product_notemporary.cpp
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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 MatrixType> void product_notemporary(const MatrixType& m)
15 {
16  /* This test checks the number of temporaries created
17  * during the evaluation of a complex expression */
18  typedef typename MatrixType::Scalar Scalar;
19  typedef typename MatrixType::RealScalar RealScalar;
20  typedef Matrix<Scalar, 1, Dynamic> RowVectorType;
21  typedef Matrix<Scalar, Dynamic, 1> ColVectorType;
22  typedef Matrix<Scalar, Dynamic, Dynamic, ColMajor> ColMajorMatrixType;
23  typedef Matrix<Scalar, Dynamic, Dynamic, RowMajor> RowMajorMatrixType;
24 
25  Index rows = m.rows();
26  Index cols = m.cols();
27 
28  ColMajorMatrixType m1 = MatrixType::Random(rows, cols),
29  m2 = MatrixType::Random(rows, cols),
30  m3(rows, cols);
31  RowVectorType rv1 = RowVectorType::Random(rows), rvres(rows);
32  ColVectorType cv1 = ColVectorType::Random(cols), cvres(cols);
33  RowMajorMatrixType rm3(rows, cols);
34 
35  Scalar s1 = internal::random<Scalar>(),
36  s2 = internal::random<Scalar>(),
37  s3 = internal::random<Scalar>();
38 
39  Index c0 = internal::random<Index>(4,cols-8),
40  c1 = internal::random<Index>(8,cols-c0),
41  r0 = internal::random<Index>(4,cols-8),
42  r1 = internal::random<Index>(8,rows-r0);
43 
44  VERIFY_EVALUATION_COUNT( m3 = (m1 * m2.adjoint()), 1);
45  VERIFY_EVALUATION_COUNT( m3 = (m1 * m2.adjoint()).transpose(), 1);
46  VERIFY_EVALUATION_COUNT( m3.noalias() = m1 * m2.adjoint(), 0);
47 
48  VERIFY_EVALUATION_COUNT( m3 = s1 * (m1 * m2.transpose()), 1);
49 // VERIFY_EVALUATION_COUNT( m3 = m3 + s1 * (m1 * m2.transpose()), 1);
50  VERIFY_EVALUATION_COUNT( m3.noalias() = s1 * (m1 * m2.transpose()), 0);
51 
52  VERIFY_EVALUATION_COUNT( m3 = m3 + (m1 * m2.adjoint()), 1);
53  VERIFY_EVALUATION_COUNT( m3 = m3 - (m1 * m2.adjoint()), 1);
54 
55  VERIFY_EVALUATION_COUNT( m3 = m3 + (m1 * m2.adjoint()).transpose(), 1);
56  VERIFY_EVALUATION_COUNT( m3.noalias() = m3 + m1 * m2.transpose(), 0);
57  VERIFY_EVALUATION_COUNT( m3.noalias() += m3 + m1 * m2.transpose(), 0);
58  VERIFY_EVALUATION_COUNT( m3.noalias() -= m3 + m1 * m2.transpose(), 0);
59  VERIFY_EVALUATION_COUNT( m3.noalias() = m3 - m1 * m2.transpose(), 0);
60  VERIFY_EVALUATION_COUNT( m3.noalias() += m3 - m1 * m2.transpose(), 0);
61  VERIFY_EVALUATION_COUNT( m3.noalias() -= m3 - m1 * m2.transpose(), 0);
62 
63  VERIFY_EVALUATION_COUNT( m3.noalias() = s1 * m1 * s2 * m2.adjoint(), 0);
64  VERIFY_EVALUATION_COUNT( m3.noalias() = s1 * m1 * s2 * (m1*s3+m2*s2).adjoint(), 1);
65  VERIFY_EVALUATION_COUNT( m3.noalias() = (s1 * m1).adjoint() * s2 * m2, 0);
66  VERIFY_EVALUATION_COUNT( m3.noalias() += s1 * (-m1*s3).adjoint() * (s2 * m2 * s3), 0);
67  VERIFY_EVALUATION_COUNT( m3.noalias() -= s1 * (m1.transpose() * m2), 0);
68 
69  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);
70  VERIFY_EVALUATION_COUNT(( m3.block(r0,r0,r1,r1).noalias() -= s1 * m1.block(r0,c0,r1,c1) * m2.block(c0,r0,c1,r1) ), 0);
71 
72  // NOTE this is because the Block expression is not handled yet by our expression analyser
73  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);
74 
75  VERIFY_EVALUATION_COUNT( m3.noalias() -= (s1 * m1).template triangularView<Lower>() * m2, 0);
76  VERIFY_EVALUATION_COUNT( rm3.noalias() = (s1 * m1.adjoint()).template triangularView<Upper>() * (m2+m2), 1);
77  VERIFY_EVALUATION_COUNT( rm3.noalias() = (s1 * m1.adjoint()).template triangularView<UnitUpper>() * m2.adjoint(), 0);
78 
79  VERIFY_EVALUATION_COUNT( m3.template triangularView<Upper>() = (m1 * m2.adjoint()), 0);
80  VERIFY_EVALUATION_COUNT( m3.template triangularView<Upper>() -= (m1 * m2.adjoint()), 0);
81 
82  // 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
83  VERIFY_EVALUATION_COUNT( rm3.col(c0).noalias() = (s1 * m1.adjoint()).template triangularView<UnitUpper>() * (s2*m2.row(c0)).adjoint(), 1);
84 
85  VERIFY_EVALUATION_COUNT( m1.template triangularView<Lower>().solveInPlace(m3), 0);
86  VERIFY_EVALUATION_COUNT( m1.adjoint().template triangularView<Lower>().solveInPlace(m3.transpose()), 0);
87 
88  VERIFY_EVALUATION_COUNT( m3.noalias() -= (s1 * m1).adjoint().template selfadjointView<Lower>() * (-m2*s3).adjoint(), 0);
89  VERIFY_EVALUATION_COUNT( m3.noalias() = s2 * m2.adjoint() * (s1 * m1.adjoint()).template selfadjointView<Upper>(), 0);
90  VERIFY_EVALUATION_COUNT( rm3.noalias() = (s1 * m1.adjoint()).template selfadjointView<Lower>() * m2.adjoint(), 0);
91 
92  // 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
93  VERIFY_EVALUATION_COUNT( m3.col(c0).noalias() = (s1 * m1).adjoint().template selfadjointView<Lower>() * (-m2.row(c0)*s3).adjoint(), 1);
94  VERIFY_EVALUATION_COUNT( m3.col(c0).noalias() -= (s1 * m1).adjoint().template selfadjointView<Upper>() * (-m2.row(c0)*s3).adjoint(), 1);
95 
96  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);
97  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);
98 
99  VERIFY_EVALUATION_COUNT( m3.template selfadjointView<Lower>().rankUpdate(m2.adjoint()), 0);
100 
101  // Here we will get 1 temporary for each resize operation of the lhs operator; resize(r1,c1) would lead to zero temporaries
102  m3.resize(1,1);
103  VERIFY_EVALUATION_COUNT( m3.noalias() = m1.block(r0,r0,r1,r1).template selfadjointView<Lower>() * m2.block(r0,c0,r1,c1), 1);
104  m3.resize(1,1);
105  VERIFY_EVALUATION_COUNT( m3.noalias() = m1.block(r0,r0,r1,r1).template triangularView<UnitUpper>() * m2.block(r0,c0,r1,c1), 1);
106 
107  // Zero temporaries for lazy products ...
108  VERIFY_EVALUATION_COUNT( Scalar tmp = 0; tmp += Scalar(RealScalar(1)) / (m3.transpose().lazyProduct(m3)).diagonal().sum(), 0 );
109 
110  // ... and even no temporary for even deeply (>=2) nested products
111  VERIFY_EVALUATION_COUNT( Scalar tmp = 0; tmp += Scalar(RealScalar(1)) / (m3.transpose() * m3).diagonal().sum(), 0 );
112  VERIFY_EVALUATION_COUNT( Scalar tmp = 0; tmp += Scalar(RealScalar(1)) / (m3.transpose() * m3).diagonal().array().abs().sum(), 0 );
113 
114  // Zero temporaries for ... CoeffBasedProductMode
115  VERIFY_EVALUATION_COUNT( m3.col(0).template head<5>() * m3.col(0).transpose() + m3.col(0).template head<5>() * m3.col(0).transpose(), 0 );
116 
117  // Check matrix * vectors
118  VERIFY_EVALUATION_COUNT( cvres.noalias() = m1 * cv1, 0 );
119  VERIFY_EVALUATION_COUNT( cvres.noalias() -= m1 * cv1, 0 );
120  VERIFY_EVALUATION_COUNT( cvres.noalias() -= m1 * m2.col(0), 0 );
121  VERIFY_EVALUATION_COUNT( cvres.noalias() -= m1 * rv1.adjoint(), 0 );
122  VERIFY_EVALUATION_COUNT( cvres.noalias() -= m1 * m2.row(0).transpose(), 0 );
123 
124  VERIFY_EVALUATION_COUNT( cvres.noalias() = (m1+m1) * cv1, 0 );
125  VERIFY_EVALUATION_COUNT( cvres.noalias() = (rm3+rm3) * cv1, 0 );
126  VERIFY_EVALUATION_COUNT( cvres.noalias() = (m1+m1) * (m1*cv1), 1 );
127  VERIFY_EVALUATION_COUNT( cvres.noalias() = (rm3+rm3) * (m1*cv1), 1 );
128 
129  // Check outer products
130  m3 = cv1 * rv1;
131  VERIFY_EVALUATION_COUNT( m3.noalias() = cv1 * rv1, 0 );
132  VERIFY_EVALUATION_COUNT( m3.noalias() = (cv1+cv1) * (rv1+rv1), 1 );
133  VERIFY_EVALUATION_COUNT( m3.noalias() = (m1*cv1) * (rv1), 1 );
134  VERIFY_EVALUATION_COUNT( m3.noalias() += (m1*cv1) * (rv1), 1 );
135  VERIFY_EVALUATION_COUNT( rm3.noalias() = (cv1) * (rv1 * m1), 1 );
136  VERIFY_EVALUATION_COUNT( rm3.noalias() -= (cv1) * (rv1 * m1), 1 );
137  VERIFY_EVALUATION_COUNT( rm3.noalias() = (m1*cv1) * (rv1 * m1), 2 );
138  VERIFY_EVALUATION_COUNT( rm3.noalias() += (m1*cv1) * (rv1 * m1), 2 );
139 
140  // Check nested products
141  VERIFY_EVALUATION_COUNT( cvres.noalias() = m1.adjoint() * m1 * cv1, 1 );
142  VERIFY_EVALUATION_COUNT( rvres.noalias() = rv1 * (m1 * m2.adjoint()), 1 );
143 }
144 
145 void test_product_notemporary()
146 {
147  int s;
148  for(int i = 0; i < g_repeat; i++) {
149  s = internal::random<int>(16,EIGEN_TEST_MAX_SIZE);
150  CALL_SUBTEST_1( product_notemporary(MatrixXf(s, s)) );
151  CALL_SUBTEST_2( product_notemporary(MatrixXd(s, s)) );
152  TEST_SET_BUT_UNUSED_VARIABLE(s)
153 
154  s = internal::random<int>(16,EIGEN_TEST_MAX_SIZE/2);
155  CALL_SUBTEST_3( product_notemporary(MatrixXcf(s,s)) );
156  CALL_SUBTEST_4( product_notemporary(MatrixXcd(s,s)) );
157  TEST_SET_BUT_UNUSED_VARIABLE(s)
158  }
159 }
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void product_notemporary(const MatrixType &m)
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autogenerated on Sat May 8 2021 02:43:33