product_notemporary.cpp (10988B)
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 #define TEST_ENABLE_TEMPORARY_TRACKING 11 12 #include "main.h" 13 14 template<typename Dst, typename Lhs, typename Rhs> 15 void check_scalar_multiple3(Dst &dst, const Lhs& A, const Rhs& B) 16 { 17 VERIFY_EVALUATION_COUNT( (dst.noalias() = A * B), 0); 18 VERIFY_IS_APPROX( dst, (A.eval() * B.eval()).eval() ); 19 VERIFY_EVALUATION_COUNT( (dst.noalias() += A * B), 0); 20 VERIFY_IS_APPROX( dst, 2*(A.eval() * B.eval()).eval() ); 21 VERIFY_EVALUATION_COUNT( (dst.noalias() -= A * B), 0); 22 VERIFY_IS_APPROX( dst, (A.eval() * B.eval()).eval() ); 23 } 24 25 template<typename Dst, typename Lhs, typename Rhs, typename S2> 26 void check_scalar_multiple2(Dst &dst, const Lhs& A, const Rhs& B, S2 s2) 27 { 28 CALL_SUBTEST( check_scalar_multiple3(dst, A, B) ); 29 CALL_SUBTEST( check_scalar_multiple3(dst, A, -B) ); 30 CALL_SUBTEST( check_scalar_multiple3(dst, A, s2*B) ); 31 CALL_SUBTEST( check_scalar_multiple3(dst, A, B*s2) ); 32 CALL_SUBTEST( check_scalar_multiple3(dst, A, (B*s2).conjugate()) ); 33 } 34 35 template<typename Dst, typename Lhs, typename Rhs, typename S1, typename S2> 36 void check_scalar_multiple1(Dst &dst, const Lhs& A, const Rhs& B, S1 s1, S2 s2) 37 { 38 CALL_SUBTEST( check_scalar_multiple2(dst, A, B, s2) ); 39 CALL_SUBTEST( check_scalar_multiple2(dst, -A, B, s2) ); 40 CALL_SUBTEST( check_scalar_multiple2(dst, s1*A, B, s2) ); 41 CALL_SUBTEST( check_scalar_multiple2(dst, A*s1, B, s2) ); 42 CALL_SUBTEST( check_scalar_multiple2(dst, (A*s1).conjugate(), B, s2) ); 43 } 44 45 template<typename MatrixType> void product_notemporary(const MatrixType& m) 46 { 47 /* This test checks the number of temporaries created 48 * during the evaluation of a complex expression */ 49 typedef typename MatrixType::Scalar Scalar; 50 typedef typename MatrixType::RealScalar RealScalar; 51 typedef Matrix<Scalar, 1, Dynamic> RowVectorType; 52 typedef Matrix<Scalar, Dynamic, 1> ColVectorType; 53 typedef Matrix<Scalar, Dynamic, Dynamic, ColMajor> ColMajorMatrixType; 54 typedef Matrix<Scalar, Dynamic, Dynamic, RowMajor> RowMajorMatrixType; 55 56 Index rows = m.rows(); 57 Index cols = m.cols(); 58 59 ColMajorMatrixType m1 = MatrixType::Random(rows, cols), 60 m2 = MatrixType::Random(rows, cols), 61 m3(rows, cols); 62 RowVectorType rv1 = RowVectorType::Random(rows), rvres(rows); 63 ColVectorType cv1 = ColVectorType::Random(cols), cvres(cols); 64 RowMajorMatrixType rm3(rows, cols); 65 66 Scalar s1 = internal::random<Scalar>(), 67 s2 = internal::random<Scalar>(), 68 s3 = internal::random<Scalar>(); 69 70 Index c0 = internal::random<Index>(4,cols-8), 71 c1 = internal::random<Index>(8,cols-c0), 72 r0 = internal::random<Index>(4,cols-8), 73 r1 = internal::random<Index>(8,rows-r0); 74 75 VERIFY_EVALUATION_COUNT( m3 = (m1 * m2.adjoint()), 1); 76 VERIFY_EVALUATION_COUNT( m3 = (m1 * m2.adjoint()).transpose(), 1); 77 VERIFY_EVALUATION_COUNT( m3.noalias() = m1 * m2.adjoint(), 0); 78 79 VERIFY_EVALUATION_COUNT( m3 = s1 * (m1 * m2.transpose()), 1); 80 // VERIFY_EVALUATION_COUNT( m3 = m3 + s1 * (m1 * m2.transpose()), 1); 81 VERIFY_EVALUATION_COUNT( m3.noalias() = s1 * (m1 * m2.transpose()), 0); 82 83 VERIFY_EVALUATION_COUNT( m3 = m3 + (m1 * m2.adjoint()), 1); 84 VERIFY_EVALUATION_COUNT( m3 = m3 - (m1 * m2.adjoint()), 1); 85 86 VERIFY_EVALUATION_COUNT( m3 = m3 + (m1 * m2.adjoint()).transpose(), 1); 87 VERIFY_EVALUATION_COUNT( m3.noalias() = m3 + m1 * m2.transpose(), 0); 88 VERIFY_EVALUATION_COUNT( m3.noalias() += m3 + m1 * m2.transpose(), 0); 89 VERIFY_EVALUATION_COUNT( m3.noalias() -= m3 + m1 * m2.transpose(), 0); 90 VERIFY_EVALUATION_COUNT( m3.noalias() = m3 - m1 * m2.transpose(), 0); 91 VERIFY_EVALUATION_COUNT( m3.noalias() += m3 - m1 * m2.transpose(), 0); 92 VERIFY_EVALUATION_COUNT( m3.noalias() -= m3 - m1 * m2.transpose(), 0); 93 94 VERIFY_EVALUATION_COUNT( m3.noalias() = s1 * m1 * s2 * m2.adjoint(), 0); 95 VERIFY_EVALUATION_COUNT( m3.noalias() = s1 * m1 * s2 * (m1*s3+m2*s2).adjoint(), 1); 96 VERIFY_EVALUATION_COUNT( m3.noalias() = (s1 * m1).adjoint() * s2 * m2, 0); 97 VERIFY_EVALUATION_COUNT( m3.noalias() += s1 * (-m1*s3).adjoint() * (s2 * m2 * s3), 0); 98 VERIFY_EVALUATION_COUNT( m3.noalias() -= s1 * (m1.transpose() * m2), 0); 99 100 VERIFY_EVALUATION_COUNT(( m3.block(r0,r0,r1,r1).noalias() += -m1.block(r0,c0,r1,c1) * (s2*m2.block(r0,c0,r1,c1)).adjoint() ), 0); 101 VERIFY_EVALUATION_COUNT(( m3.block(r0,r0,r1,r1).noalias() -= s1 * m1.block(r0,c0,r1,c1) * m2.block(c0,r0,c1,r1) ), 0); 102 103 // NOTE this is because the Block expression is not handled yet by our expression analyser 104 VERIFY_EVALUATION_COUNT(( m3.block(r0,r0,r1,r1).noalias() = s1 * m1.block(r0,c0,r1,c1) * (s1*m2).block(c0,r0,c1,r1) ), 1); 105 106 VERIFY_EVALUATION_COUNT( m3.noalias() -= (s1 * m1).template triangularView<Lower>() * m2, 0); 107 VERIFY_EVALUATION_COUNT( rm3.noalias() = (s1 * m1.adjoint()).template triangularView<Upper>() * (m2+m2), 1); 108 VERIFY_EVALUATION_COUNT( rm3.noalias() = (s1 * m1.adjoint()).template triangularView<UnitUpper>() * m2.adjoint(), 0); 109 110 VERIFY_EVALUATION_COUNT( m3.template triangularView<Upper>() = (m1 * m2.adjoint()), 0); 111 VERIFY_EVALUATION_COUNT( m3.template triangularView<Upper>() -= (m1 * m2.adjoint()), 0); 112 113 // NOTE this is because the blas_traits require innerstride==1 to avoid a temporary, but that doesn't seem to be actually needed for the triangular products 114 VERIFY_EVALUATION_COUNT( rm3.col(c0).noalias() = (s1 * m1.adjoint()).template triangularView<UnitUpper>() * (s2*m2.row(c0)).adjoint(), 1); 115 116 VERIFY_EVALUATION_COUNT( m1.template triangularView<Lower>().solveInPlace(m3), 0); 117 VERIFY_EVALUATION_COUNT( m1.adjoint().template triangularView<Lower>().solveInPlace(m3.transpose()), 0); 118 119 VERIFY_EVALUATION_COUNT( m3.noalias() -= (s1 * m1).adjoint().template selfadjointView<Lower>() * (-m2*s3).adjoint(), 0); 120 VERIFY_EVALUATION_COUNT( m3.noalias() = s2 * m2.adjoint() * (s1 * m1.adjoint()).template selfadjointView<Upper>(), 0); 121 VERIFY_EVALUATION_COUNT( rm3.noalias() = (s1 * m1.adjoint()).template selfadjointView<Lower>() * m2.adjoint(), 0); 122 123 // NOTE this is because the blas_traits require innerstride==1 to avoid a temporary, but that doesn't seem to be actually needed for the triangular products 124 VERIFY_EVALUATION_COUNT( m3.col(c0).noalias() = (s1 * m1).adjoint().template selfadjointView<Lower>() * (-m2.row(c0)*s3).adjoint(), 1); 125 VERIFY_EVALUATION_COUNT( m3.col(c0).noalias() -= (s1 * m1).adjoint().template selfadjointView<Upper>() * (-m2.row(c0)*s3).adjoint(), 1); 126 127 VERIFY_EVALUATION_COUNT( m3.block(r0,c0,r1,c1).noalias() += m1.block(r0,r0,r1,r1).template selfadjointView<Upper>() * (s1*m2.block(r0,c0,r1,c1)), 0); 128 VERIFY_EVALUATION_COUNT( m3.block(r0,c0,r1,c1).noalias() = m1.block(r0,r0,r1,r1).template selfadjointView<Upper>() * m2.block(r0,c0,r1,c1), 0); 129 130 VERIFY_EVALUATION_COUNT( m3.template selfadjointView<Lower>().rankUpdate(m2.adjoint()), 0); 131 132 // Here we will get 1 temporary for each resize operation of the lhs operator; resize(r1,c1) would lead to zero temporaries 133 m3.resize(1,1); 134 VERIFY_EVALUATION_COUNT( m3.noalias() = m1.block(r0,r0,r1,r1).template selfadjointView<Lower>() * m2.block(r0,c0,r1,c1), 1); 135 m3.resize(1,1); 136 VERIFY_EVALUATION_COUNT( m3.noalias() = m1.block(r0,r0,r1,r1).template triangularView<UnitUpper>() * m2.block(r0,c0,r1,c1), 1); 137 138 // Zero temporaries for lazy products ... 139 m3.setRandom(rows,cols); 140 VERIFY_EVALUATION_COUNT( Scalar tmp = 0; tmp += Scalar(RealScalar(1)) / (m3.transpose().lazyProduct(m3)).diagonal().sum(), 0 ); 141 VERIFY_EVALUATION_COUNT( m3.noalias() = m1.conjugate().lazyProduct(m2.conjugate()), 0); 142 143 // ... and even no temporary for even deeply (>=2) nested products 144 VERIFY_EVALUATION_COUNT( Scalar tmp = 0; tmp += Scalar(RealScalar(1)) / (m3.transpose() * m3).diagonal().sum(), 0 ); 145 VERIFY_EVALUATION_COUNT( Scalar tmp = 0; tmp += Scalar(RealScalar(1)) / (m3.transpose() * m3).diagonal().array().abs().sum(), 0 ); 146 147 // Zero temporaries for ... CoeffBasedProductMode 148 VERIFY_EVALUATION_COUNT( m3.col(0).template head<5>() * m3.col(0).transpose() + m3.col(0).template head<5>() * m3.col(0).transpose(), 0 ); 149 150 // Check matrix * vectors 151 VERIFY_EVALUATION_COUNT( cvres.noalias() = m1 * cv1, 0 ); 152 VERIFY_EVALUATION_COUNT( cvres.noalias() -= m1 * cv1, 0 ); 153 VERIFY_EVALUATION_COUNT( cvres.noalias() -= m1 * m2.col(0), 0 ); 154 VERIFY_EVALUATION_COUNT( cvres.noalias() -= m1 * rv1.adjoint(), 0 ); 155 VERIFY_EVALUATION_COUNT( cvres.noalias() -= m1 * m2.row(0).transpose(), 0 ); 156 157 VERIFY_EVALUATION_COUNT( cvres.noalias() = (m1+m1) * cv1, 0 ); 158 VERIFY_EVALUATION_COUNT( cvres.noalias() = (rm3+rm3) * cv1, 0 ); 159 VERIFY_EVALUATION_COUNT( cvres.noalias() = (m1+m1) * (m1*cv1), 1 ); 160 VERIFY_EVALUATION_COUNT( cvres.noalias() = (rm3+rm3) * (m1*cv1), 1 ); 161 162 // Check outer products 163 #ifdef EIGEN_ALLOCA 164 bool temp_via_alloca = m3.rows()*sizeof(Scalar) <= EIGEN_STACK_ALLOCATION_LIMIT; 165 #else 166 bool temp_via_alloca = false; 167 #endif 168 m3 = cv1 * rv1; 169 VERIFY_EVALUATION_COUNT( m3.noalias() = cv1 * rv1, 0 ); 170 VERIFY_EVALUATION_COUNT( m3.noalias() = (cv1+cv1) * (rv1+rv1), temp_via_alloca ? 0 : 1 ); 171 VERIFY_EVALUATION_COUNT( m3.noalias() = (m1*cv1) * (rv1), 1 ); 172 VERIFY_EVALUATION_COUNT( m3.noalias() += (m1*cv1) * (rv1), 1 ); 173 rm3 = cv1 * rv1; 174 VERIFY_EVALUATION_COUNT( rm3.noalias() = cv1 * rv1, 0 ); 175 VERIFY_EVALUATION_COUNT( rm3.noalias() = (cv1+cv1) * (rv1+rv1), temp_via_alloca ? 0 : 1 ); 176 VERIFY_EVALUATION_COUNT( rm3.noalias() = (cv1) * (rv1 * m1), 1 ); 177 VERIFY_EVALUATION_COUNT( rm3.noalias() -= (cv1) * (rv1 * m1), 1 ); 178 VERIFY_EVALUATION_COUNT( rm3.noalias() = (m1*cv1) * (rv1 * m1), 2 ); 179 VERIFY_EVALUATION_COUNT( rm3.noalias() += (m1*cv1) * (rv1 * m1), 2 ); 180 181 // Check nested products 182 VERIFY_EVALUATION_COUNT( cvres.noalias() = m1.adjoint() * m1 * cv1, 1 ); 183 VERIFY_EVALUATION_COUNT( rvres.noalias() = rv1 * (m1 * m2.adjoint()), 1 ); 184 185 // exhaustively check all scalar multiple combinations: 186 { 187 // Generic path: 188 check_scalar_multiple1(m3, m1, m2, s1, s2); 189 // Force fall back to coeff-based: 190 typename ColMajorMatrixType::BlockXpr m3_blck = m3.block(r0,r0,1,1); 191 check_scalar_multiple1(m3_blck, m1.block(r0,c0,1,1), m2.block(c0,r0,1,1), s1, s2); 192 } 193 } 194 195 EIGEN_DECLARE_TEST(product_notemporary) 196 { 197 int s; 198 for(int i = 0; i < g_repeat; i++) { 199 s = internal::random<int>(16,EIGEN_TEST_MAX_SIZE); 200 CALL_SUBTEST_1( product_notemporary(MatrixXf(s, s)) ); 201 CALL_SUBTEST_2( product_notemporary(MatrixXd(s, s)) ); 202 TEST_SET_BUT_UNUSED_VARIABLE(s) 203 204 s = internal::random<int>(16,EIGEN_TEST_MAX_SIZE/2); 205 CALL_SUBTEST_3( product_notemporary(MatrixXcf(s,s)) ); 206 CALL_SUBTEST_4( product_notemporary(MatrixXcd(s,s)) ); 207 TEST_SET_BUT_UNUSED_VARIABLE(s) 208 } 209 }