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
13template<typename Derived1, typename Derived2>
14bool 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
20template<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::Index Index;
26  typedef typename MatrixType::Scalar Scalar;
27  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> RowVectorType;
28  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> ColVectorType;
29  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> RowSquareMatrixType;
30  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> ColSquareMatrixType;
31  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime,
32                         MatrixType::Flags&RowMajorBit?ColMajor:RowMajor> OtherMajorMatrixType;
33
34  Index rows = m.rows();
35  Index cols = m.cols();
36
37  // this test relies a lot on Random.h, and there's not much more that we can do
38  // to test it, hence I consider that we will have tested Random.h
39  MatrixType m1 = MatrixType::Random(rows, cols),
40             m2 = MatrixType::Random(rows, cols),
41             m3(rows, cols);
42  RowSquareMatrixType
43             identity = RowSquareMatrixType::Identity(rows, rows),
44             square = RowSquareMatrixType::Random(rows, rows),
45             res = RowSquareMatrixType::Random(rows, rows);
46  ColSquareMatrixType
47             square2 = ColSquareMatrixType::Random(cols, cols),
48             res2 = ColSquareMatrixType::Random(cols, cols);
49  RowVectorType v1 = RowVectorType::Random(rows);
50  ColVectorType vc2 = ColVectorType::Random(cols), vcres(cols);
51  OtherMajorMatrixType tm1 = m1;
52
53  Scalar s1 = internal::random<Scalar>();
54
55  Index r  = internal::random<Index>(0, rows-1),
56        c  = internal::random<Index>(0, cols-1),
57        c2 = internal::random<Index>(0, cols-1);
58
59  // begin testing Product.h: only associativity for now
60  // (we use Transpose.h but this doesn't count as a test for it)
61  VERIFY_IS_APPROX((m1*m1.transpose())*m2,  m1*(m1.transpose()*m2));
62  m3 = m1;
63  m3 *= m1.transpose() * m2;
64  VERIFY_IS_APPROX(m3,                      m1 * (m1.transpose()*m2));
65  VERIFY_IS_APPROX(m3,                      m1 * (m1.transpose()*m2));
66
67  // continue testing Product.h: distributivity
68  VERIFY_IS_APPROX(square*(m1 + m2),        square*m1+square*m2);
69  VERIFY_IS_APPROX(square*(m1 - m2),        square*m1-square*m2);
70
71  // continue testing Product.h: compatibility with ScalarMultiple.h
72  VERIFY_IS_APPROX(s1*(square*m1),          (s1*square)*m1);
73  VERIFY_IS_APPROX(s1*(square*m1),          square*(m1*s1));
74
75  // test Product.h together with Identity.h
76  VERIFY_IS_APPROX(v1,                      identity*v1);
77  VERIFY_IS_APPROX(v1.transpose(),          v1.transpose() * identity);
78  // again, test operator() to check const-qualification
79  VERIFY_IS_APPROX(MatrixType::Identity(rows, cols)(r,c), static_cast<Scalar>(r==c));
80
81  if (rows!=cols)
82     VERIFY_RAISES_ASSERT(m3 = m1*m1);
83
84  // test the previous tests were not screwed up because operator* returns 0
85  // (we use the more accurate default epsilon)
86  if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1)
87  {
88    VERIFY(areNotApprox(m1.transpose()*m2,m2.transpose()*m1));
89  }
90
91  // test optimized operator+= path
92  res = square;
93  res.noalias() += m1 * m2.transpose();
94  VERIFY_IS_APPROX(res, square + m1 * m2.transpose());
95  if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1)
96  {
97    VERIFY(areNotApprox(res,square + m2 * m1.transpose()));
98  }
99  vcres = vc2;
100  vcres.noalias() += m1.transpose() * v1;
101  VERIFY_IS_APPROX(vcres, vc2 + m1.transpose() * v1);
102
103  // test optimized operator-= path
104  res = square;
105  res.noalias() -= m1 * m2.transpose();
106  VERIFY_IS_APPROX(res, square - (m1 * m2.transpose()));
107  if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1)
108  {
109    VERIFY(areNotApprox(res,square - m2 * m1.transpose()));
110  }
111  vcres = vc2;
112  vcres.noalias() -= m1.transpose() * v1;
113  VERIFY_IS_APPROX(vcres, vc2 - m1.transpose() * v1);
114
115  tm1 = m1;
116  VERIFY_IS_APPROX(tm1.transpose() * v1, m1.transpose() * v1);
117  VERIFY_IS_APPROX(v1.transpose() * tm1, v1.transpose() * m1);
118
119  // test submatrix and matrix/vector product
120  for (int i=0; i<rows; ++i)
121    res.row(i) = m1.row(i) * m2.transpose();
122  VERIFY_IS_APPROX(res, m1 * m2.transpose());
123  // the other way round:
124  for (int i=0; i<rows; ++i)
125    res.col(i) = m1 * m2.transpose().col(i);
126  VERIFY_IS_APPROX(res, m1 * m2.transpose());
127
128  res2 = square2;
129  res2.noalias() += m1.transpose() * m2;
130  VERIFY_IS_APPROX(res2, square2 + m1.transpose() * m2);
131  if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1)
132  {
133    VERIFY(areNotApprox(res2,square2 + m2.transpose() * m1));
134  }
135
136  VERIFY_IS_APPROX(res.col(r).noalias() = square.adjoint() * square.col(r), (square.adjoint() * square.col(r)).eval());
137  VERIFY_IS_APPROX(res.col(r).noalias() = square * square.col(r), (square * square.col(r)).eval());
138
139  // inner product
140  Scalar x = square2.row(c) * square2.col(c2);
141  VERIFY_IS_APPROX(x, square2.row(c).transpose().cwiseProduct(square2.col(c2)).sum());
142}
143