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      1 // This file is part of Eigen, a lightweight C++ template library
      2 // for linear algebra.
      3 //
      4 // Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud (at) inria.fr>
      5 // Copyright (C) 2008 Benoit Jacob <jacob.benoit.1 (at) gmail.com>
      6 //
      7 // This Source Code Form is subject to the terms of the Mozilla
      8 // Public License v. 2.0. If a copy of the MPL was not distributed
      9 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
     10 
     11 // work around "uninitialized" warnings and give that option some testing
     12 #define EIGEN_INITIALIZE_MATRICES_BY_ZERO
     13 
     14 #ifndef EIGEN_NO_STATIC_ASSERT
     15 #define EIGEN_NO_STATIC_ASSERT // turn static asserts into runtime asserts in order to check them
     16 #endif
     17 
     18 #if defined(EIGEN_TEST_PART_1) || defined(EIGEN_TEST_PART_2) || defined(EIGEN_TEST_PART_3)
     19 
     20 #ifndef EIGEN_DONT_VECTORIZE
     21 #define EIGEN_DONT_VECTORIZE
     22 #endif
     23 
     24 #endif
     25 
     26 static bool g_called;
     27 #define EIGEN_SCALAR_BINARY_OP_PLUGIN { g_called |= (!internal::is_same<LhsScalar,RhsScalar>::value); }
     28 
     29 #include "main.h"
     30 
     31 using namespace std;
     32 
     33 #define VERIFY_MIX_SCALAR(XPR,REF) \
     34   g_called = false; \
     35   VERIFY_IS_APPROX(XPR,REF); \
     36   VERIFY( g_called && #XPR" not properly optimized");
     37 
     38 template<int SizeAtCompileType> void mixingtypes(int size = SizeAtCompileType)
     39 {
     40   typedef std::complex<float>   CF;
     41   typedef std::complex<double>  CD;
     42   typedef Matrix<float, SizeAtCompileType, SizeAtCompileType> Mat_f;
     43   typedef Matrix<double, SizeAtCompileType, SizeAtCompileType> Mat_d;
     44   typedef Matrix<std::complex<float>, SizeAtCompileType, SizeAtCompileType> Mat_cf;
     45   typedef Matrix<std::complex<double>, SizeAtCompileType, SizeAtCompileType> Mat_cd;
     46   typedef Matrix<float, SizeAtCompileType, 1> Vec_f;
     47   typedef Matrix<double, SizeAtCompileType, 1> Vec_d;
     48   typedef Matrix<std::complex<float>, SizeAtCompileType, 1> Vec_cf;
     49   typedef Matrix<std::complex<double>, SizeAtCompileType, 1> Vec_cd;
     50 
     51   Mat_f mf    = Mat_f::Random(size,size);
     52   Mat_d md    = mf.template cast<double>();
     53   //Mat_d rd    = md;
     54   Mat_cf mcf  = Mat_cf::Random(size,size);
     55   Mat_cd mcd  = mcf.template cast<complex<double> >();
     56   Mat_cd rcd = mcd;
     57   Vec_f vf    = Vec_f::Random(size,1);
     58   Vec_d vd    = vf.template cast<double>();
     59   Vec_cf vcf  = Vec_cf::Random(size,1);
     60   Vec_cd vcd  = vcf.template cast<complex<double> >();
     61   float           sf  = internal::random<float>();
     62   double          sd  = internal::random<double>();
     63   complex<float>  scf = internal::random<complex<float> >();
     64   complex<double> scd = internal::random<complex<double> >();
     65 
     66   mf+mf;
     67 
     68   float  epsf = std::sqrt(std::numeric_limits<float> ::min EIGEN_EMPTY ());
     69   double epsd = std::sqrt(std::numeric_limits<double>::min EIGEN_EMPTY ());
     70 
     71   while(std::abs(sf )<epsf) sf  = internal::random<float>();
     72   while(std::abs(sd )<epsd) sf  = internal::random<double>();
     73   while(std::abs(scf)<epsf) scf = internal::random<CF>();
     74   while(std::abs(scd)<epsd) scd = internal::random<CD>();
     75 
     76 //   VERIFY_RAISES_ASSERT(mf+md); // does not even compile
     77 
     78 #ifdef EIGEN_DONT_VECTORIZE
     79   VERIFY_RAISES_ASSERT(vf=vd);
     80   VERIFY_RAISES_ASSERT(vf+=vd);
     81 #endif
     82 
     83   // check scalar products
     84   VERIFY_MIX_SCALAR(vcf * sf , vcf * complex<float>(sf));
     85   VERIFY_MIX_SCALAR(sd * vcd , complex<double>(sd) * vcd);
     86   VERIFY_MIX_SCALAR(vf * scf , vf.template cast<complex<float> >() * scf);
     87   VERIFY_MIX_SCALAR(scd * vd , scd * vd.template cast<complex<double> >());
     88 
     89   VERIFY_MIX_SCALAR(vcf * 2 , vcf * complex<float>(2));
     90   VERIFY_MIX_SCALAR(vcf * 2.1 , vcf * complex<float>(2.1));
     91   VERIFY_MIX_SCALAR(2 * vcf, vcf * complex<float>(2));
     92   VERIFY_MIX_SCALAR(2.1 * vcf , vcf * complex<float>(2.1));
     93 
     94   // check scalar quotients
     95   VERIFY_MIX_SCALAR(vcf / sf , vcf / complex<float>(sf));
     96   VERIFY_MIX_SCALAR(vf / scf , vf.template cast<complex<float> >() / scf);
     97   VERIFY_MIX_SCALAR(vf.array()  / scf, vf.template cast<complex<float> >().array() / scf);
     98   VERIFY_MIX_SCALAR(scd / vd.array() , scd / vd.template cast<complex<double> >().array());
     99 
    100   // check scalar increment
    101   VERIFY_MIX_SCALAR(vcf.array() + sf , vcf.array() + complex<float>(sf));
    102   VERIFY_MIX_SCALAR(sd  + vcd.array(), complex<double>(sd) + vcd.array());
    103   VERIFY_MIX_SCALAR(vf.array()  + scf, vf.template cast<complex<float> >().array() + scf);
    104   VERIFY_MIX_SCALAR(scd + vd.array() , scd + vd.template cast<complex<double> >().array());
    105 
    106   // check scalar subtractions
    107   VERIFY_MIX_SCALAR(vcf.array() - sf , vcf.array() - complex<float>(sf));
    108   VERIFY_MIX_SCALAR(sd  - vcd.array(), complex<double>(sd) - vcd.array());
    109   VERIFY_MIX_SCALAR(vf.array()  - scf, vf.template cast<complex<float> >().array() - scf);
    110   VERIFY_MIX_SCALAR(scd - vd.array() , scd - vd.template cast<complex<double> >().array());
    111 
    112   // check scalar powers
    113   VERIFY_MIX_SCALAR( pow(vcf.array(), sf),        Eigen::pow(vcf.array(), complex<float>(sf)) );
    114   VERIFY_MIX_SCALAR( vcf.array().pow(sf) ,        Eigen::pow(vcf.array(), complex<float>(sf)) );
    115   VERIFY_MIX_SCALAR( pow(sd, vcd.array()),        Eigen::pow(complex<double>(sd), vcd.array()) );
    116   VERIFY_MIX_SCALAR( Eigen::pow(vf.array(), scf), Eigen::pow(vf.template cast<complex<float> >().array(), scf) );
    117   VERIFY_MIX_SCALAR( vf.array().pow(scf) ,        Eigen::pow(vf.template cast<complex<float> >().array(), scf) );
    118   VERIFY_MIX_SCALAR( Eigen::pow(scd, vd.array()), Eigen::pow(scd, vd.template cast<complex<double> >().array()) );
    119 
    120   // check dot product
    121   vf.dot(vf);
    122 #if 0 // we get other compilation errors here than just static asserts
    123   VERIFY_RAISES_ASSERT(vd.dot(vf));
    124 #endif
    125   VERIFY_IS_APPROX(vcf.dot(vf), vcf.dot(vf.template cast<complex<float> >()));
    126 
    127   // check diagonal product
    128   VERIFY_IS_APPROX(vf.asDiagonal() * mcf, vf.template cast<complex<float> >().asDiagonal() * mcf);
    129   VERIFY_IS_APPROX(vcd.asDiagonal() * md, vcd.asDiagonal() * md.template cast<complex<double> >());
    130   VERIFY_IS_APPROX(mcf * vf.asDiagonal(), mcf * vf.template cast<complex<float> >().asDiagonal());
    131   VERIFY_IS_APPROX(md * vcd.asDiagonal(), md.template cast<complex<double> >() * vcd.asDiagonal());
    132 
    133 //   vd.asDiagonal() * mf;    // does not even compile
    134 //   vcd.asDiagonal() * mf;   // does not even compile
    135 
    136   // check inner product
    137   VERIFY_IS_APPROX((vf.transpose() * vcf).value(), (vf.template cast<complex<float> >().transpose() * vcf).value());
    138 
    139   // check outer product
    140   VERIFY_IS_APPROX((vf * vcf.transpose()).eval(), (vf.template cast<complex<float> >() * vcf.transpose()).eval());
    141 
    142   // coeff wise product
    143 
    144   VERIFY_IS_APPROX((vf * vcf.transpose()).eval(), (vf.template cast<complex<float> >() * vcf.transpose()).eval());
    145 
    146   Mat_cd mcd2 = mcd;
    147   VERIFY_IS_APPROX(mcd.array() *= md.array(), mcd2.array() *= md.array().template cast<std::complex<double> >());
    148 
    149   // check matrix-matrix products
    150   VERIFY_IS_APPROX(sd*md*mcd, (sd*md).template cast<CD>().eval()*mcd);
    151   VERIFY_IS_APPROX(sd*mcd*md, sd*mcd*md.template cast<CD>());
    152   VERIFY_IS_APPROX(scd*md*mcd, scd*md.template cast<CD>().eval()*mcd);
    153   VERIFY_IS_APPROX(scd*mcd*md, scd*mcd*md.template cast<CD>());
    154 
    155   VERIFY_IS_APPROX(sf*mf*mcf, sf*mf.template cast<CF>()*mcf);
    156   VERIFY_IS_APPROX(sf*mcf*mf, sf*mcf*mf.template cast<CF>());
    157   VERIFY_IS_APPROX(scf*mf*mcf, scf*mf.template cast<CF>()*mcf);
    158   VERIFY_IS_APPROX(scf*mcf*mf, scf*mcf*mf.template cast<CF>());
    159 
    160   VERIFY_IS_APPROX(sd*md.adjoint()*mcd, (sd*md).template cast<CD>().eval().adjoint()*mcd);
    161   VERIFY_IS_APPROX(sd*mcd.adjoint()*md, sd*mcd.adjoint()*md.template cast<CD>());
    162   VERIFY_IS_APPROX(sd*md.adjoint()*mcd.adjoint(), (sd*md).template cast<CD>().eval().adjoint()*mcd.adjoint());
    163   VERIFY_IS_APPROX(sd*mcd.adjoint()*md.adjoint(), sd*mcd.adjoint()*md.template cast<CD>().adjoint());
    164   VERIFY_IS_APPROX(sd*md*mcd.adjoint(), (sd*md).template cast<CD>().eval()*mcd.adjoint());
    165   VERIFY_IS_APPROX(sd*mcd*md.adjoint(), sd*mcd*md.template cast<CD>().adjoint());
    166 
    167   VERIFY_IS_APPROX(sf*mf.adjoint()*mcf, (sf*mf).template cast<CF>().eval().adjoint()*mcf);
    168   VERIFY_IS_APPROX(sf*mcf.adjoint()*mf, sf*mcf.adjoint()*mf.template cast<CF>());
    169   VERIFY_IS_APPROX(sf*mf.adjoint()*mcf.adjoint(), (sf*mf).template cast<CF>().eval().adjoint()*mcf.adjoint());
    170   VERIFY_IS_APPROX(sf*mcf.adjoint()*mf.adjoint(), sf*mcf.adjoint()*mf.template cast<CF>().adjoint());
    171   VERIFY_IS_APPROX(sf*mf*mcf.adjoint(), (sf*mf).template cast<CF>().eval()*mcf.adjoint());
    172   VERIFY_IS_APPROX(sf*mcf*mf.adjoint(), sf*mcf*mf.template cast<CF>().adjoint());
    173 
    174   VERIFY_IS_APPROX(sf*mf*vcf, (sf*mf).template cast<CF>().eval()*vcf);
    175   VERIFY_IS_APPROX(scf*mf*vcf,(scf*mf.template cast<CF>()).eval()*vcf);
    176   VERIFY_IS_APPROX(sf*mcf*vf, sf*mcf*vf.template cast<CF>());
    177   VERIFY_IS_APPROX(scf*mcf*vf,scf*mcf*vf.template cast<CF>());
    178 
    179   VERIFY_IS_APPROX(sf*vcf.adjoint()*mf,  sf*vcf.adjoint()*mf.template cast<CF>().eval());
    180   VERIFY_IS_APPROX(scf*vcf.adjoint()*mf, scf*vcf.adjoint()*mf.template cast<CF>().eval());
    181   VERIFY_IS_APPROX(sf*vf.adjoint()*mcf,  sf*vf.adjoint().template cast<CF>().eval()*mcf);
    182   VERIFY_IS_APPROX(scf*vf.adjoint()*mcf, scf*vf.adjoint().template cast<CF>().eval()*mcf);
    183 
    184   VERIFY_IS_APPROX(sd*md*vcd, (sd*md).template cast<CD>().eval()*vcd);
    185   VERIFY_IS_APPROX(scd*md*vcd,(scd*md.template cast<CD>()).eval()*vcd);
    186   VERIFY_IS_APPROX(sd*mcd*vd, sd*mcd*vd.template cast<CD>().eval());
    187   VERIFY_IS_APPROX(scd*mcd*vd,scd*mcd*vd.template cast<CD>().eval());
    188 
    189   VERIFY_IS_APPROX(sd*vcd.adjoint()*md,  sd*vcd.adjoint()*md.template cast<CD>().eval());
    190   VERIFY_IS_APPROX(scd*vcd.adjoint()*md, scd*vcd.adjoint()*md.template cast<CD>().eval());
    191   VERIFY_IS_APPROX(sd*vd.adjoint()*mcd,  sd*vd.adjoint().template cast<CD>().eval()*mcd);
    192   VERIFY_IS_APPROX(scd*vd.adjoint()*mcd, scd*vd.adjoint().template cast<CD>().eval()*mcd);
    193 
    194   VERIFY_IS_APPROX( sd*vcd.adjoint()*md.template triangularView<Upper>(),  sd*vcd.adjoint()*md.template cast<CD>().eval().template triangularView<Upper>());
    195   VERIFY_IS_APPROX(scd*vcd.adjoint()*md.template triangularView<Lower>(), scd*vcd.adjoint()*md.template cast<CD>().eval().template triangularView<Lower>());
    196   VERIFY_IS_APPROX( sd*vcd.adjoint()*md.transpose().template triangularView<Upper>(),  sd*vcd.adjoint()*md.transpose().template cast<CD>().eval().template triangularView<Upper>());
    197   VERIFY_IS_APPROX(scd*vcd.adjoint()*md.transpose().template triangularView<Lower>(), scd*vcd.adjoint()*md.transpose().template cast<CD>().eval().template triangularView<Lower>());
    198   VERIFY_IS_APPROX( sd*vd.adjoint()*mcd.template triangularView<Lower>(),  sd*vd.adjoint().template cast<CD>().eval()*mcd.template triangularView<Lower>());
    199   VERIFY_IS_APPROX(scd*vd.adjoint()*mcd.template triangularView<Upper>(), scd*vd.adjoint().template cast<CD>().eval()*mcd.template triangularView<Upper>());
    200   VERIFY_IS_APPROX( sd*vd.adjoint()*mcd.transpose().template triangularView<Lower>(),  sd*vd.adjoint().template cast<CD>().eval()*mcd.transpose().template triangularView<Lower>());
    201   VERIFY_IS_APPROX(scd*vd.adjoint()*mcd.transpose().template triangularView<Upper>(), scd*vd.adjoint().template cast<CD>().eval()*mcd.transpose().template triangularView<Upper>());
    202 
    203   // Not supported yet: trmm
    204 //   VERIFY_IS_APPROX(sd*mcd*md.template triangularView<Lower>(),  sd*mcd*md.template cast<CD>().eval().template triangularView<Lower>());
    205 //   VERIFY_IS_APPROX(scd*mcd*md.template triangularView<Upper>(), scd*mcd*md.template cast<CD>().eval().template triangularView<Upper>());
    206 //   VERIFY_IS_APPROX(sd*md*mcd.template triangularView<Lower>(),  sd*md.template cast<CD>().eval()*mcd.template triangularView<Lower>());
    207 //   VERIFY_IS_APPROX(scd*md*mcd.template triangularView<Upper>(), scd*md.template cast<CD>().eval()*mcd.template triangularView<Upper>());
    208 
    209   // Not supported yet: symv
    210 //   VERIFY_IS_APPROX(sd*vcd.adjoint()*md.template selfadjointView<Upper>(),  sd*vcd.adjoint()*md.template cast<CD>().eval().template selfadjointView<Upper>());
    211 //   VERIFY_IS_APPROX(scd*vcd.adjoint()*md.template selfadjointView<Lower>(), scd*vcd.adjoint()*md.template cast<CD>().eval().template selfadjointView<Lower>());
    212 //   VERIFY_IS_APPROX(sd*vd.adjoint()*mcd.template selfadjointView<Lower>(),  sd*vd.adjoint().template cast<CD>().eval()*mcd.template selfadjointView<Lower>());
    213 //   VERIFY_IS_APPROX(scd*vd.adjoint()*mcd.template selfadjointView<Upper>(), scd*vd.adjoint().template cast<CD>().eval()*mcd.template selfadjointView<Upper>());
    214 
    215   // Not supported yet: symm
    216 //   VERIFY_IS_APPROX(sd*vcd.adjoint()*md.template selfadjointView<Upper>(),  sd*vcd.adjoint()*md.template cast<CD>().eval().template selfadjointView<Upper>());
    217 //   VERIFY_IS_APPROX(scd*vcd.adjoint()*md.template selfadjointView<Upper>(), scd*vcd.adjoint()*md.template cast<CD>().eval().template selfadjointView<Upper>());
    218 //   VERIFY_IS_APPROX(sd*vd.adjoint()*mcd.template selfadjointView<Upper>(),  sd*vd.adjoint().template cast<CD>().eval()*mcd.template selfadjointView<Upper>());
    219 //   VERIFY_IS_APPROX(scd*vd.adjoint()*mcd.template selfadjointView<Upper>(), scd*vd.adjoint().template cast<CD>().eval()*mcd.template selfadjointView<Upper>());
    220 
    221   rcd.setZero();
    222   VERIFY_IS_APPROX(Mat_cd(rcd.template triangularView<Upper>() = sd * mcd * md),
    223                    Mat_cd((sd * mcd * md.template cast<CD>().eval()).template triangularView<Upper>()));
    224   VERIFY_IS_APPROX(Mat_cd(rcd.template triangularView<Upper>() = sd * md * mcd),
    225                    Mat_cd((sd * md.template cast<CD>().eval() * mcd).template triangularView<Upper>()));
    226   VERIFY_IS_APPROX(Mat_cd(rcd.template triangularView<Upper>() = scd * mcd * md),
    227                    Mat_cd((scd * mcd * md.template cast<CD>().eval()).template triangularView<Upper>()));
    228   VERIFY_IS_APPROX(Mat_cd(rcd.template triangularView<Upper>() = scd * md * mcd),
    229                    Mat_cd((scd * md.template cast<CD>().eval() * mcd).template triangularView<Upper>()));
    230 
    231 
    232   VERIFY_IS_APPROX( md.array()  * mcd.array(), md.template cast<CD>().eval().array() * mcd.array() );
    233   VERIFY_IS_APPROX( mcd.array() * md.array(),  mcd.array() * md.template cast<CD>().eval().array() );
    234 
    235   VERIFY_IS_APPROX( md.array()  + mcd.array(), md.template cast<CD>().eval().array() + mcd.array() );
    236   VERIFY_IS_APPROX( mcd.array() + md.array(),  mcd.array() + md.template cast<CD>().eval().array() );
    237 
    238   VERIFY_IS_APPROX( md.array()  - mcd.array(), md.template cast<CD>().eval().array() - mcd.array() );
    239   VERIFY_IS_APPROX( mcd.array() - md.array(),  mcd.array() - md.template cast<CD>().eval().array() );
    240 
    241   if(mcd.array().abs().minCoeff()>epsd)
    242   {
    243     VERIFY_IS_APPROX( md.array() / mcd.array(), md.template cast<CD>().eval().array() / mcd.array() );
    244   }
    245   if(md.array().abs().minCoeff()>epsd)
    246   {
    247     VERIFY_IS_APPROX( mcd.array() / md.array(), mcd.array() / md.template cast<CD>().eval().array() );
    248   }
    249 
    250   if(md.array().abs().minCoeff()>epsd || mcd.array().abs().minCoeff()>epsd)
    251   {
    252     VERIFY_IS_APPROX( md.array().pow(mcd.array()), md.template cast<CD>().eval().array().pow(mcd.array()) );
    253     VERIFY_IS_APPROX( mcd.array().pow(md.array()),  mcd.array().pow(md.template cast<CD>().eval().array()) );
    254 
    255     VERIFY_IS_APPROX( pow(md.array(),mcd.array()), md.template cast<CD>().eval().array().pow(mcd.array()) );
    256     VERIFY_IS_APPROX( pow(mcd.array(),md.array()),  mcd.array().pow(md.template cast<CD>().eval().array()) );
    257   }
    258 
    259   rcd = mcd;
    260   VERIFY_IS_APPROX( rcd = md, md.template cast<CD>().eval() );
    261   rcd = mcd;
    262   VERIFY_IS_APPROX( rcd += md, mcd + md.template cast<CD>().eval() );
    263   rcd = mcd;
    264   VERIFY_IS_APPROX( rcd -= md, mcd - md.template cast<CD>().eval() );
    265   rcd = mcd;
    266   VERIFY_IS_APPROX( rcd.array() *= md.array(), mcd.array() * md.template cast<CD>().eval().array() );
    267   rcd = mcd;
    268   if(md.array().abs().minCoeff()>epsd)
    269   {
    270     VERIFY_IS_APPROX( rcd.array() /= md.array(), mcd.array() / md.template cast<CD>().eval().array() );
    271   }
    272 
    273   rcd = mcd;
    274   VERIFY_IS_APPROX( rcd.noalias() += md + mcd*md, mcd + (md.template cast<CD>().eval()) + mcd*(md.template cast<CD>().eval()));
    275 
    276   VERIFY_IS_APPROX( rcd.noalias()  = md*md,       ((md*md).eval().template cast<CD>()) );
    277   rcd = mcd;
    278   VERIFY_IS_APPROX( rcd.noalias() += md*md, mcd + ((md*md).eval().template cast<CD>()) );
    279   rcd = mcd;
    280   VERIFY_IS_APPROX( rcd.noalias() -= md*md, mcd - ((md*md).eval().template cast<CD>()) );
    281 
    282   VERIFY_IS_APPROX( rcd.noalias()  = mcd + md*md,       mcd + ((md*md).eval().template cast<CD>()) );
    283   rcd = mcd;
    284   VERIFY_IS_APPROX( rcd.noalias() += mcd + md*md, mcd + mcd + ((md*md).eval().template cast<CD>()) );
    285   rcd = mcd;
    286   VERIFY_IS_APPROX( rcd.noalias() -= mcd + md*md,           - ((md*md).eval().template cast<CD>()) );
    287 }
    288 
    289 void test_mixingtypes()
    290 {
    291   for(int i = 0; i < g_repeat; i++) {
    292     CALL_SUBTEST_1(mixingtypes<3>());
    293     CALL_SUBTEST_2(mixingtypes<4>());
    294     CALL_SUBTEST_3(mixingtypes<Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE)));
    295 
    296     CALL_SUBTEST_4(mixingtypes<3>());
    297     CALL_SUBTEST_5(mixingtypes<4>());
    298     CALL_SUBTEST_6(mixingtypes<Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE)));
    299   }
    300 }
    301