update

2025.09.22_cpp_with_eigen_package/Eigen/src/CholmodSupport/CholmodSupport.h

@@ -0,0 +1,738 @@
+// 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

2025.09.22_cpp_with_eigen_package/Eigen/src/CholmodSupport/InternalHeaderCheck.h

@@ -0,0 +1,3 @@
+#ifndef EIGEN_CHOLMODSUPPORT_MODULE_H
+#error "Please include Eigen/CholmodSupport instead of including headers inside the src directory directly."
+#endif