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 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