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 
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::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 d ?= a+b*c rules
115  res.noalias() = square + m1 * m2.transpose();
116  VERIFY_IS_APPROX(res, square + m1 * m2.transpose());
117  res.noalias() += square + m1 * m2.transpose();
118  VERIFY_IS_APPROX(res, 2*(square + m1 * m2.transpose()));
119  res.noalias() -= square + m1 * m2.transpose();
120  VERIFY_IS_APPROX(res, square + m1 * m2.transpose());
121 
122  // test d ?= a-b*c rules
123  res.noalias() = square - m1 * m2.transpose();
124  VERIFY_IS_APPROX(res, square - m1 * m2.transpose());
125  res.noalias() += square - m1 * m2.transpose();
126  VERIFY_IS_APPROX(res, 2*(square - m1 * m2.transpose()));
127  res.noalias() -= square - m1 * m2.transpose();
128  VERIFY_IS_APPROX(res, square - m1 * m2.transpose());
129 
130 
131  tm1 = m1;
132  VERIFY_IS_APPROX(tm1.transpose() * v1, m1.transpose() * v1);
133  VERIFY_IS_APPROX(v1.transpose() * tm1, v1.transpose() * m1);
134 
135  // test submatrix and matrix/vector product
136  for (int i=0; i<rows; ++i)
137  res.row(i) = m1.row(i) * m2.transpose();
138  VERIFY_IS_APPROX(res, m1 * m2.transpose());
139  // the other way round:
140  for (int i=0; i<rows; ++i)
141  res.col(i) = m1 * m2.transpose().col(i);
142  VERIFY_IS_APPROX(res, m1 * m2.transpose());
143 
144  res2 = square2;
145  res2.noalias() += m1.transpose() * m2;
146  VERIFY_IS_APPROX(res2, square2 + m1.transpose() * m2);
147  if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1)
148  {
149  VERIFY(areNotApprox(res2,square2 + m2.transpose() * m1));
150  }
151 
152  VERIFY_IS_APPROX(res.col(r).noalias() = square.adjoint() * square.col(r), (square.adjoint() * square.col(r)).eval());
153  VERIFY_IS_APPROX(res.col(r).noalias() = square * square.col(r), (square * square.col(r)).eval());
154 
155  // vector at runtime (see bug 1166)
156  {
157  RowSquareMatrixType ref(square);
158  ColSquareMatrixType ref2(square2);
159  ref = res = square;
160  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()));
161  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()));
162  VERIFY_IS_APPROX(res.block(0,0,1,rows).noalias() = m1.col(0).transpose() * square, (ref.row(0) = m1.col(0).transpose() * square));
163  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));
164  ref2 = res2 = square2;
165  VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.row(0) * square2.transpose(), (ref2.row(0) = m1.row(0) * square2.transpose()));
166  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()));
167  VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.row(0) * square2, (ref2.row(0) = m1.row(0) * square2));
168  VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.block(0,0,1,cols) * square2, (ref2.row(0) = m1.row(0) * square2));
169  }
170 
171  // vector.block() (see bug 1283)
172  {
173  RowVectorType w1(rows);
174  VERIFY_IS_APPROX(square * v1.block(0,0,rows,1), square * v1);
175  VERIFY_IS_APPROX(w1.noalias() = square * v1.block(0,0,rows,1), square * v1);
176  VERIFY_IS_APPROX(w1.block(0,0,rows,1).noalias() = square * v1.block(0,0,rows,1), square * v1);
177 
178  Matrix<Scalar,1,MatrixType::ColsAtCompileTime> w2(cols);
179  VERIFY_IS_APPROX(vc2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2);
180  VERIFY_IS_APPROX(w2.noalias() = vc2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2);
181  VERIFY_IS_APPROX(w2.block(0,0,1,cols).noalias() = vc2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2);
182 
183  vc2 = square2.block(0,0,1,cols).transpose();
184  VERIFY_IS_APPROX(square2.block(0,0,1,cols) * square2, vc2.transpose() * square2);
185  VERIFY_IS_APPROX(w2.noalias() = square2.block(0,0,1,cols) * square2, vc2.transpose() * square2);
186  VERIFY_IS_APPROX(w2.block(0,0,1,cols).noalias() = square2.block(0,0,1,cols) * square2, vc2.transpose() * square2);
187 
188  vc2 = square2.block(0,0,cols,1);
189  VERIFY_IS_APPROX(square2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2);
190  VERIFY_IS_APPROX(w2.noalias() = square2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2);
191  VERIFY_IS_APPROX(w2.block(0,0,1,cols).noalias() = square2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2);
192  }
193 
194  // inner product
195  {
196  Scalar x = square2.row(c) * square2.col(c2);
197  VERIFY_IS_APPROX(x, square2.row(c).transpose().cwiseProduct(square2.col(c2)).sum());
198  }
199 
200  // outer product
201  {
202  VERIFY_IS_APPROX(m1.col(c) * m1.row(r), m1.block(0,c,rows,1) * m1.block(r,0,1,cols));
203  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());
204  VERIFY_IS_APPROX(m1.block(0,c,rows,1) * m1.row(r), m1.block(0,c,rows,1) * m1.block(r,0,1,cols));
205  VERIFY_IS_APPROX(m1.col(c) * m1.block(r,0,1,cols), m1.block(0,c,rows,1) * m1.block(r,0,1,cols));
206  VERIFY_IS_APPROX(m1.leftCols(1) * m1.row(r), m1.block(0,0,rows,1) * m1.block(r,0,1,cols));
207  VERIFY_IS_APPROX(m1.col(c) * m1.topRows(1), m1.block(0,c,rows,1) * m1.block(0,0,1,cols));
208  }
209 
210  // Aliasing
211  {
212  ColVectorType x(cols); x.setRandom();
213  ColVectorType z(x);
214  ColVectorType y(cols); y.setZero();
215  ColSquareMatrixType A(cols,cols); A.setRandom();
216  // CwiseBinaryOp
217  VERIFY_IS_APPROX(x = y + A*x, A*z);
218  x = z;
219  // CwiseUnaryOp
220  VERIFY_IS_APPROX(x = Scalar(1.)*(A*x), A*z);
221  }
222 
223  // regression for blas_trais
224  {
225  VERIFY_IS_APPROX(square * (square*square).transpose(), square * square.transpose() * square.transpose());
226  VERIFY_IS_APPROX(square * (-(square*square)), -square * square * square);
227  VERIFY_IS_APPROX(square * (s1*(square*square)), s1 * square * square * square);
228  VERIFY_IS_APPROX(square * (square*square).conjugate(), square * square.conjugate() * square.conjugate());
229  }
230 
231 }
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