1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra. Eigen itself is part of the KDE project.
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/Array>
12#include <Eigen/QR>
13
14template<typename Derived1, typename Derived2>
15bool areNotApprox(const MatrixBase<Derived1>& m1, const MatrixBase<Derived2>& m2, typename Derived1::RealScalar epsilon = precision<typename Derived1::RealScalar>())
16{
17  return !((m1-m2).cwise().abs2().maxCoeff() < epsilon * epsilon
18                          * std::max(m1.cwise().abs2().maxCoeff(), m2.cwise().abs2().maxCoeff()));
19}
20
21template<typename MatrixType> void product(const MatrixType& m)
22{
23  /* this test covers the following files:
24     Identity.h Product.h
25  */
26
27  typedef typename MatrixType::Scalar Scalar;
28  typedef typename NumTraits<Scalar>::FloatingPoint FloatingPoint;
29  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> RowVectorType;
30  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> ColVectorType;
31  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> RowSquareMatrixType;
32  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> ColSquareMatrixType;
33  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime,
34                         MatrixType::Options^RowMajor> OtherMajorMatrixType;
35
36  int rows = m.rows();
37  int cols = m.cols();
38
39  // this test relies a lot on Random.h, and there's not much more that we can do
40  // to test it, hence I consider that we will have tested Random.h
41  MatrixType m1 = MatrixType::Random(rows, cols),
42             m2 = MatrixType::Random(rows, cols),
43             m3(rows, cols),
44             mzero = MatrixType::Zero(rows, cols);
45  RowSquareMatrixType
46             identity = RowSquareMatrixType::Identity(rows, rows),
47             square = RowSquareMatrixType::Random(rows, rows),
48             res = RowSquareMatrixType::Random(rows, rows);
49  ColSquareMatrixType
50             square2 = ColSquareMatrixType::Random(cols, cols),
51             res2 = ColSquareMatrixType::Random(cols, cols);
52  RowVectorType v1 = RowVectorType::Random(rows),
53             v2 = RowVectorType::Random(rows),
54             vzero = RowVectorType::Zero(rows);
55  ColVectorType vc2 = ColVectorType::Random(cols), vcres(cols);
56  OtherMajorMatrixType tm1 = m1;
57
58  Scalar s1 = ei_random<Scalar>();
59
60  int r = ei_random<int>(0, rows-1),
61      c = ei_random<int>(0, cols-1);
62
63  // begin testing Product.h: only associativity for now
64  // (we use Transpose.h but this doesn't count as a test for it)
65
66  VERIFY_IS_APPROX((m1*m1.transpose())*m2,  m1*(m1.transpose()*m2));
67  m3 = m1;
68  m3 *= m1.transpose() * m2;
69  VERIFY_IS_APPROX(m3,                      m1 * (m1.transpose()*m2));
70  VERIFY_IS_APPROX(m3,                      m1.lazy() * (m1.transpose()*m2));
71
72  // continue testing Product.h: distributivity
73  VERIFY_IS_APPROX(square*(m1 + m2),        square*m1+square*m2);
74  VERIFY_IS_APPROX(square*(m1 - m2),        square*m1-square*m2);
75
76  // continue testing Product.h: compatibility with ScalarMultiple.h
77  VERIFY_IS_APPROX(s1*(square*m1),          (s1*square)*m1);
78  VERIFY_IS_APPROX(s1*(square*m1),          square*(m1*s1));
79
80  // again, test operator() to check const-qualification
81  s1 += (square.lazy() * m1)(r,c);
82
83  // test Product.h together with Identity.h
84  VERIFY_IS_APPROX(v1,                      identity*v1);
85  VERIFY_IS_APPROX(v1.transpose(),          v1.transpose() * identity);
86  // again, test operator() to check const-qualification
87  VERIFY_IS_APPROX(MatrixType::Identity(rows, cols)(r,c), static_cast<Scalar>(r==c));
88
89  if (rows!=cols)
90     VERIFY_RAISES_ASSERT(m3 = m1*m1);
91
92  // test the previous tests were not screwed up because operator* returns 0
93  // (we use the more accurate default epsilon)
94  if (NumTraits<Scalar>::HasFloatingPoint && std::min(rows,cols)>1)
95  {
96    VERIFY(areNotApprox(m1.transpose()*m2,m2.transpose()*m1));
97  }
98
99  // test optimized operator+= path
100  res = square;
101  res += (m1 * m2.transpose()).lazy();
102  VERIFY_IS_APPROX(res, square + m1 * m2.transpose());
103  if (NumTraits<Scalar>::HasFloatingPoint && std::min(rows,cols)>1)
104  {
105    VERIFY(areNotApprox(res,square + m2 * m1.transpose()));
106  }
107  vcres = vc2;
108  vcres += (m1.transpose() * v1).lazy();
109  VERIFY_IS_APPROX(vcres, vc2 + m1.transpose() * v1);
110  tm1 = m1;
111  VERIFY_IS_APPROX(tm1.transpose() * v1, m1.transpose() * v1);
112  VERIFY_IS_APPROX(v1.transpose() * tm1, v1.transpose() * m1);
113
114  // test submatrix and matrix/vector product
115  for (int i=0; i<rows; ++i)
116    res.row(i) = m1.row(i) * m2.transpose();
117  VERIFY_IS_APPROX(res, m1 * m2.transpose());
118  // the other way round:
119  for (int i=0; i<rows; ++i)
120    res.col(i) = m1 * m2.transpose().col(i);
121  VERIFY_IS_APPROX(res, m1 * m2.transpose());
122
123  res2 = square2;
124  res2 += (m1.transpose() * m2).lazy();
125  VERIFY_IS_APPROX(res2, square2 + m1.transpose() * m2);
126
127  if (NumTraits<Scalar>::HasFloatingPoint && std::min(rows,cols)>1)
128  {
129    VERIFY(areNotApprox(res2,square2 + m2.transpose() * m1));
130  }
131}
132
133