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source: pacpussensors/trunk/Vislab/lib3dv/eigen/test/product.h@ 136

Last change on this file since 136 was 136, checked in by ldecherf, 7 years ago
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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
13	template<typename Derived1, typename Derived2>
14	bool 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
20	template<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((m1m1.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), squarem1+square*m2);
69	VERIFY_IS_APPROX(square(m1 - m2), squarem1-square*m2);
70
71	// continue testing Product.h: compatibility with ScalarMultiple.h
72	VERIFY_IS_APPROX(s1(squarem1), (s1square)m1);
73	VERIFY_IS_APPROX(s1(squarem1), square(m1s1));
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	// vector at runtime (see bug 1166)
140	{
141	RowSquareMatrixType ref(square);
142	ColSquareMatrixType ref2(square2);
143	ref = res = square;
144	VERIFY_IS_APPROX(res.block(0,0,1,rows).noalias() = m1.col(0).transpose() * square.transpose(), (ref.row(0) = m1.col(0).transpose() * square.transpose()));
145	VERIFY_IS_APPROX(res.block(0,0,1,rows).noalias() = m1.block(0,0,rows,1).transpose() * square.transpose(), (ref.row(0) = m1.col(0).transpose() * square.transpose()));
146	VERIFY_IS_APPROX(res.block(0,0,1,rows).noalias() = m1.col(0).transpose() * square, (ref.row(0) = m1.col(0).transpose() * square));
147	VERIFY_IS_APPROX(res.block(0,0,1,rows).noalias() = m1.block(0,0,rows,1).transpose() * square, (ref.row(0) = m1.col(0).transpose() * square));
148	ref2 = res2 = square2;
149	VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.row(0) * square2.transpose(), (ref2.row(0) = m1.row(0) * square2.transpose()));
150	VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.block(0,0,1,cols) * square2.transpose(), (ref2.row(0) = m1.row(0) * square2.transpose()));
151	VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.row(0) * square2, (ref2.row(0) = m1.row(0) * square2));
152	VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.block(0,0,1,cols) * square2, (ref2.row(0) = m1.row(0) * square2));
153	}
154
155	// inner product
156	{
157	Scalar x = square2.row(c) * square2.col(c2);
158	VERIFY_IS_APPROX(x, square2.row(c).transpose().cwiseProduct(square2.col(c2)).sum());
159	}
160
161	// outer product
162	VERIFY_IS_APPROX(m1.col(c) * m1.row(r), m1.block(0,c,rows,1) * m1.block(r,0,1,cols));
163	VERIFY_IS_APPROX(m1.row(r).transpose() * m1.col(c).transpose(), m1.block(r,0,1,cols).transpose() * m1.block(0,c,rows,1).transpose());
164	VERIFY_IS_APPROX(m1.block(0,c,rows,1) * m1.row(r), m1.block(0,c,rows,1) * m1.block(r,0,1,cols));
165	VERIFY_IS_APPROX(m1.col(c) * m1.block(r,0,1,cols), m1.block(0,c,rows,1) * m1.block(r,0,1,cols));
166	VERIFY_IS_APPROX(m1.leftCols(1) * m1.row(r), m1.block(0,0,rows,1) * m1.block(r,0,1,cols));
167	VERIFY_IS_APPROX(m1.col(c) * m1.topRows(1), m1.block(0,c,rows,1) * m1.block(0,0,1,cols));
168
169	// Aliasing
170	{
171	ColVectorType x(cols); x.setRandom();
172	ColVectorType z(x);
173	ColVectorType y(cols); y.setZero();
174	ColSquareMatrixType A(cols,cols); A.setRandom();
175	// CwiseBinaryOp
176	VERIFY_IS_APPROX(x = y + Ax, Az);
177	x = z;
178	// CwiseUnaryOp
179	VERIFY_IS_APPROX(x = Scalar(1.)(Ax), A*z);
180	}
181
182	// regression for blas_trais
183	{
184	VERIFY_IS_APPROX(square * (squaresquare).transpose(), square square.transpose() * square.transpose());
185	VERIFY_IS_APPROX(square * (-(squaresquare)), -square square * square);
186	VERIFY_IS_APPROX(square * (s1(squaresquare)), s1 * square * square * square);
187	VERIFY_IS_APPROX(square * (squaresquare).conjugate(), square square.conjugate() * square.conjugate());
188	}
189	}

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