN_DEVICE_FUNC constexpr static int run() { return std::numeric_limits<T>::digits10; }
};
template <typename T>
struct default_digits10_impl<T, false, false> // Floating point
{
EIGEN_DEVICE_FUNC constexpr static int run() {
using std::floor;
using std::log10;
typedef typename NumTraits<T>::Real Real;
return int(floor((internal::default_digits_impl<Real>::run() - 1) * log10(2)));
}
};
template <typename T>
struct default_digits10_impl<T, false, true> // Integer
{
EIGEN_DEVICE_FUNC constexpr static int run() { return 0; }
};
// default implementation of max_digits10(), based on numeric_limits if specialized,
// 0 for integer types, and log10(2) * digits() + 1 otherwise.
template <typename T, bool use_numeric_limits = std::numeric_limits<T>::is_specialized,
bool is_integer = NumTraits<T>::IsInteger>
struct default_max_digits10_impl {
EIGEN_DEVICE_FUNC constexpr static int run() { return std::numeric_limits<T>::max_digits10; }
};
template <typename T>
struct default_max_digits10_impl<T, false, false> // Floating point
{
EIGEN_DEVICE_FUNC constexpr static int run() {
using std::ceil;
using std::log10;
typedef typename NumTraits<T>::Real Real;
return int(ceil(internal::default_digits_impl<Real>::run() * log10(2) + 1));
}
};
template <typename T>
struct default_max_digits10_impl<T, false, true> // Integer
{
EIGEN_DEVICE_FUNC constexpr static int run() { return 0; }
};
} // end namespace internal
namespace numext {
/** \internal bit-wise cast without changing the underlying bit representation. */
#if defined(__cpp_lib_bit_cast) && __cpp_lib_bit_cast >= 201806L
template <typename Tgt, typename Src>
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC constexpr Tgt bit_cast(const Src& src) {
return std::bit_cast<Tgt>(src);
}
#elif EIGEN_HAS_BUILTIN(__builtin_bit_cast)
template <typename Tgt, typename Src>
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC constexpr Tgt bit_cast(const Src& src) {
EIGEN_STATIC_ASSERT(std::is_trivially_copyable<Src>::value, THIS_TYPE_IS_NOT_SUPPORTED)
EIGEN_STATIC_ASSERT(std::is_trivially_copyable<Tgt>::value, THIS_TYPE_IS_NOT_SUPPORTED)
EIGEN_STATIC_ASSERT(sizeof(Src) == sizeof(Tgt), THIS_TYPE_IS_NOT_SUPPORTED)
return __builtin_bit_cast(Tgt, src);
}
#else
template <typename Tgt, typename Src>
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Tgt bit_cast(const Src& src) {
// The behaviour of memcpy is not specified for non-trivially copyable types
EIGEN_STATIC_ASSERT(std::is_trivially_copyable<Src>::value, THIS_TYPE_IS_NOT_SUPPORTED)
EIGEN_STATIC_ASSERT(std::is_trivially_copyable<Tgt>::value && std::is_default_constructible<Tgt>::value,
THIS_TYPE_IS_NOT_SUPPORTED)
EIGEN_STATIC_ASSERT(sizeof(Src) == sizeof(Tgt), THIS_TYPE_IS_NOT_SUPPORTED)
Tgt tgt;
// Load src into registers first. This allows the memcpy to be elided by CUDA.
const Src staged = src;
EIGEN_USING_STD(memcpy)
memcpy(static_cast<void*>(&tgt), static_cast<const void*>(&staged), sizeof(Tgt));
return tgt;
}
#endif
} // namespace numext
// clang-format off
/** \class NumTraits
* \ingroup Core_Module
*
* \brief Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
*
* \tparam T the numeric type at hand
*
* This class stores enums, typedefs and static methods giving information about a numeric type.
*
* The provided data consists of:
* \li A typedef \c Real, giving the "real part" type of \a T. If \a T is already real,
* then \c Real is just a typedef to \a T. If \a T is `std::complex<U>` then \c Real
* is a typedef to \a U.
* \li A typedef \c NonInteger, giving the type that should be used for operations producing non-integral values,
* such as quotients, square roots, etc. If \a T is a floating-point type, then this typedef just gives
* \a T again. Note however that many Eigen functions such as internal::sqrt simply refuse to
* take integers. Outside of a few cases, Eigen doesn't do automatic type promotion. Thus, this typedef is
* only intended as a helper for code that needs to explicitly promote types.
* \li A typedef \c Literal giving the type to use for numeric literals such as "2" or "0.5". For instance, for
* `std::complex<U>`, Literal is defined as \a U. Of course, this type must be fully compatible with \a T. In doubt,
* just use \a T here.
* \li A typedef \c Nested giving the type to use to nest a value inside of the expression tree. If you don't know what
* this means, just use \a T here.
* \li An enum value \c IsComplex. It is equal to 1 if \a T is a \c std::complex type, and to 0 otherwise.
* \li An enum value \c IsInteger. It is equal to \c 1 if \a T is an integer type such as \c int, and to \c 0 otherwise.
* \li Enum values \c ReadCost, \c AddCost and \c MulCost representing a rough estimate of the number of CPU cycles needed to by
* move / add / mul instructions respectively, assuming the data is already stored in CPU registers. Stay vague here.
* No need to do architecture-specific stuff. If you don't know what this means, just use \c Eigen::HugeCost.
* \li An enum value \c IsSigned. It is equal to \c 1 if \a T is a signed type and to 0 if \a T is unsigned.
* \li An enum value \c RequireInitialization. It is equal to \c 1 if the constructor of the numeric type \a T must be
* called, and to 0 if it is safe not to call it. Default is 0 if \a T is an arithmetic type, and 1 otherwise.
* \li An epsilon() function which, unlike <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/epsilon">
* `std::numeric_limits::epsilon()`</a>, it returns a \c Real instead of a \a T.
* \li A dummy_precision() function returning a weak epsilon value. It is mainly used as a default value by the fuzzy
* comparison operators.
* \li highest() and lowest() functions returning the highest and lowest possible values respectively.
* \li digits() function returning the number of radix digits (non-sign digits for integers, mantissa for floating-point).
* This is the analogue of <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/digits">
* `std::numeric_limits<T>::digits`</a> which is used as the default implementation if specialized.
* \li digits10() function returning the number of decimal digits that can be represented without change. This is the
* analogue of <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/digits10">
* `std::numeric_limits<T>::digits10`</a> which is used as the default implementation if specialized.
* \li max_digits10() function returning the number of decimal digits required to uniquely represent all distinct values
* of the type. This is the analogue of <a
* href="http://en.cppreference.com/w/cpp/types/numeric_limits/max_digits10">`std::numeric_limits<T>::max_digits10`</a>
* which is used as the default implementation if specialized.
* \li min_exponent() and max_exponent() functions returning the highest and lowest possible values, respectively,
* such that the radix raised to the power exponent-1 is a normalized floating-point number. These are equivalent
* to <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/min_exponent">
* `std::numeric_limits<T>::min_exponent`</a>/<a
* href="http://en.cppreference.com/w/cpp/types/numeric_limits/max_exponent">`std::numeric_limits<T>::max_exponent`</a>.
* \li infinity() function returning a representation of positive infinity, if available.
* \li quiet_NaN() function returning a non-signaling "not-a-number", if available.
*/
// clang-format on
template <typename T>
struct GenericNumTraits {
enum {
IsInteger = std::numeric_limits<T>::is_integer,
IsSigned = std::numeric_limits<T>::is_signed,
IsComplex = 0,
RequireInitialization = internal::is_arithmetic<T>::value ? 0 : 1,
ReadCost = 1,
AddCost = 1,
MulCost = 1
};
typedef T Real;
typedef std::conditional_t<IsInteger, std::conditional_t<sizeof(T) <= 2, float, double>, T> NonInteger;
typedef T Nested;
typedef T Literal;
EIGEN_DEVICE_FUNC constexpr static Real epsilon() { return numext::numeric_limits<T>::epsilon(); }
EIGEN_DEVICE_FUNC constexpr static int digits10() { return internal::default_digits10_impl<T>::run(); }
EIGEN_DEVICE_FUNC constexpr static int max_digits10() { return internal::default_max_digits10_impl<T>::run(); }
EIGEN_DEVICE_FUNC constexpr static int digits() { return internal::default_digits_impl<T>::run(); }
EIGEN_DEVICE_FUNC constexpr static int min_exponent() { return numext::numeric_limits<T>::min_exponent; }
EIGEN_DEVICE_FUNC constexpr static int max_exponent() { return numext::numeric_limits<T>::max_exponent; }
EIGEN_DEVICE_FUNC constexpr static Real dummy_precision() {
// make sure to override this for floating-point types
return Real(0);
}
EIGEN_DEVICE_FUNC constexpr static T highest() { return (numext::numeric_limits<T>::max)(); }
EIGEN_DEVICE_FUNC constexpr static T lowest() { return (numext::numeric_limits<T>::lowest)(); }
EIGEN_DEVICE_FUNC constexpr static T infinity() { return numext::numeric_limits<T>::infinity(); }
EIGEN_DEVICE_FUNC constexpr static T quiet_NaN() { return numext::numeric_limits<T>::quiet_NaN(); }
};
template <typename T>
struct NumTraits : GenericNumTraits<T> {};
template <>
struct NumTraits<float> : GenericNumTraits<float> {
EIGEN_DEVICE_FUNC constexpr static float dummy_precision() { return 1e-5f; }
};
template <>
struct NumTraits<double> : GenericNumTraits<double> {
EIGEN_DEVICE_FUNC constexpr static double dummy_precision() { return 1e-12; }
};
// GPU devices treat `long double` as `double`.
#ifndef EIGEN_GPU_COMPILE_PHASE
template <>
struct NumTraits<long double> : GenericNumTraits<long double> {
EIGEN_DEVICE_FUNC constexpr static long double dummy_precision() { return static_cast<long double>(1e-15l); }
#if defined(EIGEN_ARCH_PPC) && (__LDBL_MANT_DIG__ == 106)
// PowerPC double double causes issues with some values
EIGEN_DEVICE_FUNC constexpr static long double epsilon() {
// 2^(-(__LDBL_MANT_DIG__)+1)
return static_cast<long double>(2.4651903288156618919116517665087e-32l);
}
#endif
};
#endif
template <typename Real_>
struct NumTraits<std::complex<Real_> > : GenericNumTraits<std::complex<Real_> > {
typedef Real_ Real;
typedef typename NumTraits<Real_>::Literal Literal;
enum {
IsComplex = 1,
IsSigned = NumTraits<Real_>::IsSigned,
RequireInitialization = NumTraits<Real_>::RequireInitialization,
ReadCost = 2 * NumTraits<Real_>::ReadCost,
AddCost = 2 * NumTraits<Real>::AddCost,
MulCost = 4 * NumTraits<Real>::MulCost + 2 * NumTraits<Real>::AddCost
};
EIGEN_DEVICE_FUNC constexpr static Real epsilon() { return NumTraits<Real>::epsilon(); }
EIGEN_DEVICE_FUNC constexpr static Real dummy_precision() { return NumTraits<Real>::dummy_precision(); }
EIGEN_DEVICE_FUNC constexpr static int digits10() { return NumTraits<Real>::digits10(); }
EIGEN_DEVICE_FUNC constexpr static int max_digits10() { return NumTraits<Real>::max_digits10(); }
};
template <typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
struct NumTraits<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> > {
typedef Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> ArrayType;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Array<RealScalar, Rows, Cols, Options, MaxRows, MaxCols> Real;
typedef typename NumTraits<Scalar>::NonInteger NonIntegerScalar;
typedef Array<NonIntegerScalar, Rows, Cols, Options, MaxRows, MaxCols> NonInteger;
typedef ArrayType& Nested;
typedef typename NumTraits<Scalar>::Literal Literal;
enum {
IsComplex = NumTraits<Scalar>::IsComplex,
IsInteger = NumTraits<Scalar>::IsInteger,
IsSigned = NumTraits<Scalar>::IsSigned,
RequireInitialization = 1,
ReadCost = ArrayType::SizeAtCompileTime == Dynamic
? HugeCost
: ArrayType::SizeAtCompileTime * int(NumTraits<Scalar>::ReadCost),
AddCost = ArrayType::SizeAtCompileTime == Dynamic ? HugeCost
: ArrayType::SizeAtCompileTime * int(NumTraits<Scalar>::AddCost),
MulCost = ArrayType::SizeAtCompileTime == Dynamic ? HugeCost
: ArrayType::SizeAtCompileTime * int(NumTraits<Scalar>::MulCost)
};
EIGEN_DEVICE_FUNC constexpr static RealScalar epsilon() { return NumTraits<RealScalar>::epsilon(); }
EIGEN_DEVICE_FUNC constexpr static RealScalar dummy_precision() { return NumTraits<RealScalar>::dummy_precision(); }
constexpr static int digits10() { return NumTraits<Scalar>::digits10(); }
constexpr static int max_digits10() { return NumTraits<Scalar>::max_digits10(); }
};
template <>
struct NumTraits<std::string> : GenericNumTraits<std::string> {
enum { RequireInitialization = 1, ReadCost = HugeCost, AddCost = HugeCost, MulCost = HugeCost };
constexpr static int digits10() { return 0; }
constexpr static int max_digits10() { return 0; }
private:
static inline std::string epsilon();
static inline std::string dummy_precision();
static inline std::string lowest();
static inline std::string highest();
static inline std::string infinity();
static inline std::string quiet_NaN();
};
// Empty specialization for void to allow template specialization based on NumTraits<T>::Real with T==void and SFINAE.
template <>
struct NumTraits<void> {};
template <>
struct NumTraits<bool> : GenericNumTraits<bool> {};
} // end namespace Eigen
#endif // EIGEN_NUMTRAITS_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2011-2018 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_PARTIALREDUX_H
#define EIGEN_PARTIALREDUX_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
/***************************************************************************
*
* This file provides evaluators for partial reductions.
* There are two modes:
*
* - scalar path: simply calls the respective function on the column or row.
* -> nothing special here, all the tricky part is handled by the return
* types of VectorwiseOp's members. They embed the functor calling the
* respective DenseBase's member function.
*
* - vectorized path: implements a packet-wise reductions followed by
* some (optional) processing of the outcome, e.g., division by n for mean.
*
* For the vectorized path let's observe that the packet-size and outer-unrolling
* are both decided by the assignment logic. So all we have to do is to decide
* on the inner unrolling.
*
* For the unrolling, we can reuse "internal::redux_vec_unroller" from Redux.h,
* but be need to be careful to specify correct increment.
*
***************************************************************************/
/* logic deciding a strategy for unrolling of vectorized paths */
template <typename Func, typename Evaluator>
struct packetwise_redux_traits {
enum {
OuterSize = int(Evaluator::IsRowMajor) ? Evaluator::RowsAtCompileTime : Evaluator::ColsAtCompileTime,
Cost = OuterSize == Dynamic ? HugeCost
: OuterSize * Evaluator::CoeffReadCost + (OuterSize - 1) * functor_traits<Func>::Cost,
Unrolling = Cost <= EIGEN_UNROLLING_LIMIT ? CompleteUnrolling : NoUnrolling
};
};
/* Value to be returned when size==0 , by default let's return 0 */
template <typename PacketType, typename Func>
EIGEN_DEVICE_FUNC PacketType packetwise_redux_empty_value(const Func&) {
const typename unpacket_traits<PacketType>::type zero(0);
return pset1<PacketType>(zero);
}
/* For products the default is 1 */
template <typename PacketType, typename Scalar>
EIGEN_DEVICE_FUNC PacketType packetwise_redux_empty_value(const scalar_product_op<Scalar, Scalar>&) {
return pset1<PacketType>(Scalar(1));
}
/* Perform the actual reduction */
template <typename Func, typename Evaluator, int Unrolling = packetwise_redux_traits<Func, Evaluator>::Unrolling>
struct packetwise_redux_impl;
/* Perform the actual reduction with unrolling */
template <typename Func, typename Evaluator>
struct packetwise_redux_impl<Func, Evaluator, CompleteUnrolling> {
typedef redux_novec_unroller<Func, Evaluator, 0, Evaluator::SizeAtCompileTime> Base;
typedef typename Evaluator::Scalar Scalar;
template <typename PacketType>
EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE PacketType run(const Evaluator& eval, const Func& func, Index /*size*/) {
return redux_vec_unroller<Func, Evaluator, 0,
packetwise_redux_traits<Func, Evaluator>::OuterSize>::template run<PacketType>(eval,
func);
}
};
/* Add a specialization of redux_vec_unroller for size==0 at compiletime.
* This specialization is not required for general reductions, which is
* why it is defined here.
*/
template <typename Func, typename Evaluator, Index Start>
struct redux_vec_unroller<Func, Evaluator, Start, 0> {
template <typename PacketType>
EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE PacketType run(const Evaluator&, const Func& f) {
return packetwise_redux_empty_value<PacketType>(f);
}
};
/* Perform the actual reduction for dynamic sizes */
template <typename Func, typename Evaluator>
struct packetwise_redux_impl<Func, Evaluator, NoUnrolling> {
typedef typename Evaluator::Scalar Scalar;
typedef typename redux_traits<Func, Evaluator>::PacketType PacketScalar;
template <typename PacketType>
EIGEN_DEVICE_FUNC static PacketType run(const Evaluator& eval, const Func& func, Index size) {
if (size == 0) return packetwise_redux_empty_value<PacketType>(func);
const Index size4 = 1 + numext::round_down(size - 1, 4);
PacketType p = eval.template packetByOuterInner<Unaligned, PacketType>(0, 0);
// This loop is optimized for instruction pipelining:
// - each iteration generates two independent instructions
// - thanks to branch prediction and out-of-order execution we have independent instructions across loops
for (Index i = 1; i < size4; i += 4)
p = func.packetOp(
p, func.packetOp(func.packetOp(eval.template packetByOuterInner<Unaligned, PacketType>(i + 0, 0),
eval.template packetByOuterInner<Unaligned, PacketType>(i + 1, 0)),
func.packetOp(eval.template packetByOuterInner<Unaligned, PacketType>(i + 2, 0),
eval.template packetByOuterInner<Unaligned, PacketType>(i + 3, 0))));
for (Index i = size4; i < size; ++i)
p = func.packetOp(p, eval.template packetByOuterInner<Unaligned, PacketType>(i, 0));
return p;
}
};
template <typename Func, typename Evaluator>
struct packetwise_segment_redux_impl {
typedef typename Evaluator::Scalar Scalar;
typedef typename redux_traits<Func, Evaluator>::PacketType PacketScalar;
template <typename PacketType>
EIGEN_DEVICE_FUNC static PacketType run(const Evaluator& eval, const Func& func, Index size, Index begin,
Index count) {
if (size == 0) return packetwise_redux_empty_value<PacketType>(func);
PacketType p = eval.template packetSegmentByOuterInner<Unaligned, PacketType>(0, 0, begin, count);
for (Index i = 1; i < size; ++i)
p = func.packetOp(p, eval.template packetSegmentByOuterInner<Unaligned, PacketType>(i, 0, begin, count));
return p;
}
};
template <typename ArgType, typename MemberOp, int Direction>
struct evaluator<PartialReduxExpr<ArgType, MemberOp, Direction> >
: evaluator_base<PartialReduxExpr<ArgType, MemberOp, Direction> > {
typedef PartialReduxExpr<ArgType, MemberOp, Direction> XprType;
typedef typename internal::nested_eval<ArgType, 1>::type ArgTypeNested;
typedef add_const_on_value_type_t<ArgTypeNested> ConstArgTypeNested;
typedef internal::remove_all_t<ArgTypeNested> ArgTypeNestedCleaned;
typedef typename ArgType::Scalar InputScalar;
typedef typename XprType::Scalar Scalar;
enum {
TraversalSize = Direction == int(Vertical) ? int(ArgType::RowsAtCompileTime) : int(ArgType::ColsAtCompileTime)
};
typedef typename MemberOp::template Cost<int(TraversalSize)> CostOpType;
enum {
CoeffReadCost = TraversalSize == Dynamic ? HugeCost
: TraversalSize == 0
? 1
: int(TraversalSize) * int(evaluator<ArgType>::CoeffReadCost) + int(CostOpType::value),
ArgFlags_ = evaluator<ArgType>::Flags,
Vectorizable_ = bool(int(ArgFlags_) & PacketAccessBit) && bool(MemberOp::Vectorizable) &&
(Direction == int(Vertical) ? bool(ArgFlags_ & RowMajorBit) : (ArgFlags_ & RowMajorBit) == 0) &&
(TraversalSize != 0),
Flags = (traits<XprType>::Flags & RowMajorBit) | (evaluator<ArgType>::Flags & (HereditaryBits & (~RowMajorBit))) |
(Vectorizable_ ? PacketAccessBit : 0) | LinearAccessBit,
Alignment = 0 // FIXME this will need to be improved once PartialReduxExpr is vectorized
};
EIGEN_DEVICE_FUNC explicit evaluator(const XprType xpr) : m_arg(xpr.nestedExpression()), m_functor(xpr.functor()) {
EIGEN_INTERNAL_CHECK_COST_VALUE(TraversalSize == Dynamic ? HugeCost
: (TraversalSize == 0 ? 1 : int(CostOpType::value)));
EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
}
typedef typename XprType::CoeffReturnType CoeffReturnType;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar coeff(Index i, Index j) const {
return coeff(Direction == Vertical ? j : i);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar coeff(Index index) const {
return m_functor(m_arg.template subVector<DirectionType(Direction)>(index));
}
template <int LoadMode, typename PacketType>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(Index i, Index j) const {
return packet<LoadMode, PacketType>(Direction == Vertical ? j : i);
}
template <int LoadMode, typename PacketType>
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC PacketType packet(Index idx) const {
static constexpr int PacketSize = internal::unpacket_traits<PacketType>::size;
static constexpr int PanelRows = Direction == Vertical ? ArgType::RowsAtCompileTime : PacketSize;
static constexpr int PanelCols = Direction == Vertical ? PacketSize : ArgType::ColsAtCompileTime;
using PanelType = Block<const ArgTypeNestedCleaned, PanelRows, PanelCols, true /* InnerPanel */>;
using PanelEvaluator = typename internal::redux_evaluator<PanelType>;
using BinaryOp = typename MemberOp::BinaryOp;
using Impl = internal::packetwise_redux_impl<BinaryOp, PanelEvaluator>;
// FIXME
// See bug 1612, currently if PacketSize==1 (i.e. complex<double> with 128bits registers) then the storage-order of
// panel get reversed and methods like packetByOuterInner do not make sense anymore in this context. So let's just
// by pass "vectorization" in this case:
if (PacketSize == 1) return internal::pset1<PacketType>(coeff(idx));
Index startRow = Direction == Vertical ? 0 : idx;
Index startCol = Direction == Vertical ? idx : 0;
Index numRows = Direction == Vertical ? m_arg.rows() : PacketSize;
Index numCols = Direction == Vertical ? PacketSize : m_arg.cols();
PanelType panel(m_arg, startRow, startCol, numRows, numCols);
PanelEvaluator panel_eval(panel);
PacketType p = Impl::template run<PacketType>(panel_eval, m_functor.binaryFunc(), m_arg.outerSize());
return p;
}
template <int LoadMode, typename PacketType>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packetSegment(Index i, Index j, Index begin, Index count) const {
return packetSegment<LoadMode, PacketType>(Direction == Vertical ? j : i, begin, count);
}
template <int LoadMode, typename PacketType>
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC PacketType packetSegment(Index idx, Index begin, Index count) const {
static constexpr int PanelRows = Direction == Vertical ? ArgType::RowsAtCompileTime : Dynamic;
static constexpr int PanelCols = Direction == Vertical ? Dynamic : ArgType::ColsAtCompileTime;
using PanelType = Block<const ArgTypeNestedCleaned, PanelRows, PanelCols, true /* InnerPanel */>;
using PanelEvaluator = typename internal::redux_evaluator<PanelType>;
using BinaryOp = typename MemberOp::BinaryOp;
using Impl = internal::packetwise_segment_redux_impl<BinaryOp, PanelEvaluator>;
Index startRow = Direction == Vertical ? 0 : idx;
Index startCol = Direction == Vertical ? idx : 0;
Index numRows = Direction == Vertical ? m_arg.rows() : begin + count;
Index numCols = Direction == Vertical ? begin + count : m_arg.cols();
PanelType panel(m_arg, startRow, startCol, numRows, numCols);
PanelEvaluator panel_eval(panel);
PacketType p = Impl::template run<PacketType>(panel_eval, m_functor.binaryFunc(), m_arg.outerSize(), begin, count);
return p;
}
protected:
ConstArgTypeNested m_arg;
const MemberOp m_functor;
};
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_PARTIALREDUX_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2009-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_PERMUTATIONMATRIX_H
#define EIGEN_PERMUTATIONMATRIX_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
enum PermPermProduct_t { PermPermProduct };
} // end namespace internal
/** \class PermutationBase
* \ingroup Core_Module
*
* \brief Base class for permutations
*
* \tparam Derived the derived class
*
* This class is the base class for all expressions representing a permutation matrix,
* internally stored as a vector of integers.
* The convention followed here is that if \f$ \sigma \f$ is a permutation, the corresponding permutation matrix
* \f$ P_\sigma \f$ is such that if \f$ (e_1,\ldots,e_p) \f$ is the canonical basis, we have:
* \f[ P_\sigma(e_i) = e_{\sigma(i)}. \f]
* This convention ensures that for any two permutations \f$ \sigma, \tau \f$, we have:
* \f[ P_{\sigma\circ\tau} = P_\sigma P_\tau. \f]
*
* Permutation matrices are square and invertible.
*
* Notice that in addition to the member functions and operators listed here, there also are non-member
* operator* to multiply any kind of permutation object with any kind of matrix expression (MatrixBase)
* on either side.
*
* \sa class PermutationMatrix, class PermutationWrapper
*/
template <typename Derived>
class PermutationBase : public EigenBase<Derived> {
typedef internal::traits<Derived> Traits;
typedef EigenBase<Derived> Base;
public:
#ifndef EIGEN_PARSED_BY_DOXYGEN
typedef typename Traits::IndicesType IndicesType;
enum {
Flags = Traits::Flags,
RowsAtCompileTime = Traits::RowsAtCompileTime,
ColsAtCompileTime = Traits::ColsAtCompileTime,
MaxRowsAtCompileTime = Traits::MaxRowsAtCompileTime,
MaxColsAtCompileTime = Traits::MaxColsAtCompileTime
};
typedef typename Traits::StorageIndex StorageIndex;
typedef Matrix<StorageIndex, RowsAtCompileTime, ColsAtCompileTime, 0, MaxRowsAtCompileTime, MaxColsAtCompileTime>
DenseMatrixType;
typedef PermutationMatrix<IndicesType::SizeAtCompileTime, IndicesType::MaxSizeAtCompileTime, StorageIndex>
PlainPermutationType;
typedef PlainPermutationType PlainObject;
using Base::derived;
typedef Inverse<Derived> InverseReturnType;
typedef void Scalar;
#endif
/** Copies the other permutation into *this */
template <typename OtherDerived>
Derived& operator=(const PermutationBase<OtherDerived>& other) {
indices() = other.indices();
return derived();
}
/** Assignment from the Transpositions \a tr */
template <typename OtherDerived>
Derived& operator=(const TranspositionsBase<OtherDerived>& tr) {
setIdentity(tr.size());
for (Index k = size() - 1; k >= 0; --k) applyTranspositionOnTheRight(k, tr.coeff(k));
return derived();
}
/** \returns the number of rows */
inline EIGEN_DEVICE_FUNC Index rows() const { return Index(indices().size()); }
/** \returns the number of columns */
inline EIGEN_DEVICE_FUNC Index cols() const { return Index(indices().size()); }
/** \returns the size of a side of the respective square matrix, i.e., the number of indices */
inline EIGEN_DEVICE_FUNC Index size() const { return Index(indices().size()); }
#ifndef EIGEN_PARSED_BY_DOXYGEN
template <typename DenseDerived>
void evalTo(MatrixBase<DenseDerived>& other) const {
other.setZero();
for (Index i = 0; i < rows(); ++i) other.coeffRef(indices().coeff(i), i) = typename DenseDerived::Scalar(1);
}
#endif
/** \returns a Matrix object initialized from this permutation matrix. Notice that it
* is inefficient to return this Matrix object by value. For efficiency, favor using
* the Matrix constructor taking EigenBase objects.
*/
DenseMatrixType toDenseMatrix() const { return derived(); }
/** const version of indices(). */
const IndicesType& indices() const { return derived().indices(); }
/** \returns a reference to the stored array representing the permutation. */
IndicesType& indices() { return derived().indices(); }
/** Resizes to given size.
*/
inline void resize(Index newSize) { indices().resize(newSize); }
/** Sets *this to be the identity permutation matrix */
void setIdentity() {
StorageIndex n = StorageIndex(size());
for (StorageIndex i = 0; i < n; ++i) indices().coeffRef(i) = i;
}
/** Sets *this to be the identity permutation matrix of given size.
*/
void setIdentity(Index newSize) {
resize(newSize);
setIdentity();
}
/** Multiplies *this by the transposition \f$(ij)\f$ on the left.
*
* \returns a reference to *this.
*
* \warning This is much slower than applyTranspositionOnTheRight(Index,Index):
* this has linear complexity and requires a lot of branching.
*
* \sa applyTranspositionOnTheRight(Index,Index)
*/
Derived& applyTranspositionOnTheLeft(Index i, Index j) {
eigen_assert(i >= 0 && j >= 0 && i < size() && j < size());
for (Index k = 0; k < size(); ++k) {
if (indices().coeff(k) == i)
indices().coeffRef(k) = StorageIndex(j);
else if (indices().coeff(k) == j)
indices().coeffRef(k) = StorageIndex(i);
}
return derived();
}
/** Multiplies *this by the transposition \f$(ij)\f$ on the right.
*
* \returns a reference to *this.
*
* This is a fast operation, it only consists in swapping two indices.
*
* \sa applyTranspositionOnTheLeft(Index,Index)
*/
Derived& applyTranspositionOnTheRight(Index i, Index j) {
eigen_assert(i >= 0 && j >= 0 && i < size() && j < size());
std::swap(indices().coeffRef(i), indices().coeffRef(j));
return derived();
}
/** \returns the inverse permutation matrix.
*
* \note \blank \note_try_to_help_rvo
*/
inline InverseReturnType inverse() const { return InverseReturnType(derived()); }
/** \returns the transpose permutation matrix.
*
* \note \blank \note_try_to_help_rvo
*/
inline InverseReturnType transpose() const { return InverseReturnType(derived()); }
/**** multiplication helpers to hopefully get RVO ****/
#ifndef EIGEN_PARSED_BY_DOXYGEN
protected:
template <typename OtherDerived>
void assignTranspose(const PermutationBase<OtherDerived>& other) {
for (Index i = 0; i < rows(); ++i) indices().coeffRef(other.indices().coeff(i)) = i;
}
template <typename Lhs, typename Rhs>
void assignProduct(const Lhs& lhs, const Rhs& rhs) {
eigen_assert(lhs.cols() == rhs.rows());
for (Index i = 0; i < rows(); ++i) indices().coeffRef(i) = lhs.indices().coeff(rhs.indices().coeff(i));
}
#endif
public:
/** \returns the product permutation matrix.
*
* \note \blank \note_try_to_help_rvo
*/
template <typename Other>
inline PlainPermutationType operator*(const PermutationBase<Other>& other) const {
return PlainPermutationType(internal::PermPermProduct, derived(), other.derived());
}
/** \returns the product of a permutation with another inverse permutation.
*
* \note \blank \note_try_to_help_rvo
*/
template <typename Other>
inline PlainPermutationType operator*(const InverseImpl<Other, PermutationStorage>& other) const {
return PlainPermutationType(internal::PermPermProduct, *this, other.eval());
}
/** \returns the product of an inverse permutation with another permutation.
*
* \note \blank \note_try_to_help_rvo
*/
template <typename Other>
friend inline PlainPermutationType operator*(const InverseImpl<Other, PermutationStorage>& other,
const PermutationBase& perm) {
return PlainPermutationType(internal::PermPermProduct, other.eval(), perm);
}
/** \returns the determinant of the permutation matrix, which is either 1 or -1 depending on the parity of the
* permutation.
*
* This function is O(\c n) procedure allocating a buffer of \c n booleans.
*/
Index determinant() const {
Index res = 1;
Index n = size();
Matrix<bool, RowsAtCompileTime, 1, 0, MaxRowsAtCompileTime> mask(n);
mask.fill(false);
Index r = 0;
while (r < n) {
// search for the next seed
while (r < n && mask[r]) r++;
if (r >= n) break;
// we got one, let's follow it until we are back to the seed
Index k0 = r++;
mask.coeffRef(k0) = true;
for (Index k = indices().coeff(k0); k != k0; k = indices().coeff(k)) {
mask.coeffRef(k) = true;
res = -res;
}
}
return res;
}
protected:
};
namespace internal {
template <int SizeAtCompileTime, int MaxSizeAtCompileTime, typename StorageIndex_>
struct traits<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_> >
: traits<
Matrix<StorageIndex_, SizeAtCompileTime, SizeAtCompileTime, 0, MaxSizeAtCompileTime, MaxSizeAtCompileTime> > {
typedef PermutationStorage StorageKind;
typedef Matrix<StorageIndex_, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1> IndicesType;
typedef StorageIndex_ StorageIndex;
typedef void Scalar;
};
} // namespace internal
/** \class PermutationMatrix
* \ingroup Core_Module
*
* \brief Permutation matrix
*
* \tparam SizeAtCompileTime the number of rows/cols, or Dynamic
* \tparam MaxSizeAtCompileTime the maximum number of rows/cols, or Dynamic. This optional parameter defaults to
* SizeAtCompileTime. Most of the time, you should not have to specify it. \tparam StorageIndex_ the integer type of the
* indices
*
* This class represents a permutation matrix, internally stored as a vector of integers.
*
* \sa class PermutationBase, class PermutationWrapper, class DiagonalMatrix
*/
template <int SizeAtCompileTime, int MaxSizeAtCompileTime, typename StorageIndex_>
class PermutationMatrix
: public PermutationBase<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_> > {
typedef PermutationBase<PermutationMatrix> Base;
typedef internal::traits<PermutationMatrix> Traits;
public:
typedef const PermutationMatrix& Nested;
#ifndef EIGEN_PARSED_BY_DOXYGEN
typedef typename Traits::IndicesType IndicesType;
typedef typename Traits::StorageIndex StorageIndex;
#endif
inline PermutationMatrix() {}
/** Constructs an uninitialized permutation matrix of given size.
*/
explicit inline PermutationMatrix(Index size) : m_indices(size) {
eigen_internal_assert(size <= NumTraits<StorageIndex>::highest());
}
/** Copy constructor. */
template <typename OtherDerived>
inline PermutationMatrix(const PermutationBase<OtherDerived>& other) : m_indices(other.indices()) {}
/** Generic constructor from expression of the indices. The indices
* array has the meaning that the permutations sends each integer i to indices[i].
*
* \warning It is your responsibility to check that the indices array that you passes actually
* describes a permutation, i.e., each value between 0 and n-1 occurs exactly once, where n is the
* array's size.
*/
template <typename Other>
explicit inline PermutationMatrix(const MatrixBase<Other>& indices) : m_indices(indices) {}
/** Convert the Transpositions \a tr to a permutation matrix */
template <typename Other>
explicit PermutationMatrix(const TranspositionsBase<Other>& tr) : m_indices(tr.size()) {
*this = tr;
}
/** Copies the other permutation into *this */
template <typename Other>
PermutationMatrix& operator=(const PermutationBase<Other>& other) {
m_indices = other.indices();
return *this;
}
/** Assignment from the Transpositions \a tr */
template <typename Other>
PermutationMatrix& operator=(const TranspositionsBase<Other>& tr) {
return Base::operator=(tr.derived());
}
/** const version of indices(). */
const IndicesType& indices() const { return m_indices; }
/** \returns a reference to the stored array representing the permutation. */
IndicesType& indices() { return m_indices; }
/**** multiplication helpers to hopefully get RVO ****/
#ifndef EIGEN_PARSED_BY_DOXYGEN
template <typename Other>
PermutationMatrix(const InverseImpl<Other, PermutationStorage>& other)
: m_indices(other.derived().nestedExpression().size()) {
eigen_internal_assert(m_indices.size() <= NumTraits<StorageIndex>::highest());
StorageIndex end = StorageIndex(m_indices.size());
for (StorageIndex i = 0; i < end; ++i)
m_indices.coeffRef(other.derived().nestedExpression().indices().coeff(i)) = i;
}
template <typename Lhs, typename Rhs>
PermutationMatrix(internal::PermPermProduct_t, const Lhs& lhs, const Rhs& rhs) : m_indices(lhs.indices().size()) {
Base::assignProduct(lhs, rhs);
}
#endif
protected:
IndicesType m_indices;
};
namespace internal {
template <int SizeAtCompileTime, int MaxSizeAtCompileTime, typename StorageIndex_, int PacketAccess_>
struct traits<Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_>, PacketAccess_> >
: traits<
Matrix<StorageIndex_, SizeAtCompileTime, SizeAtCompileTime, 0, MaxSizeAtCompileTime, MaxSizeAtCompileTime> > {
typedef PermutationStorage StorageKind;
typedef Map<const Matrix<StorageIndex_, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1>, PacketAccess_> IndicesType;
typedef StorageIndex_ StorageIndex;
typedef void Scalar;
};
} // namespace internal
template <int SizeAtCompileTime, int MaxSizeAtCompileTime, typename StorageIndex_, int PacketAccess_>
class Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_>, PacketAccess_>
: public PermutationBase<
Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_>, PacketAccess_> > {
typedef PermutationBase<Map> Base;
typedef internal::traits<Map> Traits;
public:
#ifndef EIGEN_PARSED_BY_DOXYGEN
typedef typename Traits::IndicesType IndicesType;
typedef typename IndicesType::Scalar StorageIndex;
#endif
inline Map(const StorageIndex* indicesPtr) : m_indices(indicesPtr) {}
inline Map(const StorageIndex* indicesPtr, Index size) : m_indices(indicesPtr, size) {}
/** Copies the other permutation into *this */
template <typename Other>
Map& operator=(const PermutationBase<Other>& other) {
return Base::operator=(other.derived());
}
/** Assignment from the Transpositions \a tr */
template <typename Other>
Map& operator=(const TranspositionsBase<Other>& tr) {
return Base::operator=(tr.derived());
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** This is a special case of the templated operator=. Its purpose is to
* prevent a default operator= from hiding the templated operator=.
*/
Map& operator=(const Map& other) {
m_indices = other.m_indices;
return *this;
}
#endif
/** const version of indices(). */
const IndicesType& indices() const { return m_indices; }
/** \returns a reference to the stored array representing the permutation. */
IndicesType& indices() { return m_indices; }
protected:
IndicesType m_indices;
};
template <typename IndicesType_>
class TranspositionsWrapper;
namespace internal {
template <typename IndicesType_>
struct traits<PermutationWrapper<IndicesType_> > {
typedef PermutationStorage StorageKind;
typedef void Scalar;
typedef typename IndicesType_::Scalar StorageIndex;
typedef IndicesType_ IndicesType;
enum {
RowsAtCompileTime = IndicesType_::SizeAtCompileTime,
ColsAtCompileTime = IndicesType_::SizeAtCompileTime,
MaxRowsAtCompileTime = IndicesType::MaxSizeAtCompileTime,
MaxColsAtCompileTime = IndicesType::MaxSizeAtCompileTime,
Flags = 0
};
};
} // namespace internal
/** \class PermutationWrapper
* \ingroup Core_Module
*
* \brief Class to view a vector of integers as a permutation matrix
*
* \tparam IndicesType_ the type of the vector of integer (can be any compatible expression)
*
* This class allows to view any vector expression of integers as a permutation matrix.
*
* \sa class PermutationBase, class PermutationMatrix
*/
template <typename IndicesType_>
class PermutationWrapper : public PermutationBase<PermutationWrapper<IndicesType_> > {
typedef PermutationBase<PermutationWrapper> Base;
typedef internal::traits<PermutationWrapper> Traits;
public:
#ifndef EIGEN_PARSED_BY_DOXYGEN
typedef typename Traits::IndicesType IndicesType;
#endif
inline PermutationWrapper(const IndicesType& indices) : m_indices(indices) {}
/** const version of indices(). */
const internal::remove_all_t<typename IndicesType::Nested>& indices() const { return m_indices; }
protected:
typename IndicesType::Nested m_indices;
};
/** \returns the matrix with the permutation applied to the columns.
*/
template <typename MatrixDerived, typename PermutationDerived>
EIGEN_DEVICE_FUNC const Product<MatrixDerived, PermutationDerived, DefaultProduct> operator*(
const MatrixBase<MatrixDerived>& matrix, const PermutationBase<PermutationDerived>& permutation) {
return Product<MatrixDerived, PermutationDerived, DefaultProduct>(matrix.derived(), permutation.derived());
}
/** \returns the matrix with the permutation applied to the rows.
*/
template <typename PermutationDerived, typename MatrixDerived>
EIGEN_DEVICE_FUNC const Product<PermutationDerived, MatrixDerived, DefaultProduct> operator*(
const PermutationBase<PermutationDerived>& permutation, const MatrixBase<MatrixDerived>& matrix) {
return Product<PermutationDerived, MatrixDerived, DefaultProduct>(permutation.derived(), matrix.derived());
}
template <typename PermutationType>
class InverseImpl<PermutationType, PermutationStorage> : public EigenBase<Inverse<PermutationType> > {
typedef typename PermutationType::PlainPermutationType PlainPermutationType;
typedef internal::traits<PermutationType> PermTraits;
protected:
InverseImpl() {}
public:
typedef Inverse<PermutationType> InverseType;
using EigenBase<Inverse<PermutationType> >::derived;
#ifndef EIGEN_PARSED_BY_DOXYGEN
typedef typename PermutationType::DenseMatrixType DenseMatrixType;
enum {
RowsAtCompileTime = PermTraits::RowsAtCompileTime,
ColsAtCompileTime = PermTraits::ColsAtCompileTime,
MaxRowsAtCompileTime = PermTraits::MaxRowsAtCompileTime,
MaxColsAtCompileTime = PermTraits::MaxColsAtCompileTime
};
#endif
#ifndef EIGEN_PARSED_BY_DOXYGEN
template <typename DenseDerived>
void evalTo(MatrixBase<DenseDerived>& other) const {
other.setZero();
for (Index i = 0; i < derived().rows(); ++i)
other.coeffRef(i, derived().nestedExpression().indices().coeff(i)) = typename DenseDerived::Scalar(1);
}
#endif
/** \return the equivalent permutation matrix */
PlainPermutationType eval() const { return derived(); }
DenseMatrixType toDenseMatrix() const { return derived(); }
/** \returns the matrix with the inverse permutation applied to the columns.
*/
template <typename OtherDerived>
friend const Product<OtherDerived, InverseType, DefaultProduct> operator*(const MatrixBase<OtherDerived>& matrix,
const InverseType& trPerm) {
return Product<OtherDerived, InverseType, DefaultProduct>(matrix.derived(), trPerm.derived());
}
/** \returns the matrix with the inverse permutation applied to the rows.
*/
template <typename OtherDerived>
const Product<InverseType, OtherDerived, DefaultProduct> operator*(const MatrixBase<OtherDerived>& matrix) const {
return Product<InverseType, OtherDerived, DefaultProduct>(derived(), matrix.derived());
}
};
template <typename Derived>
const PermutationWrapper<const Derived> MatrixBase<Derived>::asPermutation() const {
return derived();
}
namespace internal {
template <>
struct AssignmentKind<DenseShape, PermutationShape> {
typedef EigenBase2EigenBase Kind;
};
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_PERMUTATIONMATRIX_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_PRODUCT_H
#define EIGEN_PRODUCT_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
template <typename Lhs, typename Rhs, int Option, typename StorageKind>
class ProductImpl;
namespace internal {
template <typename Lhs, typename Rhs, int Option>
struct traits<Product<Lhs, Rhs, Option>> {
typedef remove_all_t<Lhs> LhsCleaned;
typedef remove_all_t<Rhs> RhsCleaned;
typedef traits<LhsCleaned> LhsTraits;
typedef traits<RhsCleaned> RhsTraits;
typedef MatrixXpr XprKind;
typedef typename ScalarBinaryOpTraits<typename traits<LhsCleaned>::Scalar,
typename traits<RhsCleaned>::Scalar>::ReturnType Scalar;
typedef typename product_promote_storage_type<typename LhsTraits::StorageKind, typename RhsTraits::StorageKind,
internal::product_type<Lhs, Rhs>::ret>::ret StorageKind;
typedef typename promote_index_type<typename LhsTraits::StorageIndex, typename RhsTraits::StorageIndex>::type
StorageIndex;
enum {
RowsAtCompileTime = LhsTraits::RowsAtCompileTime,
ColsAtCompileTime = RhsTraits::ColsAtCompileTime,
MaxRowsAtCompileTime = LhsTraits::MaxRowsAtCompileTime,
MaxColsAtCompileTime = RhsTraits::MaxColsAtCompileTime,
// FIXME: only needed by GeneralMatrixMatrixTriangular
InnerSize = min_size_prefer_fixed(LhsTraits::ColsAtCompileTime, RhsTraits::RowsAtCompileTime),
// The storage order is somewhat arbitrary here. The correct one will be determined through the evaluator.
Flags = (MaxRowsAtCompileTime == 1 && MaxColsAtCompileTime != 1) ? RowMajorBit
: (MaxColsAtCompileTime == 1 && MaxRowsAtCompileTime != 1) ? 0
: (((LhsTraits::Flags & NoPreferredStorageOrderBit) && (RhsTraits::Flags & RowMajorBit)) ||
((RhsTraits::Flags & NoPreferredStorageOrderBit) && (LhsTraits::Flags & RowMajorBit)))
? RowMajorBit
: NoPreferredStorageOrderBit
};
};
struct TransposeProductEnum {
// convenience enumerations to specialize transposed products
enum : int {
Default = 0x00,
Matrix = 0x01,
Permutation = 0x02,
MatrixMatrix = (Matrix << 8) | Matrix,
MatrixPermutation = (Matrix << 8) | Permutation,
PermutationMatrix = (Permutation << 8) | Matrix
};
};
template <typename Xpr>
struct TransposeKind {
static constexpr int Kind = is_matrix_base_xpr<Xpr>::value ? TransposeProductEnum::Matrix
: is_permutation_base_xpr<Xpr>::value ? TransposeProductEnum::Permutation
: TransposeProductEnum::Default;
};
template <typename Lhs, typename Rhs>
struct TransposeProductKind {
static constexpr int Kind = (TransposeKind<Lhs>::Kind << 8) | TransposeKind<Rhs>::Kind;
};
template <typename Lhs, typename Rhs, int Option, int Kind = TransposeProductKind<Lhs, Rhs>::Kind>
struct product_transpose_helper {
// by default, don't optimize the transposed product
using Derived = Product<Lhs, Rhs, Option>;
using Scalar = typename Derived::Scalar;
using TransposeType = Transpose<const Derived>;
using ConjugateTransposeType = CwiseUnaryOp<scalar_conjugate_op<Scalar>, TransposeType>;
using AdjointType = std::conditional_t<NumTraits<Scalar>::IsComplex, ConjugateTransposeType, TransposeType>;
// return (lhs * rhs)^T
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TransposeType run_transpose(const Derived& derived) {
return TransposeType(derived);
}
// return (lhs * rhs)^H
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE AdjointType run_adjoint(const Derived& derived) {
return AdjointType(TransposeType(derived));
}
};
template <typename Lhs, typename Rhs, int Option>
struct product_transpose_helper<Lhs, Rhs, Option, TransposeProductEnum::MatrixMatrix> {
// expand the transposed matrix-matrix product
using Derived = Product<Lhs, Rhs, Option>;
using LhsScalar = typename traits<Lhs>::Scalar;
using LhsTransposeType = typename DenseBase<Lhs>::ConstTransposeReturnType;
using LhsConjugateTransposeType = CwiseUnaryOp<scalar_conjugate_op<LhsScalar>, LhsTransposeType>;
using LhsAdjointType =
std::conditional_t<NumTraits<LhsScalar>::IsComplex, LhsConjugateTransposeType, LhsTransposeType>;
using RhsScalar = typename traits<Rhs>::Scalar;
using RhsTransposeType = typename DenseBase<Rhs>::ConstTransposeReturnType;
using RhsConjugateTransposeType = CwiseUnaryOp<scalar_conjugate_op<RhsScalar>, RhsTransposeType>;
using RhsAdjointType =
std::conditional_t<NumTraits<RhsScalar>::IsComplex, RhsConjugateTransposeType, RhsTransposeType>;
using TransposeType = Product<RhsTransposeType, LhsTransposeType, Option>;
using AdjointType = Product<RhsAdjointType, LhsAdjointType, Option>;
// return rhs^T * lhs^T
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TransposeType run_transpose(const Derived& derived) {
return TransposeType(RhsTransposeType(derived.rhs()), LhsTransposeType(derived.lhs()));
}
// return rhs^H * lhs^H
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE AdjointType run_adjoint(const Derived& derived) {
return AdjointType(RhsAdjointType(RhsTransposeType(derived.rhs())),
LhsAdjointType(LhsTransposeType(derived.lhs())));
}
};
template <typename Lhs, typename Rhs, int Option>
struct product_transpose_helper<Lhs, Rhs, Option, TransposeProductEnum::PermutationMatrix> {
// expand the transposed permutation-matrix product
using Derived = Product<Lhs, Rhs, Option>;
using LhsInverseType = typename PermutationBase<Lhs>::InverseReturnType;
using RhsScalar = typename traits<Rhs>::Scalar;
using RhsTransposeType = typename DenseBase<Rhs>::ConstTransposeReturnType;
using RhsConjugateTransposeType = CwiseUnaryOp<scalar_conjugate_op<RhsScalar>, RhsTransposeType>;
using RhsAdjointType =
std::conditional_t<NumTraits<RhsScalar>::IsComplex, RhsConjugateTransposeType, RhsTransposeType>;
using TransposeType = Product<RhsTransposeType, LhsInverseType, Option>;
using AdjointType = Product<RhsAdjointType, LhsInverseType, Option>;
// return rhs^T * lhs^-1
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TransposeType run_transpose(const Derived& derived) {
return TransposeType(RhsTransposeType(derived.rhs()), LhsInverseType(derived.lhs()));
}
// return rhs^H * lhs^-1
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE AdjointType run_adjoint(const Derived& derived) {
return AdjointType(RhsAdjointType(RhsTransposeType(derived.rhs())), LhsInverseType(derived.lhs()));
}
};
template <typename Lhs, typename Rhs, int Option>
struct product_transpose_helper<Lhs, Rhs, Option, TransposeProductEnum::MatrixPermutation> {
// expand the transposed matrix-permutation product
using Derived = Product<Lhs, Rhs, Option>;
using LhsScalar = typename traits<Lhs>::Scalar;
using LhsTransposeType = typename DenseBase<Lhs>::ConstTransposeReturnType;
using LhsConjugateTransposeType = CwiseUnaryOp<scalar_conjugate_op<LhsScalar>, LhsTransposeType>;
using LhsAdjointType =
std::conditional_t<NumTraits<LhsScalar>::IsComplex, LhsConjugateTransposeType, LhsTransposeType>;
using RhsInverseType = typename PermutationBase<Rhs>::InverseReturnType;
using TransposeType = Product<RhsInverseType, LhsTransposeType, Option>;
using AdjointType = Product<RhsInverseType, LhsAdjointType, Option>;
// return rhs^-1 * lhs^T
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TransposeType run_transpose(const Derived& derived) {
return TransposeType(RhsInverseType(derived.rhs()), LhsTransposeType(derived.lhs()));
}
// return rhs^-1 * lhs^H
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE AdjointType run_adjoint(const Derived& derived) {
return AdjointType(RhsInverseType(derived.rhs()), LhsAdjointType(LhsTransposeType(derived.lhs())));
}
};
} // end namespace internal
/** \class Product
* \ingroup Core_Module
*
* \brief Expression of the product of two arbitrary matrices or vectors
*
* \tparam Lhs_ the type of the left-hand side expression
* \tparam Rhs_ the type of the right-hand side expression
*
* This class represents an expression of the product of two arbitrary matrices.
*
* The other template parameters are:
* \tparam Option can be DefaultProduct, AliasFreeProduct, or LazyProduct
*
*/
template <typename Lhs_, typename Rhs_, int Option>
class Product
: public ProductImpl<Lhs_, Rhs_, Option,
typename internal::product_promote_storage_type<
typename internal::traits<Lhs_>::StorageKind, typename internal::traits<Rhs_>::StorageKind,
internal::product_type<Lhs_, Rhs_>::ret>::ret> {
public:
typedef Lhs_ Lhs;
typedef Rhs_ Rhs;
typedef
typename ProductImpl<Lhs, Rhs, Option,
typename internal::product_promote_storage_type<
typename internal::traits<Lhs>::StorageKind, typename internal::traits<Rhs>::StorageKind,
internal::product_type<Lhs, Rhs>::ret>::ret>::Base Base;
EIGEN_GENERIC_PUBLIC_INTERFACE(Product)
typedef typename internal::ref_selector<Lhs>::type LhsNested;
typedef typename internal::ref_selector<Rhs>::type RhsNested;
typedef internal::remove_all_t<LhsNested> LhsNestedCleaned;
typedef internal::remove_all_t<RhsNested> RhsNestedCleaned;
using TransposeReturnType = typename internal::product_transpose_helper<Lhs, Rhs, Option>::TransposeType;
using AdjointReturnType = typename internal::product_transpose_helper<Lhs, Rhs, Option>::AdjointType;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Product(const Lhs& lhs, const Rhs& rhs) : m_lhs(lhs), m_rhs(rhs) {
eigen_assert(lhs.cols() == rhs.rows() && "invalid matrix product" &&
"if you wanted a coeff-wise or a dot product use the respective explicit functions");
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index rows() const noexcept { return m_lhs.rows(); }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index cols() const noexcept { return m_rhs.cols(); }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const LhsNestedCleaned& lhs() const { return m_lhs; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const RhsNestedCleaned& rhs() const { return m_rhs; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TransposeReturnType transpose() const {
return internal::product_transpose_helper<Lhs, Rhs, Option>::run_transpose(*this);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE AdjointReturnType adjoint() const {
return internal::product_transpose_helper<Lhs, Rhs, Option>::run_adjoint(*this);
}
protected:
LhsNested m_lhs;
RhsNested m_rhs;
};
namespace internal {
template <typename Lhs, typename Rhs, int Option, int ProductTag = internal::product_type<Lhs, Rhs>::ret>
class dense_product_base : public internal::dense_xpr_base<Product<Lhs, Rhs, Option>>::type {};
/** Conversion to scalar for inner-products */
template <typename Lhs, typename Rhs, int Option>
class dense_product_base<Lhs, Rhs, Option, InnerProduct>
: public internal::dense_xpr_base<Product<Lhs, Rhs, Option>>::type {
typedef Product<Lhs, Rhs, Option> ProductXpr;
typedef typename internal::dense_xpr_base<ProductXpr>::type Base;
public:
using Base::derived;
typedef typename Base::Scalar Scalar;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE operator const Scalar() const {
return internal::evaluator<ProductXpr>(derived()).coeff(0, 0);
}
};
} // namespace internal
// Generic API dispatcher
template <typename Lhs, typename Rhs, int Option, typename StorageKind>
class ProductImpl : public internal::generic_xpr_base<Product<Lhs, Rhs, Option>, MatrixXpr, StorageKind>::type {
public:
typedef typename internal::generic_xpr_base<Product<Lhs, Rhs, Option>, MatrixXpr, StorageKind>::type Base;
};
template <typename Lhs, typename Rhs, int Option>
class ProductImpl<Lhs, Rhs, Option, Dense> : public internal::dense_product_base<Lhs, Rhs, Option> {
typedef Product<Lhs, Rhs, Option> Derived;
public:
typedef typename internal::dense_product_base<Lhs, Rhs, Option> Base;
EIGEN_DENSE_PUBLIC_INTERFACE(Derived)
protected:
enum {
IsOneByOne = (RowsAtCompileTime == 1 || RowsAtCompileTime == Dynamic) &&
(ColsAtCompileTime == 1 || ColsAtCompileTime == Dynamic),
EnableCoeff = IsOneByOne || Option == LazyProduct
};
public:
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(Index row, Index col) const {
EIGEN_STATIC_ASSERT(EnableCoeff, THIS_METHOD_IS_ONLY_FOR_INNER_OR_LAZY_PRODUCTS);
eigen_assert((Option == LazyProduct) || (this->rows() == 1 && this->cols() == 1));
return internal::evaluator<Derived>(derived()).coeff(row, col);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(Index i) const {
EIGEN_STATIC_ASSERT(EnableCoeff, THIS_METHOD_IS_ONLY_FOR_INNER_OR_LAZY_PRODUCTS);
eigen_assert((Option == LazyProduct) || (this->rows() == 1 && this->cols() == 1));
return internal::evaluator<Derived>(derived()).coeff(i);
}
};
} // end namespace Eigen
#endif // EIGEN_PRODUCT_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_RANDOM_H
#define EIGEN_RANDOM_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
template <typename Scalar>
struct scalar_random_op {
inline const Scalar operator()() const { return random<Scalar>(); }
};
template <typename Scalar>
struct functor_traits<scalar_random_op<Scalar> > {
enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = false, IsRepeatable = false };
};
} // end namespace internal
/** \returns a random matrix expression
*
* Numbers are uniformly spread through their whole definition range for integer types,
* and in the [-1:1] range for floating point scalar types.
*
* The parameters \a rows and \a cols are the number of rows and of columns of
* the returned matrix. Must be compatible with this MatrixBase type.
*
* \not_reentrant
*
* This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
* it is redundant to pass \a rows and \a cols as arguments, so Random() should be used
* instead.
*
*
* Example: \include MatrixBase_random_int_int.cpp
* Output: \verbinclude MatrixBase_random_int_int.out
*
* This expression has the "evaluate before nesting" flag so that it will be evaluated into
* a temporary matrix whenever it is nested in a larger expression. This prevents unexpected
* behavior with expressions involving random matrices.
*
* See DenseBase::NullaryExpr(Index, const CustomNullaryOp&) for an example using C++11 random generators.
*
* \sa DenseBase::setRandom(), DenseBase::Random(Index), DenseBase::Random()
*/
template <typename Derived>
inline const typename DenseBase<Derived>::RandomReturnType DenseBase<Derived>::Random(Index rows, Index cols) {
return NullaryExpr(rows, cols, internal::scalar_random_op<Scalar>());
}
/** \returns a random vector expression
*
* Numbers are uniformly spread through their whole definition range for integer types,
* and in the [-1:1] range for floating point scalar types.
*
* The parameter \a size is the size of the returned vector.
* Must be compatible with this MatrixBase type.
*
* \only_for_vectors
* \not_reentrant
*
* This variant is meant to be used for dynamic-size vector types. For fixed-size types,
* it is redundant to pass \a size as argument, so Random() should be used
* instead.
*
* Example: \include MatrixBase_random_int.cpp
* Output: \verbinclude MatrixBase_random_int.out
*
* This expression has the "evaluate before nesting" flag so that it will be evaluated into
* a temporary vector whenever it is nested in a larger expression. This prevents unexpected
* behavior with expressions involving random matrices.
*
* \sa DenseBase::setRandom(), DenseBase::Random(Index,Index), DenseBase::Random()
*/
template <typename Derived>
inline const typename DenseBase<Derived>::RandomReturnType DenseBase<Derived>::Random(Index size) {
return NullaryExpr(size, internal::scalar_random_op<Scalar>());
}
/** \returns a fixed-size random matrix or vector expression
*
* Numbers are uniformly spread through their whole definition range for integer types,
* and in the [-1:1] range for floating point scalar types.
*
* This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
* need to use the variants taking size arguments.
*
* Example: \include MatrixBase_random.cpp
* Output: \verbinclude MatrixBase_random.out
*
* This expression has the "evaluate before nesting" flag so that it will be evaluated into
* a temporary matrix whenever it is nested in a larger expression. This prevents unexpected
* behavior with expressions involving random matrices.
*
* \not_reentrant
*
* \sa DenseBase::setRandom(), DenseBase::Random(Index,Index), DenseBase::Random(Index)
*/
template <typename Derived>
inline const typename DenseBase<Derived>::RandomReturnType DenseBase<Derived>::Random() {
return NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, internal::scalar_random_op<Scalar>());
}
/** Sets all coefficients in this expression to random values.
*
* Numbers are uniformly spread through their whole definition range for integer types,
* and in the [-1:1] range for floating point scalar types.
*
* \not_reentrant
*
* Example: \include MatrixBase_setRandom.cpp
* Output: \verbinclude MatrixBase_setRandom.out
*
* \sa class CwiseNullaryOp, setRandom(Index), setRandom(Index,Index)
*/
template <typename Derived>
EIGEN_DEVICE_FUNC inline Derived& DenseBase<Derived>::setRandom() {
return *this = Random(rows(), cols());
}
/** Resizes to the given \a newSize, and sets all coefficients in this expression to random values.
*
* Numbers are uniformly spread through their whole definition range for integer types,
* and in the [-1:1] range for floating point scalar types.
*
* \only_for_vectors
* \not_reentrant
*
* Example: \include Matrix_setRandom_int.cpp
* Output: \verbinclude Matrix_setRandom_int.out
*
* \sa DenseBase::setRandom(), setRandom(Index,Index), class CwiseNullaryOp, DenseBase::Random()
*/
template <typename Derived>
EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setRandom(Index newSize) {
resize(newSize);
return setRandom();
}
/** Resizes to the given size, and sets all coefficients in this expression to random values.
*
* Numbers are uniformly spread through their whole definition range for integer types,
* and in the [-1:1] range for floating point scalar types.
*
* \not_reentrant
*
* \param rows the new number of rows
* \param cols the new number of columns
*
* Example: \include Matrix_setRandom_int_int.cpp
* Output: \verbinclude Matrix_setRandom_int_int.out
*
* \sa DenseBase::setRandom(), setRandom(Index), class CwiseNullaryOp, DenseBase::Random()
*/
template <typename Derived>
EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setRandom(Index rows, Index cols) {
resize(rows, cols);
return setRandom();
}
/** Resizes to the given size, changing only the number of columns, and sets all
* coefficients in this expression to random values. For the parameter of type
* NoChange_t, just pass the special value \c NoChange.
*
* Numbers are uniformly spread through their whole definition range for integer types,
* and in the [-1:1] range for floating point scalar types.
*
* \not_reentrant
*
* \sa DenseBase::setRandom(), setRandom(Index), setRandom(Index, NoChange_t), class CwiseNullaryOp, DenseBase::Random()
*/
template <typename Derived>
EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setRandom(NoChange_t, Index cols) {
return setRandom(rows(), cols);
}
/** Resizes to the given size, changing only the number of rows, and sets all
* coefficients in this expression to random values. For the parameter of type
* NoChange_t, just pass the special value \c NoChange.
*
* Numbers are uniformly spread through their whole definition range for integer types,
* and in the [-1:1] range for floating point scalar types.
*
* \not_reentrant
*
* \sa DenseBase::setRandom(), setRandom(Index), setRandom(NoChange_t, Index), class CwiseNullaryOp, DenseBase::Random()
*/
template <typename Derived>
EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setRandom(Index rows, NoChange_t) {
return setRandom(rows, cols());
}
} // end namespace Eigen
#endif // EIGEN_RANDOM_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2024 Charles Schlosser <cs.schlosser@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_RANDOM_IMPL_H
#define EIGEN_RANDOM_IMPL_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
/****************************************************************************
* Implementation of random *
****************************************************************************/
template <typename Scalar, bool IsComplex, bool IsInteger>
struct random_default_impl {};
template <typename Scalar>
struct random_impl : random_default_impl<Scalar, NumTraits<Scalar>::IsComplex, NumTraits<Scalar>::IsInteger> {};
template <typename Scalar>
struct random_retval {
typedef Scalar type;
};
template <typename Scalar>
inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random(const Scalar& x, const Scalar& y) {
return EIGEN_MATHFUNC_IMPL(random, Scalar)::run(x, y);
}
template <typename Scalar>
inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random() {
return EIGEN_MATHFUNC_IMPL(random, Scalar)::run();
}
// TODO: replace or provide alternatives to this, e.g. std::random_device
struct eigen_random_device {
using ReturnType = int;
static constexpr int Entropy = meta_floor_log2<(unsigned int)(RAND_MAX) + 1>::value;
static constexpr ReturnType Highest = RAND_MAX;
static EIGEN_DEVICE_FUNC inline ReturnType run() { return std::rand(); }
};
// Fill a built-in unsigned integer with numRandomBits beginning with the least significant bit
template <typename Scalar>
struct random_bits_impl {
EIGEN_STATIC_ASSERT(std::is_unsigned<Scalar>::value, SCALAR MUST BE A BUILT - IN UNSIGNED INTEGER)
using RandomDevice = eigen_random_device;
using RandomReturnType = typename RandomDevice::ReturnType;
static constexpr int kEntropy = RandomDevice::Entropy;
static constexpr int kTotalBits = sizeof(Scalar) * CHAR_BIT;
// return a Scalar filled with numRandomBits beginning from the least significant bit
static EIGEN_DEVICE_FUNC inline Scalar run(int numRandomBits) {
eigen_assert((numRandomBits >= 0) && (numRandomBits <= kTotalBits));
const Scalar mask = Scalar(-1) >> ((kTotalBits - numRandomBits) & (kTotalBits - 1));
Scalar randomBits = 0;
for (int shift = 0; shift < numRandomBits; shift += kEntropy) {
RandomReturnType r = RandomDevice::run();
randomBits |= static_cast<Scalar>(r) << shift;
}
// clear the excess bits
randomBits &= mask;
return randomBits;
}
};
template <typename BitsType>
EIGEN_DEVICE_FUNC inline BitsType getRandomBits(int numRandomBits) {
return random_bits_impl<BitsType>::run(numRandomBits);
}
// random implementation for a built-in floating point type
template <typename Scalar, bool BuiltIn = std::is_floating_point<Scalar>::value>
struct random_float_impl {
using BitsType = typename numext::get_integer_by_size<sizeof(Scalar)>::unsigned_type;
static constexpr EIGEN_DEVICE_FUNC inline int mantissaBits() {
const int digits = NumTraits<Scalar>::digits();
return digits - 1;
}
static EIGEN_DEVICE_FUNC inline Scalar run(int numRandomBits) {
eigen_assert(numRandomBits >= 0 && numRandomBits <= mantissaBits());
BitsType randomBits = getRandomBits<BitsType>(numRandomBits);
// if fewer than MantissaBits is requested, shift them to the left
randomBits <<= (mantissaBits() - numRandomBits);
// randomBits is in the half-open interval [2,4)
randomBits |= numext::bit_cast<BitsType>(Scalar(2));
// result is in the half-open interval [-1,1)
Scalar result = numext::bit_cast<Scalar>(randomBits) - Scalar(3);
return result;
}
};
// random implementation for a custom floating point type
// uses double as the implementation with a mantissa with a size equal to either the target scalar's mantissa or that of
// double, whichever is smaller
template <typename Scalar>
struct random_float_impl<Scalar, false> {
static EIGEN_DEVICE_FUNC inline int mantissaBits() {
const int digits = NumTraits<Scalar>::digits();
constexpr int kDoubleDigits = NumTraits<double>::digits();
return numext::mini(digits, kDoubleDigits) - 1;
}
static EIGEN_DEVICE_FUNC inline Scalar run(int numRandomBits) {
eigen_assert(numRandomBits >= 0 && numRandomBits <= mantissaBits());
Scalar result = static_cast<Scalar>(random_float_impl<double>::run(numRandomBits));
return result;
}
};
#if !EIGEN_COMP_NVCC
// random implementation for long double
// this specialization is not compatible with double-double scalars
template <bool Specialize = (sizeof(long double) == 2 * sizeof(uint64_t)) &&
((std::numeric_limits<long double>::digits != (2 * std::numeric_limits<double>::digits)))>
struct random_longdouble_impl {
static constexpr int Size = sizeof(long double);
static constexpr EIGEN_DEVICE_FUNC int mantissaBits() { return NumTraits<long double>::digits() - 1; }
static EIGEN_DEVICE_FUNC inline long double run(int numRandomBits) {
eigen_assert(numRandomBits >= 0 && numRandomBits <= mantissaBits());
EIGEN_USING_STD(memcpy);
int numLowBits = numext::mini(numRandomBits, 64);
int numHighBits = numext::maxi(numRandomBits - 64, 0);
uint64_t randomBits[2];
long double result = 2.0L;
memcpy(&randomBits, &result, Size);
#if __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__
randomBits[0] |= getRandomBits<uint64_t>(numLowBits);
randomBits[1] |= getRandomBits<uint64_t>(numHighBits);
#elif __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__
randomBits[0] |= getRandomBits<uint64_t>(numHighBits);
randomBits[1] |= getRandomBits<uint64_t>(numLowBits);
#else
#error Unexpected or undefined __BYTE_ORDER__
#endif
memcpy(&result, &randomBits, Size);
result -= 3.0L;
return result;
}
};
template <>
struct random_longdouble_impl<false> {
static constexpr EIGEN_DEVICE_FUNC int mantissaBits() { return NumTraits<double>::digits() - 1; }
static EIGEN_DEVICE_FUNC inline long double run(int numRandomBits) {
return static_cast<long double>(random_float_impl<double>::run(numRandomBits));
}
};
template <>
struct random_float_impl<long double> : random_longdouble_impl<> {};
#endif
template <typename Scalar>
struct random_default_impl<Scalar, false, false> {
using Impl = random_float_impl<Scalar>;
static EIGEN_DEVICE_FUNC inline Scalar run(const Scalar& x, const Scalar& y, int numRandomBits) {
Scalar half_x = Scalar(0.5) * x;
Scalar half_y = Scalar(0.5) * y;
Scalar result = (half_x + half_y) + (half_y - half_x) * run(numRandomBits);
// result is in the half-open interval [x, y) -- provided that x < y
return result;
}
static EIGEN_DEVICE_FUNC inline Scalar run(const Scalar& x, const Scalar& y) {
return run(x, y, Impl::mantissaBits());
}
static EIGEN_DEVICE_FUNC inline Scalar run(int numRandomBits) { return Impl::run(numRandomBits); }
static EIGEN_DEVICE_FUNC inline Scalar run() { return run(Impl::mantissaBits()); }
};
template <typename Scalar, bool IsSigned = NumTraits<Scalar>::IsSigned, bool BuiltIn = std::is_integral<Scalar>::value>
struct random_int_impl;
// random implementation for a built-in unsigned integer type
template <typename Scalar>
struct random_int_impl<Scalar, false, true> {
static constexpr int kTotalBits = sizeof(Scalar) * CHAR_BIT;
static EIGEN_DEVICE_FUNC inline Scalar run(const Scalar& x, const Scalar& y) {
if (y <= x) return x;
Scalar range = y - x;
// handle edge case where [x,y] spans the entire range of Scalar
if (range == NumTraits<Scalar>::highest()) return run();
Scalar count = range + 1;
// calculate the number of random bits needed to fill range
int numRandomBits = log2_ceil(count);
Scalar randomBits;
do {
randomBits = getRandomBits<Scalar>(numRandomBits);
// if the random draw is outside [0, range), try again (rejection sampling)
// in the worst-case scenario, the probability of rejection is: 1/2 - 1/2^numRandomBits < 50%
} while (randomBits >= count);
Scalar result = x + randomBits;
return result;
}
static EIGEN_DEVICE_FUNC inline Scalar run() { return getRandomBits<Scalar>(kTotalBits); }
};
// random implementation for a built-in signed integer type
template <typename Scalar>
struct random_int_impl<Scalar, true, true> {
static constexpr int kTotalBits = sizeof(Scalar) * CHAR_BIT;
using BitsType = typename make_unsigned<Scalar>::type;
static EIGEN_DEVICE_FUNC inline Scalar run(const Scalar& x, const Scalar& y) {
if (y <= x) return x;
// Avoid overflow by representing `range` as an unsigned type
BitsType range = static_cast<BitsType>(y) - static_cast<BitsType>(x);
BitsType randomBits = random_int_impl<BitsType>::run(0, range);
// Avoid overflow in the case where `x` is negative and there is a large range so
// `randomBits` would also be negative if cast to `Scalar` first.
Scalar result = static_cast<Scalar>(static_cast<BitsType>(x) + randomBits);
return result;
}
static EIGEN_DEVICE_FUNC inline Scalar run() { return static_cast<Scalar>(getRandomBits<BitsType>(kTotalBits)); }
};
// todo: custom integers
template <typename Scalar, bool IsSigned>
struct random_int_impl<Scalar, IsSigned, false> {
static EIGEN_DEVICE_FUNC inline Scalar run(const Scalar&, const Scalar&) { return run(); }
static EIGEN_DEVICE_FUNC inline Scalar run() {
eigen_assert(std::false_type::value && "RANDOM FOR CUSTOM INTEGERS NOT YET SUPPORTED");
return Scalar(0);
}
};
template <typename Scalar>
struct random_default_impl<Scalar, false, true> : random_int_impl<Scalar> {};
template <>
struct random_impl<bool> {
static EIGEN_DEVICE_FUNC inline bool run(const bool& x, const bool& y) {
if (y <= x) return x;
return run();
}
static EIGEN_DEVICE_FUNC inline bool run() { return getRandomBits<unsigned>(1) ? true : false; }
};
template <typename Scalar>
struct random_default_impl<Scalar, true, false> {
typedef typename NumTraits<Scalar>::Real RealScalar;
using Impl = random_impl<RealScalar>;
static EIGEN_DEVICE_FUNC inline Scalar run(const Scalar& x, const Scalar& y, int numRandomBits) {
return Scalar(Impl::run(x.real(), y.real(), numRandomBits), Impl::run(x.imag(), y.imag(), numRandomBits));
}
static EIGEN_DEVICE_FUNC inline Scalar run(const Scalar& x, const Scalar& y) {
return Scalar(Impl::run(x.real(), y.real()), Impl::run(x.imag(), y.imag()));
}
static EIGEN_DEVICE_FUNC inline Scalar run(int numRandomBits) {
return Scalar(Impl::run(numRandomBits), Impl::run(numRandomBits));
}
static EIGEN_DEVICE_FUNC inline Scalar run() { return Scalar(Impl::run(), Impl::run()); }
};
} // namespace internal
} // namespace Eigen
#endif // EIGEN_RANDOM_IMPL_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2025 Charlie Schlosser <cs.schlosser@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_REALVIEW_H
#define EIGEN_REALVIEW_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
// Vectorized assignment to RealView requires array-oriented access to the real and imaginary components.
// From https://en.cppreference.com/w/cpp/numeric/complex.html:
// For any pointer to an element of an array of std::complex<T> named p and any valid array index i,
// reinterpret_cast<T*>(p)[2 * i] is the real part of the complex number p[i], and
// reinterpret_cast<T*>(p)[2 * i + 1] is the imaginary part of the complex number p[i].
template <typename ComplexScalar>
struct complex_array_access : std::false_type {};
template <>
struct complex_array_access<std::complex<float>> : std::true_type {};
template <>
struct complex_array_access<std::complex<double>> : std::true_type {};
template <>
struct complex_array_access<std::complex<long double>> : std::true_type {};
template <typename Xpr>
struct traits<RealView<Xpr>> : public traits<Xpr> {
template <typename T>
static constexpr int double_size(T size, bool times_two) {
int size_as_int = int(size);
if (size_as_int == Dynamic) return Dynamic;
return times_two ? (2 * size_as_int) : size_as_int;
}
using Base = traits<Xpr>;
using ComplexScalar = typename Base::Scalar;
using Scalar = typename NumTraits<ComplexScalar>::Real;
static constexpr int ActualDirectAccessBit = complex_array_access<ComplexScalar>::value ? DirectAccessBit : 0;
static constexpr int ActualPacketAccessBit = packet_traits<Scalar>::Vectorizable ? PacketAccessBit : 0;
static constexpr int FlagMask =
ActualDirectAccessBit | ActualPacketAccessBit | HereditaryBits | LinearAccessBit | LvalueBit;
static constexpr int BaseFlags = int(evaluator<Xpr>::Flags) | int(Base::Flags);
static constexpr int Flags = BaseFlags & FlagMask;
static constexpr bool IsRowMajor = Flags & RowMajorBit;
static constexpr int RowsAtCompileTime = double_size(Base::RowsAtCompileTime, !IsRowMajor);
static constexpr int ColsAtCompileTime = double_size(Base::ColsAtCompileTime, IsRowMajor);
static constexpr int SizeAtCompileTime = size_at_compile_time(RowsAtCompileTime, ColsAtCompileTime);
static constexpr int MaxRowsAtCompileTime = double_size(Base::MaxRowsAtCompileTime, !IsRowMajor);
static constexpr int MaxColsAtCompileTime = double_size(Base::MaxColsAtCompileTime, IsRowMajor);
static constexpr int MaxSizeAtCompileTime = size_at_compile_time(MaxRowsAtCompileTime, MaxColsAtCompileTime);
static constexpr int OuterStrideAtCompileTime = double_size(outer_stride_at_compile_time<Xpr>::ret, true);
static constexpr int InnerStrideAtCompileTime = inner_stride_at_compile_time<Xpr>::ret;
};
template <typename Xpr>
struct evaluator<RealView<Xpr>> : private evaluator<Xpr> {
using BaseEvaluator = evaluator<Xpr>;
using XprType = RealView<Xpr>;
using ExpressionTraits = traits<XprType>;
using ComplexScalar = typename ExpressionTraits::ComplexScalar;
using ComplexCoeffReturnType = typename BaseEvaluator::CoeffReturnType;
using Scalar = typename ExpressionTraits::Scalar;
static constexpr bool IsRowMajor = ExpressionTraits::IsRowMajor;
static constexpr int Flags = ExpressionTraits::Flags;
static constexpr int CoeffReadCost = BaseEvaluator::CoeffReadCost;
static constexpr int Alignment = BaseEvaluator::Alignment;
EIGEN_DEVICE_FUNC explicit evaluator(XprType realView) : BaseEvaluator(realView.m_xpr) {}
template <bool Enable = std::is_reference<ComplexCoeffReturnType>::value, typename = std::enable_if_t<!Enable>>
constexpr EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(Index row, Index col) const {
ComplexCoeffReturnType cscalar = BaseEvaluator::coeff(IsRowMajor ? row : row / 2, IsRowMajor ? col / 2 : col);
Index p = (IsRowMajor ? col : row) & 1;
return p ? numext::real(cscalar) : numext::imag(cscalar);
}
template <bool Enable = std::is_reference<ComplexCoeffReturnType>::value, typename = std::enable_if_t<Enable>>
constexpr EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& coeff(Index row, Index col) const {
ComplexCoeffReturnType cscalar = BaseEvaluator::coeff(IsRowMajor ? row : row / 2, IsRowMajor ? col / 2 : col);
Index p = (IsRowMajor ? col : row) & 1;
return reinterpret_cast<const Scalar(&)[2]>(cscalar)[p];
}
constexpr EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index row, Index col) {
ComplexScalar& cscalar = BaseEvaluator::coeffRef(IsRowMajor ? row : row / 2, IsRowMajor ? col / 2 : col);
Index p = (IsRowMajor ? col : row) & 1;
return reinterpret_cast<Scalar(&)[2]>(cscalar)[p];
}
template <bool Enable = std::is_reference<ComplexCoeffReturnType>::value, typename = std::enable_if_t<!Enable>>
constexpr EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(Index index) const {
ComplexCoeffReturnType cscalar = BaseEvaluator::coeff(index / 2);
Index p = index & 1;
return p ? numext::real(cscalar) : numext::imag(cscalar);
}
template <bool Enable = std::is_reference<ComplexCoeffReturnType>::value, typename = std::enable_if_t<Enable>>
constexpr EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& coeff(Index index) const {
ComplexCoeffReturnType cscalar = BaseEvaluator::coeff(index / 2);
Index p = index & 1;
return reinterpret_cast<const Scalar(&)[2]>(cscalar)[p];
}
constexpr EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index index) {
ComplexScalar& cscalar = BaseEvaluator::coeffRef(index / 2);
Index p = index & 1;
return reinterpret_cast<Scalar(&)[2]>(cscalar)[p];
}
template <int LoadMode, typename PacketType>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(Index row, Index col) const {
constexpr int RealPacketSize = unpacket_traits<PacketType>::size;
using ComplexPacket = typename find_packet_by_size<ComplexScalar, RealPacketSize / 2>::type;
EIGEN_STATIC_ASSERT((find_packet_by_size<ComplexScalar, RealPacketSize / 2>::value),
MISSING COMPATIBLE COMPLEX PACKET TYPE)
eigen_assert(((IsRowMajor ? col : row) % 2 == 0) && "the inner index must be even");
Index crow = IsRowMajor ? row : row / 2;
Index ccol = IsRowMajor ? col / 2 : col;
ComplexPacket cpacket = BaseEvaluator::template packet<LoadMode, ComplexPacket>(crow, ccol);
return preinterpret<PacketType, ComplexPacket>(cpacket);
}
template <int LoadMode, typename PacketType>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(Index index) const {
constexpr int RealPacketSize = unpacket_traits<PacketType>::size;
using ComplexPacket = typename find_packet_by_size<ComplexScalar, RealPacketSize / 2>::type;
EIGEN_STATIC_ASSERT((find_packet_by_size<ComplexScalar, RealPacketSize / 2>::value),
MISSING COMPATIBLE COMPLEX PACKET TYPE)
eigen_assert((index % 2 == 0) && "the index must be even");
Index cindex = index / 2;
ComplexPacket cpacket = BaseEvaluator::template packet<LoadMode, ComplexPacket>(cindex);
return preinterpret<PacketType, ComplexPacket>(cpacket);
}
template <int LoadMode, typename PacketType>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packetSegment(Index row, Index col, Index begin, Index count) const {
constexpr int RealPacketSize = unpacket_traits<PacketType>::size;
using ComplexPacket = typename find_packet_by_size<ComplexScalar, RealPacketSize / 2>::type;
EIGEN_STATIC_ASSERT((find_packet_by_size<ComplexScalar, RealPacketSize / 2>::value),
MISSING COMPATIBLE COMPLEX PACKET TYPE)
eigen_assert(((IsRowMajor ? col : row) % 2 == 0) && "the inner index must be even");
eigen_assert((begin % 2 == 0) && (count % 2 == 0) && "begin and count must be even");
Index crow = IsRowMajor ? row : row / 2;
Index ccol = IsRowMajor ? col / 2 : col;
Index cbegin = begin / 2;
Index ccount = count / 2;
ComplexPacket cpacket = BaseEvaluator::template packetSegment<LoadMode, ComplexPacket>(crow, ccol, cbegin, ccount);
return preinterpret<PacketType, ComplexPacket>(cpacket);
}
template <int LoadMode, typename PacketType>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packetSegment(Index index, Index begin, Index count) const {
constexpr int RealPacketSize = unpacket_traits<PacketType>::size;
using ComplexPacket = typename find_packet_by_size<ComplexScalar, RealPacketSize / 2>::type;
EIGEN_STATIC_ASSERT((find_packet_by_size<ComplexScalar, RealPacketSize / 2>::value),
MISSING COMPATIBLE COMPLEX PACKET TYPE)
eigen_assert((index % 2 == 0) && "the index must be even");
eigen_assert((begin % 2 == 0) && (count % 2 == 0) && "begin and count must be even");
Index cindex = index / 2;
Index cbegin = begin / 2;
Index ccount = count / 2;
ComplexPacket cpacket = BaseEvaluator::template packetSegment<LoadMode, ComplexPacket>(cindex, cbegin, ccount);
return preinterpret<PacketType, ComplexPacket>(cpacket);
}
};
} // namespace internal
template <typename Xpr>
class RealView : public internal::dense_xpr_base<RealView<Xpr>>::type {
using ExpressionTraits = internal::traits<RealView>;
EIGEN_STATIC_ASSERT(NumTraits<typename Xpr::Scalar>::IsComplex, SCALAR MUST BE COMPLEX)
public:
using Scalar = typename ExpressionTraits::Scalar;
using Nested = RealView;
EIGEN_DEVICE_FUNC explicit RealView(Xpr& xpr) : m_xpr(xpr) {}
EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return Xpr::IsRowMajor ? m_xpr.rows() : 2 * m_xpr.rows(); }
EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return Xpr::IsRowMajor ? 2 * m_xpr.cols() : m_xpr.cols(); }
EIGEN_DEVICE_FUNC constexpr Index size() const noexcept { return 2 * m_xpr.size(); }
EIGEN_DEVICE_FUNC constexpr Index innerStride() const noexcept { return m_xpr.innerStride(); }
EIGEN_DEVICE_FUNC constexpr Index outerStride() const noexcept { return 2 * m_xpr.outerStride(); }
EIGEN_DEVICE_FUNC void resize(Index rows, Index cols) {
m_xpr.resize(Xpr::IsRowMajor ? rows : rows / 2, Xpr::IsRowMajor ? cols / 2 : cols);
}
EIGEN_DEVICE_FUNC void resize(Index size) { m_xpr.resize(size / 2); }
EIGEN_DEVICE_FUNC Scalar* data() { return reinterpret_cast<Scalar*>(m_xpr.data()); }
EIGEN_DEVICE_FUNC const Scalar* data() const { return reinterpret_cast<const Scalar*>(m_xpr.data()); }
EIGEN_DEVICE_FUNC RealView(const RealView&) = default;
EIGEN_DEVICE_FUNC RealView& operator=(const RealView& other);
template <typename OtherDerived>
EIGEN_DEVICE_FUNC RealView& operator=(const RealView<OtherDerived>& other);
template <typename OtherDerived>
EIGEN_DEVICE_FUNC RealView& operator=(const DenseBase<OtherDerived>& other);
protected:
friend struct internal::evaluator<RealView<Xpr>>;
Xpr& m_xpr;
};
template <typename Xpr>
EIGEN_DEVICE_FUNC RealView<Xpr>& RealView<Xpr>::operator=(const RealView& other) {
internal::call_assignment(*this, other);
return *this;
}
template <typename Xpr>
template <typename OtherDerived>
EIGEN_DEVICE_FUNC RealView<Xpr>& RealView<Xpr>::operator=(const RealView<OtherDerived>& other) {
internal::call_assignment(*this, other);
return *this;
}
template <typename Xpr>
template <typename OtherDerived>
EIGEN_DEVICE_FUNC RealView<Xpr>& RealView<Xpr>::operator=(const DenseBase<OtherDerived>& other) {
internal::call_assignment(*this, other.derived());
return *this;
}
template <typename Derived>
EIGEN_DEVICE_FUNC typename DenseBase<Derived>::RealViewReturnType DenseBase<Derived>::realView() {
return RealViewReturnType(derived());
}
template <typename Derived>
EIGEN_DEVICE_FUNC typename DenseBase<Derived>::ConstRealViewReturnType DenseBase<Derived>::realView() const {
return ConstRealViewReturnType(derived());
}
} // namespace Eigen
#endif // EIGEN_REALVIEW_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_REDUX_H
#define EIGEN_REDUX_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
// TODO
// * implement other kind of vectorization
// * factorize code
/***************************************************************************
* Part 1 : the logic deciding a strategy for vectorization and unrolling
***************************************************************************/
template <typename Func, typename Evaluator>
struct redux_traits {
public:
typedef typename find_best_packet<typename Evaluator::Scalar, Evaluator::SizeAtCompileTime>::type PacketType;
enum {
PacketSize = unpacket_traits<PacketType>::size,
InnerMaxSize = int(Evaluator::IsRowMajor) ? Evaluator::MaxColsAtCompileTime : Evaluator::MaxRowsAtCompileTime,
OuterMaxSize = int(Evaluator::IsRowMajor) ? Evaluator::MaxRowsAtCompileTime : Evaluator::MaxColsAtCompileTime,
SliceVectorizedWork = int(InnerMaxSize) == Dynamic ? Dynamic
: int(OuterMaxSize) == Dynamic ? (int(InnerMaxSize) >= int(PacketSize) ? Dynamic : 0)
: (int(InnerMaxSize) / int(PacketSize)) * int(OuterMaxSize)
};
enum {
MayLinearize = (int(Evaluator::Flags) & LinearAccessBit),
MightVectorize = (int(Evaluator::Flags) & ActualPacketAccessBit) && (functor_traits<Func>::PacketAccess),
MayLinearVectorize = bool(MightVectorize) && bool(MayLinearize),
MaySliceVectorize = bool(MightVectorize) && (int(SliceVectorizedWork) == Dynamic || int(SliceVectorizedWork) >= 3)
};
public:
enum {
Traversal = int(MayLinearVectorize) ? int(LinearVectorizedTraversal)
: int(MaySliceVectorize) ? int(SliceVectorizedTraversal)
: int(MayLinearize) ? int(LinearTraversal)
: int(DefaultTraversal)
};
public:
enum {
Cost = Evaluator::SizeAtCompileTime == Dynamic
? HugeCost
: int(Evaluator::SizeAtCompileTime) * int(Evaluator::CoeffReadCost) +
(Evaluator::SizeAtCompileTime - 1) * functor_traits<Func>::Cost,
UnrollingLimit = EIGEN_UNROLLING_LIMIT * (int(Traversal) == int(DefaultTraversal) ? 1 : int(PacketSize))
};
public:
enum { Unrolling = Cost <= UnrollingLimit ? CompleteUnrolling : NoUnrolling };
#ifdef EIGEN_DEBUG_ASSIGN
static void debug() {
std::cerr << "Xpr: " << typeid(typename Evaluator::XprType).name() << std::endl;
std::cerr.setf(std::ios::hex, std::ios::basefield);
EIGEN_DEBUG_VAR(Evaluator::Flags)
std::cerr.unsetf(std::ios::hex);
EIGEN_DEBUG_VAR(InnerMaxSize)
EIGEN_DEBUG_VAR(OuterMaxSize)
EIGEN_DEBUG_VAR(SliceVectorizedWork)
EIGEN_DEBUG_VAR(PacketSize)
EIGEN_DEBUG_VAR(MightVectorize)
EIGEN_DEBUG_VAR(MayLinearVectorize)
EIGEN_DEBUG_VAR(MaySliceVectorize)
std::cerr << "Traversal"
<< " = " << Traversal << " (" << demangle_traversal(Traversal) << ")" << std::endl;
EIGEN_DEBUG_VAR(UnrollingLimit)
std::cerr << "Unrolling"
<< " = " << Unrolling << " (" << demangle_unrolling(Unrolling) << ")" << std::endl;
std::cerr << std::endl;
}
#endif
};
/***************************************************************************
* Part 2 : unrollers
***************************************************************************/
/*** no vectorization ***/
template <typename Func, typename Evaluator, Index Start, Index Length>
struct redux_novec_unroller {
static constexpr Index HalfLength = Length / 2;
typedef typename Evaluator::Scalar Scalar;
EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Scalar run(const Evaluator& eval, const Func& func) {
return func(redux_novec_unroller<Func, Evaluator, Start, HalfLength>::run(eval, func),
redux_novec_unroller<Func, Evaluator, Start + HalfLength, Length - HalfLength>::run(eval, func));
}
};
template <typename Func, typename Evaluator, Index Start>
struct redux_novec_unroller<Func, Evaluator, Start, 1> {
static constexpr Index outer = Start / Evaluator::InnerSizeAtCompileTime;
static constexpr Index inner = Start % Evaluator::InnerSizeAtCompileTime;
typedef typename Evaluator::Scalar Scalar;
EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Scalar run(const Evaluator& eval, const Func&) {
return eval.coeffByOuterInner(outer, inner);
}
};
// This is actually dead code and will never be called. It is required
// to prevent false warnings regarding failed inlining though
// for 0 length run() will never be called at all.
template <typename Func, typename Evaluator, Index Start>
struct redux_novec_unroller<Func, Evaluator, Start, 0> {
typedef typename Evaluator::Scalar Scalar;
EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Scalar run(const Evaluator&, const Func&) { return Scalar(); }
};
template <typename Func, typename Evaluator, Index Start, Index Length>
struct redux_novec_linear_unroller {
static constexpr Index HalfLength = Length / 2;
typedef typename Evaluator::Scalar Scalar;
EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Scalar run(const Evaluator& eval, const Func& func) {
return func(redux_novec_linear_unroller<Func, Evaluator, Start, HalfLength>::run(eval, func),
redux_novec_linear_unroller<Func, Evaluator, Start + HalfLength, Length - HalfLength>::run(eval, func));
}
};
template <typename Func, typename Evaluator, Index Start>
struct redux_novec_linear_unroller<Func, Evaluator, Start, 1> {
typedef typename Evaluator::Scalar Scalar;
EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Scalar run(const Evaluator& eval, const Func&) {
return eval.coeff(Start);
}
};
// This is actually dead code and will never be called. It is required
// to prevent false warnings regarding failed inlining though
// for 0 length run() will never be called at all.
template <typename Func, typename Evaluator, Index Start>
struct redux_novec_linear_unroller<Func, Evaluator, Start, 0> {
typedef typename Evaluator::Scalar Scalar;
EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Scalar run(const Evaluator&, const Func&) { return Scalar(); }
};
/*** vectorization ***/
template <typename Func, typename Evaluator, Index Start, Index Length>
struct redux_vec_unroller {
template <typename PacketType>
EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE PacketType run(const Evaluator& eval, const Func& func) {
constexpr Index HalfLength = Length / 2;
return func.packetOp(
redux_vec_unroller<Func, Evaluator, Start, HalfLength>::template run<PacketType>(eval, func),
redux_vec_unroller<Func, Evaluator, Start + HalfLength, Length - HalfLength>::template run<PacketType>(eval,
func));
}
};
template <typename Func, typename Evaluator, Index Start>
struct redux_vec_unroller<Func, Evaluator, Start, 1> {
template <typename PacketType>
EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE PacketType run(const Evaluator& eval, const Func&) {
constexpr Index PacketSize = unpacket_traits<PacketType>::size;
constexpr Index index = Start * PacketSize;
constexpr Index outer = index / int(Evaluator::InnerSizeAtCompileTime);
constexpr Index inner = index % int(Evaluator::InnerSizeAtCompileTime);
constexpr int alignment = Evaluator::Alignment;
return eval.template packetByOuterInner<alignment, PacketType>(outer, inner);
}
};
template <typename Func, typename Evaluator, Index Start, Index Length>
struct redux_vec_linear_unroller {
template <typename PacketType>
EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE PacketType run(const Evaluator& eval, const Func& func) {
constexpr Index HalfLength = Length / 2;
return func.packetOp(
redux_vec_linear_unroller<Func, Evaluator, Start, HalfLength>::template run<PacketType>(eval, func),
redux_vec_linear_unroller<Func, Evaluator, Start + HalfLength, Length - HalfLength>::template run<PacketType>(
eval, func));
}
};
template <typename Func, typename Evaluator, Index Start>
struct redux_vec_linear_unroller<Func, Evaluator, Start, 1> {
template <typename PacketType>
EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE PacketType run(const Evaluator& eval, const Func&) {
constexpr Index PacketSize = unpacket_traits<PacketType>::size;
constexpr Index index = (Start * PacketSize);
constexpr int alignment = Evaluator::Alignment;
return eval.template packet<alignment, PacketType>(index);
}
};
/***************************************************************************
* Part 3 : implementation of all cases
***************************************************************************/
template <typename Func, typename Evaluator, int Traversal = redux_traits<Func, Evaluator>::Traversal,
int Unrolling = redux_traits<Func, Evaluator>::Unrolling>
struct redux_impl;
template <typename Func, typename Evaluator>
struct redux_impl<Func, Evaluator, DefaultTraversal, NoUnrolling> {
typedef typename Evaluator::Scalar Scalar;
template <typename XprType>
EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Scalar run(const Evaluator& eval, const Func& func, const XprType& xpr) {
eigen_assert(xpr.rows() > 0 && xpr.cols() > 0 && "you are using an empty matrix");
Scalar res = eval.coeffByOuterInner(0, 0);
for (Index i = 1; i < xpr.innerSize(); ++i) res = func(res, eval.coeffByOuterInner(0, i));
for (Index i = 1; i < xpr.outerSize(); ++i)
for (Index j = 0; j < xpr.innerSize(); ++j) res = func(res, eval.coeffByOuterInner(i, j));
return res;
}
};
template <typename Func, typename Evaluator>
struct redux_impl<Func, Evaluator, LinearTraversal, NoUnrolling> {
typedef typename Evaluator::Scalar Scalar;
template <typename XprType>
EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Scalar run(const Evaluator& eval, const Func& func, const XprType& xpr) {
eigen_assert(xpr.size() > 0 && "you are using an empty matrix");
Scalar res = eval.coeff(0);
for (Index k = 1; k < xpr.size(); ++k) res = func(res, eval.coeff(k));
return res;
}
};
template <typename Func, typename Evaluator>
struct redux_impl<Func, Evaluator, DefaultTraversal, CompleteUnrolling>
: redux_novec_unroller<Func, Evaluator, 0, Evaluator::SizeAtCompileTime> {
typedef redux_novec_unroller<Func, Evaluator, 0, Evaluator::SizeAtCompileTime> Base;
typedef typename Evaluator::Scalar Scalar;
template <typename XprType>
EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Scalar run(const Evaluator& eval, const Func& func,
const XprType& /*xpr*/) {
return Base::run(eval, func);
}
};
template <typename Func, typename Evaluator>
struct redux_impl<Func, Evaluator, LinearTraversal, CompleteUnrolling>
: redux_novec_linear_unroller<Func, Evaluator, 0, Evaluator::SizeAtCompileTime> {
typedef redux_novec_linear_unroller<Func, Evaluator, 0, Evaluator::SizeAtCompileTime> Base;
typedef typename Evaluator::Scalar Scalar;
template <typename XprType>
EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Scalar run(const Evaluator& eval, const Func& func,
const XprType& /*xpr*/) {
return Base::run(eval, func);
}
};
template <typename Func, typename Evaluator>
struct redux_impl<Func, Evaluator, LinearVectorizedTraversal, NoUnrolling> {
typedef typename Evaluator::Scalar Scalar;
typedef typename redux_traits<Func, Evaluator>::PacketType PacketScalar;
template <typename XprType>
static Scalar run(const Evaluator& eval, const Func& func, const XprType& xpr) {
const Index size = xpr.size();
constexpr Index packetSize = redux_traits<Func, Evaluator>::PacketSize;
constexpr int packetAlignment = unpacket_traits<PacketScalar>::alignment;
constexpr int alignment0 =
(bool(Evaluator::Flags & DirectAccessBit) && bool(packet_traits<Scalar>::AlignedOnScalar))
? int(packetAlignment)
: int(Unaligned);
constexpr int alignment = plain_enum_max(alignment0, Evaluator::Alignment);
const Index alignedStart = internal::first_default_aligned(xpr);
const Index alignedSize2 = ((size - alignedStart) / (2 * packetSize)) * (2 * packetSize);
const Index alignedSize = ((size - alignedStart) / (packetSize)) * (packetSize);
const Index alignedEnd2 = alignedStart + alignedSize2;
const Index alignedEnd = alignedStart + alignedSize;
Scalar res;
if (alignedSize) {
PacketScalar packet_res0 = eval.template packet<alignment, PacketScalar>(alignedStart);
if (alignedSize > packetSize) // we have at least two packets to partly unroll the loop
{
PacketScalar packet_res1 = eval.template packet<alignment, PacketScalar>(alignedStart + packetSize);
for (Index index = alignedStart + 2 * packetSize; index < alignedEnd2; index += 2 * packetSize) {
packet_res0 = func.packetOp(packet_res0, eval.template packet<alignment, PacketScalar>(index));
packet_res1 = func.packetOp(packet_res1, eval.template packet<alignment, PacketScalar>(index + packetSize));
}
packet_res0 = func.packetOp(packet_res0, packet_res1);
if (alignedEnd > alignedEnd2)
packet_res0 = func.packetOp(packet_res0, eval.template packet<alignment, PacketScalar>(alignedEnd2));
}
res = func.predux(packet_res0);
for (Index index = 0; index < alignedStart; ++index) res = func(res, eval.coeff(index));
for (Index index = alignedEnd; index < size; ++index) res = func(res, eval.coeff(index));
} else // too small to vectorize anything.
// since this is dynamic-size hence inefficient anyway for such small sizes, don't try to optimize.
{
res = eval.coeff(0);
for (Index index = 1; index < size; ++index) res = func(res, eval.coeff(index));
}
return res;
}
};
// NOTE: for SliceVectorizedTraversal we simply bypass unrolling
template <typename Func, typename Evaluator, int Unrolling>
struct redux_impl<Func, Evaluator, SliceVectorizedTraversal, Unrolling> {
typedef typename Evaluator::Scalar Scalar;
typedef typename redux_traits<Func, Evaluator>::PacketType PacketType;
template <typename XprType>
EIGEN_DEVICE_FUNC static Scalar run(const Evaluator& eval, const Func& func, const XprType& xpr) {
eigen_assert(xpr.rows() > 0 && xpr.cols() > 0 && "you are using an empty matrix");
constexpr Index packetSize = redux_traits<Func, Evaluator>::PacketSize;
const Index innerSize = xpr.innerSize();
const Index outerSize = xpr.outerSize();
const Index packetedInnerSize = ((innerSize) / packetSize) * packetSize;
Scalar res;
if (packetedInnerSize) {
PacketType packet_res = eval.template packet<Unaligned, PacketType>(0, 0);
for (Index j = 0; j < outerSize; ++j)
for (Index i = (j == 0 ? packetSize : 0); i < packetedInnerSize; i += Index(packetSize))
packet_res = func.packetOp(packet_res, eval.template packetByOuterInner<Unaligned, PacketType>(j, i));
res = func.predux(packet_res);
for (Index j = 0; j < outerSize; ++j)
for (Index i = packetedInnerSize; i < innerSize; ++i) res = func(res, eval.coeffByOuterInner(j, i));
} else // too small to vectorize anything.
// since this is dynamic-size hence inefficient anyway for such small sizes, don't try to optimize.
{
res = redux_impl<Func, Evaluator, DefaultTraversal, NoUnrolling>::run(eval, func, xpr);
}
return res;
}
};
template <typename Func, typename Evaluator>
struct redux_impl<Func, Evaluator, LinearVectorizedTraversal, CompleteUnrolling> {
typedef typename Evaluator::Scalar Scalar;
typedef typename redux_traits<Func, Evaluator>::PacketType PacketType;
static constexpr Index PacketSize = redux_traits<Func, Evaluator>::PacketSize;
static constexpr Index Size = Evaluator::SizeAtCompileTime;
static constexpr Index VectorizedSize = (int(Size) / int(PacketSize)) * int(PacketSize);
template <typename XprType>
EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Scalar run(const Evaluator& eval, const Func& func, const XprType& xpr) {
EIGEN_ONLY_USED_FOR_DEBUG(xpr)
eigen_assert(xpr.rows() > 0 && xpr.cols() > 0 && "you are using an empty matrix");
if (VectorizedSize > 0) {
Scalar res = func.predux(
redux_vec_linear_unroller<Func, Evaluator, 0, Size / PacketSize>::template run<PacketType>(eval, func));
if (VectorizedSize != Size)
res = func(
res, redux_novec_linear_unroller<Func, Evaluator, VectorizedSize, Size - VectorizedSize>::run(eval, func));
return res;
} else {
return redux_novec_linear_unroller<Func, Evaluator, 0, Size>::run(eval, func);
}
}
};
// evaluator adaptor
template <typename XprType_>
class redux_evaluator : public internal::evaluator<XprType_> {
typedef internal::evaluator<XprType_> Base;
public:
typedef XprType_ XprType;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit redux_evaluator(const XprType& xpr) : Base(xpr) {}
typedef typename XprType::Scalar Scalar;
typedef typename XprType::CoeffReturnType CoeffReturnType;
typedef typename XprType::PacketScalar PacketScalar;
enum {
MaxRowsAtCompileTime = XprType::MaxRowsAtCompileTime,
MaxColsAtCompileTime = XprType::MaxColsAtCompileTime,
// TODO we should not remove DirectAccessBit and rather find an elegant way to query the alignment offset at runtime
// from the evaluator
Flags = Base::Flags & ~DirectAccessBit,
IsRowMajor = XprType::IsRowMajor,
SizeAtCompileTime = XprType::SizeAtCompileTime,
InnerSizeAtCompileTime = XprType::InnerSizeAtCompileTime
};
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeffByOuterInner(Index outer, Index inner) const {
return Base::coeff(IsRowMajor ? outer : inner, IsRowMajor ? inner : outer);
}
template <int LoadMode, typename PacketType>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packetByOuterInner(Index outer, Index inner) const {
return Base::template packet<LoadMode, PacketType>(IsRowMajor ? outer : inner, IsRowMajor ? inner : outer);
}
template <int LoadMode, typename PacketType>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packetSegmentByOuterInner(Index outer, Index inner, Index begin,
Index count) const {
return Base::template packetSegment<LoadMode, PacketType>(IsRowMajor ? outer : inner, IsRowMajor ? inner : outer,
begin, count);
}
};
} // end namespace internal
/***************************************************************************
* Part 4 : public API
***************************************************************************/
/** \returns the result of a full redux operation on the whole matrix or vector using \a func
*
* The template parameter \a BinaryOp is the type of the functor \a func which must be
* an associative operator. Both current C++98 and C++11 functor styles are handled.
*
* \warning the matrix must be not empty, otherwise an assertion is triggered.
*
* \sa DenseBase::sum(), DenseBase::minCoeff(), DenseBase::maxCoeff(), MatrixBase::colwise(), MatrixBase::rowwise()
*/
template <typename Derived>
template <typename Func>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar DenseBase<Derived>::redux(
const Func& func) const {
eigen_assert(this->rows() > 0 && this->cols() > 0 && "you are using an empty matrix");
typedef typename internal::redux_evaluator<Derived> ThisEvaluator;
ThisEvaluator thisEval(derived());
// The initial expression is passed to the reducer as an additional argument instead of
// passing it as a member of redux_evaluator to help
return internal::redux_impl<Func, ThisEvaluator>::run(thisEval, func, derived());
}
/** \returns the minimum of all coefficients of \c *this.
* In case \c *this contains NaN, NaNPropagation determines the behavior:
* NaNPropagation == PropagateFast : undefined
* NaNPropagation == PropagateNaN : result is NaN
* NaNPropagation == PropagateNumbers : result is minimum of elements that are not NaN
* \warning the matrix must be not empty, otherwise an assertion is triggered.
*/
template <typename Derived>
template <int NaNPropagation>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar DenseBase<Derived>::minCoeff() const {
return derived().redux(Eigen::internal::scalar_min_op<Scalar, Scalar, NaNPropagation>());
}
/** \returns the maximum of all coefficients of \c *this.
* In case \c *this contains NaN, NaNPropagation determines the behavior:
* NaNPropagation == PropagateFast : undefined
* NaNPropagation == PropagateNaN : result is NaN
* NaNPropagation == PropagateNumbers : result is maximum of elements that are not NaN
* \warning the matrix must be not empty, otherwise an assertion is triggered.
*/
template <typename Derived>
template <int NaNPropagation>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar DenseBase<Derived>::maxCoeff() const {
return derived().redux(Eigen::internal::scalar_max_op<Scalar, Scalar, NaNPropagation>());
}
/** \returns the sum of all coefficients of \c *this
*
* If \c *this is empty, then the value 0 is returned.
*
* \sa trace(), prod(), mean()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar DenseBase<Derived>::sum() const {
if (SizeAtCompileTime == 0 || (SizeAtCompileTime == Dynamic && size() == 0)) return Scalar(0);
return derived().redux(Eigen::internal::scalar_sum_op<Scalar, Scalar>());
}
/** \returns the mean of all coefficients of *this
*
* \sa trace(), prod(), sum()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar DenseBase<Derived>::mean() const {
#ifdef __INTEL_COMPILER
#pragma warning push
#pragma warning(disable : 2259)
#endif
return Scalar(derived().redux(Eigen::internal::scalar_sum_op<Scalar, Scalar>())) / Scalar(this->size());
#ifdef __INTEL_COMPILER
#pragma warning pop
#endif
}
/** \returns the product of all coefficients of *this
*
* Example: \include MatrixBase_prod.cpp
* Output: \verbinclude MatrixBase_prod.out
*
* \sa sum(), mean(), trace()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar DenseBase<Derived>::prod() const {
if (SizeAtCompileTime == 0 || (SizeAtCompileTime == Dynamic && size() == 0)) return Scalar(1);
return derived().redux(Eigen::internal::scalar_product_op<Scalar>());
}
/** \returns the trace of \c *this, i.e. the sum of the coefficients on the main diagonal.
*
* \c *this can be any matrix, not necessarily square.
*
* \sa diagonal(), sum()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar MatrixBase<Derived>::trace() const {
return derived().diagonal().sum();
}
} // end namespace Eigen
#endif // EIGEN_REDUX_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_REF_H
#define EIGEN_REF_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
template <typename PlainObjectType_, int Options_, typename StrideType_>
struct traits<Ref<PlainObjectType_, Options_, StrideType_> >
: public traits<Map<PlainObjectType_, Options_, StrideType_> > {
typedef PlainObjectType_ PlainObjectType;
typedef StrideType_ StrideType;
enum {
Options = Options_,
Flags = traits<Map<PlainObjectType_, Options_, StrideType_> >::Flags | NestByRefBit,
Alignment = traits<Map<PlainObjectType_, Options_, StrideType_> >::Alignment,
InnerStrideAtCompileTime = traits<Map<PlainObjectType_, Options_, StrideType_> >::InnerStrideAtCompileTime,
OuterStrideAtCompileTime = traits<Map<PlainObjectType_, Options_, StrideType_> >::OuterStrideAtCompileTime
};
template <typename Derived>
struct match {
enum {
IsVectorAtCompileTime = PlainObjectType::IsVectorAtCompileTime || Derived::IsVectorAtCompileTime,
HasDirectAccess = internal::has_direct_access<Derived>::ret,
StorageOrderMatch =
IsVectorAtCompileTime || ((PlainObjectType::Flags & RowMajorBit) == (Derived::Flags & RowMajorBit)),
InnerStrideMatch = int(InnerStrideAtCompileTime) == int(Dynamic) ||
int(InnerStrideAtCompileTime) == int(Derived::InnerStrideAtCompileTime) ||
(int(InnerStrideAtCompileTime) == 0 && int(Derived::InnerStrideAtCompileTime) == 1),
OuterStrideMatch = IsVectorAtCompileTime || int(OuterStrideAtCompileTime) == int(Dynamic) ||
int(OuterStrideAtCompileTime) == int(Derived::OuterStrideAtCompileTime),
// NOTE, this indirection of evaluator<Derived>::Alignment is needed
// to workaround a very strange bug in MSVC related to the instantiation
// of has_*ary_operator in evaluator<CwiseNullaryOp>.
// This line is surprisingly very sensitive. For instance, simply adding parenthesis
// as "DerivedAlignment = (int(evaluator<Derived>::Alignment))," will make MSVC fail...
DerivedAlignment = int(evaluator<Derived>::Alignment),
AlignmentMatch = (int(traits<PlainObjectType>::Alignment) == int(Unaligned)) ||
(DerivedAlignment >= int(Alignment)), // FIXME the first condition is not very clear, it should
// be replaced by the required alignment
ScalarTypeMatch = internal::is_same<typename PlainObjectType::Scalar, typename Derived::Scalar>::value,
MatchAtCompileTime = HasDirectAccess && StorageOrderMatch && InnerStrideMatch && OuterStrideMatch &&
AlignmentMatch && ScalarTypeMatch
};
typedef std::conditional_t<MatchAtCompileTime, internal::true_type, internal::false_type> type;
};
};
template <typename Derived>
struct traits<RefBase<Derived> > : public traits<Derived> {};
} // namespace internal
template <typename Derived>
class RefBase : public MapBase<Derived> {
typedef typename internal::traits<Derived>::PlainObjectType PlainObjectType;
typedef typename internal::traits<Derived>::StrideType StrideType;
public:
typedef MapBase<Derived> Base;
EIGEN_DENSE_PUBLIC_INTERFACE(RefBase)
EIGEN_DEVICE_FUNC constexpr Index innerStride() const {
return StrideType::InnerStrideAtCompileTime != 0 ? m_stride.inner() : 1;
}
EIGEN_DEVICE_FUNC constexpr Index outerStride() const {
return StrideType::OuterStrideAtCompileTime != 0 ? m_stride.outer()
: IsVectorAtCompileTime ? this->size()
: int(Flags) & RowMajorBit ? this->cols()
: this->rows();
}
EIGEN_DEVICE_FUNC RefBase()
: Base(0, RowsAtCompileTime == Dynamic ? 0 : RowsAtCompileTime,
ColsAtCompileTime == Dynamic ? 0 : ColsAtCompileTime),
// Stride<> does not allow default ctor for Dynamic strides, so let' initialize it with dummy values:
m_stride(StrideType::OuterStrideAtCompileTime == Dynamic ? 0 : StrideType::OuterStrideAtCompileTime,
StrideType::InnerStrideAtCompileTime == Dynamic ? 0 : StrideType::InnerStrideAtCompileTime) {}
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(RefBase)
protected:
typedef Stride<StrideType::OuterStrideAtCompileTime, StrideType::InnerStrideAtCompileTime> StrideBase;
// Resolves inner stride if default 0.
static EIGEN_DEVICE_FUNC constexpr Index resolveInnerStride(Index inner) { return inner == 0 ? 1 : inner; }
// Resolves outer stride if default 0.
static EIGEN_DEVICE_FUNC constexpr Index resolveOuterStride(Index inner, Index outer, Index rows, Index cols,
bool isVectorAtCompileTime, bool isRowMajor) {
return outer == 0 ? isVectorAtCompileTime ? inner * rows * cols : isRowMajor ? inner * cols : inner * rows : outer;
}
// Returns true if construction is valid, false if there is a stride mismatch,
// and fails if there is a size mismatch.
template <typename Expression>
EIGEN_DEVICE_FUNC bool construct(Expression& expr) {
// Check matrix sizes. If this is a compile-time vector, we do allow
// implicitly transposing.
EIGEN_STATIC_ASSERT(EIGEN_PREDICATE_SAME_MATRIX_SIZE(PlainObjectType, Expression)
// If it is a vector, the transpose sizes might match.
|| (PlainObjectType::IsVectorAtCompileTime &&
((int(PlainObjectType::RowsAtCompileTime) == Eigen::Dynamic ||
int(Expression::ColsAtCompileTime) == Eigen::Dynamic ||
int(PlainObjectType::RowsAtCompileTime) == int(Expression::ColsAtCompileTime)) &&
(int(PlainObjectType::ColsAtCompileTime) == Eigen::Dynamic ||
int(Expression::RowsAtCompileTime) == Eigen::Dynamic ||
int(PlainObjectType::ColsAtCompileTime) == int(Expression::RowsAtCompileTime)))),
YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES)
// Determine runtime rows and columns.
Index rows = expr.rows();
Index cols = expr.cols();
if (PlainObjectType::RowsAtCompileTime == 1) {
eigen_assert(expr.rows() == 1 || expr.cols() == 1);
rows = 1;
cols = expr.size();
} else if (PlainObjectType::ColsAtCompileTime == 1) {
eigen_assert(expr.rows() == 1 || expr.cols() == 1);
rows = expr.size();
cols = 1;
}
// Verify that the sizes are valid.
eigen_assert((PlainObjectType::RowsAtCompileTime == Dynamic) || (PlainObjectType::RowsAtCompileTime == rows));
eigen_assert((PlainObjectType::ColsAtCompileTime == Dynamic) || (PlainObjectType::ColsAtCompileTime == cols));
// If this is a vector, we might be transposing, which means that stride should swap.
const bool transpose = PlainObjectType::IsVectorAtCompileTime && (rows != expr.rows());
// If the storage format differs, we also need to swap the stride.
const bool row_major = ((PlainObjectType::Flags)&RowMajorBit) != 0;
const bool expr_row_major = (Expression::Flags & RowMajorBit) != 0;
const bool storage_differs = (row_major != expr_row_major);
const bool swap_stride = (transpose != storage_differs);
// Determine expr's actual strides, resolving any defaults if zero.
const Index expr_inner_actual = resolveInnerStride(expr.innerStride());
const Index expr_outer_actual = resolveOuterStride(expr_inner_actual, expr.outerStride(), expr.rows(), expr.cols(),
Expression::IsVectorAtCompileTime != 0, expr_row_major);
// If this is a column-major row vector or row-major column vector, the inner-stride
// is arbitrary, so set it to either the compile-time inner stride or 1.
const bool row_vector = (rows == 1);
const bool col_vector = (cols == 1);
const Index inner_stride =
((!row_major && row_vector) || (row_major && col_vector))
? (StrideType::InnerStrideAtCompileTime > 0 ? Index(StrideType::InnerStrideAtCompileTime) : 1)
: swap_stride ? expr_outer_actual
: expr_inner_actual;
// If this is a column-major column vector or row-major row vector, the outer-stride
// is arbitrary, so set it to either the compile-time outer stride or vector size.
const Index outer_stride =
((!row_major && col_vector) || (row_major && row_vector))
? (StrideType::OuterStrideAtCompileTime > 0 ? Index(StrideType::OuterStrideAtCompileTime)
: rows * cols * inner_stride)
: swap_stride ? expr_inner_actual
: expr_outer_actual;
// Check if given inner/outer strides are compatible with compile-time strides.
const bool inner_valid = (StrideType::InnerStrideAtCompileTime == Dynamic) ||
(resolveInnerStride(Index(StrideType::InnerStrideAtCompileTime)) == inner_stride);
if (!inner_valid) {
return false;
}
const bool outer_valid =
(StrideType::OuterStrideAtCompileTime == Dynamic) ||
(resolveOuterStride(inner_stride, Index(StrideType::OuterStrideAtCompileTime), rows, cols,
PlainObjectType::IsVectorAtCompileTime != 0, row_major) == outer_stride);
if (!outer_valid) {
return false;
}
internal::construct_at<Base>(this, expr.data(), rows, cols);
internal::construct_at(&m_stride, (StrideType::OuterStrideAtCompileTime == 0) ? 0 : outer_stride,
(StrideType::InnerStrideAtCompileTime == 0) ? 0 : inner_stride);
return true;
}
StrideBase m_stride;
};
/** \class Ref
* \ingroup Core_Module
*
* \brief A matrix or vector expression mapping an existing expression
*
* \tparam PlainObjectType the equivalent matrix type of the mapped data
* \tparam Options specifies the pointer alignment in bytes. It can be: \c #Aligned128, , \c #Aligned64, \c #Aligned32,
* \c #Aligned16, \c #Aligned8 or \c #Unaligned. The default is \c #Unaligned. \tparam StrideType optionally specifies
* strides. By default, Ref implies a contiguous storage along the inner dimension (inner stride==1), but accepts a
* variable outer stride (leading dimension). This can be overridden by specifying strides. The type passed here must be
* a specialization of the Stride template, see examples below.
*
* This class provides a way to write non-template functions taking Eigen objects as parameters while limiting the
* number of copies. A Ref<> object can represent either a const expression or a l-value: \code
* // in-out argument:
* void foo1(Ref<VectorXf> x);
*
* // read-only const argument:
* void foo2(const Ref<const VectorXf>& x);
* \endcode
*
* In the in-out case, the input argument must satisfy the constraints of the actual Ref<> type, otherwise a compilation
* issue will be triggered. By default, a Ref<VectorXf> can reference any dense vector expression of float having a
* contiguous memory layout. Likewise, a Ref<MatrixXf> can reference any column-major dense matrix expression of float
* whose column's elements are contiguously stored with the possibility to have a constant space in-between each column,
* i.e. the inner stride must be equal to 1, but the outer stride (or leading dimension) can be greater than the number
* of rows.
*
* In the const case, if the input expression does not match the above requirement, then it is evaluated into a
* temporary before being passed to the function. Here are some examples: \code MatrixXf A; VectorXf a; foo1(a.head());
* // OK foo1(A.col()); // OK foo1(A.row()); // Compilation error because here innerstride!=1
* foo2(A.row()); // Compilation error because A.row() is a 1xN object while foo2 is expecting a Nx1 object
* foo2(A.row().transpose()); // The row is copied into a contiguous temporary
* foo2(2*a); // The expression is evaluated into a temporary
* foo2(A.col().segment(2,4)); // No temporary
* \endcode
*
* The range of inputs that can be referenced without temporary can be enlarged using the last two template parameters.
* Here is an example accepting an innerstride!=1:
* \code
* // in-out argument:
* void foo3(Ref<VectorXf,0,InnerStride<> > x);
* foo3(A.row()); // OK
* \endcode
* The downside here is that the function foo3 might be significantly slower than foo1 because it won't be able to
* exploit vectorization, and will involve more expensive address computations even if the input is contiguously stored
* in memory. To overcome this issue, one might propose to overload internally calling a template function, e.g.: \code
* // in the .h:
* void foo(const Ref<MatrixXf>& A);
* void foo(const Ref<MatrixXf,0,Stride<> >& A);
*
* // in the .cpp:
* template<typename TypeOfA> void foo_impl(const TypeOfA& A) {
* ... // crazy code goes here
* }
* void foo(const Ref<MatrixXf>& A) { foo_impl(A); }
* void foo(const Ref<MatrixXf,0,Stride<> >& A) { foo_impl(A); }
* \endcode
*
* See also the following stackoverflow questions for further references:
* - <a href="http://stackoverflow.com/questions/21132538/correct-usage-of-the-eigenref-class">Correct usage of the
* Eigen::Ref<> class</a>
*
* \sa PlainObjectBase::Map(), \ref TopicStorageOrders
*/
template <typename PlainObjectType, int Options, typename StrideType>
class Ref : public RefBase<Ref<PlainObjectType, Options, StrideType> > {
private:
typedef internal::traits<Ref> Traits;
template <typename Derived>
EIGEN_DEVICE_FUNC inline Ref(
const PlainObjectBase<Derived>& expr,
std::enable_if_t<bool(Traits::template match<Derived>::MatchAtCompileTime), Derived>* = 0);
public:
typedef RefBase<Ref> Base;
EIGEN_DENSE_PUBLIC_INTERFACE(Ref)
#ifndef EIGEN_PARSED_BY_DOXYGEN
template <typename Derived>
EIGEN_DEVICE_FUNC inline Ref(
PlainObjectBase<Derived>& expr,
std::enable_if_t<bool(Traits::template match<Derived>::MatchAtCompileTime), Derived>* = 0) {
EIGEN_STATIC_ASSERT(bool(Traits::template match<Derived>::MatchAtCompileTime), STORAGE_LAYOUT_DOES_NOT_MATCH);
// Construction must pass since we will not create temporary storage in the non-const case.
const bool success = Base::construct(expr.derived());
EIGEN_UNUSED_VARIABLE(success)
eigen_assert(success);
}
template <typename Derived>
EIGEN_DEVICE_FUNC inline Ref(
const DenseBase<Derived>& expr,
std::enable_if_t<bool(Traits::template match<Derived>::MatchAtCompileTime), Derived>* = 0)
#else
/** Implicit constructor from any dense expression */
template <typename Derived>
inline Ref(DenseBase<Derived>& expr)
#endif
{
EIGEN_STATIC_ASSERT(bool(internal::is_lvalue<Derived>::value), THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY);
EIGEN_STATIC_ASSERT(bool(Traits::template match<Derived>::MatchAtCompileTime), STORAGE_LAYOUT_DOES_NOT_MATCH);
EIGEN_STATIC_ASSERT(!Derived::IsPlainObjectBase, THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY);
// Construction must pass since we will not create temporary storage in the non-const case.
const bool success = Base::construct(expr.const_cast_derived());
EIGEN_UNUSED_VARIABLE(success)
eigen_assert(success);
}
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Ref)
};
// this is the const ref version
template <typename TPlainObjectType, int Options, typename StrideType>
class Ref<const TPlainObjectType, Options, StrideType>
: public RefBase<Ref<const TPlainObjectType, Options, StrideType> > {
typedef internal::traits<Ref> Traits;
static constexpr bool may_map_m_object_successfully =
(static_cast<int>(StrideType::InnerStrideAtCompileTime) == 0 ||
static_cast<int>(StrideType::InnerStrideAtCompileTime) == 1 ||
static_cast<int>(StrideType::InnerStrideAtCompileTime) == Dynamic) &&
(TPlainObjectType::IsVectorAtCompileTime || static_cast<int>(StrideType::OuterStrideAtCompileTime) == 0 ||
static_cast<int>(StrideType::OuterStrideAtCompileTime) == Dynamic ||
static_cast<int>(StrideType::OuterStrideAtCompileTime) ==
static_cast<int>(TPlainObjectType::InnerSizeAtCompileTime) ||
static_cast<int>(TPlainObjectType::InnerSizeAtCompileTime) == Dynamic);
public:
typedef RefBase<Ref> Base;
EIGEN_DENSE_PUBLIC_INTERFACE(Ref)
template <typename Derived>
EIGEN_DEVICE_FUNC inline Ref(const DenseBase<Derived>& expr,
std::enable_if_t<bool(Traits::template match<Derived>::ScalarTypeMatch), Derived>* = 0) {
// std::cout << match_helper<Derived>::HasDirectAccess << "," << match_helper<Derived>::OuterStrideMatch << ","
// << match_helper<Derived>::InnerStrideMatch << "\n"; std::cout << int(StrideType::OuterStrideAtCompileTime)
// << " - " << int(Derived::OuterStrideAtCompileTime) << "\n"; std::cout <<
// int(StrideType::InnerStrideAtCompileTime) << " - " << int(Derived::InnerStrideAtCompileTime) << "\n";
EIGEN_STATIC_ASSERT(Traits::template match<Derived>::type::value || may_map_m_object_successfully,
STORAGE_LAYOUT_DOES_NOT_MATCH);
construct(expr.derived(), typename Traits::template match<Derived>::type());
}
EIGEN_DEVICE_FUNC inline Ref(const Ref& other) : Base(other) {
// copy constructor shall not copy the m_object, to avoid unnecessary malloc and copy
}
EIGEN_DEVICE_FUNC inline Ref(Ref&& other) {
if (other.data() == other.m_object.data()) {
m_object = std::move(other.m_object);
Base::construct(m_object);
} else
Base::construct(other);
}
template <typename OtherRef>
EIGEN_DEVICE_FUNC inline Ref(const RefBase<OtherRef>& other) {
EIGEN_STATIC_ASSERT(Traits::template match<OtherRef>::type::value || may_map_m_object_successfully,
STORAGE_LAYOUT_DOES_NOT_MATCH);
construct(other.derived(), typename Traits::template match<OtherRef>::type());
}
protected:
template <typename Expression>
EIGEN_DEVICE_FUNC void construct(const Expression& expr, internal::true_type) {
// Check if we can use the underlying expr's storage directly, otherwise call the copy version.
if (!Base::construct(expr)) {
construct(expr, internal::false_type());
}
}
template <typename Expression>
EIGEN_DEVICE_FUNC void construct(const Expression& expr, internal::false_type) {
internal::call_assignment_no_alias(m_object, expr, internal::assign_op<Scalar, Scalar>());
const bool success = Base::construct(m_object);
EIGEN_ONLY_USED_FOR_DEBUG(success)
eigen_assert(success);
}
protected:
TPlainObjectType m_object;
};
} // end namespace Eigen
#endif // EIGEN_REF_H

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_REPLICATE_H
#define EIGEN_REPLICATE_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
template <typename MatrixType, int RowFactor, int ColFactor>
struct traits<Replicate<MatrixType, RowFactor, ColFactor> > : traits<MatrixType> {
typedef typename MatrixType::Scalar Scalar;
typedef typename traits<MatrixType>::StorageKind StorageKind;
typedef typename traits<MatrixType>::XprKind XprKind;
typedef typename ref_selector<MatrixType>::type MatrixTypeNested;
typedef std::remove_reference_t<MatrixTypeNested> MatrixTypeNested_;
enum {
RowsAtCompileTime = RowFactor == Dynamic || int(MatrixType::RowsAtCompileTime) == Dynamic
? Dynamic
: RowFactor * MatrixType::RowsAtCompileTime,
ColsAtCompileTime = ColFactor == Dynamic || int(MatrixType::ColsAtCompileTime) == Dynamic
? Dynamic
: ColFactor * MatrixType::ColsAtCompileTime,
// FIXME we don't propagate the max sizes !!!
MaxRowsAtCompileTime = RowsAtCompileTime,
MaxColsAtCompileTime = ColsAtCompileTime,
IsRowMajor = MaxRowsAtCompileTime == 1 && MaxColsAtCompileTime != 1 ? 1
: MaxColsAtCompileTime == 1 && MaxRowsAtCompileTime != 1 ? 0
: (MatrixType::Flags & RowMajorBit) ? 1
: 0,
// FIXME enable DirectAccess with negative strides?
Flags = IsRowMajor ? RowMajorBit : 0
};
};
} // namespace internal
/**
* \class Replicate
* \ingroup Core_Module
*
* \brief Expression of the multiple replication of a matrix or vector
*
* \tparam MatrixType the type of the object we are replicating
* \tparam RowFactor number of repetitions at compile time along the vertical direction, can be Dynamic.
* \tparam ColFactor number of repetitions at compile time along the horizontal direction, can be Dynamic.
*
* This class represents an expression of the multiple replication of a matrix or vector.
* It is the return type of DenseBase::replicate() and most of the time
* this is the only way it is used.
*
* \sa DenseBase::replicate()
*/
template <typename MatrixType, int RowFactor, int ColFactor>
class Replicate : public internal::dense_xpr_base<Replicate<MatrixType, RowFactor, ColFactor> >::type {
typedef typename internal::traits<Replicate>::MatrixTypeNested MatrixTypeNested;
typedef typename internal::traits<Replicate>::MatrixTypeNested_ MatrixTypeNested_;
public:
typedef typename internal::dense_xpr_base<Replicate>::type Base;
EIGEN_DENSE_PUBLIC_INTERFACE(Replicate)
typedef internal::remove_all_t<MatrixType> NestedExpression;
template <typename OriginalMatrixType>
EIGEN_DEVICE_FUNC inline explicit Replicate(const OriginalMatrixType& matrix)
: m_matrix(matrix), m_rowFactor(RowFactor), m_colFactor(ColFactor) {
EIGEN_STATIC_ASSERT((internal::is_same<std::remove_const_t<MatrixType>, OriginalMatrixType>::value),
THE_MATRIX_OR_EXPRESSION_THAT_YOU_PASSED_DOES_NOT_HAVE_THE_EXPECTED_TYPE)
eigen_assert(RowFactor != Dynamic && ColFactor != Dynamic);
}
template <typename OriginalMatrixType>
EIGEN_DEVICE_FUNC inline Replicate(const OriginalMatrixType& matrix, Index rowFactor, Index colFactor)
: m_matrix(matrix), m_rowFactor(rowFactor), m_colFactor(colFactor) {
EIGEN_STATIC_ASSERT((internal::is_same<std::remove_const_t<MatrixType>, OriginalMatrixType>::value),
THE_MATRIX_OR_EXPRESSION_THAT_YOU_PASSED_DOES_NOT_HAVE_THE_EXPECTED_TYPE)
}
EIGEN_DEVICE_FUNC constexpr Index rows() const { return m_matrix.rows() * m_rowFactor.value(); }
EIGEN_DEVICE_FUNC constexpr Index cols() const { return m_matrix.cols() * m_colFactor.value(); }
EIGEN_DEVICE_FUNC const MatrixTypeNested_& nestedExpression() const { return m_matrix; }
protected:
MatrixTypeNested m_matrix;
const internal::variable_if_dynamic<Index, RowFactor> m_rowFactor;
const internal::variable_if_dynamic<Index, ColFactor> m_colFactor;
};
/**
* \return an expression of the replication of \c *this
*
* Example: \include MatrixBase_replicate.cpp
* Output: \verbinclude MatrixBase_replicate.out
*
* \sa VectorwiseOp::replicate(), DenseBase::replicate(Index,Index), class Replicate
*/
template <typename Derived>
template <int RowFactor, int ColFactor>
EIGEN_DEVICE_FUNC const Replicate<Derived, RowFactor, ColFactor> DenseBase<Derived>::replicate() const {
return Replicate<Derived, RowFactor, ColFactor>(derived());
}
/**
* \return an expression of the replication of each column (or row) of \c *this
*
* Example: \include DirectionWise_replicate_int.cpp
* Output: \verbinclude DirectionWise_replicate_int.out
*
* \sa VectorwiseOp::replicate(), DenseBase::replicate(), class Replicate
*/
template <typename ExpressionType, int Direction>
EIGEN_DEVICE_FUNC const typename VectorwiseOp<ExpressionType, Direction>::ReplicateReturnType
VectorwiseOp<ExpressionType, Direction>::replicate(Index factor) const {
return typename VectorwiseOp<ExpressionType, Direction>::ReplicateReturnType(
_expression(), Direction == Vertical ? factor : 1, Direction == Horizontal ? factor : 1);
}
} // end namespace Eigen
#endif // EIGEN_REPLICATE_H

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