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::Scalar Scalar; 26 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> RowVectorType; 27 typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> ColVectorType; 28 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> RowSquareMatrixType; 29 typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> ColSquareMatrixType; 30 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime, 31 MatrixType::Flags&RowMajorBit?ColMajor:RowMajor> OtherMajorMatrixType; 32 33 Index rows = m.rows(); 34 Index cols = m.cols(); 35 36 // this test relies a lot on Random.h, and there's not much more that we can do 37 // to test it, hence I consider that we will have tested Random.h 38 MatrixType m1 = MatrixType::Random(rows, cols), 39 m2 = MatrixType::Random(rows, cols), 40 m3(rows, cols); 41 RowSquareMatrixType 42 identity = RowSquareMatrixType::Identity(rows, rows), 43 square = RowSquareMatrixType::Random(rows, rows), 44 res = RowSquareMatrixType::Random(rows, rows); 45 ColSquareMatrixType 46 square2 = ColSquareMatrixType::Random(cols, cols), 47 res2 = ColSquareMatrixType::Random(cols, cols); 48 RowVectorType v1 = RowVectorType::Random(rows); 49 ColVectorType vc2 = ColVectorType::Random(cols), vcres(cols); 50 OtherMajorMatrixType tm1 = m1; 51 52 Scalar s1 = internal::random<Scalar>(); 53 54 Index r = internal::random<Index>(0, rows-1), 55 c = internal::random<Index>(0, cols-1), 56 c2 = internal::random<Index>(0, cols-1); 57 58 // begin testing Product.h: only associativity for now 59 // (we use Transpose.h but this doesn't count as a test for it) 60 VERIFY_IS_APPROX((m1*m1.transpose())*m2, m1*(m1.transpose()*m2)); 61 m3 = m1; 62 m3 *= m1.transpose() * m2; 63 VERIFY_IS_APPROX(m3, m1 * (m1.transpose()*m2)); 64 VERIFY_IS_APPROX(m3, m1 * (m1.transpose()*m2)); 65 66 // continue testing Product.h: distributivity 67 VERIFY_IS_APPROX(square*(m1 + m2), square*m1+square*m2); 68 VERIFY_IS_APPROX(square*(m1 - m2), square*m1-square*m2); 69 70 // continue testing Product.h: compatibility with ScalarMultiple.h 71 VERIFY_IS_APPROX(s1*(square*m1), (s1*square)*m1); 72 VERIFY_IS_APPROX(s1*(square*m1), square*(m1*s1)); 73 74 // test Product.h together with Identity.h 75 VERIFY_IS_APPROX(v1, identity*v1); 76 VERIFY_IS_APPROX(v1.transpose(), v1.transpose() * identity); 77 // again, test operator() to check const-qualification 78 VERIFY_IS_APPROX(MatrixType::Identity(rows, cols)(r,c), static_cast<Scalar>(r==c)); 79 80 if (rows!=cols) 81 VERIFY_RAISES_ASSERT(m3 = m1*m1); 82 83 // test the previous tests were not screwed up because operator* returns 0 84 // (we use the more accurate default epsilon) 85 if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1) 86 { 87 VERIFY(areNotApprox(m1.transpose()*m2,m2.transpose()*m1)); 88 } 89 90 // test optimized operator+= path 91 res = square; 92 res.noalias() += m1 * m2.transpose(); 93 VERIFY_IS_APPROX(res, square + m1 * m2.transpose()); 94 if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1) 95 { 96 VERIFY(areNotApprox(res,square + m2 * m1.transpose())); 97 } 98 vcres = vc2; 99 vcres.noalias() += m1.transpose() * v1; 100 VERIFY_IS_APPROX(vcres, vc2 + m1.transpose() * v1); 101 102 // test optimized operator-= path 103 res = square; 104 res.noalias() -= m1 * m2.transpose(); 105 VERIFY_IS_APPROX(res, square - (m1 * m2.transpose())); 106 if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1) 107 { 108 VERIFY(areNotApprox(res,square - m2 * m1.transpose())); 109 } 110 vcres = vc2; 111 vcres.noalias() -= m1.transpose() * v1; 112 VERIFY_IS_APPROX(vcres, vc2 - m1.transpose() * v1); 113 114 // test d ?= a+b*c rules 115 res.noalias() = square + m1 * m2.transpose(); 116 VERIFY_IS_APPROX(res, square + m1 * m2.transpose()); 117 res.noalias() += square + m1 * m2.transpose(); 118 VERIFY_IS_APPROX(res, 2*(square + m1 * m2.transpose())); 119 res.noalias() -= square + m1 * m2.transpose(); 120 VERIFY_IS_APPROX(res, square + m1 * m2.transpose()); 121 122 // test d ?= a-b*c rules 123 res.noalias() = square - m1 * m2.transpose(); 124 VERIFY_IS_APPROX(res, square - m1 * m2.transpose()); 125 res.noalias() += square - m1 * m2.transpose(); 126 VERIFY_IS_APPROX(res, 2*(square - m1 * m2.transpose())); 127 res.noalias() -= square - m1 * m2.transpose(); 128 VERIFY_IS_APPROX(res, square - m1 * m2.transpose()); 129 130 131 tm1 = m1; 132 VERIFY_IS_APPROX(tm1.transpose() * v1, m1.transpose() * v1); 133 VERIFY_IS_APPROX(v1.transpose() * tm1, v1.transpose() * m1); 134 135 // test submatrix and matrix/vector product 136 for (int i=0; i<rows; ++i) 137 res.row(i) = m1.row(i) * m2.transpose(); 138 VERIFY_IS_APPROX(res, m1 * m2.transpose()); 139 // the other way round: 140 for (int i=0; i<rows; ++i) 141 res.col(i) = m1 * m2.transpose().col(i); 142 VERIFY_IS_APPROX(res, m1 * m2.transpose()); 143 144 res2 = square2; 145 res2.noalias() += m1.transpose() * m2; 146 VERIFY_IS_APPROX(res2, square2 + m1.transpose() * m2); 147 if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1) 148 { 149 VERIFY(areNotApprox(res2,square2 + m2.transpose() * m1)); 150 } 151 152 VERIFY_IS_APPROX(res.col(r).noalias() = square.adjoint() * square.col(r), (square.adjoint() * square.col(r)).eval()); 153 VERIFY_IS_APPROX(res.col(r).noalias() = square * square.col(r), (square * square.col(r)).eval()); 154 155 // vector at runtime (see bug 1166) 156 { 157 RowSquareMatrixType ref(square); 158 ColSquareMatrixType ref2(square2); 159 ref = res = square; 160 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())); 161 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())); 162 VERIFY_IS_APPROX(res.block(0,0,1,rows).noalias() = m1.col(0).transpose() * square, (ref.row(0) = m1.col(0).transpose() * square)); 163 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)); 164 ref2 = res2 = square2; 165 VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.row(0) * square2.transpose(), (ref2.row(0) = m1.row(0) * square2.transpose())); 166 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())); 167 VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.row(0) * square2, (ref2.row(0) = m1.row(0) * square2)); 168 VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.block(0,0,1,cols) * square2, (ref2.row(0) = m1.row(0) * square2)); 169 } 170 171 // vector.block() (see bug 1283) 172 { 173 RowVectorType w1(rows); 174 VERIFY_IS_APPROX(square * v1.block(0,0,rows,1), square * v1); 175 VERIFY_IS_APPROX(w1.noalias() = square * v1.block(0,0,rows,1), square * v1); 176 VERIFY_IS_APPROX(w1.block(0,0,rows,1).noalias() = square * v1.block(0,0,rows,1), square * v1); 177 178 Matrix<Scalar,1,MatrixType::ColsAtCompileTime> w2(cols); 179 VERIFY_IS_APPROX(vc2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2); 180 VERIFY_IS_APPROX(w2.noalias() = vc2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2); 181 VERIFY_IS_APPROX(w2.block(0,0,1,cols).noalias() = vc2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2); 182 183 vc2 = square2.block(0,0,1,cols).transpose(); 184 VERIFY_IS_APPROX(square2.block(0,0,1,cols) * square2, vc2.transpose() * square2); 185 VERIFY_IS_APPROX(w2.noalias() = square2.block(0,0,1,cols) * square2, vc2.transpose() * square2); 186 VERIFY_IS_APPROX(w2.block(0,0,1,cols).noalias() = square2.block(0,0,1,cols) * square2, vc2.transpose() * square2); 187 188 vc2 = square2.block(0,0,cols,1); 189 VERIFY_IS_APPROX(square2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2); 190 VERIFY_IS_APPROX(w2.noalias() = square2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2); 191 VERIFY_IS_APPROX(w2.block(0,0,1,cols).noalias() = square2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2); 192 } 193 194 // inner product 195 { 196 Scalar x = square2.row(c) * square2.col(c2); 197 VERIFY_IS_APPROX(x, square2.row(c).transpose().cwiseProduct(square2.col(c2)).sum()); 198 } 199 200 // outer product 201 { 202 VERIFY_IS_APPROX(m1.col(c) * m1.row(r), m1.block(0,c,rows,1) * m1.block(r,0,1,cols)); 203 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()); 204 VERIFY_IS_APPROX(m1.block(0,c,rows,1) * m1.row(r), m1.block(0,c,rows,1) * m1.block(r,0,1,cols)); 205 VERIFY_IS_APPROX(m1.col(c) * m1.block(r,0,1,cols), m1.block(0,c,rows,1) * m1.block(r,0,1,cols)); 206 VERIFY_IS_APPROX(m1.leftCols(1) * m1.row(r), m1.block(0,0,rows,1) * m1.block(r,0,1,cols)); 207 VERIFY_IS_APPROX(m1.col(c) * m1.topRows(1), m1.block(0,c,rows,1) * m1.block(0,0,1,cols)); 208 } 209 210 // Aliasing 211 { 212 ColVectorType x(cols); x.setRandom(); 213 ColVectorType z(x); 214 ColVectorType y(cols); y.setZero(); 215 ColSquareMatrixType A(cols,cols); A.setRandom(); 216 // CwiseBinaryOp 217 VERIFY_IS_APPROX(x = y + A*x, A*z); 218 x = z; 219 // CwiseUnaryOp 220 VERIFY_IS_APPROX(x = Scalar(1.)*(A*x), A*z); 221 } 222 223 // regression for blas_trais 224 { 225 VERIFY_IS_APPROX(square * (square*square).transpose(), square * square.transpose() * square.transpose()); 226 VERIFY_IS_APPROX(square * (-(square*square)), -square * square * square); 227 VERIFY_IS_APPROX(square * (s1*(square*square)), s1 * square * square * square); 228 VERIFY_IS_APPROX(square * (square*square).conjugate(), square * square.conjugate() * square.conjugate()); 229 } 230 231 } 232
