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
10static int nb_temporaries;
11
12inline void on_temporary_creation(int size) {
13  // here's a great place to set a breakpoint when debugging failures in this test!
14  if(size!=0) nb_temporaries++;
15}
16
17
18#define EIGEN_DENSE_STORAGE_CTOR_PLUGIN { on_temporary_creation(size); }
19
20#include "main.h"
21
22#define VERIFY_EVALUATION_COUNT(XPR,N) {\
23    nb_temporaries = 0; \
24    XPR; \
25    if(nb_temporaries!=N) std::cerr << "nb_temporaries == " << nb_temporaries << "\n"; \
26    VERIFY( (#XPR) && nb_temporaries==N ); \
27  }
28
29template<typename MatrixType> void product_notemporary(const MatrixType& m)
30{
31  /* This test checks the number of temporaries created
32   * during the evaluation of a complex expression */
33  typedef typename MatrixType::Index Index;
34  typedef typename MatrixType::Scalar Scalar;
35  typedef typename MatrixType::RealScalar RealScalar;
36  typedef Matrix<Scalar, 1, Dynamic> RowVectorType;
37  typedef Matrix<Scalar, Dynamic, 1> ColVectorType;
38  typedef Matrix<Scalar, Dynamic, Dynamic, ColMajor> ColMajorMatrixType;
39  typedef Matrix<Scalar, Dynamic, Dynamic, RowMajor> RowMajorMatrixType;
40
41  Index rows = m.rows();
42  Index cols = m.cols();
43
44  ColMajorMatrixType m1 = MatrixType::Random(rows, cols),
45                     m2 = MatrixType::Random(rows, cols),
46                     m3(rows, cols);
47  RowVectorType rv1 = RowVectorType::Random(rows), rvres(rows);
48  ColVectorType cv1 = ColVectorType::Random(cols), cvres(cols);
49  RowMajorMatrixType rm3(rows, cols);
50
51  Scalar s1 = internal::random<Scalar>(),
52         s2 = internal::random<Scalar>(),
53         s3 = internal::random<Scalar>();
54
55  Index c0 = internal::random<Index>(4,cols-8),
56        c1 = internal::random<Index>(8,cols-c0),
57        r0 = internal::random<Index>(4,cols-8),
58        r1 = internal::random<Index>(8,rows-r0);
59
60  VERIFY_EVALUATION_COUNT( m3 = (m1 * m2.adjoint()), 1);
61  VERIFY_EVALUATION_COUNT( m3.noalias() = m1 * m2.adjoint(), 0);
62
63  VERIFY_EVALUATION_COUNT( m3.noalias() = s1 * (m1 * m2.transpose()), 0);
64
65  VERIFY_EVALUATION_COUNT( m3.noalias() = s1 * m1 * s2 * m2.adjoint(), 0);
66  VERIFY_EVALUATION_COUNT( m3.noalias() = s1 * m1 * s2 * (m1*s3+m2*s2).adjoint(), 1);
67  VERIFY_EVALUATION_COUNT( m3.noalias() = (s1 * m1).adjoint() * s2 * m2, 0);
68  VERIFY_EVALUATION_COUNT( m3.noalias() += s1 * (-m1*s3).adjoint() * (s2 * m2 * s3), 0);
69  VERIFY_EVALUATION_COUNT( m3.noalias() -= s1 * (m1.transpose() * m2), 0);
70
71  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);
72  VERIFY_EVALUATION_COUNT(( m3.block(r0,r0,r1,r1).noalias() -= s1 * m1.block(r0,c0,r1,c1) * m2.block(c0,r0,c1,r1) ), 0);
73
74  // NOTE this is because the Block expression is not handled yet by our expression analyser
75  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);
76
77  VERIFY_EVALUATION_COUNT( m3.noalias() -= (s1 * m1).template triangularView<Lower>() * m2, 0);
78  VERIFY_EVALUATION_COUNT( rm3.noalias() = (s1 * m1.adjoint()).template triangularView<Upper>() * (m2+m2), 1);
79  VERIFY_EVALUATION_COUNT( rm3.noalias() = (s1 * m1.adjoint()).template triangularView<UnitUpper>() * m2.adjoint(), 0);
80
81  VERIFY_EVALUATION_COUNT( m3.template triangularView<Upper>() = (m1 * m2.adjoint()), 0);
82  VERIFY_EVALUATION_COUNT( m3.template triangularView<Upper>() -= (m1 * m2.adjoint()), 0);
83
84  // 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
85  VERIFY_EVALUATION_COUNT( rm3.col(c0).noalias() = (s1 * m1.adjoint()).template triangularView<UnitUpper>() * (s2*m2.row(c0)).adjoint(), 1);
86
87  VERIFY_EVALUATION_COUNT( m1.template triangularView<Lower>().solveInPlace(m3), 0);
88  VERIFY_EVALUATION_COUNT( m1.adjoint().template triangularView<Lower>().solveInPlace(m3.transpose()), 0);
89
90  VERIFY_EVALUATION_COUNT( m3.noalias() -= (s1 * m1).adjoint().template selfadjointView<Lower>() * (-m2*s3).adjoint(), 0);
91  VERIFY_EVALUATION_COUNT( m3.noalias() = s2 * m2.adjoint() * (s1 * m1.adjoint()).template selfadjointView<Upper>(), 0);
92  VERIFY_EVALUATION_COUNT( rm3.noalias() = (s1 * m1.adjoint()).template selfadjointView<Lower>() * m2.adjoint(), 0);
93
94  // 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
95  VERIFY_EVALUATION_COUNT( m3.col(c0).noalias() = (s1 * m1).adjoint().template selfadjointView<Lower>() * (-m2.row(c0)*s3).adjoint(), 1);
96  VERIFY_EVALUATION_COUNT( m3.col(c0).noalias() -= (s1 * m1).adjoint().template selfadjointView<Upper>() * (-m2.row(c0)*s3).adjoint(), 1);
97
98  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);
99  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);
100
101  VERIFY_EVALUATION_COUNT( m3.template selfadjointView<Lower>().rankUpdate(m2.adjoint()), 0);
102
103  // Here we will get 1 temporary for each resize operation of the lhs operator; resize(r1,c1) would lead to zero temporaries
104  m3.resize(1,1);
105  VERIFY_EVALUATION_COUNT( m3.noalias() = m1.block(r0,r0,r1,r1).template selfadjointView<Lower>() * m2.block(r0,c0,r1,c1), 1);
106  m3.resize(1,1);
107  VERIFY_EVALUATION_COUNT( m3.noalias() = m1.block(r0,r0,r1,r1).template triangularView<UnitUpper>()  * m2.block(r0,c0,r1,c1), 1);
108
109  // Zero temporaries for lazy products ...
110  VERIFY_EVALUATION_COUNT( Scalar tmp = 0; tmp += Scalar(RealScalar(1)) /  (m3.transpose().lazyProduct(m3)).diagonal().sum(), 0 );
111
112  // ... and even no temporary for even deeply (>=2) nested products
113  VERIFY_EVALUATION_COUNT( Scalar tmp = 0; tmp += Scalar(RealScalar(1)) /  (m3.transpose() * m3).diagonal().sum(), 0 );
114  VERIFY_EVALUATION_COUNT( Scalar tmp = 0; tmp += Scalar(RealScalar(1)) /  (m3.transpose() * m3).diagonal().array().abs().sum(), 0 );
115
116  // Zero temporaries for ... CoeffBasedProductMode
117  // - does not work with GCC because of the <..>, we'ld need variadic macros ...
118  //VERIFY_EVALUATION_COUNT( m3.col(0).head<5>() * m3.col(0).transpose() + m3.col(0).head<5>() * m3.col(0).transpose(), 0 );
119
120  // Check matrix * vectors
121  VERIFY_EVALUATION_COUNT( cvres.noalias() = m1 * cv1, 0 );
122  VERIFY_EVALUATION_COUNT( cvres.noalias() -= m1 * cv1, 0 );
123  VERIFY_EVALUATION_COUNT( cvres.noalias() -= m1 * m2.col(0), 0 );
124  VERIFY_EVALUATION_COUNT( cvres.noalias() -= m1 * rv1.adjoint(), 0 );
125  VERIFY_EVALUATION_COUNT( cvres.noalias() -= m1 * m2.row(0).transpose(), 0 );
126}
127
128void test_product_notemporary()
129{
130  int s;
131  for(int i = 0; i < g_repeat; i++) {
132    s = internal::random<int>(16,EIGEN_TEST_MAX_SIZE);
133    CALL_SUBTEST_1( product_notemporary(MatrixXf(s, s)) );
134    s = internal::random<int>(16,EIGEN_TEST_MAX_SIZE);
135    CALL_SUBTEST_2( product_notemporary(MatrixXd(s, s)) );
136    s = internal::random<int>(16,EIGEN_TEST_MAX_SIZE/2);
137    CALL_SUBTEST_3( product_notemporary(MatrixXcf(s,s)) );
138    s = internal::random<int>(16,EIGEN_TEST_MAX_SIZE/2);
139    CALL_SUBTEST_4( product_notemporary(MatrixXcd(s,s)) );
140  }
141}
142