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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
// work around "uninitialized" warnings and give that option some testing
#define EIGEN_INITIALIZE_MATRICES_BY_ZERO
#ifndef EIGEN_NO_STATIC_ASSERT
#define EIGEN_NO_STATIC_ASSERT // turn static asserts into runtime asserts in order to check them
#endif
#if defined(EIGEN_TEST_PART_1) || defined(EIGEN_TEST_PART_2) || defined(EIGEN_TEST_PART_3)
#ifndef EIGEN_DONT_VECTORIZE
#define EIGEN_DONT_VECTORIZE
#endif
#endif
static bool g_called;
#define EIGEN_SCALAR_BINARY_OP_PLUGIN { g_called |= (!internal::is_same<LhsScalar,RhsScalar>::value); }
#include "main.h"
using namespace std;
#define VERIFY_MIX_SCALAR(XPR,REF) \
g_called = false; \
VERIFY_IS_APPROX(XPR,REF); \
VERIFY( g_called && #XPR" not properly optimized");
template<int SizeAtCompileType> void mixingtypes(int size = SizeAtCompileType)
{
typedef std::complex<float> CF;
typedef std::complex<double> CD;
typedef Matrix<float, SizeAtCompileType, SizeAtCompileType> Mat_f;
typedef Matrix<double, SizeAtCompileType, SizeAtCompileType> Mat_d;
typedef Matrix<std::complex<float>, SizeAtCompileType, SizeAtCompileType> Mat_cf;
typedef Matrix<std::complex<double>, SizeAtCompileType, SizeAtCompileType> Mat_cd;
typedef Matrix<float, SizeAtCompileType, 1> Vec_f;
typedef Matrix<double, SizeAtCompileType, 1> Vec_d;
typedef Matrix<std::complex<float>, SizeAtCompileType, 1> Vec_cf;
typedef Matrix<std::complex<double>, SizeAtCompileType, 1> Vec_cd;
Mat_f mf = Mat_f::Random(size,size);
Mat_d md = mf.template cast<double>();
//Mat_d rd = md;
Mat_cf mcf = Mat_cf::Random(size,size);
Mat_cd mcd = mcf.template cast<complex<double> >();
Mat_cd rcd = mcd;
Vec_f vf = Vec_f::Random(size,1);
Vec_d vd = vf.template cast<double>();
Vec_cf vcf = Vec_cf::Random(size,1);
Vec_cd vcd = vcf.template cast<complex<double> >();
float sf = internal::random<float>();
double sd = internal::random<double>();
complex<float> scf = internal::random<complex<float> >();
complex<double> scd = internal::random<complex<double> >();
mf+mf;
float epsf = std::sqrt(std::numeric_limits<float> ::min EIGEN_EMPTY ());
double epsd = std::sqrt(std::numeric_limits<double>::min EIGEN_EMPTY ());
while(std::abs(sf )<epsf) sf = internal::random<float>();
while(std::abs(sd )<epsd) sd = internal::random<double>();
while(std::abs(scf)<epsf) scf = internal::random<CF>();
while(std::abs(scd)<epsd) scd = internal::random<CD>();
// VERIFY_RAISES_ASSERT(mf+md); // does not even compile
#ifdef EIGEN_DONT_VECTORIZE
VERIFY_RAISES_ASSERT(vf=vd);
VERIFY_RAISES_ASSERT(vf+=vd);
#endif
// check scalar products
VERIFY_MIX_SCALAR(vcf * sf , vcf * complex<float>(sf));
VERIFY_MIX_SCALAR(sd * vcd , complex<double>(sd) * vcd);
VERIFY_MIX_SCALAR(vf * scf , vf.template cast<complex<float> >() * scf);
VERIFY_MIX_SCALAR(scd * vd , scd * vd.template cast<complex<double> >());
VERIFY_MIX_SCALAR(vcf * 2 , vcf * complex<float>(2));
VERIFY_MIX_SCALAR(vcf * 2.1 , vcf * complex<float>(2.1));
VERIFY_MIX_SCALAR(2 * vcf, vcf * complex<float>(2));
VERIFY_MIX_SCALAR(2.1 * vcf , vcf * complex<float>(2.1));
// check scalar quotients
VERIFY_MIX_SCALAR(vcf / sf , vcf / complex<float>(sf));
VERIFY_MIX_SCALAR(vf / scf , vf.template cast<complex<float> >() / scf);
VERIFY_MIX_SCALAR(vf.array() / scf, vf.template cast<complex<float> >().array() / scf);
VERIFY_MIX_SCALAR(scd / vd.array() , scd / vd.template cast<complex<double> >().array());
// check scalar increment
VERIFY_MIX_SCALAR(vcf.array() + sf , vcf.array() + complex<float>(sf));
VERIFY_MIX_SCALAR(sd + vcd.array(), complex<double>(sd) + vcd.array());
VERIFY_MIX_SCALAR(vf.array() + scf, vf.template cast<complex<float> >().array() + scf);
VERIFY_MIX_SCALAR(scd + vd.array() , scd + vd.template cast<complex<double> >().array());
// check scalar subtractions
VERIFY_MIX_SCALAR(vcf.array() - sf , vcf.array() - complex<float>(sf));
VERIFY_MIX_SCALAR(sd - vcd.array(), complex<double>(sd) - vcd.array());
VERIFY_MIX_SCALAR(vf.array() - scf, vf.template cast<complex<float> >().array() - scf);
VERIFY_MIX_SCALAR(scd - vd.array() , scd - vd.template cast<complex<double> >().array());
// check scalar powers
VERIFY_MIX_SCALAR( pow(vcf.array(), sf), Eigen::pow(vcf.array(), complex<float>(sf)) );
VERIFY_MIX_SCALAR( vcf.array().pow(sf) , Eigen::pow(vcf.array(), complex<float>(sf)) );
VERIFY_MIX_SCALAR( pow(sd, vcd.array()), Eigen::pow(complex<double>(sd), vcd.array()) );
VERIFY_MIX_SCALAR( Eigen::pow(vf.array(), scf), Eigen::pow(vf.template cast<complex<float> >().array(), scf) );
VERIFY_MIX_SCALAR( vf.array().pow(scf) , Eigen::pow(vf.template cast<complex<float> >().array(), scf) );
VERIFY_MIX_SCALAR( Eigen::pow(scd, vd.array()), Eigen::pow(scd, vd.template cast<complex<double> >().array()) );
// check dot product
vf.dot(vf);
#if 0 // we get other compilation errors here than just static asserts
VERIFY_RAISES_ASSERT(vd.dot(vf));
#endif
VERIFY_IS_APPROX(vcf.dot(vf), vcf.dot(vf.template cast<complex<float> >()));
// check diagonal product
VERIFY_IS_APPROX(vf.asDiagonal() * mcf, vf.template cast<complex<float> >().asDiagonal() * mcf);
VERIFY_IS_APPROX(vcd.asDiagonal() * md, vcd.asDiagonal() * md.template cast<complex<double> >());
VERIFY_IS_APPROX(mcf * vf.asDiagonal(), mcf * vf.template cast<complex<float> >().asDiagonal());
VERIFY_IS_APPROX(md * vcd.asDiagonal(), md.template cast<complex<double> >() * vcd.asDiagonal());
// vd.asDiagonal() * mf; // does not even compile
// vcd.asDiagonal() * mf; // does not even compile
// check inner product
VERIFY_IS_APPROX((vf.transpose() * vcf).value(), (vf.template cast<complex<float> >().transpose() * vcf).value());
// check outer product
VERIFY_IS_APPROX((vf * vcf.transpose()).eval(), (vf.template cast<complex<float> >() * vcf.transpose()).eval());
// coeff wise product
VERIFY_IS_APPROX((vf * vcf.transpose()).eval(), (vf.template cast<complex<float> >() * vcf.transpose()).eval());
Mat_cd mcd2 = mcd;
VERIFY_IS_APPROX(mcd.array() *= md.array(), mcd2.array() *= md.array().template cast<std::complex<double> >());
// check matrix-matrix products
VERIFY_IS_APPROX(sd*md*mcd, (sd*md).template cast<CD>().eval()*mcd);
VERIFY_IS_APPROX(sd*mcd*md, sd*mcd*md.template cast<CD>());
VERIFY_IS_APPROX(scd*md*mcd, scd*md.template cast<CD>().eval()*mcd);
VERIFY_IS_APPROX(scd*mcd*md, scd*mcd*md.template cast<CD>());
VERIFY_IS_APPROX(sf*mf*mcf, sf*mf.template cast<CF>()*mcf);
VERIFY_IS_APPROX(sf*mcf*mf, sf*mcf*mf.template cast<CF>());
VERIFY_IS_APPROX(scf*mf*mcf, scf*mf.template cast<CF>()*mcf);
VERIFY_IS_APPROX(scf*mcf*mf, scf*mcf*mf.template cast<CF>());
VERIFY_IS_APPROX(sd*md.adjoint()*mcd, (sd*md).template cast<CD>().eval().adjoint()*mcd);
VERIFY_IS_APPROX(sd*mcd.adjoint()*md, sd*mcd.adjoint()*md.template cast<CD>());
VERIFY_IS_APPROX(sd*md.adjoint()*mcd.adjoint(), (sd*md).template cast<CD>().eval().adjoint()*mcd.adjoint());
VERIFY_IS_APPROX(sd*mcd.adjoint()*md.adjoint(), sd*mcd.adjoint()*md.template cast<CD>().adjoint());
VERIFY_IS_APPROX(sd*md*mcd.adjoint(), (sd*md).template cast<CD>().eval()*mcd.adjoint());
VERIFY_IS_APPROX(sd*mcd*md.adjoint(), sd*mcd*md.template cast<CD>().adjoint());
VERIFY_IS_APPROX(sf*mf.adjoint()*mcf, (sf*mf).template cast<CF>().eval().adjoint()*mcf);
VERIFY_IS_APPROX(sf*mcf.adjoint()*mf, sf*mcf.adjoint()*mf.template cast<CF>());
VERIFY_IS_APPROX(sf*mf.adjoint()*mcf.adjoint(), (sf*mf).template cast<CF>().eval().adjoint()*mcf.adjoint());
VERIFY_IS_APPROX(sf*mcf.adjoint()*mf.adjoint(), sf*mcf.adjoint()*mf.template cast<CF>().adjoint());
VERIFY_IS_APPROX(sf*mf*mcf.adjoint(), (sf*mf).template cast<CF>().eval()*mcf.adjoint());
VERIFY_IS_APPROX(sf*mcf*mf.adjoint(), sf*mcf*mf.template cast<CF>().adjoint());
VERIFY_IS_APPROX(sf*mf*vcf, (sf*mf).template cast<CF>().eval()*vcf);
VERIFY_IS_APPROX(scf*mf*vcf,(scf*mf.template cast<CF>()).eval()*vcf);
VERIFY_IS_APPROX(sf*mcf*vf, sf*mcf*vf.template cast<CF>());
VERIFY_IS_APPROX(scf*mcf*vf,scf*mcf*vf.template cast<CF>());
VERIFY_IS_APPROX(sf*vcf.adjoint()*mf, sf*vcf.adjoint()*mf.template cast<CF>().eval());
VERIFY_IS_APPROX(scf*vcf.adjoint()*mf, scf*vcf.adjoint()*mf.template cast<CF>().eval());
VERIFY_IS_APPROX(sf*vf.adjoint()*mcf, sf*vf.adjoint().template cast<CF>().eval()*mcf);
VERIFY_IS_APPROX(scf*vf.adjoint()*mcf, scf*vf.adjoint().template cast<CF>().eval()*mcf);
VERIFY_IS_APPROX(sd*md*vcd, (sd*md).template cast<CD>().eval()*vcd);
VERIFY_IS_APPROX(scd*md*vcd,(scd*md.template cast<CD>()).eval()*vcd);
VERIFY_IS_APPROX(sd*mcd*vd, sd*mcd*vd.template cast<CD>().eval());
VERIFY_IS_APPROX(scd*mcd*vd,scd*mcd*vd.template cast<CD>().eval());
VERIFY_IS_APPROX(sd*vcd.adjoint()*md, sd*vcd.adjoint()*md.template cast<CD>().eval());
VERIFY_IS_APPROX(scd*vcd.adjoint()*md, scd*vcd.adjoint()*md.template cast<CD>().eval());
VERIFY_IS_APPROX(sd*vd.adjoint()*mcd, sd*vd.adjoint().template cast<CD>().eval()*mcd);
VERIFY_IS_APPROX(scd*vd.adjoint()*mcd, scd*vd.adjoint().template cast<CD>().eval()*mcd);
VERIFY_IS_APPROX( sd*vcd.adjoint()*md.template triangularView<Upper>(), sd*vcd.adjoint()*md.template cast<CD>().eval().template triangularView<Upper>());
VERIFY_IS_APPROX(scd*vcd.adjoint()*md.template triangularView<Lower>(), scd*vcd.adjoint()*md.template cast<CD>().eval().template triangularView<Lower>());
VERIFY_IS_APPROX( sd*vcd.adjoint()*md.transpose().template triangularView<Upper>(), sd*vcd.adjoint()*md.transpose().template cast<CD>().eval().template triangularView<Upper>());
VERIFY_IS_APPROX(scd*vcd.adjoint()*md.transpose().template triangularView<Lower>(), scd*vcd.adjoint()*md.transpose().template cast<CD>().eval().template triangularView<Lower>());
VERIFY_IS_APPROX( sd*vd.adjoint()*mcd.template triangularView<Lower>(), sd*vd.adjoint().template cast<CD>().eval()*mcd.template triangularView<Lower>());
VERIFY_IS_APPROX(scd*vd.adjoint()*mcd.template triangularView<Upper>(), scd*vd.adjoint().template cast<CD>().eval()*mcd.template triangularView<Upper>());
VERIFY_IS_APPROX( sd*vd.adjoint()*mcd.transpose().template triangularView<Lower>(), sd*vd.adjoint().template cast<CD>().eval()*mcd.transpose().template triangularView<Lower>());
VERIFY_IS_APPROX(scd*vd.adjoint()*mcd.transpose().template triangularView<Upper>(), scd*vd.adjoint().template cast<CD>().eval()*mcd.transpose().template triangularView<Upper>());
// Not supported yet: trmm
// VERIFY_IS_APPROX(sd*mcd*md.template triangularView<Lower>(), sd*mcd*md.template cast<CD>().eval().template triangularView<Lower>());
// VERIFY_IS_APPROX(scd*mcd*md.template triangularView<Upper>(), scd*mcd*md.template cast<CD>().eval().template triangularView<Upper>());
// VERIFY_IS_APPROX(sd*md*mcd.template triangularView<Lower>(), sd*md.template cast<CD>().eval()*mcd.template triangularView<Lower>());
// VERIFY_IS_APPROX(scd*md*mcd.template triangularView<Upper>(), scd*md.template cast<CD>().eval()*mcd.template triangularView<Upper>());
// Not supported yet: symv
// VERIFY_IS_APPROX(sd*vcd.adjoint()*md.template selfadjointView<Upper>(), sd*vcd.adjoint()*md.template cast<CD>().eval().template selfadjointView<Upper>());
// VERIFY_IS_APPROX(scd*vcd.adjoint()*md.template selfadjointView<Lower>(), scd*vcd.adjoint()*md.template cast<CD>().eval().template selfadjointView<Lower>());
// VERIFY_IS_APPROX(sd*vd.adjoint()*mcd.template selfadjointView<Lower>(), sd*vd.adjoint().template cast<CD>().eval()*mcd.template selfadjointView<Lower>());
// VERIFY_IS_APPROX(scd*vd.adjoint()*mcd.template selfadjointView<Upper>(), scd*vd.adjoint().template cast<CD>().eval()*mcd.template selfadjointView<Upper>());
// Not supported yet: symm
// VERIFY_IS_APPROX(sd*vcd.adjoint()*md.template selfadjointView<Upper>(), sd*vcd.adjoint()*md.template cast<CD>().eval().template selfadjointView<Upper>());
// VERIFY_IS_APPROX(scd*vcd.adjoint()*md.template selfadjointView<Upper>(), scd*vcd.adjoint()*md.template cast<CD>().eval().template selfadjointView<Upper>());
// VERIFY_IS_APPROX(sd*vd.adjoint()*mcd.template selfadjointView<Upper>(), sd*vd.adjoint().template cast<CD>().eval()*mcd.template selfadjointView<Upper>());
// VERIFY_IS_APPROX(scd*vd.adjoint()*mcd.template selfadjointView<Upper>(), scd*vd.adjoint().template cast<CD>().eval()*mcd.template selfadjointView<Upper>());
rcd.setZero();
VERIFY_IS_APPROX(Mat_cd(rcd.template triangularView<Upper>() = sd * mcd * md),
Mat_cd((sd * mcd * md.template cast<CD>().eval()).template triangularView<Upper>()));
VERIFY_IS_APPROX(Mat_cd(rcd.template triangularView<Upper>() = sd * md * mcd),
Mat_cd((sd * md.template cast<CD>().eval() * mcd).template triangularView<Upper>()));
VERIFY_IS_APPROX(Mat_cd(rcd.template triangularView<Upper>() = scd * mcd * md),
Mat_cd((scd * mcd * md.template cast<CD>().eval()).template triangularView<Upper>()));
VERIFY_IS_APPROX(Mat_cd(rcd.template triangularView<Upper>() = scd * md * mcd),
Mat_cd((scd * md.template cast<CD>().eval() * mcd).template triangularView<Upper>()));
VERIFY_IS_APPROX( md.array() * mcd.array(), md.template cast<CD>().eval().array() * mcd.array() );
VERIFY_IS_APPROX( mcd.array() * md.array(), mcd.array() * md.template cast<CD>().eval().array() );
VERIFY_IS_APPROX( md.array() + mcd.array(), md.template cast<CD>().eval().array() + mcd.array() );
VERIFY_IS_APPROX( mcd.array() + md.array(), mcd.array() + md.template cast<CD>().eval().array() );
VERIFY_IS_APPROX( md.array() - mcd.array(), md.template cast<CD>().eval().array() - mcd.array() );
VERIFY_IS_APPROX( mcd.array() - md.array(), mcd.array() - md.template cast<CD>().eval().array() );
if(mcd.array().abs().minCoeff()>epsd)
{
VERIFY_IS_APPROX( md.array() / mcd.array(), md.template cast<CD>().eval().array() / mcd.array() );
}
if(md.array().abs().minCoeff()>epsd)
{
VERIFY_IS_APPROX( mcd.array() / md.array(), mcd.array() / md.template cast<CD>().eval().array() );
}
if(md.array().abs().minCoeff()>epsd || mcd.array().abs().minCoeff()>epsd)
{
VERIFY_IS_APPROX( md.array().pow(mcd.array()), md.template cast<CD>().eval().array().pow(mcd.array()) );
VERIFY_IS_APPROX( mcd.array().pow(md.array()), mcd.array().pow(md.template cast<CD>().eval().array()) );
VERIFY_IS_APPROX( pow(md.array(),mcd.array()), md.template cast<CD>().eval().array().pow(mcd.array()) );
VERIFY_IS_APPROX( pow(mcd.array(),md.array()), mcd.array().pow(md.template cast<CD>().eval().array()) );
}
rcd = mcd;
VERIFY_IS_APPROX( rcd = md, md.template cast<CD>().eval() );
rcd = mcd;
VERIFY_IS_APPROX( rcd += md, mcd + md.template cast<CD>().eval() );
rcd = mcd;
VERIFY_IS_APPROX( rcd -= md, mcd - md.template cast<CD>().eval() );
rcd = mcd;
VERIFY_IS_APPROX( rcd.array() *= md.array(), mcd.array() * md.template cast<CD>().eval().array() );
rcd = mcd;
if(md.array().abs().minCoeff()>epsd)
{
VERIFY_IS_APPROX( rcd.array() /= md.array(), mcd.array() / md.template cast<CD>().eval().array() );
}
rcd = mcd;
VERIFY_IS_APPROX( rcd.noalias() += md + mcd*md, mcd + (md.template cast<CD>().eval()) + mcd*(md.template cast<CD>().eval()));
VERIFY_IS_APPROX( rcd.noalias() = md*md, ((md*md).eval().template cast<CD>()) );
rcd = mcd;
VERIFY_IS_APPROX( rcd.noalias() += md*md, mcd + ((md*md).eval().template cast<CD>()) );
rcd = mcd;
VERIFY_IS_APPROX( rcd.noalias() -= md*md, mcd - ((md*md).eval().template cast<CD>()) );
VERIFY_IS_APPROX( rcd.noalias() = mcd + md*md, mcd + ((md*md).eval().template cast<CD>()) );
rcd = mcd;
VERIFY_IS_APPROX( rcd.noalias() += mcd + md*md, mcd + mcd + ((md*md).eval().template cast<CD>()) );
rcd = mcd;
VERIFY_IS_APPROX( rcd.noalias() -= mcd + md*md, - ((md*md).eval().template cast<CD>()) );
}
void test_mixingtypes()
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1(mixingtypes<3>());
CALL_SUBTEST_2(mixingtypes<4>());
CALL_SUBTEST_3(mixingtypes<Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE)));
CALL_SUBTEST_4(mixingtypes<3>());
CALL_SUBTEST_5(mixingtypes<4>());
CALL_SUBTEST_6(mixingtypes<Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE)));
}
}
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