text: /*
      tests/eigen.cpp -- automatic conversion of Eigen types
  
      Copyright (c) 2016 Wenzel Jakob <wenzel.jakob@epfl.ch>
  
      All rights reserved. Use of this source code is governed by a
      BSD-style license that can be found in the LICENSE file.
  */
  
  #include "pybind11_tests.h"
  #include "constructor_stats.h"
  #include <pybind11/eigen.h>
  #include <pybind11/stl.h>
  
  #if defined(_MSC_VER)
  #if _MSC_VER < 1910  // VS 2015's MSVC
  #  pragma warning(disable: 4127) // C4127: conditional expression is constant
  #endif
  #  pragma warning(disable: 4996) // C4996: std::unary_negation is deprecated
  #endif
  
  #include <Eigen/Cholesky>
  
  using MatrixXdR = Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>;
  
  
  
  // Sets/resets a testing reference matrix to have values of 10*r + c, where r and c are the
  // (1-based) row/column number.
  template <typename M> void reset_ref(M &x) {
      for (int i = 0; i < x.rows(); i++) for (int j = 0; j < x.cols(); j++)
          x(i, j) = 11 + 10*i + j;
  }
  
  // Returns a static, column-major matrix
  Eigen::MatrixXd &get_cm() {
      static Eigen::MatrixXd *x;
      if (!x) {
          x = new Eigen::MatrixXd(3, 3);
          reset_ref(*x);
      }
      return *x;
  }
  // Likewise, but row-major
  MatrixXdR &get_rm() {
      static MatrixXdR *x;
      if (!x) {
          x = new MatrixXdR(3, 3);
          reset_ref(*x);
      }
      return *x;
  }
  // Resets the values of the static matrices returned by get_cm()/get_rm()
  void reset_refs() {
      reset_ref(get_cm());
      reset_ref(get_rm());
  }
  
  // Returns element 2,1 from a matrix (used to test copy/nocopy)
  double get_elem(const Eigen::Ref<const Eigen::MatrixXd> &m) { return m(2, 1); };
  
  // Returns a matrix with 10*r + 100*c added to each matrix element (to help test that the matrix
  // reference is referencing rows/columns correctly).
  template <typename MatrixArgType> Eigen::MatrixXd adjust_matrix(MatrixArgType m) {
      Eigen::MatrixXd ret(m);
      for (int c = 0; c < m.cols(); c++)
          for (int r = 0; r < m.rows(); r++)
              ret(r, c) += 10*r + 100*c;  // NOLINT(clang-analyzer-core.uninitialized.Assign)
      return ret;
  }
  
  struct CustomOperatorNew {
      CustomOperatorNew() = default;
  
      Eigen::Matrix4d a = Eigen::Matrix4d::Zero();
      Eigen::Matrix4d b = Eigen::Matrix4d::Identity();
  
      EIGEN_MAKE_ALIGNED_OPERATOR_NEW;
  };
  
  TEST_SUBMODULE(eigen, m) {
      using FixedMatrixR = Eigen::Matrix<float, 5, 6, Eigen::RowMajor>;
      using FixedMatrixC = Eigen::Matrix<float, 5, 6>;
      using DenseMatrixR = Eigen::Matrix<float, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>;
      using DenseMatrixC = Eigen::Matrix<float, Eigen::Dynamic, Eigen::Dynamic>;
      using FourRowMatrixC = Eigen::Matrix<float, 4, Eigen::Dynamic>;
      using FourColMatrixC = Eigen::Matrix<float, Eigen::Dynamic, 4>;
      using FourRowMatrixR = Eigen::Matrix<float, 4, Eigen::Dynamic>;
      using FourColMatrixR = Eigen::Matrix<float, Eigen::Dynamic, 4>;
      using SparseMatrixR = Eigen::SparseMatrix<float, Eigen::RowMajor>;
      using SparseMatrixC = Eigen::SparseMatrix<float>;
  
      // various tests
      m.def("double_col", [](const Eigen::VectorXf &x) -> Eigen::VectorXf { return 2.0f * x; });
      m.def("double_row", [](const Eigen::RowVectorXf &x) -> Eigen::RowVectorXf { return 2.0f * x; });
      m.def("double_complex", [](const Eigen::VectorXcf &x) -> Eigen::VectorXcf { return 2.0f * x; });
      m.def("double_threec", [](py::EigenDRef<Eigen::Vector3f> x) { x *= 2; });
      m.def("double_threer", [](py::EigenDRef<Eigen::RowVector3f> x) { x *= 2; });
      m.def("double_mat_cm", [](const Eigen::MatrixXf &x) -> Eigen::MatrixXf { return 2.0f * x; });
      m.def("double_mat_rm", [](const DenseMatrixR &x) -> DenseMatrixR { return 2.0f * x; });
  
      // test_eigen_ref_to_python
      // Different ways of passing via Eigen::Ref; the first and second are the Eigen-recommended
      m.def("cholesky1",
            [](const Eigen::Ref<MatrixXdR> &x) -> Eigen::MatrixXd { return x.llt().matrixL(); });
      m.def("cholesky2", [](const Eigen::Ref<const MatrixXdR> &x) -> Eigen::MatrixXd { return x.llt().matrixL(); });
      m.def("cholesky3", [](const Eigen::Ref<MatrixXdR> &x) -> Eigen::MatrixXd { return x.llt().matrixL(); });
      m.def("cholesky4", [](const Eigen::Ref<const MatrixXdR> &x) -> Eigen::MatrixXd {
          return x.llt().matrixL();
      });
  
      // test_eigen_ref_mutators
      // Mutators: these add some value to the given element using Eigen, but Eigen should be mapping into
      // the numpy array data and so the result should show up there.  There are three versions: one that
      // works on a contiguous-row matrix (numpy's default), one for a contiguous-column matrix, and one
      // for any matrix.
      auto add_rm = [](Eigen::Ref<MatrixXdR> x, int r, int c, double v) { x(r,c) += v; };
      auto add_cm = [](Eigen::Ref<Eigen::MatrixXd> x, int r, int c, double v) { x(r,c) += v; };
  
      // Mutators (Eigen maps into numpy variables):
      m.def("add_rm", add_rm); // Only takes row-contiguous
      m.def("add_cm", add_cm); // Only takes column-contiguous
      // Overloaded versions that will accept either row or column contiguous:
      m.def("add1", add_rm);
      m.def("add1", add_cm);
      m.def("add2", add_cm);
      m.def("add2", add_rm);
      // This one accepts a matrix of any stride:
      m.def("add_any", [](py::EigenDRef<Eigen::MatrixXd> x, int r, int c, double v) { x(r,c) += v; });
  
      // Return mutable references (numpy maps into eigen variables)
      m.def("get_cm_ref", []() { return Eigen::Ref<Eigen::MatrixXd>(get_cm()); });
      m.def("get_rm_ref", []() { return Eigen::Ref<MatrixXdR>(get_rm()); });
      // The same references, but non-mutable (numpy maps into eigen variables, but is !writeable)
      m.def("get_cm_const_ref", []() { return Eigen::Ref<const Eigen::MatrixXd>(get_cm()); });
      m.def("get_rm_const_ref", []() { return Eigen::Ref<const MatrixXdR>(get_rm()); });
  
      m.def("reset_refs", reset_refs); // Restores get_{cm,rm}_ref to original values
  
      // Increments and returns ref to (same) matrix
      m.def("incr_matrix", [](Eigen::Ref<Eigen::MatrixXd> m, double v) {
          m += Eigen::MatrixXd::Constant(m.rows(), m.cols(), v);
          return m;
      }, py::return_value_policy::reference);
  
      // Same, but accepts a matrix of any strides
      m.def("incr_matrix_any", [](py::EigenDRef<Eigen::MatrixXd> m, double v) {
          m += Eigen::MatrixXd::Constant(m.rows(), m.cols(), v);
          return m;
      }, py::return_value_policy::reference);
  
      // Returns an eigen slice of even rows
      m.def("even_rows", [](py::EigenDRef<Eigen::MatrixXd> m) {
          return py::EigenDMap<Eigen::MatrixXd>(
                  m.data(), (m.rows() + 1) / 2, m.cols(),
                  py::EigenDStride(m.outerStride(), 2 * m.innerStride()));
      }, py::return_value_policy::reference);
  
      // Returns an eigen slice of even columns
      m.def("even_cols", [](py::EigenDRef<Eigen::MatrixXd> m) {
          return py::EigenDMap<Eigen::MatrixXd>(
                  m.data(), m.rows(), (m.cols() + 1) / 2,
                  py::EigenDStride(2 * m.outerStride(), m.innerStride()));
      }, py::return_value_policy::reference);
  
      // Returns diagonals: a vector-like object with an inner stride != 1
      m.def("diagonal", [](const Eigen::Ref<const Eigen::MatrixXd> &x) { return x.diagonal(); });
      m.def("diagonal_1", [](const Eigen::Ref<const Eigen::MatrixXd> &x) { return x.diagonal<1>(); });
      m.def("diagonal_n", [](const Eigen::Ref<const Eigen::MatrixXd> &x, int index) { return x.diagonal(index); });
  
      // Return a block of a matrix (gives non-standard strides)
      m.def("block", [](const Eigen::Ref<const Eigen::MatrixXd> &x, int start_row, int start_col, int block_rows, int block_cols) {
          return x.block(start_row, start_col, block_rows, block_cols);
      });
  
      // test_eigen_return_references, test_eigen_keepalive
      // return value referencing/copying tests:
      class ReturnTester {
          Eigen::MatrixXd mat = create();
      public:
          ReturnTester() { print_created(this); }
          ~ReturnTester() { print_destroyed(this); }
          static Eigen::MatrixXd create() { return Eigen::MatrixXd::Ones(10, 10); }
          // NOLINTNEXTLINE(readability-const-return-type)
          static const Eigen::MatrixXd createConst() { return Eigen::MatrixXd::Ones(10, 10); }
          Eigen::MatrixXd &get() { return mat; }
          Eigen::MatrixXd *getPtr() { return &mat; }
          const Eigen::MatrixXd &view() { return mat; }
          const Eigen::MatrixXd *viewPtr() { return &mat; }
          Eigen::Ref<Eigen::MatrixXd> ref() { return mat; }
          Eigen::Ref<const Eigen::MatrixXd> refConst() { return mat; }
          Eigen::Block<Eigen::MatrixXd> block(int r, int c, int nrow, int ncol) { return mat.block(r, c, nrow, ncol); }
          Eigen::Block<const Eigen::MatrixXd> blockConst(int r, int c, int nrow, int ncol) const { return mat.block(r, c, nrow, ncol); }
          py::EigenDMap<Eigen::Matrix2d> corners() { return py::EigenDMap<Eigen::Matrix2d>(mat.data(),
                      py::EigenDStride(mat.outerStride() * (mat.outerSize()-1), mat.innerStride() * (mat.innerSize()-1))); }
          py::EigenDMap<const Eigen::Matrix2d> cornersConst() const { return py::EigenDMap<const Eigen::Matrix2d>(mat.data(),
                      py::EigenDStride(mat.outerStride() * (mat.outerSize()-1), mat.innerStride() * (mat.innerSize()-1))); }
      };
      using rvp = py::return_value_policy;
      py::class_<ReturnTester>(m, "ReturnTester")
          .def(py::init<>())
          .def_static("create", &ReturnTester::create)
          .def_static("create_const", &ReturnTester::createConst)
          .def("get", &ReturnTester::get, rvp::reference_internal)
          .def("get_ptr", &ReturnTester::getPtr, rvp::reference_internal)
          .def("view", &ReturnTester::view, rvp::reference_internal)
          .def("view_ptr", &ReturnTester::view, rvp::reference_internal)
          .def("copy_get", &ReturnTester::get)   // Default rvp: copy
          .def("copy_view", &ReturnTester::view) //         "
          .def("ref", &ReturnTester::ref) // Default for Ref is to reference
          .def("ref_const", &ReturnTester::refConst) // Likewise, but const
          .def("ref_safe", &ReturnTester::ref, rvp::reference_internal)
          .def("ref_const_safe", &ReturnTester::refConst, rvp::reference_internal)
          .def("copy_ref", &ReturnTester::ref, rvp::copy)
          .def("copy_ref_const", &ReturnTester::refConst, rvp::copy)
          .def("block", &ReturnTester::block)
          .def("block_safe", &ReturnTester::block, rvp::reference_internal)
          .def("block_const", &ReturnTester::blockConst, rvp::reference_internal)
          .def("copy_block", &ReturnTester::block, rvp::copy)
          .def("corners", &ReturnTester::corners, rvp::reference_internal)
          .def("corners_const", &ReturnTester::cornersConst, rvp::reference_internal)
          ;
  
      // test_special_matrix_objects
      // Returns a DiagonalMatrix with diagonal (1,2,3,...)
      m.def("incr_diag", [](int k) {
          Eigen::DiagonalMatrix<int, Eigen::Dynamic> m(k);
          for (int i = 0; i < k; i++) m.diagonal()[i] = i+1;
          return m;
      });
  
      // Returns a SelfAdjointView referencing the lower triangle of m
      m.def("symmetric_lower", [](const Eigen::MatrixXi &m) {
              return m.selfadjointView<Eigen::Lower>();
      });
      // Returns a SelfAdjointView referencing the lower triangle of m
      m.def("symmetric_upper", [](const Eigen::MatrixXi &m) {
              return m.selfadjointView<Eigen::Upper>();
      });
  
      // Test matrix for various functions below.
      Eigen::MatrixXf mat(5, 6);
      mat << 0,  3,  0,  0,  0, 11,
             22, 0,  0,  0, 17, 11,
             7,  5,  0,  1,  0, 11,
             0,  0,  0,  0,  0, 11,
             0,  0, 14,  0,  8, 11;
  
      // test_fixed, and various other tests
      m.def("fixed_r", [mat]() -> FixedMatrixR { return FixedMatrixR(mat); });
      // Our Eigen does a hack which respects constness through the numpy writeable flag.
      // Therefore, the const return actually affects this type despite being an rvalue.
      // NOLINTNEXTLINE(readability-const-return-type)
      m.def("fixed_r_const", [mat]() -> const FixedMatrixR { return FixedMatrixR(mat); });
      m.def("fixed_c", [mat]() -> FixedMatrixC { return FixedMatrixC(mat); });
      m.def("fixed_copy_r", [](const FixedMatrixR &m) -> FixedMatrixR { return m; });
      m.def("fixed_copy_c", [](const FixedMatrixC &m) -> FixedMatrixC { return m; });
      // test_mutator_descriptors
      m.def("fixed_mutator_r", [](const Eigen::Ref<FixedMatrixR> &) {});
      m.def("fixed_mutator_c", [](const Eigen::Ref<FixedMatrixC> &) {});
      m.def("fixed_mutator_a", [](const py::EigenDRef<FixedMatrixC> &) {});
      // test_dense
      m.def("dense_r", [mat]() -> DenseMatrixR { return DenseMatrixR(mat); });
      m.def("dense_c", [mat]() -> DenseMatrixC { return DenseMatrixC(mat); });
      m.def("dense_copy_r", [](const DenseMatrixR &m) -> DenseMatrixR { return m; });
      m.def("dense_copy_c", [](const DenseMatrixC &m) -> DenseMatrixC { return m; });
      // test_sparse, test_sparse_signature
      m.def("sparse_r", [mat]() -> SparseMatrixR {
          // NOLINTNEXTLINE(clang-analyzer-core.uninitialized.UndefReturn)
          return Eigen::SparseView<Eigen::MatrixXf>(mat);
      });
      m.def("sparse_c", [mat]() -> SparseMatrixC { return Eigen::SparseView<Eigen::MatrixXf>(mat); });
      m.def("sparse_copy_r", [](const SparseMatrixR &m) -> SparseMatrixR { return m; });
      m.def("sparse_copy_c", [](const SparseMatrixC &m) -> SparseMatrixC { return m; });
      // test_partially_fixed
      m.def("partial_copy_four_rm_r", [](const FourRowMatrixR &m) -> FourRowMatrixR { return m; });
      m.def("partial_copy_four_rm_c", [](const FourColMatrixR &m) -> FourColMatrixR { return m; });
      m.def("partial_copy_four_cm_r", [](const FourRowMatrixC &m) -> FourRowMatrixC { return m; });
      m.def("partial_copy_four_cm_c", [](const FourColMatrixC &m) -> FourColMatrixC { return m; });
  
      // test_cpp_casting
      // Test that we can cast a numpy object to a Eigen::MatrixXd explicitly
      m.def("cpp_copy", [](py::handle m) { return m.cast<Eigen::MatrixXd>()(1, 0); });
      m.def("cpp_ref_c", [](py::handle m) { return m.cast<Eigen::Ref<Eigen::MatrixXd>>()(1, 0); });
      m.def("cpp_ref_r", [](py::handle m) { return m.cast<Eigen::Ref<MatrixXdR>>()(1, 0); });
      m.def("cpp_ref_any", [](py::handle m) { return m.cast<py::EigenDRef<Eigen::MatrixXd>>()(1, 0); });
  
      // [workaround(intel)] ICC 20/21 breaks with py::arg().stuff, using py::arg{}.stuff works.
  
      // test_nocopy_wrapper
      // Test that we can prevent copying into an argument that would normally copy: First a version
      // that would allow copying (if types or strides don't match) for comparison:
      m.def("get_elem", &get_elem);
      // Now this alternative that calls the tells pybind to fail rather than copy:
      m.def(
          "get_elem_nocopy",
          [](const Eigen::Ref<const Eigen::MatrixXd> &m) -> double { return get_elem(m); },
          py::arg{}.noconvert());
      // Also test a row-major-only no-copy const ref:
      m.def("get_elem_rm_nocopy", [](Eigen::Ref<const Eigen::Matrix<long, -1, -1, Eigen::RowMajor>> &m) -> long { return m(2, 1); },
              py::arg{}.noconvert());
  
      // test_issue738
      // Issue #738: 1xN or Nx1 2D matrices were neither accepted nor properly copied with an
      // incompatible stride value on the length-1 dimension--but that should be allowed (without
      // requiring a copy!) because the stride value can be safely ignored on a size-1 dimension.
      m.def("iss738_f1", &adjust_matrix<const Eigen::Ref<const Eigen::MatrixXd> &>, py::arg{}.noconvert());
      m.def("iss738_f2", &adjust_matrix<const Eigen::Ref<const Eigen::Matrix<double, -1, -1, Eigen::RowMajor>> &>, py::arg{}.noconvert());
  
      // test_issue1105
      // Issue #1105: when converting from a numpy two-dimensional (Nx1) or (1xN) value into a dense
      // eigen Vector or RowVector, the argument would fail to load because the numpy copy would
      // fail: numpy won't broadcast a Nx1 into a 1-dimensional vector.
      m.def("iss1105_col", [](const Eigen::VectorXd &) { return true; });
      m.def("iss1105_row", [](const Eigen::RowVectorXd &) { return true; });
  
      // test_named_arguments
      // Make sure named arguments are working properly:
      m.def(
          "matrix_multiply",
          [](const py::EigenDRef<const Eigen::MatrixXd> &A,
             const py::EigenDRef<const Eigen::MatrixXd> &B) -> Eigen::MatrixXd {
              if (A.cols() != B.rows())
                  throw std::domain_error("Nonconformable matrices!");
              return A * B;
          },
          py::arg("A"),
          py::arg("B"));
  
      // test_custom_operator_new
      py::class_<CustomOperatorNew>(m, "CustomOperatorNew")
          .def(py::init<>())
          .def_readonly("a", &CustomOperatorNew::a)
          .def_readonly("b", &CustomOperatorNew::b);
  
      // test_eigen_ref_life_support
      // In case of a failure (the caster's temp array does not live long enough), creating
      // a new array (np.ones(10)) increases the chances that the temp array will be garbage
      // collected and/or that its memory will be overridden with different values.
      m.def("get_elem_direct", [](const Eigen::Ref<const Eigen::VectorXd> &v) {
          py::module_::import("numpy").attr("ones")(10);
          return v(5);
      });
      m.def("get_elem_indirect", [](std::vector<Eigen::Ref<const Eigen::VectorXd>> v) {
          py::module_::import("numpy").attr("ones")(10);
          return v[0](5);
      });
  }
  