test_eigen_matrix.cpp

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/*
    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/eigen/matrix.h>
#include <pybind11/stl.h>
 
#include "constructor_stats.h"
#include "pybind11_tests.h"
 
PYBIND11_WARNING_DISABLE_MSVC(4996)
 
#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_matrix, 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",
          [m](const py::object &x_obj,
              int start_row,
              int start_col,
              int block_rows,
              int block_cols) {
              return m.attr("_block")(x_obj, x_obj, start_row, start_col, block_rows, block_cols);
          });
 
    m.def(
        "_block",
        [](const py::object &x_obj,
           const Eigen::Ref<const Eigen::MatrixXd> &x,
           int start_row,
           int start_col,
           int block_rows,
           int block_cols) {
            // See PR #4217 for background. This test is a bit over the top, but might be useful
            // as a concrete example to point to when explaining the dangling reference trap.
            auto i0 = py::make_tuple(0, 0);
            auto x0_orig = x_obj[*i0].cast<double>();
            if (x(0, 0) != x0_orig) {
                throw std::runtime_error(
                    "Something in the type_caster for Eigen::Ref is terribly wrong.");
            }
            double x0_mod = x0_orig + 1;
            x_obj[*i0] = x0_mod;
            auto copy_detected = (x(0, 0) != x0_mod);
            x_obj[*i0] = x0_orig;
            if (copy_detected) {
                throw std::runtime_error("type_caster for Eigen::Ref made a copy.");
            }
            return x.block(start_row, start_col, block_rows, block_cols);
        },
        py::keep_alive<0, 1>());
 
    // 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_defaults
    bool have_numpy = true;
    try {
        py::module_::import("numpy");
    } catch (const py::error_already_set &) {
        have_numpy = false;
    }
    if (have_numpy) {
        py::module_::import("numpy");
        Eigen::Matrix<double, 3, 3> defaultMatrix = Eigen::Matrix3d::Identity();
        m.def("defaults_mat", [](const Eigen::Matrix3d &) {}, py::arg("mat") = defaultMatrix);
 
        Eigen::VectorXd defaultVector = Eigen::VectorXd::Ones(32);
        m.def("defaults_vec", [](const Eigen::VectorXd &) {}, py::arg("vec") = defaultMatrix);
    }
    // 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, test_zero_length
    // Issue #738: 1×N or N×1 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.
    // Similarly, 0×N or N×0 matrices were not accepted--again, these should be allowed since
    // they contain no data. This particularly affects numpy ≥ 1.23, which sets the strides to
    // 0 if any dimension size is 0.
    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);
    });
}