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 
product(const MatrixType & m)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 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     // CwiseUnaryOp
231     VERIFY_IS_APPROX(x = Scalar(1.)*(A*x), A*z);
232   }
233 
234   // regression for blas_trais
235   {
236     VERIFY_IS_APPROX(square * (square*square).transpose(), square * square.transpose() * square.transpose());
237     VERIFY_IS_APPROX(square * (-(square*square)), -square * square * square);
238     VERIFY_IS_APPROX(square * (s1*(square*square)), s1 * square * square * square);
239     VERIFY_IS_APPROX(square * (square*square).conjugate(), square * square.conjugate() * square.conjugate());
240   }
241 
242   // destination with a non-default inner-stride
243   // see bug 1741
244   if(!MatrixType::IsRowMajor)
245   {
246     typedef Matrix<Scalar,Dynamic,Dynamic> MatrixX;
247     MatrixX buffer(2*rows,2*rows);
248     Map<RowSquareMatrixType,0,Stride<Dynamic,2> > map1(buffer.data(),rows,rows,Stride<Dynamic,2>(2*rows,2));
249     buffer.setZero();
250     VERIFY_IS_APPROX(map1 = m1 * m2.transpose(), (m1 * m2.transpose()).eval());
251     buffer.setZero();
252     VERIFY_IS_APPROX(map1.noalias() = m1 * m2.transpose(), (m1 * m2.transpose()).eval());
253     buffer.setZero();
254     VERIFY_IS_APPROX(map1.noalias() += m1 * m2.transpose(), (m1 * m2.transpose()).eval());
255   }
256 
257 }
258