product.h (11880B)
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@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 scaled products 115 res = square; 116 res.noalias() = s1 * m1 * m2.transpose(); 117 VERIFY_IS_APPROX(res, ((s1*m1).eval() * m2.transpose())); 118 res = square; 119 res.noalias() += s1 * m1 * m2.transpose(); 120 VERIFY_IS_APPROX(res, square + ((s1*m1).eval() * m2.transpose())); 121 res = square; 122 res.noalias() -= s1 * m1 * m2.transpose(); 123 VERIFY_IS_APPROX(res, square - ((s1*m1).eval() * m2.transpose())); 124 125 // test d ?= a+b*c rules 126 res.noalias() = square + m1 * m2.transpose(); 127 VERIFY_IS_APPROX(res, square + m1 * m2.transpose()); 128 res.noalias() += square + m1 * m2.transpose(); 129 VERIFY_IS_APPROX(res, 2*(square + m1 * m2.transpose())); 130 res.noalias() -= square + m1 * m2.transpose(); 131 VERIFY_IS_APPROX(res, square + m1 * m2.transpose()); 132 133 // test d ?= a-b*c rules 134 res.noalias() = square - m1 * m2.transpose(); 135 VERIFY_IS_APPROX(res, square - m1 * m2.transpose()); 136 res.noalias() += square - m1 * m2.transpose(); 137 VERIFY_IS_APPROX(res, 2*(square - m1 * m2.transpose())); 138 res.noalias() -= square - m1 * m2.transpose(); 139 VERIFY_IS_APPROX(res, square - m1 * m2.transpose()); 140 141 142 tm1 = m1; 143 VERIFY_IS_APPROX(tm1.transpose() * v1, m1.transpose() * v1); 144 VERIFY_IS_APPROX(v1.transpose() * tm1, v1.transpose() * m1); 145 146 // test submatrix and matrix/vector product 147 for (int i=0; i<rows; ++i) 148 res.row(i) = m1.row(i) * m2.transpose(); 149 VERIFY_IS_APPROX(res, m1 * m2.transpose()); 150 // the other way round: 151 for (int i=0; i<rows; ++i) 152 res.col(i) = m1 * m2.transpose().col(i); 153 VERIFY_IS_APPROX(res, m1 * m2.transpose()); 154 155 res2 = square2; 156 res2.noalias() += m1.transpose() * m2; 157 VERIFY_IS_APPROX(res2, square2 + m1.transpose() * m2); 158 if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1) 159 { 160 VERIFY(areNotApprox(res2,square2 + m2.transpose() * m1)); 161 } 162 163 VERIFY_IS_APPROX(res.col(r).noalias() = square.adjoint() * square.col(r), (square.adjoint() * square.col(r)).eval()); 164 VERIFY_IS_APPROX(res.col(r).noalias() = square * square.col(r), (square * square.col(r)).eval()); 165 166 // vector at runtime (see bug 1166) 167 { 168 RowSquareMatrixType ref(square); 169 ColSquareMatrixType ref2(square2); 170 ref = res = square; 171 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())); 172 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())); 173 VERIFY_IS_APPROX(res.block(0,0,1,rows).noalias() = m1.col(0).transpose() * square, (ref.row(0) = m1.col(0).transpose() * square)); 174 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)); 175 ref2 = res2 = square2; 176 VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.row(0) * square2.transpose(), (ref2.row(0) = m1.row(0) * square2.transpose())); 177 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())); 178 VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.row(0) * square2, (ref2.row(0) = m1.row(0) * square2)); 179 VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.block(0,0,1,cols) * square2, (ref2.row(0) = m1.row(0) * square2)); 180 } 181 182 // vector.block() (see bug 1283) 183 { 184 RowVectorType w1(rows); 185 VERIFY_IS_APPROX(square * v1.block(0,0,rows,1), square * v1); 186 VERIFY_IS_APPROX(w1.noalias() = square * v1.block(0,0,rows,1), square * v1); 187 VERIFY_IS_APPROX(w1.block(0,0,rows,1).noalias() = square * v1.block(0,0,rows,1), square * v1); 188 189 Matrix<Scalar,1,MatrixType::ColsAtCompileTime> w2(cols); 190 VERIFY_IS_APPROX(vc2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2); 191 VERIFY_IS_APPROX(w2.noalias() = vc2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2); 192 VERIFY_IS_APPROX(w2.block(0,0,1,cols).noalias() = vc2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2); 193 194 vc2 = square2.block(0,0,1,cols).transpose(); 195 VERIFY_IS_APPROX(square2.block(0,0,1,cols) * square2, vc2.transpose() * square2); 196 VERIFY_IS_APPROX(w2.noalias() = square2.block(0,0,1,cols) * square2, vc2.transpose() * square2); 197 VERIFY_IS_APPROX(w2.block(0,0,1,cols).noalias() = square2.block(0,0,1,cols) * square2, vc2.transpose() * square2); 198 199 vc2 = square2.block(0,0,cols,1); 200 VERIFY_IS_APPROX(square2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2); 201 VERIFY_IS_APPROX(w2.noalias() = square2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2); 202 VERIFY_IS_APPROX(w2.block(0,0,1,cols).noalias() = square2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2); 203 } 204 205 // inner product 206 { 207 Scalar x = square2.row(c) * square2.col(c2); 208 VERIFY_IS_APPROX(x, square2.row(c).transpose().cwiseProduct(square2.col(c2)).sum()); 209 } 210 211 // outer product 212 { 213 VERIFY_IS_APPROX(m1.col(c) * m1.row(r), m1.block(0,c,rows,1) * m1.block(r,0,1,cols)); 214 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()); 215 VERIFY_IS_APPROX(m1.block(0,c,rows,1) * m1.row(r), m1.block(0,c,rows,1) * m1.block(r,0,1,cols)); 216 VERIFY_IS_APPROX(m1.col(c) * m1.block(r,0,1,cols), m1.block(0,c,rows,1) * m1.block(r,0,1,cols)); 217 VERIFY_IS_APPROX(m1.leftCols(1) * m1.row(r), m1.block(0,0,rows,1) * m1.block(r,0,1,cols)); 218 VERIFY_IS_APPROX(m1.col(c) * m1.topRows(1), m1.block(0,c,rows,1) * m1.block(0,0,1,cols)); 219 } 220 221 // Aliasing 222 { 223 ColVectorType x(cols); x.setRandom(); 224 ColVectorType z(x); 225 ColVectorType y(cols); y.setZero(); 226 ColSquareMatrixType A(cols,cols); A.setRandom(); 227 // CwiseBinaryOp 228 VERIFY_IS_APPROX(x = y + A*x, A*z); 229 x = z; 230 VERIFY_IS_APPROX(x = y - A*x, A*(-z)); 231 x = z; 232 // CwiseUnaryOp 233 VERIFY_IS_APPROX(x = Scalar(1.)*(A*x), A*z); 234 } 235 236 // regression for blas_trais 237 { 238 VERIFY_IS_APPROX(square * (square*square).transpose(), square * square.transpose() * square.transpose()); 239 VERIFY_IS_APPROX(square * (-(square*square)), -square * square * square); 240 VERIFY_IS_APPROX(square * (s1*(square*square)), s1 * square * square * square); 241 VERIFY_IS_APPROX(square * (square*square).conjugate(), square * square.conjugate() * square.conjugate()); 242 } 243 244 // destination with a non-default inner-stride 245 // see bug 1741 246 if(!MatrixType::IsRowMajor) 247 { 248 typedef Matrix<Scalar,Dynamic,Dynamic> MatrixX; 249 MatrixX buffer(2*rows,2*rows); 250 Map<RowSquareMatrixType,0,Stride<Dynamic,2> > map1(buffer.data(),rows,rows,Stride<Dynamic,2>(2*rows,2)); 251 buffer.setZero(); 252 VERIFY_IS_APPROX(map1 = m1 * m2.transpose(), (m1 * m2.transpose()).eval()); 253 buffer.setZero(); 254 VERIFY_IS_APPROX(map1.noalias() = m1 * m2.transpose(), (m1 * m2.transpose()).eval()); 255 buffer.setZero(); 256 VERIFY_IS_APPROX(map1.noalias() += m1 * m2.transpose(), (m1 * m2.transpose()).eval()); 257 } 258 259 }