product_extra.cpp
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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 
12 template<typename MatrixType> void product_extra(const MatrixType& m)
13 {
14  typedef typename MatrixType::Scalar Scalar;
15  typedef Matrix<Scalar, 1, Dynamic> RowVectorType;
16  typedef Matrix<Scalar, Dynamic, 1> ColVectorType;
17  typedef Matrix<Scalar, Dynamic, Dynamic,
18  MatrixType::Flags&RowMajorBit> OtherMajorMatrixType;
19 
20  Index rows = m.rows();
21  Index cols = m.cols();
22 
23  MatrixType m1 = MatrixType::Random(rows, cols),
24  m2 = MatrixType::Random(rows, cols),
25  m3(rows, cols),
26  mzero = MatrixType::Zero(rows, cols),
27  identity = MatrixType::Identity(rows, rows),
28  square = MatrixType::Random(rows, rows),
29  res = MatrixType::Random(rows, rows),
30  square2 = MatrixType::Random(cols, cols),
31  res2 = MatrixType::Random(cols, cols);
32  RowVectorType v1 = RowVectorType::Random(rows), vrres(rows);
33  ColVectorType vc2 = ColVectorType::Random(cols), vcres(cols);
34  OtherMajorMatrixType tm1 = m1;
35 
36  Scalar s1 = internal::random<Scalar>(),
37  s2 = internal::random<Scalar>(),
38  s3 = internal::random<Scalar>();
39 
40  VERIFY_IS_APPROX(m3.noalias() = m1 * m2.adjoint(), m1 * m2.adjoint().eval());
41  VERIFY_IS_APPROX(m3.noalias() = m1.adjoint() * square.adjoint(), m1.adjoint().eval() * square.adjoint().eval());
42  VERIFY_IS_APPROX(m3.noalias() = m1.adjoint() * m2, m1.adjoint().eval() * m2);
43  VERIFY_IS_APPROX(m3.noalias() = (s1 * m1.adjoint()) * m2, (s1 * m1.adjoint()).eval() * m2);
44  VERIFY_IS_APPROX(m3.noalias() = ((s1 * m1).adjoint()) * m2, (numext::conj(s1) * m1.adjoint()).eval() * m2);
45  VERIFY_IS_APPROX(m3.noalias() = (- m1.adjoint() * s1) * (s3 * m2), (- m1.adjoint() * s1).eval() * (s3 * m2).eval());
46  VERIFY_IS_APPROX(m3.noalias() = (s2 * m1.adjoint() * s1) * m2, (s2 * m1.adjoint() * s1).eval() * m2);
47  VERIFY_IS_APPROX(m3.noalias() = (-m1*s2) * s1*m2.adjoint(), (-m1*s2).eval() * (s1*m2.adjoint()).eval());
48 
49  // a very tricky case where a scale factor has to be automatically conjugated:
50  VERIFY_IS_APPROX( m1.adjoint() * (s1*m2).conjugate(), (m1.adjoint()).eval() * ((s1*m2).conjugate()).eval());
51 
52 
53  // test all possible conjugate combinations for the four matrix-vector product cases:
54 
55  VERIFY_IS_APPROX((-m1.conjugate() * s2) * (s1 * vc2),
56  (-m1.conjugate()*s2).eval() * (s1 * vc2).eval());
57  VERIFY_IS_APPROX((-m1 * s2) * (s1 * vc2.conjugate()),
58  (-m1*s2).eval() * (s1 * vc2.conjugate()).eval());
59  VERIFY_IS_APPROX((-m1.conjugate() * s2) * (s1 * vc2.conjugate()),
60  (-m1.conjugate()*s2).eval() * (s1 * vc2.conjugate()).eval());
61 
62  VERIFY_IS_APPROX((s1 * vc2.transpose()) * (-m1.adjoint() * s2),
63  (s1 * vc2.transpose()).eval() * (-m1.adjoint()*s2).eval());
64  VERIFY_IS_APPROX((s1 * vc2.adjoint()) * (-m1.transpose() * s2),
65  (s1 * vc2.adjoint()).eval() * (-m1.transpose()*s2).eval());
66  VERIFY_IS_APPROX((s1 * vc2.adjoint()) * (-m1.adjoint() * s2),
67  (s1 * vc2.adjoint()).eval() * (-m1.adjoint()*s2).eval());
68 
69  VERIFY_IS_APPROX((-m1.adjoint() * s2) * (s1 * v1.transpose()),
70  (-m1.adjoint()*s2).eval() * (s1 * v1.transpose()).eval());
71  VERIFY_IS_APPROX((-m1.transpose() * s2) * (s1 * v1.adjoint()),
72  (-m1.transpose()*s2).eval() * (s1 * v1.adjoint()).eval());
73  VERIFY_IS_APPROX((-m1.adjoint() * s2) * (s1 * v1.adjoint()),
74  (-m1.adjoint()*s2).eval() * (s1 * v1.adjoint()).eval());
75 
76  VERIFY_IS_APPROX((s1 * v1) * (-m1.conjugate() * s2),
77  (s1 * v1).eval() * (-m1.conjugate()*s2).eval());
78  VERIFY_IS_APPROX((s1 * v1.conjugate()) * (-m1 * s2),
79  (s1 * v1.conjugate()).eval() * (-m1*s2).eval());
80  VERIFY_IS_APPROX((s1 * v1.conjugate()) * (-m1.conjugate() * s2),
81  (s1 * v1.conjugate()).eval() * (-m1.conjugate()*s2).eval());
82 
83  VERIFY_IS_APPROX((-m1.adjoint() * s2) * (s1 * v1.adjoint()),
84  (-m1.adjoint()*s2).eval() * (s1 * v1.adjoint()).eval());
85 
86  // test the vector-matrix product with non aligned starts
87  Index i = internal::random<Index>(0,m1.rows()-2);
88  Index j = internal::random<Index>(0,m1.cols()-2);
89  Index r = internal::random<Index>(1,m1.rows()-i);
90  Index c = internal::random<Index>(1,m1.cols()-j);
91  Index i2 = internal::random<Index>(0,m1.rows()-1);
92  Index j2 = internal::random<Index>(0,m1.cols()-1);
93 
94  VERIFY_IS_APPROX(m1.col(j2).adjoint() * m1.block(0,j,m1.rows(),c), m1.col(j2).adjoint().eval() * m1.block(0,j,m1.rows(),c).eval());
95  VERIFY_IS_APPROX(m1.block(i,0,r,m1.cols()) * m1.row(i2).adjoint(), m1.block(i,0,r,m1.cols()).eval() * m1.row(i2).adjoint().eval());
96 
97  // test negative strides
98  {
99  Map<MatrixType,Unaligned,Stride<Dynamic,Dynamic> > map1(&m1(rows-1,cols-1), rows, cols, Stride<Dynamic,Dynamic>(-m1.outerStride(),-1));
100  Map<MatrixType,Unaligned,Stride<Dynamic,Dynamic> > map2(&m2(rows-1,cols-1), rows, cols, Stride<Dynamic,Dynamic>(-m2.outerStride(),-1));
101  Map<RowVectorType,Unaligned,InnerStride<-1> > mapv1(&v1(v1.size()-1), v1.size(), InnerStride<-1>(-1));
102  Map<ColVectorType,Unaligned,InnerStride<-1> > mapvc2(&vc2(vc2.size()-1), vc2.size(), InnerStride<-1>(-1));
103  VERIFY_IS_APPROX(MatrixType(map1), m1.reverse());
104  VERIFY_IS_APPROX(MatrixType(map2), m2.reverse());
105  VERIFY_IS_APPROX(m3.noalias() = MatrixType(map1) * MatrixType(map2).adjoint(), m1.reverse() * m2.reverse().adjoint());
106  VERIFY_IS_APPROX(m3.noalias() = map1 * map2.adjoint(), m1.reverse() * m2.reverse().adjoint());
107  VERIFY_IS_APPROX(map1 * vc2, m1.reverse() * vc2);
108  VERIFY_IS_APPROX(m1 * mapvc2, m1 * mapvc2);
109  VERIFY_IS_APPROX(map1.adjoint() * v1.transpose(), m1.adjoint().reverse() * v1.transpose());
110  VERIFY_IS_APPROX(m1.adjoint() * mapv1.transpose(), m1.adjoint() * v1.reverse().transpose());
111  }
112 
113  // regression test
114  MatrixType tmp = m1 * m1.adjoint() * s1;
115  VERIFY_IS_APPROX(tmp, m1 * m1.adjoint() * s1);
116 
117  // regression test for bug 1343, assignment to arrays
118  Array<Scalar,Dynamic,1> a1 = m1 * vc2;
119  VERIFY_IS_APPROX(a1.matrix(),m1*vc2);
120  Array<Scalar,Dynamic,1> a2 = s1 * (m1 * vc2);
121  VERIFY_IS_APPROX(a2.matrix(),s1*m1*vc2);
122  Array<Scalar,1,Dynamic> a3 = v1 * m1;
123  VERIFY_IS_APPROX(a3.matrix(),v1*m1);
124  Array<Scalar,Dynamic,Dynamic> a4 = m1 * m2.adjoint();
125  VERIFY_IS_APPROX(a4.matrix(),m1*m2.adjoint());
126 }
127 
128 // Regression test for bug reported at http://forum.kde.org/viewtopic.php?f=74&t=96947
129 void mat_mat_scalar_scalar_product()
130 {
131  Eigen::Matrix2Xd dNdxy(2, 3);
132  dNdxy << -0.5, 0.5, 0,
133  -0.3, 0, 0.3;
134  double det = 6.0, wt = 0.5;
135  VERIFY_IS_APPROX(dNdxy.transpose()*dNdxy*det*wt, det*wt*dNdxy.transpose()*dNdxy);
136 }
137 
138 template <typename MatrixType>
139 void zero_sized_objects(const MatrixType& m)
140 {
141  typedef typename MatrixType::Scalar Scalar;
142  const int PacketSize = internal::packet_traits<Scalar>::size;
143  const int PacketSize1 = PacketSize>1 ? PacketSize-1 : 1;
144  Index rows = m.rows();
145  Index cols = m.cols();
146 
147  {
148  MatrixType res, a(rows,0), b(0,cols);
149  VERIFY_IS_APPROX( (res=a*b), MatrixType::Zero(rows,cols) );
150  VERIFY_IS_APPROX( (res=a*a.transpose()), MatrixType::Zero(rows,rows) );
151  VERIFY_IS_APPROX( (res=b.transpose()*b), MatrixType::Zero(cols,cols) );
152  VERIFY_IS_APPROX( (res=b.transpose()*a.transpose()), MatrixType::Zero(cols,rows) );
153  }
154 
155  {
156  MatrixType res, a(rows,cols), b(cols,0);
157  res = a*b;
158  VERIFY(res.rows()==rows && res.cols()==0);
159  b.resize(0,rows);
160  res = b*a;
161  VERIFY(res.rows()==0 && res.cols()==cols);
162  }
163 
164  {
165  Matrix<Scalar,PacketSize,0> a;
166  Matrix<Scalar,0,1> b;
167  Matrix<Scalar,PacketSize,1> res;
168  VERIFY_IS_APPROX( (res=a*b), MatrixType::Zero(PacketSize,1) );
169  VERIFY_IS_APPROX( (res=a.lazyProduct(b)), MatrixType::Zero(PacketSize,1) );
170  }
171 
172  {
173  Matrix<Scalar,PacketSize1,0> a;
174  Matrix<Scalar,0,1> b;
175  Matrix<Scalar,PacketSize1,1> res;
176  VERIFY_IS_APPROX( (res=a*b), MatrixType::Zero(PacketSize1,1) );
177  VERIFY_IS_APPROX( (res=a.lazyProduct(b)), MatrixType::Zero(PacketSize1,1) );
178  }
179 
180  {
181  Matrix<Scalar,PacketSize,Dynamic> a(PacketSize,0);
182  Matrix<Scalar,Dynamic,1> b(0,1);
183  Matrix<Scalar,PacketSize,1> res;
184  VERIFY_IS_APPROX( (res=a*b), MatrixType::Zero(PacketSize,1) );
185  VERIFY_IS_APPROX( (res=a.lazyProduct(b)), MatrixType::Zero(PacketSize,1) );
186  }
187 
188  {
189  Matrix<Scalar,PacketSize1,Dynamic> a(PacketSize1,0);
190  Matrix<Scalar,Dynamic,1> b(0,1);
191  Matrix<Scalar,PacketSize1,1> res;
192  VERIFY_IS_APPROX( (res=a*b), MatrixType::Zero(PacketSize1,1) );
193  VERIFY_IS_APPROX( (res=a.lazyProduct(b)), MatrixType::Zero(PacketSize1,1) );
194  }
195 }
196 
197 template<int>
198 void bug_127()
199 {
200  // Bug 127
201  //
202  // a product of the form lhs*rhs with
203  //
204  // lhs:
205  // rows = 1, cols = 4
206  // RowsAtCompileTime = 1, ColsAtCompileTime = -1
207  // MaxRowsAtCompileTime = 1, MaxColsAtCompileTime = 5
208  //
209  // rhs:
210  // rows = 4, cols = 0
211  // RowsAtCompileTime = -1, ColsAtCompileTime = -1
212  // MaxRowsAtCompileTime = 5, MaxColsAtCompileTime = 1
213  //
214  // was failing on a runtime assertion, because it had been mis-compiled as a dot product because Product.h was using the
215  // max-sizes to detect size 1 indicating vectors, and that didn't account for 0-sized object with max-size 1.
216 
217  Matrix<float,1,Dynamic,RowMajor,1,5> a(1,4);
218  Matrix<float,Dynamic,Dynamic,ColMajor,5,1> b(4,0);
219  a*b;
220 }
221 
222 template<int> void bug_817()
223 {
224  ArrayXXf B = ArrayXXf::Random(10,10), C;
225  VectorXf x = VectorXf::Random(10);
226  C = (x.transpose()*B.matrix());
227  B = (x.transpose()*B.matrix());
228  VERIFY_IS_APPROX(B,C);
229 }
230 
231 template<int>
232 void unaligned_objects()
233 {
234  // Regression test for the bug reported here:
235  // http://forum.kde.org/viewtopic.php?f=74&t=107541
236  // Recall the matrix*vector kernel avoid unaligned loads by loading two packets and then reassemble then.
237  // There was a mistake in the computation of the valid range for fully unaligned objects: in some rare cases,
238  // memory was read outside the allocated matrix memory. Though the values were not used, this might raise segfault.
239  for(int m=450;m<460;++m)
240  {
241  for(int n=8;n<12;++n)
242  {
243  MatrixXf M(m, n);
244  VectorXf v1(n), r1(500);
245  RowVectorXf v2(m), r2(16);
246 
247  M.setRandom();
248  v1.setRandom();
249  v2.setRandom();
250  for(int o=0; o<4; ++o)
251  {
252  r1.segment(o,m).noalias() = M * v1;
253  VERIFY_IS_APPROX(r1.segment(o,m), M * MatrixXf(v1));
254  r2.segment(o,n).noalias() = v2 * M;
255  VERIFY_IS_APPROX(r2.segment(o,n), MatrixXf(v2) * M);
256  }
257  }
258  }
259 }
260 
261 template<typename T>
262 EIGEN_DONT_INLINE
263 Index test_compute_block_size(Index m, Index n, Index k)
264 {
265  Index mc(m), nc(n), kc(k);
266  internal::computeProductBlockingSizes<T,T>(kc, mc, nc);
267  return kc+mc+nc;
268 }
269 
270 template<typename T>
271 Index compute_block_size()
272 {
273  Index ret = 0;
274  ret += test_compute_block_size<T>(0,1,1);
275  ret += test_compute_block_size<T>(1,0,1);
276  ret += test_compute_block_size<T>(1,1,0);
277  ret += test_compute_block_size<T>(0,0,1);
278  ret += test_compute_block_size<T>(0,1,0);
279  ret += test_compute_block_size<T>(1,0,0);
280  ret += test_compute_block_size<T>(0,0,0);
281  return ret;
282 }
283 
284 template<typename>
285 void aliasing_with_resize()
286 {
287  Index m = internal::random<Index>(10,50);
288  Index n = internal::random<Index>(10,50);
289  MatrixXd A, B, C(m,n), D(m,m);
290  VectorXd a, b, c(n);
291  C.setRandom();
292  D.setRandom();
293  c.setRandom();
294  double s = internal::random<double>(1,10);
295 
296  A = C;
297  B = A * A.transpose();
298  A = A * A.transpose();
299  VERIFY_IS_APPROX(A,B);
300 
301  A = C;
302  B = (A * A.transpose())/s;
303  A = (A * A.transpose())/s;
304  VERIFY_IS_APPROX(A,B);
305 
306  A = C;
307  B = (A * A.transpose()) + D;
308  A = (A * A.transpose()) + D;
309  VERIFY_IS_APPROX(A,B);
310 
311  A = C;
312  B = D + (A * A.transpose());
313  A = D + (A * A.transpose());
314  VERIFY_IS_APPROX(A,B);
315 
316  A = C;
317  B = s * (A * A.transpose());
318  A = s * (A * A.transpose());
319  VERIFY_IS_APPROX(A,B);
320 
321  A = C;
322  a = c;
323  b = (A * a)/s;
324  a = (A * a)/s;
325  VERIFY_IS_APPROX(a,b);
326 }
327 
328 template<int>
329 void bug_1308()
330 {
331  int n = 10;
332  MatrixXd r(n,n);
333  VectorXd v = VectorXd::Random(n);
334  r = v * RowVectorXd::Ones(n);
335  VERIFY_IS_APPROX(r, v.rowwise().replicate(n));
336  r = VectorXd::Ones(n) * v.transpose();
337  VERIFY_IS_APPROX(r, v.rowwise().replicate(n).transpose());
338 
339  Matrix4d ones44 = Matrix4d::Ones();
340  Matrix4d m44 = Matrix4d::Ones() * Matrix4d::Ones();
341  VERIFY_IS_APPROX(m44,Matrix4d::Constant(4));
342  VERIFY_IS_APPROX(m44.noalias()=ones44*Matrix4d::Ones(), Matrix4d::Constant(4));
343  VERIFY_IS_APPROX(m44.noalias()=ones44.transpose()*Matrix4d::Ones(), Matrix4d::Constant(4));
344  VERIFY_IS_APPROX(m44.noalias()=Matrix4d::Ones()*ones44, Matrix4d::Constant(4));
345  VERIFY_IS_APPROX(m44.noalias()=Matrix4d::Ones()*ones44.transpose(), Matrix4d::Constant(4));
346 
347  typedef Matrix<double,4,4,RowMajor> RMatrix4d;
348  RMatrix4d r44 = Matrix4d::Ones() * Matrix4d::Ones();
349  VERIFY_IS_APPROX(r44,Matrix4d::Constant(4));
350  VERIFY_IS_APPROX(r44.noalias()=ones44*Matrix4d::Ones(), Matrix4d::Constant(4));
351  VERIFY_IS_APPROX(r44.noalias()=ones44.transpose()*Matrix4d::Ones(), Matrix4d::Constant(4));
352  VERIFY_IS_APPROX(r44.noalias()=Matrix4d::Ones()*ones44, Matrix4d::Constant(4));
353  VERIFY_IS_APPROX(r44.noalias()=Matrix4d::Ones()*ones44.transpose(), Matrix4d::Constant(4));
354  VERIFY_IS_APPROX(r44.noalias()=ones44*RMatrix4d::Ones(), Matrix4d::Constant(4));
355  VERIFY_IS_APPROX(r44.noalias()=ones44.transpose()*RMatrix4d::Ones(), Matrix4d::Constant(4));
356  VERIFY_IS_APPROX(r44.noalias()=RMatrix4d::Ones()*ones44, Matrix4d::Constant(4));
357  VERIFY_IS_APPROX(r44.noalias()=RMatrix4d::Ones()*ones44.transpose(), Matrix4d::Constant(4));
358 
359 // RowVector4d r4;
360  m44.setOnes();
361  r44.setZero();
362  VERIFY_IS_APPROX(r44.noalias() += m44.row(0).transpose() * RowVector4d::Ones(), ones44);
363  r44.setZero();
364  VERIFY_IS_APPROX(r44.noalias() += m44.col(0) * RowVector4d::Ones(), ones44);
365  r44.setZero();
366  VERIFY_IS_APPROX(r44.noalias() += Vector4d::Ones() * m44.row(0), ones44);
367  r44.setZero();
368  VERIFY_IS_APPROX(r44.noalias() += Vector4d::Ones() * m44.col(0).transpose(), ones44);
369 }
370 
371 EIGEN_DECLARE_TEST(product_extra)
372 {
373  for(int i = 0; i < g_repeat; i++) {
374  CALL_SUBTEST_1( product_extra(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
375  CALL_SUBTEST_2( product_extra(MatrixXd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
376  CALL_SUBTEST_2( mat_mat_scalar_scalar_product() );
377  CALL_SUBTEST_3( product_extra(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2), internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))) );
378  CALL_SUBTEST_4( product_extra(MatrixXcd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2), internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))) );
379  CALL_SUBTEST_1( zero_sized_objects(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
380  }
381  CALL_SUBTEST_5( bug_127<0>() );
382  CALL_SUBTEST_5( bug_817<0>() );
383  CALL_SUBTEST_5( bug_1308<0>() );
384  CALL_SUBTEST_6( unaligned_objects<0>() );
385  CALL_SUBTEST_7( compute_block_size<float>() );
386  CALL_SUBTEST_7( compute_block_size<double>() );
387  CALL_SUBTEST_7( compute_block_size<std::complex<double> >() );
388  CALL_SUBTEST_8( aliasing_with_resize<void>() );
389 
390 }
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Definition: product_extra.cpp:12
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autogenerated on Fri Nov 1 2024 03:34:32