1 | // This file is part of Eigen, a lightweight C++ template library
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2 | // for linear algebra.
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3 | //
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4 | // Copyright (C) 2011 Kolja Brix <brix@igpm.rwth-aachen.de>
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5 | // Copyright (C) 2011 Andreas Platen <andiplaten@gmx.de>
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6 | // Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>
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7 | //
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8 | // This Source Code Form is subject to the terms of the Mozilla
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9 | // Public License v. 2.0. If a copy of the MPL was not distributed
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10 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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11 |
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12 |
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13 | #include "sparse.h"
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14 | #include <Eigen/SparseExtra>
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15 | #include <Eigen/KroneckerProduct>
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16 |
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17 |
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18 | template<typename MatrixType>
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19 | void check_dimension(const MatrixType& ab, const int rows, const int cols)
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20 | {
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21 | VERIFY_IS_EQUAL(ab.rows(), rows);
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22 | VERIFY_IS_EQUAL(ab.cols(), cols);
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23 | }
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24 |
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25 |
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26 | template<typename MatrixType>
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27 | void check_kronecker_product(const MatrixType& ab)
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28 | {
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29 | VERIFY_IS_EQUAL(ab.rows(), 6);
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30 | VERIFY_IS_EQUAL(ab.cols(), 6);
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31 | VERIFY_IS_EQUAL(ab.nonZeros(), 36);
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32 | VERIFY_IS_APPROX(ab.coeff(0,0), -0.4017367630386106);
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33 | VERIFY_IS_APPROX(ab.coeff(0,1), 0.1056863433932735);
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34 | VERIFY_IS_APPROX(ab.coeff(0,2), -0.7255206194554212);
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35 | VERIFY_IS_APPROX(ab.coeff(0,3), 0.1908653336744706);
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36 | VERIFY_IS_APPROX(ab.coeff(0,4), 0.350864567234111);
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37 | VERIFY_IS_APPROX(ab.coeff(0,5), -0.0923032108308013);
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38 | VERIFY_IS_APPROX(ab.coeff(1,0), 0.415417514804677);
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39 | VERIFY_IS_APPROX(ab.coeff(1,1), -0.2369227701722048);
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40 | VERIFY_IS_APPROX(ab.coeff(1,2), 0.7502275131458511);
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41 | VERIFY_IS_APPROX(ab.coeff(1,3), -0.4278731019742696);
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42 | VERIFY_IS_APPROX(ab.coeff(1,4), -0.3628129162264507);
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43 | VERIFY_IS_APPROX(ab.coeff(1,5), 0.2069210808481275);
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44 | VERIFY_IS_APPROX(ab.coeff(2,0), 0.05465890160863986);
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45 | VERIFY_IS_APPROX(ab.coeff(2,1), -0.2634092511419858);
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46 | VERIFY_IS_APPROX(ab.coeff(2,2), 0.09871180285793758);
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47 | VERIFY_IS_APPROX(ab.coeff(2,3), -0.4757066334017702);
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48 | VERIFY_IS_APPROX(ab.coeff(2,4), -0.04773740823058334);
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49 | VERIFY_IS_APPROX(ab.coeff(2,5), 0.2300535609645254);
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50 | VERIFY_IS_APPROX(ab.coeff(3,0), -0.8172945853260133);
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51 | VERIFY_IS_APPROX(ab.coeff(3,1), 0.2150086428359221);
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52 | VERIFY_IS_APPROX(ab.coeff(3,2), 0.5825113847292743);
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53 | VERIFY_IS_APPROX(ab.coeff(3,3), -0.1532433770097174);
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54 | VERIFY_IS_APPROX(ab.coeff(3,4), -0.329383387282399);
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55 | VERIFY_IS_APPROX(ab.coeff(3,5), 0.08665207912033064);
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56 | VERIFY_IS_APPROX(ab.coeff(4,0), 0.8451267514863225);
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57 | VERIFY_IS_APPROX(ab.coeff(4,1), -0.481996458918977);
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58 | VERIFY_IS_APPROX(ab.coeff(4,2), -0.6023482390791535);
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59 | VERIFY_IS_APPROX(ab.coeff(4,3), 0.3435339347164565);
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60 | VERIFY_IS_APPROX(ab.coeff(4,4), 0.3406002157428891);
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61 | VERIFY_IS_APPROX(ab.coeff(4,5), -0.1942526344200915);
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62 | VERIFY_IS_APPROX(ab.coeff(5,0), 0.1111982482925399);
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63 | VERIFY_IS_APPROX(ab.coeff(5,1), -0.5358806424754169);
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64 | VERIFY_IS_APPROX(ab.coeff(5,2), -0.07925446559335647);
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65 | VERIFY_IS_APPROX(ab.coeff(5,3), 0.3819388757769038);
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66 | VERIFY_IS_APPROX(ab.coeff(5,4), 0.04481475387219876);
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67 | VERIFY_IS_APPROX(ab.coeff(5,5), -0.2159688616158057);
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68 | }
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69 |
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70 |
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71 | template<typename MatrixType>
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72 | void check_sparse_kronecker_product(const MatrixType& ab)
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73 | {
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74 | VERIFY_IS_EQUAL(ab.rows(), 12);
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75 | VERIFY_IS_EQUAL(ab.cols(), 10);
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76 | VERIFY_IS_EQUAL(ab.nonZeros(), 3*2);
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77 | VERIFY_IS_APPROX(ab.coeff(3,0), -0.04);
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78 | VERIFY_IS_APPROX(ab.coeff(5,1), 0.05);
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79 | VERIFY_IS_APPROX(ab.coeff(0,6), -0.08);
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80 | VERIFY_IS_APPROX(ab.coeff(2,7), 0.10);
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81 | VERIFY_IS_APPROX(ab.coeff(6,8), 0.12);
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82 | VERIFY_IS_APPROX(ab.coeff(8,9), -0.15);
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83 | }
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84 |
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85 |
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86 | void test_kronecker_product()
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87 | {
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88 | // DM = dense matrix; SM = sparse matrix
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89 |
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90 | Matrix<double, 2, 3> DM_a;
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91 | SparseMatrix<double> SM_a(2,3);
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92 | SM_a.insert(0,0) = DM_a.coeffRef(0,0) = -0.4461540300782201;
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93 | SM_a.insert(0,1) = DM_a.coeffRef(0,1) = -0.8057364375283049;
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94 | SM_a.insert(0,2) = DM_a.coeffRef(0,2) = 0.3896572459516341;
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95 | SM_a.insert(1,0) = DM_a.coeffRef(1,0) = -0.9076572187376921;
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96 | SM_a.insert(1,1) = DM_a.coeffRef(1,1) = 0.6469156566545853;
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97 | SM_a.insert(1,2) = DM_a.coeffRef(1,2) = -0.3658010398782789;
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98 |
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99 | MatrixXd DM_b(3,2);
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100 | SparseMatrix<double> SM_b(3,2);
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101 | SM_b.insert(0,0) = DM_b.coeffRef(0,0) = 0.9004440976767099;
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102 | SM_b.insert(0,1) = DM_b.coeffRef(0,1) = -0.2368830858139832;
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103 | SM_b.insert(1,0) = DM_b.coeffRef(1,0) = -0.9311078389941825;
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104 | SM_b.insert(1,1) = DM_b.coeffRef(1,1) = 0.5310335762980047;
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105 | SM_b.insert(2,0) = DM_b.coeffRef(2,0) = -0.1225112806872035;
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106 | SM_b.insert(2,1) = DM_b.coeffRef(2,1) = 0.5903998022741264;
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107 |
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108 | SparseMatrix<double,RowMajor> SM_row_a(SM_a), SM_row_b(SM_b);
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109 |
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110 | // test kroneckerProduct(DM_block,DM,DM_fixedSize)
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111 | Matrix<double, 6, 6> DM_fix_ab = kroneckerProduct(DM_a.topLeftCorner<2,3>(),DM_b);
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112 |
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113 | CALL_SUBTEST(check_kronecker_product(DM_fix_ab));
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114 |
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115 | for(int i=0;i<DM_fix_ab.rows();++i)
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116 | for(int j=0;j<DM_fix_ab.cols();++j)
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117 | VERIFY_IS_APPROX(kroneckerProduct(DM_a,DM_b).coeff(i,j), DM_fix_ab(i,j));
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118 |
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119 | // test kroneckerProduct(DM,DM,DM_block)
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120 | MatrixXd DM_block_ab(10,15);
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121 | DM_block_ab.block<6,6>(2,5) = kroneckerProduct(DM_a,DM_b);
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122 | CALL_SUBTEST(check_kronecker_product(DM_block_ab.block<6,6>(2,5)));
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123 |
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124 | // test kroneckerProduct(DM,DM,DM)
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125 | MatrixXd DM_ab = kroneckerProduct(DM_a,DM_b);
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126 | CALL_SUBTEST(check_kronecker_product(DM_ab));
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127 |
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128 | // test kroneckerProduct(SM,DM,SM)
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129 | SparseMatrix<double> SM_ab = kroneckerProduct(SM_a,DM_b);
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130 | CALL_SUBTEST(check_kronecker_product(SM_ab));
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131 | SparseMatrix<double,RowMajor> SM_ab2 = kroneckerProduct(SM_a,DM_b);
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132 | CALL_SUBTEST(check_kronecker_product(SM_ab2));
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133 |
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134 | // test kroneckerProduct(DM,SM,SM)
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135 | SM_ab.setZero();
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136 | SM_ab.insert(0,0)=37.0;
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137 | SM_ab = kroneckerProduct(DM_a,SM_b);
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138 | CALL_SUBTEST(check_kronecker_product(SM_ab));
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139 | SM_ab2.setZero();
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140 | SM_ab2.insert(0,0)=37.0;
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141 | SM_ab2 = kroneckerProduct(DM_a,SM_b);
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142 | CALL_SUBTEST(check_kronecker_product(SM_ab2));
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143 |
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144 | // test kroneckerProduct(SM,SM,SM)
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145 | SM_ab.resize(2,33);
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146 | SM_ab.insert(0,0)=37.0;
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147 | SM_ab = kroneckerProduct(SM_a,SM_b);
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148 | CALL_SUBTEST(check_kronecker_product(SM_ab));
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149 | SM_ab2.resize(5,11);
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150 | SM_ab2.insert(0,0)=37.0;
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151 | SM_ab2 = kroneckerProduct(SM_a,SM_b);
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152 | CALL_SUBTEST(check_kronecker_product(SM_ab2));
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153 |
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154 | // test kroneckerProduct(SM,SM,SM) with sparse pattern
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155 | SM_a.resize(4,5);
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156 | SM_b.resize(3,2);
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157 | SM_a.resizeNonZeros(0);
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158 | SM_b.resizeNonZeros(0);
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159 | SM_a.insert(1,0) = -0.1;
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160 | SM_a.insert(0,3) = -0.2;
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161 | SM_a.insert(2,4) = 0.3;
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162 | SM_a.finalize();
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163 |
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164 | SM_b.insert(0,0) = 0.4;
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165 | SM_b.insert(2,1) = -0.5;
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166 | SM_b.finalize();
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167 | SM_ab.resize(1,1);
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168 | SM_ab.insert(0,0)=37.0;
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169 | SM_ab = kroneckerProduct(SM_a,SM_b);
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170 | CALL_SUBTEST(check_sparse_kronecker_product(SM_ab));
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171 |
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172 | // test dimension of result of kroneckerProduct(DM,DM,DM)
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173 | MatrixXd DM_a2(2,1);
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174 | MatrixXd DM_b2(5,4);
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175 | MatrixXd DM_ab2 = kroneckerProduct(DM_a2,DM_b2);
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176 | CALL_SUBTEST(check_dimension(DM_ab2,2*5,1*4));
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177 | DM_a2.resize(10,9);
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178 | DM_b2.resize(4,8);
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179 | DM_ab2 = kroneckerProduct(DM_a2,DM_b2);
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180 | CALL_SUBTEST(check_dimension(DM_ab2,10*4,9*8));
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181 | }
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