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 typename NumTraits<Scalar>::NonInteger NonInteger; 28 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> RowVectorType; 29 typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> ColVectorType; 30 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> RowSquareMatrixType; 31 typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> ColSquareMatrixType; 32 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime, 33 MatrixType::Flags&RowMajorBit?ColMajor:RowMajor> OtherMajorMatrixType; 34 35 Index rows = m.rows(); 36 Index cols = m.cols(); 37 38 // this test relies a lot on Random.h, and there's not much more that we can do 39 // to test it, hence I consider that we will have tested Random.h 40 MatrixType m1 = MatrixType::Random(rows, cols), 41 m2 = MatrixType::Random(rows, cols), 42 m3(rows, cols); 43 RowSquareMatrixType 44 identity = RowSquareMatrixType::Identity(rows, rows), 45 square = RowSquareMatrixType::Random(rows, rows), 46 res = RowSquareMatrixType::Random(rows, rows); 47 ColSquareMatrixType 48 square2 = ColSquareMatrixType::Random(cols, cols), 49 res2 = ColSquareMatrixType::Random(cols, cols); 50 RowVectorType v1 = RowVectorType::Random(rows); 51 ColVectorType vc2 = ColVectorType::Random(cols), vcres(cols); 52 OtherMajorMatrixType tm1 = m1; 53 54 Scalar s1 = internal::random<Scalar>(); 55 56 Index r = internal::random<Index>(0, rows-1), 57 c = internal::random<Index>(0, cols-1), 58 c2 = internal::random<Index>(0, cols-1); 59 60 // begin testing Product.h: only associativity for now 61 // (we use Transpose.h but this doesn't count as a test for it) 62 VERIFY_IS_APPROX((m1*m1.transpose())*m2, m1*(m1.transpose()*m2)); 63 m3 = m1; 64 m3 *= m1.transpose() * m2; 65 VERIFY_IS_APPROX(m3, m1 * (m1.transpose()*m2)); 66 VERIFY_IS_APPROX(m3, m1 * (m1.transpose()*m2)); 67 68 // continue testing Product.h: distributivity 69 VERIFY_IS_APPROX(square*(m1 + m2), square*m1+square*m2); 70 VERIFY_IS_APPROX(square*(m1 - m2), square*m1-square*m2); 71 72 // continue testing Product.h: compatibility with ScalarMultiple.h 73 VERIFY_IS_APPROX(s1*(square*m1), (s1*square)*m1); 74 VERIFY_IS_APPROX(s1*(square*m1), square*(m1*s1)); 75 76 // test Product.h together with Identity.h 77 VERIFY_IS_APPROX(v1, identity*v1); 78 VERIFY_IS_APPROX(v1.transpose(), v1.transpose() * identity); 79 // again, test operator() to check const-qualification 80 VERIFY_IS_APPROX(MatrixType::Identity(rows, cols)(r,c), static_cast<Scalar>(r==c)); 81 82 if (rows!=cols) 83 VERIFY_RAISES_ASSERT(m3 = m1*m1); 84 85 // test the previous tests were not screwed up because operator* returns 0 86 // (we use the more accurate default epsilon) 87 if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1) 88 { 89 VERIFY(areNotApprox(m1.transpose()*m2,m2.transpose()*m1)); 90 } 91 92 // test optimized operator+= path 93 res = square; 94 res.noalias() += m1 * m2.transpose(); 95 VERIFY_IS_APPROX(res, square + m1 * m2.transpose()); 96 if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1) 97 { 98 VERIFY(areNotApprox(res,square + m2 * m1.transpose())); 99 } 100 vcres = vc2; 101 vcres.noalias() += m1.transpose() * v1; 102 VERIFY_IS_APPROX(vcres, vc2 + m1.transpose() * v1); 103 104 // test optimized operator-= path 105 res = square; 106 res.noalias() -= m1 * m2.transpose(); 107 VERIFY_IS_APPROX(res, square - (m1 * m2.transpose())); 108 if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1) 109 { 110 VERIFY(areNotApprox(res,square - m2 * m1.transpose())); 111 } 112 vcres = vc2; 113 vcres.noalias() -= m1.transpose() * v1; 114 VERIFY_IS_APPROX(vcres, vc2 - m1.transpose() * v1); 115 116 tm1 = m1; 117 VERIFY_IS_APPROX(tm1.transpose() * v1, m1.transpose() * v1); 118 VERIFY_IS_APPROX(v1.transpose() * tm1, v1.transpose() * m1); 119 120 // test submatrix and matrix/vector product 121 for (int i=0; i<rows; ++i) 122 res.row(i) = m1.row(i) * m2.transpose(); 123 VERIFY_IS_APPROX(res, m1 * m2.transpose()); 124 // the other way round: 125 for (int i=0; i<rows; ++i) 126 res.col(i) = m1 * m2.transpose().col(i); 127 VERIFY_IS_APPROX(res, m1 * m2.transpose()); 128 129 res2 = square2; 130 res2.noalias() += m1.transpose() * m2; 131 VERIFY_IS_APPROX(res2, square2 + m1.transpose() * m2); 132 if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1) 133 { 134 VERIFY(areNotApprox(res2,square2 + m2.transpose() * m1)); 135 } 136 137 VERIFY_IS_APPROX(res.col(r).noalias() = square.adjoint() * square.col(r), (square.adjoint() * square.col(r)).eval()); 138 VERIFY_IS_APPROX(res.col(r).noalias() = square * square.col(r), (square * square.col(r)).eval()); 139 140 // inner product 141 Scalar x = square2.row(c) * square2.col(c2); 142 VERIFY_IS_APPROX(x, square2.row(c).transpose().cwiseProduct(square2.col(c2)).sum()); 143 } 144
