test/bdcsvd.cpp

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2013 Gauthier Brun <brun.gauthier@gmail.com>
// Copyright (C) 2013 Nicolas Carre <nicolas.carre@ensimag.fr>
// Copyright (C) 2013 Jean Ceccato <jean.ceccato@ensimag.fr>
// Copyright (C) 2013 Pierre Zoppitelli <pierre.zoppitelli@ensimag.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/

// discard stack allocation as that too bypasses malloc
#define EIGEN_STACK_ALLOCATION_LIMIT 0
#define EIGEN_RUNTIME_NO_MALLOC

#include "main.h"
#include <Eigen/SVD>

#define SVD_DEFAULT(M) BDCSVD<M>
#define SVD_FOR_MIN_NORM(M) BDCSVD<M>
#define SVD_STATIC_OPTIONS(M, O) BDCSVD<M, O>
#include "svd_common.h"

template <typename MatrixType>
void bdcsvd_method() {
  enum { Size = MatrixType::RowsAtCompileTime };
  typedef typename MatrixType::RealScalar RealScalar;
  typedef Matrix<RealScalar, Size, 1> RealVecType;
  MatrixType m = MatrixType::Identity();
  VERIFY_IS_APPROX(m.bdcSvd().singularValues(), RealVecType::Ones());
  VERIFY_RAISES_ASSERT(m.bdcSvd().matrixU());
  VERIFY_RAISES_ASSERT(m.bdcSvd().matrixV());
}

// compare the Singular values returned with Jacobi and Bdc
template <typename MatrixType>
void compare_bdc_jacobi(const MatrixType& a = MatrixType(), int algoswap = 16, bool random = true) {
  MatrixType m = random ? MatrixType::Random(a.rows(), a.cols()) : a;

  BDCSVD<MatrixType> bdc_svd(m.rows(), m.cols());
  bdc_svd.setSwitchSize(algoswap);
  bdc_svd.compute(m);

  JacobiSVD<MatrixType> jacobi_svd(m);
  VERIFY_IS_APPROX(bdc_svd.singularValues(), jacobi_svd.singularValues());
}

// Verifies total deflation is **not** triggered.
void compare_bdc_jacobi_instance(bool structure_as_m, int algoswap = 16) {
  MatrixXd m(4, 3);
  if (structure_as_m) {
    // The first 3 rows are the reduced form of Matrix 1 as shown below, and it
    // has nonzero elements in the first column and diagonals only.
    m << 1.056293, 0, 0, -0.336468, 0.907359, 0, -1.566245, 0, 0.149150, -0.1, 0, 0;
  } else {
    // Matrix 1.
    m << 0.882336, 18.3914, -26.7921, -5.58135, 17.1931, -24.0892, -20.794, 8.68496, -4.83103, -8.4981, -10.5451,
        23.9072;
  }
  compare_bdc_jacobi(m, algoswap, false);
}

template <typename MatrixType>
void bdcsvd_thin_options(const MatrixType& input = MatrixType()) {
  svd_thin_option_checks<MatrixType, 0>(input);
}

template <typename MatrixType>
void bdcsvd_full_options(const MatrixType& input = MatrixType()) {
  svd_option_checks_full_only<MatrixType, 0>(input);
}

template <typename MatrixType>
void bdcsvd_verify_assert(const MatrixType& input = MatrixType()) {
  svd_verify_assert<MatrixType>(input);
  svd_verify_constructor_options_assert<BDCSVD<MatrixType>>(input);
}

template <typename MatrixType>
void bdcsvd_check_convergence(const MatrixType& input) {
  BDCSVD<MatrixType, Eigen::ComputeThinU | Eigen::ComputeThinV> svd(input);
  VERIFY(svd.info() == Eigen::Success);
  MatrixType D = svd.matrixU() * svd.singularValues().asDiagonal() * svd.matrixV().transpose();
  VERIFY_IS_APPROX(input, D);
}

EIGEN_DECLARE_TEST(bdcsvd) {
  CALL_SUBTEST_1((bdcsvd_verify_assert<Matrix3f>()));
  CALL_SUBTEST_2((bdcsvd_verify_assert<Matrix4d>()));
  CALL_SUBTEST_3((bdcsvd_verify_assert<Matrix<float, 10, 7>>()));
  CALL_SUBTEST_4((bdcsvd_verify_assert<Matrix<float, 7, 10>>()));
  CALL_SUBTEST_5((bdcsvd_verify_assert<Matrix<std::complex<double>, 6, 9>>()));

  CALL_SUBTEST_6((svd_all_trivial_2x2(bdcsvd_thin_options<Matrix2cd>)));
  CALL_SUBTEST_7((svd_all_trivial_2x2(bdcsvd_full_options<Matrix2cd>)));
  CALL_SUBTEST_8((svd_all_trivial_2x2(bdcsvd_thin_options<Matrix2d>)));
  CALL_SUBTEST_9((svd_all_trivial_2x2(bdcsvd_full_options<Matrix2d>)));

  for (int i = 0; i < g_repeat; i++) {
    int r = internal::random<int>(1, EIGEN_TEST_MAX_SIZE / 2), c = internal::random<int>(1, EIGEN_TEST_MAX_SIZE / 2);

    TEST_SET_BUT_UNUSED_VARIABLE(r)
    TEST_SET_BUT_UNUSED_VARIABLE(c)

    CALL_SUBTEST_10((compare_bdc_jacobi<MatrixXf>(MatrixXf(r, c))));
    CALL_SUBTEST_11((compare_bdc_jacobi<MatrixXd>(MatrixXd(r, c))));
    CALL_SUBTEST_12((compare_bdc_jacobi<MatrixXcd>(MatrixXcd(r, c))));
    // Test on inf/nan matrix
    CALL_SUBTEST_13((svd_inf_nan<MatrixXf>()));
    CALL_SUBTEST_14((svd_inf_nan<MatrixXd>()));

    // Verify some computations using all combinations of the Options template parameter.
    CALL_SUBTEST_15((bdcsvd_thin_options<Matrix3f>()));
    CALL_SUBTEST_16((bdcsvd_full_options<Matrix3f>()));
    CALL_SUBTEST_17((bdcsvd_thin_options<Matrix<float, 2, 3>>()));
    CALL_SUBTEST_18((bdcsvd_full_options<Matrix<float, 2, 3>>()));
    CALL_SUBTEST_19((bdcsvd_thin_options<MatrixXd>(MatrixXd(20, 17))));
    CALL_SUBTEST_20((bdcsvd_full_options<MatrixXd>(MatrixXd(20, 17))));
    CALL_SUBTEST_21((bdcsvd_thin_options<MatrixXd>(MatrixXd(17, 20))));
    CALL_SUBTEST_22((bdcsvd_full_options<MatrixXd>(MatrixXd(17, 20))));
    CALL_SUBTEST_23((bdcsvd_thin_options<Matrix<double, Dynamic, 15>>(Matrix<double, Dynamic, 15>(r, 15))));
    CALL_SUBTEST_24((bdcsvd_full_options<Matrix<double, Dynamic, 15>>(Matrix<double, Dynamic, 15>(r, 15))));
    CALL_SUBTEST_25((bdcsvd_thin_options<Matrix<double, 13, Dynamic>>(Matrix<double, 13, Dynamic>(13, c))));
    CALL_SUBTEST_26((bdcsvd_full_options<Matrix<double, 13, Dynamic>>(Matrix<double, 13, Dynamic>(13, c))));
    CALL_SUBTEST_27((bdcsvd_thin_options<MatrixXf>(MatrixXf(r, c))));
    CALL_SUBTEST_28((bdcsvd_full_options<MatrixXf>(MatrixXf(r, c))));
    CALL_SUBTEST_29((bdcsvd_thin_options<MatrixXcd>(MatrixXcd(r, c))));
    CALL_SUBTEST_30((bdcsvd_full_options<MatrixXcd>(MatrixXcd(r, c))));
    CALL_SUBTEST_31((bdcsvd_thin_options<MatrixXd>(MatrixXd(r, c))));
    CALL_SUBTEST_32((bdcsvd_full_options<MatrixXd>(MatrixXd(r, c))));
    CALL_SUBTEST_33((bdcsvd_thin_options<Matrix<double, Dynamic, Dynamic, RowMajor>>(
        Matrix<double, Dynamic, Dynamic, RowMajor>(20, 27))));
    CALL_SUBTEST_34((bdcsvd_full_options<Matrix<double, Dynamic, Dynamic, RowMajor>>(
        Matrix<double, Dynamic, Dynamic, RowMajor>(20, 27))));
    CALL_SUBTEST_35((bdcsvd_thin_options<Matrix<double, Dynamic, Dynamic, RowMajor>>(
        Matrix<double, Dynamic, Dynamic, RowMajor>(27, 20))));
    CALL_SUBTEST_36((bdcsvd_full_options<Matrix<double, Dynamic, Dynamic, RowMajor>>(
        Matrix<double, Dynamic, Dynamic, RowMajor>(27, 20))));
    CALL_SUBTEST_37((
        svd_check_max_size_matrix<Matrix<float, Dynamic, Dynamic, ColMajor, 20, 35>, ColPivHouseholderQRPreconditioner>(
            r, c)));
    CALL_SUBTEST_38(
        (svd_check_max_size_matrix<Matrix<float, Dynamic, Dynamic, ColMajor, 35, 20>, HouseholderQRPreconditioner>(r,
                                                                                                                   c)));
    CALL_SUBTEST_39((
        svd_check_max_size_matrix<Matrix<float, Dynamic, Dynamic, RowMajor, 20, 35>, ColPivHouseholderQRPreconditioner>(
            r, c)));
    CALL_SUBTEST_40(
        (svd_check_max_size_matrix<Matrix<float, Dynamic, Dynamic, RowMajor, 35, 20>, HouseholderQRPreconditioner>(r,
                                                                                                                   c)));
  }

  // test matrixbase method
  CALL_SUBTEST_41((bdcsvd_method<Matrix2cd>()));
  CALL_SUBTEST_42((bdcsvd_method<Matrix3f>()));

  // Test problem size constructors
  CALL_SUBTEST_43(BDCSVD<MatrixXf>(10, 10));

  // Check that preallocation avoids subsequent mallocs
  // Disabled because not supported by BDCSVD
  // CALL_SUBTEST_9( svd_preallocate<void>() );

  CALL_SUBTEST_44(svd_underoverflow<void>());

  // Without total deflation issues.
  CALL_SUBTEST_45((compare_bdc_jacobi_instance(true)));
  CALL_SUBTEST_46((compare_bdc_jacobi_instance(false)));

  // With total deflation issues before, when it shouldn't be triggered.
  CALL_SUBTEST_47((compare_bdc_jacobi_instance(true, 3)));
  CALL_SUBTEST_48((compare_bdc_jacobi_instance(false, 3)));

  // Convergence for large constant matrix (https://gitlab.com/libeigen/eigen/-/issues/2491)
  CALL_SUBTEST_49(bdcsvd_check_convergence<MatrixXf>(MatrixXf::Constant(500, 500, 1)));
}