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product.h
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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
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::Scalar Scalar;
26 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> RowVectorType;
27 typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> ColVectorType;
28 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> RowSquareMatrixType;
29 typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> ColSquareMatrixType;
30 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime,
31 MatrixType::Flags&RowMajorBit?ColMajor:RowMajor> OtherMajorMatrixType;
32
33 Index rows = m.rows();
34 Index cols = m.cols();
35
36 // this test relies a lot on Random.h, and there's not much more that we can do
37 // to test it, hence I consider that we will have tested Random.h
38 MatrixType m1 = MatrixType::Random(rows, cols),
39 m2 = MatrixType::Random(rows, cols),
40 m3(rows, cols);
41 RowSquareMatrixType
42 identity = RowSquareMatrixType::Identity(rows, rows),
43 square = RowSquareMatrixType::Random(rows, rows),
44 res = RowSquareMatrixType::Random(rows, rows);
45 ColSquareMatrixType
46 square2 = ColSquareMatrixType::Random(cols, cols),
47 res2 = ColSquareMatrixType::Random(cols, cols);
48 RowVectorType v1 = RowVectorType::Random(rows);
49 ColVectorType vc2 = ColVectorType::Random(cols), vcres(cols);
50 OtherMajorMatrixType tm1 = m1;
51
52 Scalar s1 = internal::random<Scalar>();
53
54 Index r = internal::random<Index>(0, rows-1),
55 c = internal::random<Index>(0, cols-1),
56 c2 = internal::random<Index>(0, cols-1);
57
58 // begin testing Product.h: only associativity for now
59 // (we use Transpose.h but this doesn't count as a test for it)
60 VERIFY_IS_APPROX((m1*m1.transpose())*m2, m1*(m1.transpose()*m2));
61 m3 = m1;
62 m3 *= m1.transpose() * m2;
63 VERIFY_IS_APPROX(m3, m1 * (m1.transpose()*m2));
64 VERIFY_IS_APPROX(m3, m1 * (m1.transpose()*m2));
65
66 // continue testing Product.h: distributivity
67 VERIFY_IS_APPROX(square*(m1 + m2), square*m1+square*m2);
68 VERIFY_IS_APPROX(square*(m1 - m2), square*m1-square*m2);
69
70 // continue testing Product.h: compatibility with ScalarMultiple.h
71 VERIFY_IS_APPROX(s1*(square*m1), (s1*square)*m1);
72 VERIFY_IS_APPROX(s1*(square*m1), square*(m1*s1));
73
74 // test Product.h together with Identity.h
75 VERIFY_IS_APPROX(v1, identity*v1);
76 VERIFY_IS_APPROX(v1.transpose(), v1.transpose() * identity);
77 // again, test operator() to check const-qualification
78 VERIFY_IS_APPROX(MatrixType::Identity(rows, cols)(r,c), static_cast<Scalar>(r==c));
79
80 if (rows!=cols)
81 VERIFY_RAISES_ASSERT(m3 = m1*m1);
82
83 // test the previous tests were not screwed up because operator* returns 0
84 // (we use the more accurate default epsilon)
85 if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1)
86 {
87 VERIFY(areNotApprox(m1.transpose()*m2,m2.transpose()*m1));
88 }
89
90 // test optimized operator+= path
91 res = square;
92 res.noalias() += m1 * m2.transpose();
93 VERIFY_IS_APPROX(res, square + m1 * m2.transpose());
94 if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1)
95 {
96 VERIFY(areNotApprox(res,square + m2 * m1.transpose()));
97 }
98 vcres = vc2;
99 vcres.noalias() += m1.transpose() * v1;
100 VERIFY_IS_APPROX(vcres, vc2 + m1.transpose() * v1);
101
102 // test optimized operator-= path
103 res = square;
104 res.noalias() -= m1 * m2.transpose();
105 VERIFY_IS_APPROX(res, square - (m1 * m2.transpose()));
106 if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1)
107 {
108 VERIFY(areNotApprox(res,square - m2 * m1.transpose()));
109 }
110 vcres = vc2;
111 vcres.noalias() -= m1.transpose() * v1;
112 VERIFY_IS_APPROX(vcres, vc2 - m1.transpose() * v1);
113
114 // test scaled products
115 res = square;
116 res.noalias() = s1 * m1 * m2.transpose();
117 VERIFY_IS_APPROX(res, ((s1*m1).eval() * m2.transpose()));
118 res = square;
119 res.noalias() += s1 * m1 * m2.transpose();
120 VERIFY_IS_APPROX(res, square + ((s1*m1).eval() * m2.transpose()));
121 res = square;
122 res.noalias() -= s1 * m1 * m2.transpose();
123 VERIFY_IS_APPROX(res, square - ((s1*m1).eval() * m2.transpose()));
124
125 // test d ?= a+b*c rules
126 res.noalias() = square + m1 * m2.transpose();
127 VERIFY_IS_APPROX(res, square + m1 * m2.transpose());
128 res.noalias() += square + m1 * m2.transpose();
129 VERIFY_IS_APPROX(res, 2*(square + m1 * m2.transpose()));
130 res.noalias() -= square + m1 * m2.transpose();
131 VERIFY_IS_APPROX(res, square + m1 * m2.transpose());
132
133 // test d ?= a-b*c rules
134 res.noalias() = square - m1 * m2.transpose();
135 VERIFY_IS_APPROX(res, square - m1 * m2.transpose());
136 res.noalias() += square - m1 * m2.transpose();
137 VERIFY_IS_APPROX(res, 2*(square - m1 * m2.transpose()));
138 res.noalias() -= square - m1 * m2.transpose();
139 VERIFY_IS_APPROX(res, square - m1 * m2.transpose());
140
141
142 tm1 = m1;
143 VERIFY_IS_APPROX(tm1.transpose() * v1, m1.transpose() * v1);
144 VERIFY_IS_APPROX(v1.transpose() * tm1, v1.transpose() * m1);
145
146 // test submatrix and matrix/vector product
147 for (int i=0; i<rows; ++i)
148 res.row(i) = m1.row(i) * m2.transpose();
149 VERIFY_IS_APPROX(res, m1 * m2.transpose());
150 // the other way round:
151 for (int i=0; i<rows; ++i)
152 res.col(i) = m1 * m2.transpose().col(i);
153 VERIFY_IS_APPROX(res, m1 * m2.transpose());
154
155 res2 = square2;
156 res2.noalias() += m1.transpose() * m2;
157 VERIFY_IS_APPROX(res2, square2 + m1.transpose() * m2);
158 if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1)
159 {
160 VERIFY(areNotApprox(res2,square2 + m2.transpose() * m1));
161 }
162
163 VERIFY_IS_APPROX(res.col(r).noalias() = square.adjoint() * square.col(r), (square.adjoint() * square.col(r)).eval());
164 VERIFY_IS_APPROX(res.col(r).noalias() = square * square.col(r), (square * square.col(r)).eval());
165
166 // vector at runtime (see bug 1166)
167 {
168 RowSquareMatrixType ref(square);
169 ColSquareMatrixType ref2(square2);
170 ref = res = square;
171 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()));
172 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()));
173 VERIFY_IS_APPROX(res.block(0,0,1,rows).noalias() = m1.col(0).transpose() * square, (ref.row(0) = m1.col(0).transpose() * square));
174 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));
175 ref2 = res2 = square2;
176 VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.row(0) * square2.transpose(), (ref2.row(0) = m1.row(0) * square2.transpose()));
177 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()));
178 VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.row(0) * square2, (ref2.row(0) = m1.row(0) * square2));
179 VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.block(0,0,1,cols) * square2, (ref2.row(0) = m1.row(0) * square2));
180 }
181
182 // vector.block() (see bug 1283)
183 {
184 RowVectorType w1(rows);
185 VERIFY_IS_APPROX(square * v1.block(0,0,rows,1), square * v1);
186 VERIFY_IS_APPROX(w1.noalias() = square * v1.block(0,0,rows,1), square * v1);
187 VERIFY_IS_APPROX(w1.block(0,0,rows,1).noalias() = square * v1.block(0,0,rows,1), square * v1);
188
189 Matrix<Scalar,1,MatrixType::ColsAtCompileTime> w2(cols);
190 VERIFY_IS_APPROX(vc2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2);
191 VERIFY_IS_APPROX(w2.noalias() = vc2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2);
192 VERIFY_IS_APPROX(w2.block(0,0,1,cols).noalias() = vc2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2);
193
194 vc2 = square2.block(0,0,1,cols).transpose();
195 VERIFY_IS_APPROX(square2.block(0,0,1,cols) * square2, vc2.transpose() * square2);
196 VERIFY_IS_APPROX(w2.noalias() = square2.block(0,0,1,cols) * square2, vc2.transpose() * square2);
197 VERIFY_IS_APPROX(w2.block(0,0,1,cols).noalias() = square2.block(0,0,1,cols) * square2, vc2.transpose() * square2);
198
199 vc2 = square2.block(0,0,cols,1);
200 VERIFY_IS_APPROX(square2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2);
201 VERIFY_IS_APPROX(w2.noalias() = square2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2);
202 VERIFY_IS_APPROX(w2.block(0,0,1,cols).noalias() = square2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2);
203 }
204
205 // inner product
206 {
207 Scalar x = square2.row(c) * square2.col(c2);
208 VERIFY_IS_APPROX(x, square2.row(c).transpose().cwiseProduct(square2.col(c2)).sum());
209 }
210
211 // outer product
212 {
213 VERIFY_IS_APPROX(m1.col(c) * m1.row(r), m1.block(0,c,rows,1) * m1.block(r,0,1,cols));
214 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());
215 VERIFY_IS_APPROX(m1.block(0,c,rows,1) * m1.row(r), m1.block(0,c,rows,1) * m1.block(r,0,1,cols));
216 VERIFY_IS_APPROX(m1.col(c) * m1.block(r,0,1,cols), m1.block(0,c,rows,1) * m1.block(r,0,1,cols));
217 VERIFY_IS_APPROX(m1.leftCols(1) * m1.row(r), m1.block(0,0,rows,1) * m1.block(r,0,1,cols));
218 VERIFY_IS_APPROX(m1.col(c) * m1.topRows(1), m1.block(0,c,rows,1) * m1.block(0,0,1,cols));
219 }
220
221 // Aliasing
222 {
223 ColVectorType x(cols); x.setRandom();
224 ColVectorType z(x);
225 ColVectorType y(cols); y.setZero();
226 ColSquareMatrixType A(cols,cols); A.setRandom();
227 // CwiseBinaryOp
228 VERIFY_IS_APPROX(x = y + A*x, A*z);
229 x = z;
230 VERIFY_IS_APPROX(x = y - A*x, A*(-z));
231 x = z;
232 // CwiseUnaryOp
233 VERIFY_IS_APPROX(x = Scalar(1.)*(A*x), A*z);
234 }
235
236 // regression for blas_trais
237 {
238 VERIFY_IS_APPROX(square * (square*square).transpose(), square * square.transpose() * square.transpose());
239 VERIFY_IS_APPROX(square * (-(square*square)), -square * square * square);
240 VERIFY_IS_APPROX(square * (s1*(square*square)), s1 * square * square * square);
241 VERIFY_IS_APPROX(square * (square*square).conjugate(), square * square.conjugate() * square.conjugate());
242 }
243
244 // destination with a non-default inner-stride
245 // see bug 1741
246 if(!MatrixType::IsRowMajor)
247 {
248 typedef Matrix<Scalar,Dynamic,Dynamic> MatrixX;
249 MatrixX buffer(2*rows,2*rows);
250 Map<RowSquareMatrixType,0,Stride<Dynamic,2> > map1(buffer.data(),rows,rows,Stride<Dynamic,2>(2*rows,2));
251 buffer.setZero();
252 VERIFY_IS_APPROX(map1 = m1 * m2.transpose(), (m1 * m2.transpose()).eval());
253 buffer.setZero();
254 VERIFY_IS_APPROX(map1.noalias() = m1 * m2.transpose(), (m1 * m2.transpose()).eval());
255 buffer.setZero();
256 VERIFY_IS_APPROX(map1.noalias() += m1 * m2.transpose(), (m1 * m2.transpose()).eval());
257 }
258
259}
m
Matrix3f m
Definition AngleAxis_mimic_euler.cpp:1
square
EIGEN_DEVICE_FUNC const SquareReturnType square() const
Definition ArrayCwiseUnaryOps.h:425
i
int i
Definition BiCGSTAB_step_by_step.cpp:9
conjugate
EIGEN_DEVICE_FUNC ConjugateReturnType conjugate() const
Definition CommonCwiseUnaryOps.h:74
m1
Matrix3d m1
Definition IOFormat.cpp:2
cwiseAbs2
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseAbs2ReturnType cwiseAbs2() const
Definition MatrixCwiseUnaryOps.h:46
res
cout<< "Here is the matrix m:"<< endl<< m<< endl;Matrix< ptrdiff_t, 3, 1 > res
Definition PartialRedux_count.cpp:3
m2
MatrixType m2(n_dims)
v1
M1<< 1, 2, 3, 4, 5, 6, 7, 8, 9;Map< RowVectorXf > v1(M1.data(), M1.size())
rows
int rows
Definition Tutorial_commainit_02.cpp:1
cols
int cols
Definition Tutorial_commainit_02.cpp:1
c
Scalar Scalar * c
Definition benchVecAdd.cpp:17
Scalar
SCALAR Scalar
Definition bench_gemm.cpp:46
A
Matrix< SCALARA, Dynamic, Dynamic, opt_A > A
Definition bench_gemm.cpp:48
MatrixType
MatrixXf MatrixType
Definition benchmark-blocking-sizes.cpp:52
Eigen::Map
A matrix or vector expression mapping an existing array of data.
Definition Map.h:96
Eigen::MatrixBase
Base class for all dense matrices, vectors, and expressions.
Definition MatrixBase.h:50
Eigen::Matrix
The matrix class, also used for vectors and row-vectors.
Definition Matrix.h:180
Eigen::PlainObjectBase::setRandom
Derived & setRandom(Index size)
Definition Random.h:151
Eigen::PlainObjectBase::rows
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT
Definition PlainObjectBase.h:143
Eigen::Stride
Holds strides information for Map.
Definition Stride.h:49
VERIFY
#define VERIFY(a)
Definition main.h:380
VERIFY_RAISES_ASSERT
#define VERIFY_RAISES_ASSERT(a)
Definition main.h:340
x
set noclip points set clip one set noclip two set bar set border lt lw set xdata set ydata set zdata set x2data set y2data set boxwidth set dummy x
Definition gnuplot_common_settings.hh:12
Eigen::ColMajor
@ ColMajor
Definition Constants.h:319
Eigen::RowMajor
@ RowMajor
Definition Constants.h:321
Eigen::RowMajorBit
const unsigned int RowMajorBit
Definition Constants.h:66
VERIFY_IS_APPROX
#define VERIFY_IS_APPROX(a, b)
Definition integer_types.cpp:15
y
Scalar * y
Definition level1_cplx_impl.h:124
Eigen::Index
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition Meta.h:74
areNotApprox
bool areNotApprox(const MatrixBase< Derived1 > &m1, const MatrixBase< Derived2 > &m2, typename Derived1::RealScalar epsilon=NumTraits< typename Derived1::RealScalar >::dummy_precision())
Definition product.h:14
product
void product(const MatrixType &m)
Definition product.h:20
eval
internal::nested_eval< T, 1 >::type eval(const T &xpr)
Definition sparse_permutations.cpp:38
Eigen::NumTraits
Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
Definition NumTraits.h:233
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