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267 lines
11 KiB
C++
267 lines
11 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2013 Gauthier Brun <brun.gauthier@gmail.com>
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// Copyright (C) 2013 Nicolas Carre <nicolas.carre@ensimag.fr>
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// Copyright (C) 2013 Jean Ceccato <jean.ceccato@ensimag.fr>
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// Copyright (C) 2013 Pierre Zoppitelli <pierre.zoppitelli@ensimag.fr>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/
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// discard stack allocation as that too bypasses malloc
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#define EIGEN_STACK_ALLOCATION_LIMIT 0
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#define EIGEN_RUNTIME_NO_MALLOC
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#include "main.h"
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#include "tridiag_test_matrices.h"
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#include <Eigen/SVD>
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#define SVD_DEFAULT(M) BDCSVD<M>
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#define SVD_FOR_MIN_NORM(M) BDCSVD<M>
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#define SVD_STATIC_OPTIONS(M, O) BDCSVD<M, O>
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#include "svd_common.h"
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template <typename MatrixType>
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void bdcsvd_method() {
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enum { Size = MatrixType::RowsAtCompileTime };
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typedef typename MatrixType::RealScalar RealScalar;
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typedef Matrix<RealScalar, Size, 1> RealVecType;
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MatrixType m = MatrixType::Identity();
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VERIFY_IS_APPROX(m.bdcSvd().singularValues(), RealVecType::Ones());
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VERIFY_RAISES_ASSERT(m.bdcSvd().matrixU());
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VERIFY_RAISES_ASSERT(m.bdcSvd().matrixV());
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}
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// compare the Singular values returned with Jacobi and Bdc
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template <typename MatrixType>
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void compare_bdc_jacobi(const MatrixType& a = MatrixType(), int algoswap = 16, bool random = true) {
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MatrixType m = random ? MatrixType::Random(a.rows(), a.cols()) : a;
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BDCSVD<MatrixType> bdc_svd(m.rows(), m.cols());
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bdc_svd.setSwitchSize(algoswap);
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bdc_svd.compute(m);
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JacobiSVD<MatrixType> jacobi_svd(m);
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VERIFY_IS_APPROX(bdc_svd.singularValues(), jacobi_svd.singularValues());
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}
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// Verifies total deflation is **not** triggered.
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void compare_bdc_jacobi_instance(bool structure_as_m, int algoswap = 16) {
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MatrixXd m(4, 3);
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if (structure_as_m) {
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// The first 3 rows are the reduced form of Matrix 1 as shown below, and it
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// has nonzero elements in the first column and diagonals only.
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m << 1.056293, 0, 0, -0.336468, 0.907359, 0, -1.566245, 0, 0.149150, -0.1, 0, 0;
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} else {
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// Matrix 1.
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m << 0.882336, 18.3914, -26.7921, -5.58135, 17.1931, -24.0892, -20.794, 8.68496, -4.83103, -8.4981, -10.5451,
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23.9072;
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}
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compare_bdc_jacobi(m, algoswap, false);
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}
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template <typename MatrixType>
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void bdcsvd_thin_options(const MatrixType& input = MatrixType()) {
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svd_thin_option_checks<MatrixType, 0>(input);
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}
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template <typename MatrixType>
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void bdcsvd_full_options(const MatrixType& input = MatrixType()) {
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svd_option_checks_full_only<MatrixType, 0>(input);
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}
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template <typename MatrixType>
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void bdcsvd_verify_assert(const MatrixType& input = MatrixType()) {
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svd_verify_assert<MatrixType>(input);
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svd_verify_constructor_options_assert<BDCSVD<MatrixType>>(input);
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}
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template <typename MatrixType>
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void bdcsvd_check_convergence(const MatrixType& input) {
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BDCSVD<MatrixType, Eigen::ComputeThinU | Eigen::ComputeThinV> svd(input);
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VERIFY(svd.info() == Eigen::Success);
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MatrixType D = svd.matrixU() * svd.singularValues().asDiagonal() * svd.matrixV().transpose();
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VERIFY_IS_APPROX(input, D);
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}
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// Verify SVD of bidiagonal matrix given as diagonal + superdiagonal vectors.
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template <typename RealScalar>
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void verify_bidiagonal_svd(const Matrix<RealScalar, Dynamic, 1>& diag,
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const Matrix<RealScalar, Dynamic, 1>& superdiag) {
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typedef Matrix<RealScalar, Dynamic, Dynamic> MatrixXr;
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typedef Matrix<RealScalar, Dynamic, 1> VectorXr;
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const Index n = diag.size();
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BDCSVD<MatrixXr, ComputeFullU | ComputeFullV> bdcsvd(diag, superdiag);
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VERIFY(bdcsvd.info() == Success);
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const VectorXr& sv = bdcsvd.singularValues();
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// Singular values must be non-negative.
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for (Index i = 0; i < sv.size(); ++i) {
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VERIFY(sv(i) >= RealScalar(0));
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}
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// Singular values must be sorted descending.
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for (Index i = 1; i < sv.size(); ++i) {
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VERIFY(sv(i - 1) >= sv(i));
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}
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// Orthogonality of U and V.
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VERIFY_IS_APPROX(bdcsvd.matrixU().transpose() * bdcsvd.matrixU(), MatrixXr::Identity(n, n));
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VERIFY_IS_APPROX(bdcsvd.matrixV().transpose() * bdcsvd.matrixV(), MatrixXr::Identity(n, n));
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// Reconstruction: U * S * V^T should equal the original bidiagonal.
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MatrixXr B = MatrixXr::Zero(n, n);
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B.diagonal() = diag;
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if (n > 1) B.diagonal(1) = superdiag;
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MatrixXr recon = bdcsvd.matrixU() * sv.asDiagonal() * bdcsvd.matrixV().transpose();
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VERIFY_IS_APPROX(recon, B);
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// Cross-validate singular values against JacobiSVD.
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JacobiSVD<MatrixXr> jacobi(B);
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VERIFY_IS_APPROX(sv, jacobi.singularValues());
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}
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// Verify that bidiagonal API and matrix API produce matching singular values.
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template <typename RealScalar>
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void verify_bidiagonal_vs_matrix_svd(const Matrix<RealScalar, Dynamic, 1>& diag,
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const Matrix<RealScalar, Dynamic, 1>& superdiag) {
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typedef Matrix<RealScalar, Dynamic, Dynamic> MatrixXr;
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const Index n = diag.size();
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// Build dense bidiagonal matrix.
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MatrixXr B = MatrixXr::Zero(n, n);
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B.diagonal() = diag;
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if (n > 1) B.diagonal(1) = superdiag;
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BDCSVD<MatrixXr> bidiag_svd(diag, superdiag);
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BDCSVD<MatrixXr> matrix_svd(B);
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VERIFY(bidiag_svd.info() == Success);
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VERIFY(matrix_svd.info() == Success);
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VERIFY_IS_APPROX(bidiag_svd.singularValues(), matrix_svd.singularValues());
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}
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template <typename RealScalar>
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void bdcsvd_bidiagonal_hard_cases() {
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Eigen::internal::set_is_malloc_allowed(true);
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// Use the shared tridiagonal test matrix generators.
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// Each generator fills (diag, offdiag) which we treat as (diagonal, superdiagonal)
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// of a bidiagonal matrix.
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test::for_all_tridiag_test_matrices<RealScalar>(
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[](const auto& diag, const auto& offdiag) { verify_bidiagonal_svd<RealScalar>(diag, offdiag); });
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// Additional SVD-specific test: identity with cross-validation against full matrix SVD.
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test::for_tridiag_sizes<RealScalar>([](auto& diag, auto& offdiag) {
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test::tridiag_identity(diag, offdiag);
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verify_bidiagonal_vs_matrix_svd<RealScalar>(diag, offdiag);
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});
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// Additional SVD-specific test: scalar for n=1.
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{
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typedef Matrix<RealScalar, Dynamic, 1> VectorXr;
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VectorXr diag(1), offdiag(0);
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diag(0) = RealScalar(3.14);
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verify_bidiagonal_svd<RealScalar>(diag, offdiag);
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}
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}
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EIGEN_DECLARE_TEST(bdcsvd) {
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CALL_SUBTEST_1((bdcsvd_verify_assert<Matrix3f>()));
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CALL_SUBTEST_2((bdcsvd_verify_assert<Matrix4d>()));
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CALL_SUBTEST_3((bdcsvd_verify_assert<Matrix<float, 10, 7>>()));
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CALL_SUBTEST_4((bdcsvd_verify_assert<Matrix<float, 7, 10>>()));
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CALL_SUBTEST_5((bdcsvd_verify_assert<Matrix<std::complex<double>, 6, 9>>()));
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CALL_SUBTEST_6((svd_all_trivial_2x2(bdcsvd_thin_options<Matrix2cd>)));
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CALL_SUBTEST_7((svd_all_trivial_2x2(bdcsvd_full_options<Matrix2cd>)));
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CALL_SUBTEST_8((svd_all_trivial_2x2(bdcsvd_thin_options<Matrix2d>)));
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CALL_SUBTEST_9((svd_all_trivial_2x2(bdcsvd_full_options<Matrix2d>)));
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for (int i = 0; i < g_repeat; i++) {
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int r = internal::random<int>(1, EIGEN_TEST_MAX_SIZE / 2), c = internal::random<int>(1, EIGEN_TEST_MAX_SIZE / 2);
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TEST_SET_BUT_UNUSED_VARIABLE(r);
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TEST_SET_BUT_UNUSED_VARIABLE(c);
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CALL_SUBTEST_10((compare_bdc_jacobi<MatrixXf>(MatrixXf(r, c))));
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CALL_SUBTEST_11((compare_bdc_jacobi<MatrixXd>(MatrixXd(r, c))));
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CALL_SUBTEST_12((compare_bdc_jacobi<MatrixXcd>(MatrixXcd(r, c))));
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// Test on inf/nan matrix
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CALL_SUBTEST_13((svd_inf_nan<MatrixXf>()));
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CALL_SUBTEST_14((svd_inf_nan<MatrixXd>()));
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// Verify some computations using all combinations of the Options template parameter.
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CALL_SUBTEST_15((bdcsvd_thin_options<Matrix3f>()));
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CALL_SUBTEST_16((bdcsvd_full_options<Matrix3f>()));
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CALL_SUBTEST_17((bdcsvd_thin_options<Matrix<float, 2, 3>>()));
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CALL_SUBTEST_18((bdcsvd_full_options<Matrix<float, 2, 3>>()));
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CALL_SUBTEST_19((bdcsvd_thin_options<MatrixXd>(MatrixXd(20, 17))));
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CALL_SUBTEST_20((bdcsvd_full_options<MatrixXd>(MatrixXd(20, 17))));
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CALL_SUBTEST_21((bdcsvd_thin_options<MatrixXd>(MatrixXd(17, 20))));
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CALL_SUBTEST_22((bdcsvd_full_options<MatrixXd>(MatrixXd(17, 20))));
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CALL_SUBTEST_23((bdcsvd_thin_options<Matrix<double, Dynamic, 15>>(Matrix<double, Dynamic, 15>(r, 15))));
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CALL_SUBTEST_24((bdcsvd_full_options<Matrix<double, Dynamic, 15>>(Matrix<double, Dynamic, 15>(r, 15))));
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CALL_SUBTEST_25((bdcsvd_thin_options<Matrix<double, 13, Dynamic>>(Matrix<double, 13, Dynamic>(13, c))));
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CALL_SUBTEST_26((bdcsvd_full_options<Matrix<double, 13, Dynamic>>(Matrix<double, 13, Dynamic>(13, c))));
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CALL_SUBTEST_27((bdcsvd_thin_options<MatrixXf>(MatrixXf(r, c))));
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CALL_SUBTEST_28((bdcsvd_full_options<MatrixXf>(MatrixXf(r, c))));
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CALL_SUBTEST_29((bdcsvd_thin_options<MatrixXcd>(MatrixXcd(r, c))));
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CALL_SUBTEST_30((bdcsvd_full_options<MatrixXcd>(MatrixXcd(r, c))));
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CALL_SUBTEST_31((bdcsvd_thin_options<MatrixXd>(MatrixXd(r, c))));
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CALL_SUBTEST_32((bdcsvd_full_options<MatrixXd>(MatrixXd(r, c))));
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CALL_SUBTEST_33((bdcsvd_thin_options<Matrix<double, Dynamic, Dynamic, RowMajor>>(
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Matrix<double, Dynamic, Dynamic, RowMajor>(20, 27))));
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CALL_SUBTEST_34((bdcsvd_full_options<Matrix<double, Dynamic, Dynamic, RowMajor>>(
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Matrix<double, Dynamic, Dynamic, RowMajor>(20, 27))));
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CALL_SUBTEST_35((bdcsvd_thin_options<Matrix<double, Dynamic, Dynamic, RowMajor>>(
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Matrix<double, Dynamic, Dynamic, RowMajor>(27, 20))));
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CALL_SUBTEST_36((bdcsvd_full_options<Matrix<double, Dynamic, Dynamic, RowMajor>>(
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Matrix<double, Dynamic, Dynamic, RowMajor>(27, 20))));
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CALL_SUBTEST_37((
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svd_check_max_size_matrix<Matrix<float, Dynamic, Dynamic, ColMajor, 20, 35>, ColPivHouseholderQRPreconditioner>(
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r, c)));
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CALL_SUBTEST_38(
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(svd_check_max_size_matrix<Matrix<float, Dynamic, Dynamic, ColMajor, 35, 20>, HouseholderQRPreconditioner>(r,
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c)));
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CALL_SUBTEST_39((
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svd_check_max_size_matrix<Matrix<float, Dynamic, Dynamic, RowMajor, 20, 35>, ColPivHouseholderQRPreconditioner>(
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r, c)));
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CALL_SUBTEST_40(
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(svd_check_max_size_matrix<Matrix<float, Dynamic, Dynamic, RowMajor, 35, 20>, HouseholderQRPreconditioner>(r,
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c)));
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}
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// test matrixbase method
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CALL_SUBTEST_41((bdcsvd_method<Matrix2cd>()));
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CALL_SUBTEST_42((bdcsvd_method<Matrix3f>()));
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// Test problem size constructors
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CALL_SUBTEST_43(BDCSVD<MatrixXf>(10, 10));
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// Check that preallocation avoids subsequent mallocs
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// Disabled because not supported by BDCSVD
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// CALL_SUBTEST_9( svd_preallocate<void>() );
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CALL_SUBTEST_44(svd_underoverflow<void>());
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// Without total deflation issues.
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CALL_SUBTEST_45((compare_bdc_jacobi_instance(true)));
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CALL_SUBTEST_46((compare_bdc_jacobi_instance(false)));
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// With total deflation issues before, when it shouldn't be triggered.
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CALL_SUBTEST_47((compare_bdc_jacobi_instance(true, 3)));
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CALL_SUBTEST_48((compare_bdc_jacobi_instance(false, 3)));
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// Convergence for large constant matrix (https://gitlab.com/libeigen/eigen/-/issues/2491)
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CALL_SUBTEST_49(bdcsvd_check_convergence<MatrixXf>(MatrixXf::Constant(500, 500, 1)));
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// Bidiagonal SVD hard test cases
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CALL_SUBTEST_50((bdcsvd_bidiagonal_hard_cases<float>()));
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CALL_SUBTEST_51((bdcsvd_bidiagonal_hard_cases<double>()));
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}
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