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388 lines
16 KiB
C++
388 lines
16 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 <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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using std::abs;
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using std::cos;
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using std::pow;
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using std::sin;
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typedef Matrix<RealScalar, Dynamic, 1> VectorXr;
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Eigen::internal::set_is_malloc_allowed(true);
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const RealScalar eps = NumTraits<RealScalar>::epsilon();
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// Test sizes: cover n=1, very small, below/above algoSwap (16), and larger.
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const int sizes[] = {1, 2, 3, 5, 10, 16, 20, 50, 100};
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const int numSizes = sizeof(sizes) / sizeof(sizes[0]);
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for (int si = 0; si < numSizes; ++si) {
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const Index n = sizes[si];
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VectorXr diag(n), superdiag(n > 1 ? n - 1 : 0);
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// 1. Identity: d=[1,...,1], e=[0,...,0]
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diag.setOnes();
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superdiag.setZero();
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verify_bidiagonal_svd<RealScalar>(diag, superdiag);
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verify_bidiagonal_vs_matrix_svd<RealScalar>(diag, superdiag);
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// 2. Zero: d=[0,...,0], e=[0,...,0]
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diag.setZero();
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superdiag.setZero();
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verify_bidiagonal_svd<RealScalar>(diag, superdiag);
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// 3. Scalar (only meaningful for n=1, but runs for all)
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if (n == 1) {
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diag(0) = RealScalar(3.14);
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verify_bidiagonal_svd<RealScalar>(diag, superdiag);
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}
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// 4. Golub-Kahan: d=[1,...,1], e=[1,...,1]
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diag.setOnes();
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if (n > 1) superdiag.setOnes();
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verify_bidiagonal_svd<RealScalar>(diag, superdiag);
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// 5. Kahan matrix: d_i = s^(i-1), e_i = -c*s^(i-1)
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// Clamp exponents so condition number stays bounded by 1/eps.
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{
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const RealScalar theta = RealScalar(0.3);
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const RealScalar s = sin(theta);
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const RealScalar c = cos(theta);
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using std::log;
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const RealScalar maxPower = -log(eps) / (-log(s));
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for (Index i = 0; i < n; ++i) diag(i) = pow(s, numext::mini(RealScalar(i), maxPower));
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for (Index i = 0; i < n - 1; ++i) superdiag(i) = -c * pow(s, numext::mini(RealScalar(i), maxPower));
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verify_bidiagonal_svd<RealScalar>(diag, superdiag);
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}
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// 6. Geometric decay diagonal: d_i = 0.5^i, e=[0,...,0]
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// Clamp so condition number stays bounded by 1/eps.
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{
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using std::log;
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const RealScalar base = RealScalar(0.5);
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const RealScalar maxPower = -log(eps) / (-log(base));
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for (Index i = 0; i < n; ++i) diag(i) = pow(base, numext::mini(RealScalar(i), maxPower));
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superdiag.setZero();
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verify_bidiagonal_svd<RealScalar>(diag, superdiag);
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}
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// 7. Geometric decay superdiagonal: d=[1,...,1], e_i = 0.5^i
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diag.setOnes();
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for (Index i = 0; i < n - 1; ++i) superdiag(i) = pow(RealScalar(0.5), RealScalar(i));
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verify_bidiagonal_svd<RealScalar>(diag, superdiag);
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// 8. Clustered at 1: d_i = 1 + i*eps, e=[0,...,0]
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for (Index i = 0; i < n; ++i) diag(i) = RealScalar(1) + RealScalar(i) * eps;
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superdiag.setZero();
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verify_bidiagonal_svd<RealScalar>(diag, superdiag);
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// 9. Two clusters: half ≈ 1, half ≈ eps
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for (Index i = 0; i < n; ++i) diag(i) = (i < n / 2) ? RealScalar(1) : eps;
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superdiag.setZero();
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verify_bidiagonal_svd<RealScalar>(diag, superdiag);
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// 10. Single tiny singular value: d=[1,...,1,eps], e=[eps^2,...]
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diag.setOnes();
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diag(n - 1) = eps;
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for (Index i = 0; i < n - 1; ++i) superdiag(i) = eps * eps;
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verify_bidiagonal_svd<RealScalar>(diag, superdiag);
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// 11. Graded: d_i = 10^(-i), e_i = 10^(-i)
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for (Index i = 0; i < n; ++i) diag(i) = pow(RealScalar(10), -RealScalar(i));
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for (Index i = 0; i < n - 1; ++i) superdiag(i) = pow(RealScalar(10), -RealScalar(i));
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verify_bidiagonal_svd<RealScalar>(diag, superdiag);
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// 12. Nearly diagonal: random diag, eps * random superdiag
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diag = VectorXr::Random(n).cwiseAbs() + VectorXr::Constant(n, RealScalar(0.1));
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for (Index i = 0; i < n - 1; ++i) superdiag(i) = eps * (RealScalar(0.5) + abs(internal::random<RealScalar>()));
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verify_bidiagonal_svd<RealScalar>(diag, superdiag);
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// 13. All equal: d=[c,...,c], e=[c,...,c]
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diag.setConstant(RealScalar(2.5));
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if (n > 1) superdiag.setConstant(RealScalar(2.5));
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verify_bidiagonal_svd<RealScalar>(diag, superdiag);
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// 14. Wilkinson: d_i = |n/2 - i|, e=[1,...,1]
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for (Index i = 0; i < n; ++i) diag(i) = abs(RealScalar(n / 2) - RealScalar(i));
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if (n > 1) superdiag.setOnes();
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verify_bidiagonal_svd<RealScalar>(diag, superdiag);
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// 15. Overflow/underflow: alternating big/tiny diagonal, tiny/big superdiagonal
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{
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const RealScalar big = (std::numeric_limits<RealScalar>::max)() / RealScalar(1000);
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const RealScalar tiny = (std::numeric_limits<RealScalar>::min)() * RealScalar(1000);
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for (Index i = 0; i < n; ++i) diag(i) = (i % 2 == 0) ? big : tiny;
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for (Index i = 0; i < n - 1; ++i) superdiag(i) = (i % 2 == 0) ? tiny : big;
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verify_bidiagonal_svd<RealScalar>(diag, superdiag);
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}
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// 16. Prescribed condition number: d_i = kappa^(-i/(n-1)), e_i = eps * random
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if (n > 1) {
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const RealScalar kappa = RealScalar(1) / eps;
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for (Index i = 0; i < n; ++i) diag(i) = pow(kappa, -RealScalar(i) / RealScalar(n - 1));
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for (Index i = 0; i < n - 1; ++i) superdiag(i) = eps * abs(internal::random<RealScalar>());
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verify_bidiagonal_svd<RealScalar>(diag, superdiag);
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}
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// 17. Rank-deficient: d=[1,..,0,..,0,..,1], e=[0,...,0]
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for (Index i = 0; i < n; ++i) diag(i) = (i < n / 3 || i >= 2 * n / 3) ? RealScalar(1) : RealScalar(0);
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superdiag.setZero();
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verify_bidiagonal_svd<RealScalar>(diag, superdiag);
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// 18. Arrowhead stress: d_i = linspace(1, n), e_i = 1/(i+1)
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for (Index i = 0; i < n; ++i) diag(i) = RealScalar(1) + RealScalar(i);
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for (Index i = 0; i < n - 1; ++i) superdiag(i) = RealScalar(1) / RealScalar(i + 1);
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verify_bidiagonal_svd<RealScalar>(diag, superdiag);
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// 19. Repeated singular values: d=[1,2,3,1,2,3,...], e=[0,...,0]
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for (Index i = 0; i < n; ++i) diag(i) = RealScalar((i % 3) + 1);
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superdiag.setZero();
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verify_bidiagonal_svd<RealScalar>(diag, superdiag);
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// 20. Glued identity: d=[1,...,1], e=0 except e[n/2-1]=eps
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diag.setOnes();
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superdiag.setZero();
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if (n > 2) superdiag(n / 2 - 1) = eps;
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verify_bidiagonal_svd<RealScalar>(diag, superdiag);
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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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