1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1 (at) gmail.com> 5 // 6 // This Source Code Form is subject to the terms of the Mozilla 7 // Public License v. 2.0. If a copy of the MPL was not distributed 8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 9 10 #include "main.h" 11 #include <Eigen/QR> 12 13 template<typename Derived1, typename Derived2> 14 bool areNotApprox(const MatrixBase<Derived1>& m1, const MatrixBase<Derived2>& m2, typename Derived1::RealScalar epsilon = NumTraits<typename Derived1::RealScalar>::dummy_precision()) 15 { 16 return !((m1-m2).cwiseAbs2().maxCoeff() < epsilon * epsilon 17 * (std::max)(m1.cwiseAbs2().maxCoeff(), m2.cwiseAbs2().maxCoeff())); 18 } 19 20 template<typename MatrixType> void product(const MatrixType& m) 21 { 22 /* this test covers the following files: 23 Identity.h Product.h 24 */ 25 typedef typename MatrixType::Index Index; 26 typedef typename MatrixType::Scalar Scalar; 27 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> RowVectorType; 28 typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> ColVectorType; 29 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> RowSquareMatrixType; 30 typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> ColSquareMatrixType; 31 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime, 32 MatrixType::Flags&RowMajorBit?ColMajor:RowMajor> OtherMajorMatrixType; 33 34 Index rows = m.rows(); 35 Index cols = m.cols(); 36 37 // this test relies a lot on Random.h, and there's not much more that we can do 38 // to test it, hence I consider that we will have tested Random.h 39 MatrixType m1 = MatrixType::Random(rows, cols), 40 m2 = MatrixType::Random(rows, cols), 41 m3(rows, cols); 42 RowSquareMatrixType 43 identity = RowSquareMatrixType::Identity(rows, rows), 44 square = RowSquareMatrixType::Random(rows, rows), 45 res = RowSquareMatrixType::Random(rows, rows); 46 ColSquareMatrixType 47 square2 = ColSquareMatrixType::Random(cols, cols), 48 res2 = ColSquareMatrixType::Random(cols, cols); 49 RowVectorType v1 = RowVectorType::Random(rows); 50 ColVectorType vc2 = ColVectorType::Random(cols), vcres(cols); 51 OtherMajorMatrixType tm1 = m1; 52 53 Scalar s1 = internal::random<Scalar>(); 54 55 Index r = internal::random<Index>(0, rows-1), 56 c = internal::random<Index>(0, cols-1), 57 c2 = internal::random<Index>(0, cols-1); 58 59 // begin testing Product.h: only associativity for now 60 // (we use Transpose.h but this doesn't count as a test for it) 61 VERIFY_IS_APPROX((m1*m1.transpose())*m2, m1*(m1.transpose()*m2)); 62 m3 = m1; 63 m3 *= m1.transpose() * m2; 64 VERIFY_IS_APPROX(m3, m1 * (m1.transpose()*m2)); 65 VERIFY_IS_APPROX(m3, m1 * (m1.transpose()*m2)); 66 67 // continue testing Product.h: distributivity 68 VERIFY_IS_APPROX(square*(m1 + m2), square*m1+square*m2); 69 VERIFY_IS_APPROX(square*(m1 - m2), square*m1-square*m2); 70 71 // continue testing Product.h: compatibility with ScalarMultiple.h 72 VERIFY_IS_APPROX(s1*(square*m1), (s1*square)*m1); 73 VERIFY_IS_APPROX(s1*(square*m1), square*(m1*s1)); 74 75 // test Product.h together with Identity.h 76 VERIFY_IS_APPROX(v1, identity*v1); 77 VERIFY_IS_APPROX(v1.transpose(), v1.transpose() * identity); 78 // again, test operator() to check const-qualification 79 VERIFY_IS_APPROX(MatrixType::Identity(rows, cols)(r,c), static_cast<Scalar>(r==c)); 80 81 if (rows!=cols) 82 VERIFY_RAISES_ASSERT(m3 = m1*m1); 83 84 // test the previous tests were not screwed up because operator* returns 0 85 // (we use the more accurate default epsilon) 86 if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1) 87 { 88 VERIFY(areNotApprox(m1.transpose()*m2,m2.transpose()*m1)); 89 } 90 91 // test optimized operator+= path 92 res = square; 93 res.noalias() += m1 * m2.transpose(); 94 VERIFY_IS_APPROX(res, square + m1 * m2.transpose()); 95 if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1) 96 { 97 VERIFY(areNotApprox(res,square + m2 * m1.transpose())); 98 } 99 vcres = vc2; 100 vcres.noalias() += m1.transpose() * v1; 101 VERIFY_IS_APPROX(vcres, vc2 + m1.transpose() * v1); 102 103 // test optimized operator-= path 104 res = square; 105 res.noalias() -= m1 * m2.transpose(); 106 VERIFY_IS_APPROX(res, square - (m1 * m2.transpose())); 107 if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1) 108 { 109 VERIFY(areNotApprox(res,square - m2 * m1.transpose())); 110 } 111 vcres = vc2; 112 vcres.noalias() -= m1.transpose() * v1; 113 VERIFY_IS_APPROX(vcres, vc2 - m1.transpose() * v1); 114 115 tm1 = m1; 116 VERIFY_IS_APPROX(tm1.transpose() * v1, m1.transpose() * v1); 117 VERIFY_IS_APPROX(v1.transpose() * tm1, v1.transpose() * m1); 118 119 // test submatrix and matrix/vector product 120 for (int i=0; i<rows; ++i) 121 res.row(i) = m1.row(i) * m2.transpose(); 122 VERIFY_IS_APPROX(res, m1 * m2.transpose()); 123 // the other way round: 124 for (int i=0; i<rows; ++i) 125 res.col(i) = m1 * m2.transpose().col(i); 126 VERIFY_IS_APPROX(res, m1 * m2.transpose()); 127 128 res2 = square2; 129 res2.noalias() += m1.transpose() * m2; 130 VERIFY_IS_APPROX(res2, square2 + m1.transpose() * m2); 131 if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1) 132 { 133 VERIFY(areNotApprox(res2,square2 + m2.transpose() * m1)); 134 } 135 136 VERIFY_IS_APPROX(res.col(r).noalias() = square.adjoint() * square.col(r), (square.adjoint() * square.col(r)).eval()); 137 VERIFY_IS_APPROX(res.col(r).noalias() = square * square.col(r), (square * square.col(r)).eval()); 138 139 // inner product 140 Scalar x = square2.row(c) * square2.col(c2); 141 VERIFY_IS_APPROX(x, square2.row(c).transpose().cwiseProduct(square2.col(c2)).sum()); 142 143 // outer product 144 VERIFY_IS_APPROX(m1.col(c) * m1.row(r), m1.block(0,c,rows,1) * m1.block(r,0,1,cols)); 145 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()); 146 VERIFY_IS_APPROX(m1.block(0,c,rows,1) * m1.row(r), m1.block(0,c,rows,1) * m1.block(r,0,1,cols)); 147 VERIFY_IS_APPROX(m1.col(c) * m1.block(r,0,1,cols), m1.block(0,c,rows,1) * m1.block(r,0,1,cols)); 148 VERIFY_IS_APPROX(m1.leftCols(1) * m1.row(r), m1.block(0,0,rows,1) * m1.block(r,0,1,cols)); 149 VERIFY_IS_APPROX(m1.col(c) * m1.topRows(1), m1.block(0,c,rows,1) * m1.block(0,0,1,cols)); 150 } 151
