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
14 template<typename Derived1, typename Derived2>
15 bool 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
product(const MatrixType & m)21 template<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 RowSquareMatrixType
45 identity = RowSquareMatrixType::Identity(rows, rows),
46 square = RowSquareMatrixType::Random(rows, rows),
47 res = RowSquareMatrixType::Random(rows, rows);
48 ColSquareMatrixType
49 square2 = ColSquareMatrixType::Random(cols, cols),
50 res2 = ColSquareMatrixType::Random(cols, cols);
51 RowVectorType v1 = RowVectorType::Random(rows);
52 ColVectorType vc2 = ColVectorType::Random(cols), vcres(cols);
53 OtherMajorMatrixType tm1 = m1;
54
55 Scalar s1 = ei_random<Scalar>();
56
57 int r = ei_random<int>(0, rows-1),
58 c = ei_random<int>(0, cols-1);
59
60 // begin testing Product.h: only associativity for now
61 // (we use Transpose.h but this doesn't count as a test for it)
62
63 VERIFY_IS_APPROX((m1*m1.transpose())*m2, m1*(m1.transpose()*m2));
64 m3 = m1;
65 m3 *= m1.transpose() * m2;
66 VERIFY_IS_APPROX(m3, m1 * (m1.transpose()*m2));
67 VERIFY_IS_APPROX(m3, m1.lazy() * (m1.transpose()*m2));
68
69 // continue testing Product.h: distributivity
70 VERIFY_IS_APPROX(square*(m1 + m2), square*m1+square*m2);
71 VERIFY_IS_APPROX(square*(m1 - m2), square*m1-square*m2);
72
73 // continue testing Product.h: compatibility with ScalarMultiple.h
74 VERIFY_IS_APPROX(s1*(square*m1), (s1*square)*m1);
75 VERIFY_IS_APPROX(s1*(square*m1), square*(m1*s1));
76
77 // again, test operator() to check const-qualification
78 s1 += (square.lazy() * m1)(r,c);
79
80 // test Product.h together with Identity.h
81 VERIFY_IS_APPROX(v1, identity*v1);
82 VERIFY_IS_APPROX(v1.transpose(), v1.transpose() * identity);
83 // again, test operator() to check const-qualification
84 VERIFY_IS_APPROX(MatrixType::Identity(rows, cols)(r,c), static_cast<Scalar>(r==c));
85
86 if (rows!=cols)
87 VERIFY_RAISES_ASSERT(m3 = m1*m1);
88
89 // test the previous tests were not screwed up because operator* returns 0
90 // (we use the more accurate default epsilon)
91 if (NumTraits<Scalar>::HasFloatingPoint && std::min(rows,cols)>1)
92 {
93 VERIFY(areNotApprox(m1.transpose()*m2,m2.transpose()*m1));
94 }
95
96 // test optimized operator+= path
97 res = square;
98 res += (m1 * m2.transpose()).lazy();
99 VERIFY_IS_APPROX(res, square + m1 * m2.transpose());
100 if (NumTraits<Scalar>::HasFloatingPoint && std::min(rows,cols)>1)
101 {
102 VERIFY(areNotApprox(res,square + m2 * m1.transpose()));
103 }
104 vcres = vc2;
105 vcres += (m1.transpose() * v1).lazy();
106 VERIFY_IS_APPROX(vcres, vc2 + m1.transpose() * v1);
107 tm1 = m1;
108 VERIFY_IS_APPROX(tm1.transpose() * v1, m1.transpose() * v1);
109 VERIFY_IS_APPROX(v1.transpose() * tm1, v1.transpose() * m1);
110
111 // test submatrix and matrix/vector product
112 for (int i=0; i<rows; ++i)
113 res.row(i) = m1.row(i) * m2.transpose();
114 VERIFY_IS_APPROX(res, m1 * m2.transpose());
115 // the other way round:
116 for (int i=0; i<rows; ++i)
117 res.col(i) = m1 * m2.transpose().col(i);
118 VERIFY_IS_APPROX(res, m1 * m2.transpose());
119
120 res2 = square2;
121 res2 += (m1.transpose() * m2).lazy();
122 VERIFY_IS_APPROX(res2, square2 + m1.transpose() * m2);
123
124 if (NumTraits<Scalar>::HasFloatingPoint && std::min(rows,cols)>1)
125 {
126 VERIFY(areNotApprox(res2,square2 + m2.transpose() * m1));
127 }
128 }
129
130