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2025.09.22_cpp_with_eigen_package/Eigen/src/misc/RealSvd2x2.h

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+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2013-2016 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_REALSVD2X2_H
+#define EIGEN_REALSVD2X2_H
+
+// IWYU pragma: private
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template <typename MatrixType, typename RealScalar, typename Index>
+void real_2x2_jacobi_svd(const MatrixType &matrix, Index p, Index q, JacobiRotation<RealScalar> *j_left,
+                         JacobiRotation<RealScalar> *j_right) {
+  using std::abs;
+  using std::sqrt;
+  Matrix<RealScalar, 2, 2> m;
+  m << numext::real(matrix.coeff(p, p)), numext::real(matrix.coeff(p, q)), numext::real(matrix.coeff(q, p)),
+      numext::real(matrix.coeff(q, q));
+  JacobiRotation<RealScalar> rot1;
+  RealScalar t = m.coeff(0, 0) + m.coeff(1, 1);
+  RealScalar d = m.coeff(1, 0) - m.coeff(0, 1);
+
+  if (abs(d) < (std::numeric_limits<RealScalar>::min)()) {
+    rot1.s() = RealScalar(0);
+    rot1.c() = RealScalar(1);
+  } else {
+    // If d!=0, then t/d cannot overflow because the magnitude of the
+    // entries forming d are not too small compared to the ones forming t.
+    RealScalar u = t / d;
+    RealScalar tmp = sqrt(RealScalar(1) + numext::abs2(u));
+    rot1.s() = RealScalar(1) / tmp;
+    rot1.c() = u / tmp;
+  }
+  m.applyOnTheLeft(0, 1, rot1);
+  j_right->makeJacobi(m, 0, 1);
+  *j_left = rot1 * j_right->transpose();
+}
+
+}  // end namespace internal
+
+}  // end namespace Eigen
+
+#endif  // EIGEN_REALSVD2X2_H