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) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
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5 | //
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6 | // This Source Code Form is subject to the terms of the Mozilla
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7 | // Public License v. 2.0. If a copy of the MPL was not distributed
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8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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9 |
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10 | #include "main.h"
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11 | #include <Eigen/QR>
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12 |
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13 | template<typename Derived1, typename Derived2>
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14 | bool areNotApprox(const MatrixBase<Derived1>& m1, const MatrixBase<Derived2>& m2, typename Derived1::RealScalar epsilon = NumTraits<typename Derived1::RealScalar>::dummy_precision())
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15 | {
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16 | return !((m1-m2).cwiseAbs2().maxCoeff() < epsilon * epsilon
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17 | * (std::max)(m1.cwiseAbs2().maxCoeff(), m2.cwiseAbs2().maxCoeff()));
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18 | }
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19 |
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20 | template<typename MatrixType> void product(const MatrixType& m)
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21 | {
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22 | /* this test covers the following files:
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23 | Identity.h Product.h
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24 | */
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25 | typedef typename MatrixType::Index Index;
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26 | typedef typename MatrixType::Scalar Scalar;
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27 | typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> RowVectorType;
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28 | typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> ColVectorType;
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29 | typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> RowSquareMatrixType;
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30 | typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> ColSquareMatrixType;
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31 | typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime,
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32 | MatrixType::Flags&RowMajorBit?ColMajor:RowMajor> OtherMajorMatrixType;
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33 |
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34 | Index rows = m.rows();
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35 | Index cols = m.cols();
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36 |
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37 | // this test relies a lot on Random.h, and there's not much more that we can do
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38 | // to test it, hence I consider that we will have tested Random.h
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39 | MatrixType m1 = MatrixType::Random(rows, cols),
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40 | m2 = MatrixType::Random(rows, cols),
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41 | m3(rows, cols);
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42 | RowSquareMatrixType
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43 | identity = RowSquareMatrixType::Identity(rows, rows),
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44 | square = RowSquareMatrixType::Random(rows, rows),
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45 | res = RowSquareMatrixType::Random(rows, rows);
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46 | ColSquareMatrixType
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47 | square2 = ColSquareMatrixType::Random(cols, cols),
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48 | res2 = ColSquareMatrixType::Random(cols, cols);
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49 | RowVectorType v1 = RowVectorType::Random(rows);
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50 | ColVectorType vc2 = ColVectorType::Random(cols), vcres(cols);
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51 | OtherMajorMatrixType tm1 = m1;
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52 |
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53 | Scalar s1 = internal::random<Scalar>();
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54 |
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55 | Index r = internal::random<Index>(0, rows-1),
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56 | c = internal::random<Index>(0, cols-1),
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57 | c2 = internal::random<Index>(0, cols-1);
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58 |
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59 | // begin testing Product.h: only associativity for now
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60 | // (we use Transpose.h but this doesn't count as a test for it)
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61 | VERIFY_IS_APPROX((m1*m1.transpose())*m2, m1*(m1.transpose()*m2));
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62 | m3 = m1;
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63 | m3 *= m1.transpose() * m2;
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64 | VERIFY_IS_APPROX(m3, m1 * (m1.transpose()*m2));
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65 | VERIFY_IS_APPROX(m3, m1 * (m1.transpose()*m2));
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66 |
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67 | // continue testing Product.h: distributivity
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68 | VERIFY_IS_APPROX(square*(m1 + m2), square*m1+square*m2);
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69 | VERIFY_IS_APPROX(square*(m1 - m2), square*m1-square*m2);
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70 |
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71 | // continue testing Product.h: compatibility with ScalarMultiple.h
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72 | VERIFY_IS_APPROX(s1*(square*m1), (s1*square)*m1);
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73 | VERIFY_IS_APPROX(s1*(square*m1), square*(m1*s1));
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74 |
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75 | // test Product.h together with Identity.h
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76 | VERIFY_IS_APPROX(v1, identity*v1);
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77 | VERIFY_IS_APPROX(v1.transpose(), v1.transpose() * identity);
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78 | // again, test operator() to check const-qualification
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79 | VERIFY_IS_APPROX(MatrixType::Identity(rows, cols)(r,c), static_cast<Scalar>(r==c));
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80 |
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81 | if (rows!=cols)
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82 | VERIFY_RAISES_ASSERT(m3 = m1*m1);
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83 |
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84 | // test the previous tests were not screwed up because operator* returns 0
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85 | // (we use the more accurate default epsilon)
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86 | if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1)
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87 | {
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88 | VERIFY(areNotApprox(m1.transpose()*m2,m2.transpose()*m1));
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89 | }
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90 |
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91 | // test optimized operator+= path
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92 | res = square;
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93 | res.noalias() += m1 * m2.transpose();
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94 | VERIFY_IS_APPROX(res, square + m1 * m2.transpose());
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95 | if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1)
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96 | {
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97 | VERIFY(areNotApprox(res,square + m2 * m1.transpose()));
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98 | }
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99 | vcres = vc2;
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100 | vcres.noalias() += m1.transpose() * v1;
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101 | VERIFY_IS_APPROX(vcres, vc2 + m1.transpose() * v1);
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102 |
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103 | // test optimized operator-= path
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104 | res = square;
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105 | res.noalias() -= m1 * m2.transpose();
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106 | VERIFY_IS_APPROX(res, square - (m1 * m2.transpose()));
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107 | if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1)
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108 | {
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109 | VERIFY(areNotApprox(res,square - m2 * m1.transpose()));
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110 | }
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111 | vcres = vc2;
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112 | vcres.noalias() -= m1.transpose() * v1;
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113 | VERIFY_IS_APPROX(vcres, vc2 - m1.transpose() * v1);
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114 |
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115 | tm1 = m1;
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116 | VERIFY_IS_APPROX(tm1.transpose() * v1, m1.transpose() * v1);
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117 | VERIFY_IS_APPROX(v1.transpose() * tm1, v1.transpose() * m1);
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118 |
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119 | // test submatrix and matrix/vector product
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120 | for (int i=0; i<rows; ++i)
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121 | res.row(i) = m1.row(i) * m2.transpose();
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122 | VERIFY_IS_APPROX(res, m1 * m2.transpose());
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123 | // the other way round:
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124 | for (int i=0; i<rows; ++i)
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125 | res.col(i) = m1 * m2.transpose().col(i);
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126 | VERIFY_IS_APPROX(res, m1 * m2.transpose());
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127 |
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128 | res2 = square2;
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129 | res2.noalias() += m1.transpose() * m2;
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130 | VERIFY_IS_APPROX(res2, square2 + m1.transpose() * m2);
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131 | if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1)
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132 | {
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133 | VERIFY(areNotApprox(res2,square2 + m2.transpose() * m1));
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134 | }
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135 |
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136 | VERIFY_IS_APPROX(res.col(r).noalias() = square.adjoint() * square.col(r), (square.adjoint() * square.col(r)).eval());
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137 | VERIFY_IS_APPROX(res.col(r).noalias() = square * square.col(r), (square * square.col(r)).eval());
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138 |
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139 | // vector at runtime (see bug 1166)
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140 | {
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141 | RowSquareMatrixType ref(square);
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142 | ColSquareMatrixType ref2(square2);
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143 | ref = res = square;
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144 | VERIFY_IS_APPROX(res.block(0,0,1,rows).noalias() = m1.col(0).transpose() * square.transpose(), (ref.row(0) = m1.col(0).transpose() * square.transpose()));
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145 | VERIFY_IS_APPROX(res.block(0,0,1,rows).noalias() = m1.block(0,0,rows,1).transpose() * square.transpose(), (ref.row(0) = m1.col(0).transpose() * square.transpose()));
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146 | VERIFY_IS_APPROX(res.block(0,0,1,rows).noalias() = m1.col(0).transpose() * square, (ref.row(0) = m1.col(0).transpose() * square));
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147 | VERIFY_IS_APPROX(res.block(0,0,1,rows).noalias() = m1.block(0,0,rows,1).transpose() * square, (ref.row(0) = m1.col(0).transpose() * square));
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148 | ref2 = res2 = square2;
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149 | VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.row(0) * square2.transpose(), (ref2.row(0) = m1.row(0) * square2.transpose()));
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150 | VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.block(0,0,1,cols) * square2.transpose(), (ref2.row(0) = m1.row(0) * square2.transpose()));
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151 | VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.row(0) * square2, (ref2.row(0) = m1.row(0) * square2));
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152 | VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.block(0,0,1,cols) * square2, (ref2.row(0) = m1.row(0) * square2));
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153 | }
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154 |
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155 | // inner product
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156 | {
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157 | Scalar x = square2.row(c) * square2.col(c2);
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158 | VERIFY_IS_APPROX(x, square2.row(c).transpose().cwiseProduct(square2.col(c2)).sum());
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159 | }
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160 |
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161 | // outer product
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162 | VERIFY_IS_APPROX(m1.col(c) * m1.row(r), m1.block(0,c,rows,1) * m1.block(r,0,1,cols));
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163 | VERIFY_IS_APPROX(m1.row(r).transpose() * m1.col(c).transpose(), m1.block(r,0,1,cols).transpose() * m1.block(0,c,rows,1).transpose());
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164 | VERIFY_IS_APPROX(m1.block(0,c,rows,1) * m1.row(r), m1.block(0,c,rows,1) * m1.block(r,0,1,cols));
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165 | VERIFY_IS_APPROX(m1.col(c) * m1.block(r,0,1,cols), m1.block(0,c,rows,1) * m1.block(r,0,1,cols));
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166 | VERIFY_IS_APPROX(m1.leftCols(1) * m1.row(r), m1.block(0,0,rows,1) * m1.block(r,0,1,cols));
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167 | VERIFY_IS_APPROX(m1.col(c) * m1.topRows(1), m1.block(0,c,rows,1) * m1.block(0,0,1,cols));
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168 |
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169 | // Aliasing
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170 | {
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171 | ColVectorType x(cols); x.setRandom();
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172 | ColVectorType z(x);
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173 | ColVectorType y(cols); y.setZero();
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174 | ColSquareMatrixType A(cols,cols); A.setRandom();
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175 | // CwiseBinaryOp
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176 | VERIFY_IS_APPROX(x = y + A*x, A*z);
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177 | x = z;
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178 | // CwiseUnaryOp
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179 | VERIFY_IS_APPROX(x = Scalar(1.)*(A*x), A*z);
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180 | }
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181 |
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182 | // regression for blas_trais
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183 | {
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184 | VERIFY_IS_APPROX(square * (square*square).transpose(), square * square.transpose() * square.transpose());
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185 | VERIFY_IS_APPROX(square * (-(square*square)), -square * square * square);
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186 | VERIFY_IS_APPROX(square * (s1*(square*square)), s1 * square * square * square);
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187 | VERIFY_IS_APPROX(square * (square*square).conjugate(), square * square.conjugate() * square.conjugate());
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188 | }
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189 | }
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