ground/gcs/src/libs/eigen/test/product_extra.cpp

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