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dlma/eigen-3.4.0/test/sparse_product.cpp
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sparse_product.cpp
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// 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/.
#if defined(_MSC_VER) && (_MSC_VER==1800)
// This unit test takes forever to compile in Release mode with MSVC 2013,
// multiple hours. So let's switch off optimization for this one.
#pragma optimize("",off)
#endif
static long int nb_temporaries;
inline void on_temporary_creation() {
// here's a great place to set a breakpoint when debugging failures in this test!
nb_temporaries++;
}
#define EIGEN_SPARSE_CREATE_TEMPORARY_PLUGIN { on_temporary_creation(); }
#include "sparse.h"
#define VERIFY_EVALUATION_COUNT(XPR,N) {\
nb_temporaries = 0; \
CALL_SUBTEST( XPR ); \
if(nb_temporaries!=N) std::cerr << "nb_temporaries == " << nb_temporaries << "\n"; \
VERIFY( (#XPR) && nb_temporaries==N ); \
}
template<typename SparseMatrixType> void sparse_product()
{
typedef typename SparseMatrixType::StorageIndex StorageIndex;
Index n = 100;
const Index rows = internal::random<Index>(1,n);
const Index cols = internal::random<Index>(1,n);
const Index depth = internal::random<Index>(1,n);
typedef typename SparseMatrixType::Scalar Scalar;
enum { Flags = SparseMatrixType::Flags };
double density = (std::max)(8./(rows*cols), 0.2);
typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
typedef Matrix<Scalar,Dynamic,1> DenseVector;
typedef Matrix<Scalar,1,Dynamic> RowDenseVector;
typedef SparseVector<Scalar,0,StorageIndex> ColSpVector;
typedef SparseVector<Scalar,RowMajor,StorageIndex> RowSpVector;
Scalar s1 = internal::random<Scalar>();
Scalar s2 = internal::random<Scalar>();
// test matrix-matrix product
{
DenseMatrix refMat2 = DenseMatrix::Zero(rows, depth);
DenseMatrix refMat2t = DenseMatrix::Zero(depth, rows);
DenseMatrix refMat3 = DenseMatrix::Zero(depth, cols);
DenseMatrix refMat3t = DenseMatrix::Zero(cols, depth);
DenseMatrix refMat4 = DenseMatrix::Zero(rows, cols);
DenseMatrix refMat4t = DenseMatrix::Zero(cols, rows);
DenseMatrix refMat5 = DenseMatrix::Random(depth, cols);
DenseMatrix refMat6 = DenseMatrix::Random(rows, rows);
DenseMatrix dm4 = DenseMatrix::Zero(rows, rows);
// DenseVector dv1 = DenseVector::Random(rows);
SparseMatrixType m2 (rows, depth);
SparseMatrixType m2t(depth, rows);
SparseMatrixType m3 (depth, cols);
SparseMatrixType m3t(cols, depth);
SparseMatrixType m4 (rows, cols);
SparseMatrixType m4t(cols, rows);
SparseMatrixType m6(rows, rows);
initSparse(density, refMat2, m2);
initSparse(density, refMat2t, m2t);
initSparse(density, refMat3, m3);
initSparse(density, refMat3t, m3t);
initSparse(density, refMat4, m4);
initSparse(density, refMat4t, m4t);
initSparse(density, refMat6, m6);
// int c = internal::random<int>(0,depth-1);
// sparse * sparse
VERIFY_IS_APPROX(m4=m2*m3, refMat4=refMat2*refMat3);
VERIFY_IS_APPROX(m4=m2t.transpose()*m3, refMat4=refMat2t.transpose()*refMat3);
VERIFY_IS_APPROX(m4=m2t.transpose()*m3t.transpose(), refMat4=refMat2t.transpose()*refMat3t.transpose());
VERIFY_IS_APPROX(m4=m2*m3t.transpose(), refMat4=refMat2*refMat3t.transpose());
VERIFY_IS_APPROX(m4 = m2*m3/s1, refMat4 = refMat2*refMat3/s1);
VERIFY_IS_APPROX(m4 = m2*m3*s1, refMat4 = refMat2*refMat3*s1);
VERIFY_IS_APPROX(m4 = s2*m2*m3*s1, refMat4 = s2*refMat2*refMat3*s1);
VERIFY_IS_APPROX(m4 = (m2+m2)*m3, refMat4 = (refMat2+refMat2)*refMat3);
VERIFY_IS_APPROX(m4 = m2*m3.leftCols(cols/2), refMat4 = refMat2*refMat3.leftCols(cols/2));
VERIFY_IS_APPROX(m4 = m2*(m3+m3).leftCols(cols/2), refMat4 = refMat2*(refMat3+refMat3).leftCols(cols/2));
VERIFY_IS_APPROX(m4=(m2*m3).pruned(0), refMat4=refMat2*refMat3);
VERIFY_IS_APPROX(m4=(m2t.transpose()*m3).pruned(0), refMat4=refMat2t.transpose()*refMat3);
VERIFY_IS_APPROX(m4=(m2t.transpose()*m3t.transpose()).pruned(0), refMat4=refMat2t.transpose()*refMat3t.transpose());
VERIFY_IS_APPROX(m4=(m2*m3t.transpose()).pruned(0), refMat4=refMat2*refMat3t.transpose());
#ifndef EIGEN_SPARSE_PRODUCT_IGNORE_TEMPORARY_COUNT
// make sure the right product implementation is called:
if((!SparseMatrixType::IsRowMajor) && m2.rows()<=m3.cols())
{
VERIFY_EVALUATION_COUNT(m4 = m2*m3, 2); // 2 for transposing and get a sorted result.
VERIFY_EVALUATION_COUNT(m4 = (m2*m3).pruned(0), 1);
VERIFY_EVALUATION_COUNT(m4 = (m2*m3).eval().pruned(0), 4);
}
#endif
// and that pruning is effective:
{
DenseMatrix Ad(2,2);
Ad << -1, 1, 1, 1;
SparseMatrixType As(Ad.sparseView()), B(2,2);
VERIFY_IS_EQUAL( (As*As.transpose()).eval().nonZeros(), 4);
VERIFY_IS_EQUAL( (Ad*Ad.transpose()).eval().sparseView().eval().nonZeros(), 2);
VERIFY_IS_EQUAL( (As*As.transpose()).pruned(1e-6).eval().nonZeros(), 2);
}
// dense ?= sparse * sparse
VERIFY_IS_APPROX(dm4 =m2*m3, refMat4 =refMat2*refMat3);
VERIFY_IS_APPROX(dm4+=m2*m3, refMat4+=refMat2*refMat3);
VERIFY_IS_APPROX(dm4-=m2*m3, refMat4-=refMat2*refMat3);
VERIFY_IS_APPROX(dm4 =m2t.transpose()*m3, refMat4 =refMat2t.transpose()*refMat3);
VERIFY_IS_APPROX(dm4+=m2t.transpose()*m3, refMat4+=refMat2t.transpose()*refMat3);
VERIFY_IS_APPROX(dm4-=m2t.transpose()*m3, refMat4-=refMat2t.transpose()*refMat3);
VERIFY_IS_APPROX(dm4 =m2t.transpose()*m3t.transpose(), refMat4 =refMat2t.transpose()*refMat3t.transpose());
VERIFY_IS_APPROX(dm4+=m2t.transpose()*m3t.transpose(), refMat4+=refMat2t.transpose()*refMat3t.transpose());
VERIFY_IS_APPROX(dm4-=m2t.transpose()*m3t.transpose(), refMat4-=refMat2t.transpose()*refMat3t.transpose());
VERIFY_IS_APPROX(dm4 =m2*m3t.transpose(), refMat4 =refMat2*refMat3t.transpose());
VERIFY_IS_APPROX(dm4+=m2*m3t.transpose(), refMat4+=refMat2*refMat3t.transpose());
VERIFY_IS_APPROX(dm4-=m2*m3t.transpose(), refMat4-=refMat2*refMat3t.transpose());
VERIFY_IS_APPROX(dm4 = m2*m3*s1, refMat4 = refMat2*refMat3*s1);
// test aliasing
m4 = m2; refMat4 = refMat2;
VERIFY_IS_APPROX(m4=m4*m3, refMat4=refMat4*refMat3);
// sparse * dense matrix
VERIFY_IS_APPROX(dm4=m2*refMat3, refMat4=refMat2*refMat3);
VERIFY_IS_APPROX(dm4=m2*refMat3t.transpose(), refMat4=refMat2*refMat3t.transpose());
VERIFY_IS_APPROX(dm4=m2t.transpose()*refMat3, refMat4=refMat2t.transpose()*refMat3);
VERIFY_IS_APPROX(dm4=m2t.transpose()*refMat3t.transpose(), refMat4=refMat2t.transpose()*refMat3t.transpose());
VERIFY_IS_APPROX(dm4=m2*refMat3, refMat4=refMat2*refMat3);
VERIFY_IS_APPROX(dm4=dm4+m2*refMat3, refMat4=refMat4+refMat2*refMat3);
VERIFY_IS_APPROX(dm4+=m2*refMat3, refMat4+=refMat2*refMat3);
VERIFY_IS_APPROX(dm4-=m2*refMat3, refMat4-=refMat2*refMat3);
VERIFY_IS_APPROX(dm4.noalias()+=m2*refMat3, refMat4+=refMat2*refMat3);
VERIFY_IS_APPROX(dm4.noalias()-=m2*refMat3, refMat4-=refMat2*refMat3);
VERIFY_IS_APPROX(dm4=m2*(refMat3+refMat3), refMat4=refMat2*(refMat3+refMat3));
VERIFY_IS_APPROX(dm4=m2t.transpose()*(refMat3+refMat5)*0.5, refMat4=refMat2t.transpose()*(refMat3+refMat5)*0.5);
// sparse * dense vector
VERIFY_IS_APPROX(dm4.col(0)=m2*refMat3.col(0), refMat4.col(0)=refMat2*refMat3.col(0));
VERIFY_IS_APPROX(dm4.col(0)=m2*refMat3t.transpose().col(0), refMat4.col(0)=refMat2*refMat3t.transpose().col(0));
VERIFY_IS_APPROX(dm4.col(0)=m2t.transpose()*refMat3.col(0), refMat4.col(0)=refMat2t.transpose()*refMat3.col(0));
VERIFY_IS_APPROX(dm4.col(0)=m2t.transpose()*refMat3t.transpose().col(0), refMat4.col(0)=refMat2t.transpose()*refMat3t.transpose().col(0));
// dense * sparse
VERIFY_IS_APPROX(dm4=refMat2*m3, refMat4=refMat2*refMat3);
VERIFY_IS_APPROX(dm4=dm4+refMat2*m3, refMat4=refMat4+refMat2*refMat3);
VERIFY_IS_APPROX(dm4+=refMat2*m3, refMat4+=refMat2*refMat3);
VERIFY_IS_APPROX(dm4-=refMat2*m3, refMat4-=refMat2*refMat3);
VERIFY_IS_APPROX(dm4.noalias()+=refMat2*m3, refMat4+=refMat2*refMat3);
VERIFY_IS_APPROX(dm4.noalias()-=refMat2*m3, refMat4-=refMat2*refMat3);
VERIFY_IS_APPROX(dm4=refMat2*m3t.transpose(), refMat4=refMat2*refMat3t.transpose());
VERIFY_IS_APPROX(dm4=refMat2t.transpose()*m3, refMat4=refMat2t.transpose()*refMat3);
VERIFY_IS_APPROX(dm4=refMat2t.transpose()*m3t.transpose(), refMat4=refMat2t.transpose()*refMat3t.transpose());
// sparse * dense and dense * sparse outer product
{
Index c = internal::random<Index>(0,depth-1);
Index r = internal::random<Index>(0,rows-1);
Index c1 = internal::random<Index>(0,cols-1);
Index r1 = internal::random<Index>(0,depth-1);
DenseMatrix dm5 = DenseMatrix::Random(depth, cols);
VERIFY_IS_APPROX( m4=m2.col(c)*dm5.col(c1).transpose(), refMat4=refMat2.col(c)*dm5.col(c1).transpose());
VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
VERIFY_IS_APPROX( m4=m2.middleCols(c,1)*dm5.col(c1).transpose(), refMat4=refMat2.col(c)*dm5.col(c1).transpose());
VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
VERIFY_IS_APPROX(dm4=m2.col(c)*dm5.col(c1).transpose(), refMat4=refMat2.col(c)*dm5.col(c1).transpose());
VERIFY_IS_APPROX(m4=dm5.col(c1)*m2.col(c).transpose(), refMat4=dm5.col(c1)*refMat2.col(c).transpose());
VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
VERIFY_IS_APPROX(m4=dm5.col(c1)*m2.middleCols(c,1).transpose(), refMat4=dm5.col(c1)*refMat2.col(c).transpose());
VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
VERIFY_IS_APPROX(dm4=dm5.col(c1)*m2.col(c).transpose(), refMat4=dm5.col(c1)*refMat2.col(c).transpose());
VERIFY_IS_APPROX( m4=dm5.row(r1).transpose()*m2.col(c).transpose(), refMat4=dm5.row(r1).transpose()*refMat2.col(c).transpose());
VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
VERIFY_IS_APPROX(dm4=dm5.row(r1).transpose()*m2.col(c).transpose(), refMat4=dm5.row(r1).transpose()*refMat2.col(c).transpose());
VERIFY_IS_APPROX( m4=m2.row(r).transpose()*dm5.col(c1).transpose(), refMat4=refMat2.row(r).transpose()*dm5.col(c1).transpose());
VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
VERIFY_IS_APPROX( m4=m2.middleRows(r,1).transpose()*dm5.col(c1).transpose(), refMat4=refMat2.row(r).transpose()*dm5.col(c1).transpose());
VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
VERIFY_IS_APPROX(dm4=m2.row(r).transpose()*dm5.col(c1).transpose(), refMat4=refMat2.row(r).transpose()*dm5.col(c1).transpose());
VERIFY_IS_APPROX( m4=dm5.col(c1)*m2.row(r), refMat4=dm5.col(c1)*refMat2.row(r));
VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
VERIFY_IS_APPROX( m4=dm5.col(c1)*m2.middleRows(r,1), refMat4=dm5.col(c1)*refMat2.row(r));
VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
VERIFY_IS_APPROX(dm4=dm5.col(c1)*m2.row(r), refMat4=dm5.col(c1)*refMat2.row(r));
VERIFY_IS_APPROX( m4=dm5.row(r1).transpose()*m2.row(r), refMat4=dm5.row(r1).transpose()*refMat2.row(r));
VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
VERIFY_IS_APPROX(dm4=dm5.row(r1).transpose()*m2.row(r), refMat4=dm5.row(r1).transpose()*refMat2.row(r));
}
VERIFY_IS_APPROX(m6=m6*m6, refMat6=refMat6*refMat6);
// sparse matrix * sparse vector
ColSpVector cv0(cols), cv1;
DenseVector dcv0(cols), dcv1;
initSparse(2*density,dcv0, cv0);
RowSpVector rv0(depth), rv1;
RowDenseVector drv0(depth), drv1(rv1);
initSparse(2*density,drv0, rv0);
VERIFY_IS_APPROX(cv1=m3*cv0, dcv1=refMat3*dcv0);
VERIFY_IS_APPROX(rv1=rv0*m3, drv1=drv0*refMat3);
VERIFY_IS_APPROX(cv1=m3t.adjoint()*cv0, dcv1=refMat3t.adjoint()*dcv0);
VERIFY_IS_APPROX(cv1=rv0*m3, dcv1=drv0*refMat3);
VERIFY_IS_APPROX(rv1=m3*cv0, drv1=refMat3*dcv0);
}
// test matrix - diagonal product
{
DenseMatrix refM2 = DenseMatrix::Zero(rows, cols);
DenseMatrix refM3 = DenseMatrix::Zero(rows, cols);
DenseMatrix d3 = DenseMatrix::Zero(rows, cols);
DiagonalMatrix<Scalar,Dynamic> d1(DenseVector::Random(cols));
DiagonalMatrix<Scalar,Dynamic> d2(DenseVector::Random(rows));
SparseMatrixType m2(rows, cols);
SparseMatrixType m3(rows, cols);
initSparse<Scalar>(density, refM2, m2);
initSparse<Scalar>(density, refM3, m3);
VERIFY_IS_APPROX(m3=m2*d1, refM3=refM2*d1);
VERIFY_IS_APPROX(m3=m2.transpose()*d2, refM3=refM2.transpose()*d2);
VERIFY_IS_APPROX(m3=d2*m2, refM3=d2*refM2);
VERIFY_IS_APPROX(m3=d1*m2.transpose(), refM3=d1*refM2.transpose());
// also check with a SparseWrapper:
DenseVector v1 = DenseVector::Random(cols);
DenseVector v2 = DenseVector::Random(rows);
DenseVector v3 = DenseVector::Random(rows);
VERIFY_IS_APPROX(m3=m2*v1.asDiagonal(), refM3=refM2*v1.asDiagonal());
VERIFY_IS_APPROX(m3=m2.transpose()*v2.asDiagonal(), refM3=refM2.transpose()*v2.asDiagonal());
VERIFY_IS_APPROX(m3=v2.asDiagonal()*m2, refM3=v2.asDiagonal()*refM2);
VERIFY_IS_APPROX(m3=v1.asDiagonal()*m2.transpose(), refM3=v1.asDiagonal()*refM2.transpose());
VERIFY_IS_APPROX(m3=v2.asDiagonal()*m2*v1.asDiagonal(), refM3=v2.asDiagonal()*refM2*v1.asDiagonal());
VERIFY_IS_APPROX(v2=m2*v1.asDiagonal()*v1, refM2*v1.asDiagonal()*v1);
VERIFY_IS_APPROX(v3=v2.asDiagonal()*m2*v1, v2.asDiagonal()*refM2*v1);
// evaluate to a dense matrix to check the .row() and .col() iterator functions
VERIFY_IS_APPROX(d3=m2*d1, refM3=refM2*d1);
VERIFY_IS_APPROX(d3=m2.transpose()*d2, refM3=refM2.transpose()*d2);
VERIFY_IS_APPROX(d3=d2*m2, refM3=d2*refM2);
VERIFY_IS_APPROX(d3=d1*m2.transpose(), refM3=d1*refM2.transpose());
}
// test self-adjoint and triangular-view products
{
DenseMatrix b = DenseMatrix::Random(rows, rows);
DenseMatrix x = DenseMatrix::Random(rows, rows);
DenseMatrix refX = DenseMatrix::Random(rows, rows);
DenseMatrix refUp = DenseMatrix::Zero(rows, rows);
DenseMatrix refLo = DenseMatrix::Zero(rows, rows);
DenseMatrix refS = DenseMatrix::Zero(rows, rows);
DenseMatrix refA = DenseMatrix::Zero(rows, rows);
SparseMatrixType mUp(rows, rows);
SparseMatrixType mLo(rows, rows);
SparseMatrixType mS(rows, rows);
SparseMatrixType mA(rows, rows);
initSparse<Scalar>(density, refA, mA);
do {
initSparse<Scalar>(density, refUp, mUp, ForceRealDiag|/*ForceNonZeroDiag|*/MakeUpperTriangular);
} while (refUp.isZero());
refLo = refUp.adjoint();
mLo = mUp.adjoint();
refS = refUp + refLo;
refS.diagonal() *= 0.5;
mS = mUp + mLo;
// TODO be able to address the diagonal....
for (int k=0; k<mS.outerSize(); ++k)
for (typename SparseMatrixType::InnerIterator it(mS,k); it; ++it)
if (it.index() == k)
it.valueRef() *= Scalar(0.5);
VERIFY_IS_APPROX(refS.adjoint(), refS);
VERIFY_IS_APPROX(mS.adjoint(), mS);
VERIFY_IS_APPROX(mS, refS);
VERIFY_IS_APPROX(x=mS*b, refX=refS*b);
// sparse selfadjointView with dense matrices
VERIFY_IS_APPROX(x=mUp.template selfadjointView<Upper>()*b, refX=refS*b);
VERIFY_IS_APPROX(x=mLo.template selfadjointView<Lower>()*b, refX=refS*b);
VERIFY_IS_APPROX(x=mS.template selfadjointView<Upper|Lower>()*b, refX=refS*b);
VERIFY_IS_APPROX(x=b * mUp.template selfadjointView<Upper>(), refX=b*refS);
VERIFY_IS_APPROX(x=b * mLo.template selfadjointView<Lower>(), refX=b*refS);
VERIFY_IS_APPROX(x=b * mS.template selfadjointView<Upper|Lower>(), refX=b*refS);
VERIFY_IS_APPROX(x.noalias()+=mUp.template selfadjointView<Upper>()*b, refX+=refS*b);
VERIFY_IS_APPROX(x.noalias()-=mLo.template selfadjointView<Lower>()*b, refX-=refS*b);
VERIFY_IS_APPROX(x.noalias()+=mS.template selfadjointView<Upper|Lower>()*b, refX+=refS*b);
// sparse selfadjointView with sparse matrices
SparseMatrixType mSres(rows,rows);
VERIFY_IS_APPROX(mSres = mLo.template selfadjointView<Lower>()*mS,
refX = refLo.template selfadjointView<Lower>()*refS);
VERIFY_IS_APPROX(mSres = mS * mLo.template selfadjointView<Lower>(),
refX = refS * refLo.template selfadjointView<Lower>());
// sparse triangularView with dense matrices
VERIFY_IS_APPROX(x=mA.template triangularView<Upper>()*b, refX=refA.template triangularView<Upper>()*b);
VERIFY_IS_APPROX(x=mA.template triangularView<Lower>()*b, refX=refA.template triangularView<Lower>()*b);
VERIFY_IS_APPROX(x=b*mA.template triangularView<Upper>(), refX=b*refA.template triangularView<Upper>());
VERIFY_IS_APPROX(x=b*mA.template triangularView<Lower>(), refX=b*refA.template triangularView<Lower>());
// sparse triangularView with sparse matrices
VERIFY_IS_APPROX(mSres = mA.template triangularView<Lower>()*mS, refX = refA.template triangularView<Lower>()*refS);
VERIFY_IS_APPROX(mSres = mS * mA.template triangularView<Lower>(), refX = refS * refA.template triangularView<Lower>());
VERIFY_IS_APPROX(mSres = mA.template triangularView<Upper>()*mS, refX = refA.template triangularView<Upper>()*refS);
VERIFY_IS_APPROX(mSres = mS * mA.template triangularView<Upper>(), refX = refS * refA.template triangularView<Upper>());
}
}
// New test for Bug in SparseTimeDenseProduct
template<typename SparseMatrixType, typename DenseMatrixType> void sparse_product_regression_test()
{
// This code does not compile with afflicted versions of the bug
SparseMatrixType sm1(3,2);
DenseMatrixType m2(2,2);
sm1.setZero();
m2.setZero();
DenseMatrixType m3 = sm1*m2;
// This code produces a segfault with afflicted versions of another SparseTimeDenseProduct
// bug
SparseMatrixType sm2(20000,2);
sm2.setZero();
DenseMatrixType m4(sm2*m2);
VERIFY_IS_APPROX( m4(0,0), 0.0 );
}
template<typename Scalar>
void bug_942()
{
typedef Matrix<Scalar, Dynamic, 1> Vector;
typedef SparseMatrix<Scalar, ColMajor> ColSpMat;
typedef SparseMatrix<Scalar, RowMajor> RowSpMat;
ColSpMat cmA(1,1);
cmA.insert(0,0) = 1;
RowSpMat rmA(1,1);
rmA.insert(0,0) = 1;
Vector d(1);
d[0] = 2;
double res = 2;
VERIFY_IS_APPROX( ( cmA*d.asDiagonal() ).eval().coeff(0,0), res );
VERIFY_IS_APPROX( ( d.asDiagonal()*rmA ).eval().coeff(0,0), res );
VERIFY_IS_APPROX( ( rmA*d.asDiagonal() ).eval().coeff(0,0), res );
VERIFY_IS_APPROX( ( d.asDiagonal()*cmA ).eval().coeff(0,0), res );
}
template<typename Real>
void test_mixing_types()
{
typedef std::complex<Real> Cplx;
typedef SparseMatrix<Real> SpMatReal;
typedef SparseMatrix<Cplx> SpMatCplx;
typedef SparseMatrix<Cplx,RowMajor> SpRowMatCplx;
typedef Matrix<Real,Dynamic,Dynamic> DenseMatReal;
typedef Matrix<Cplx,Dynamic,Dynamic> DenseMatCplx;
Index n = internal::random<Index>(1,100);
double density = (std::max)(8./(n*n), 0.2);
SpMatReal sR1(n,n);
SpMatCplx sC1(n,n), sC2(n,n), sC3(n,n);
SpRowMatCplx sCR(n,n);
DenseMatReal dR1(n,n);
DenseMatCplx dC1(n,n), dC2(n,n), dC3(n,n);
initSparse<Real>(density, dR1, sR1);
initSparse<Cplx>(density, dC1, sC1);
initSparse<Cplx>(density, dC2, sC2);
VERIFY_IS_APPROX( sC2 = (sR1 * sC1), dC3 = dR1.template cast<Cplx>() * dC1 );
VERIFY_IS_APPROX( sC2 = (sC1 * sR1), dC3 = dC1 * dR1.template cast<Cplx>() );
VERIFY_IS_APPROX( sC2 = (sR1.transpose() * sC1), dC3 = dR1.template cast<Cplx>().transpose() * dC1 );
VERIFY_IS_APPROX( sC2 = (sC1.transpose() * sR1), dC3 = dC1.transpose() * dR1.template cast<Cplx>() );
VERIFY_IS_APPROX( sC2 = (sR1 * sC1.transpose()), dC3 = dR1.template cast<Cplx>() * dC1.transpose() );
VERIFY_IS_APPROX( sC2 = (sC1 * sR1.transpose()), dC3 = dC1 * dR1.template cast<Cplx>().transpose() );
VERIFY_IS_APPROX( sC2 = (sR1.transpose() * sC1.transpose()), dC3 = dR1.template cast<Cplx>().transpose() * dC1.transpose() );
VERIFY_IS_APPROX( sC2 = (sC1.transpose() * sR1.transpose()), dC3 = dC1.transpose() * dR1.template cast<Cplx>().transpose() );
VERIFY_IS_APPROX( sCR = (sR1 * sC1), dC3 = dR1.template cast<Cplx>() * dC1 );
VERIFY_IS_APPROX( sCR = (sC1 * sR1), dC3 = dC1 * dR1.template cast<Cplx>() );
VERIFY_IS_APPROX( sCR = (sR1.transpose() * sC1), dC3 = dR1.template cast<Cplx>().transpose() * dC1 );
VERIFY_IS_APPROX( sCR = (sC1.transpose() * sR1), dC3 = dC1.transpose() * dR1.template cast<Cplx>() );
VERIFY_IS_APPROX( sCR = (sR1 * sC1.transpose()), dC3 = dR1.template cast<Cplx>() * dC1.transpose() );
VERIFY_IS_APPROX( sCR = (sC1 * sR1.transpose()), dC3 = dC1 * dR1.template cast<Cplx>().transpose() );
VERIFY_IS_APPROX( sCR = (sR1.transpose() * sC1.transpose()), dC3 = dR1.template cast<Cplx>().transpose() * dC1.transpose() );
VERIFY_IS_APPROX( sCR = (sC1.transpose() * sR1.transpose()), dC3 = dC1.transpose() * dR1.template cast<Cplx>().transpose() );
VERIFY_IS_APPROX( sC2 = (sR1 * sC1).pruned(), dC3 = dR1.template cast<Cplx>() * dC1 );
VERIFY_IS_APPROX( sC2 = (sC1 * sR1).pruned(), dC3 = dC1 * dR1.template cast<Cplx>() );
VERIFY_IS_APPROX( sC2 = (sR1.transpose() * sC1).pruned(), dC3 = dR1.template cast<Cplx>().transpose() * dC1 );
VERIFY_IS_APPROX( sC2 = (sC1.transpose() * sR1).pruned(), dC3 = dC1.transpose() * dR1.template cast<Cplx>() );
VERIFY_IS_APPROX( sC2 = (sR1 * sC1.transpose()).pruned(), dC3 = dR1.template cast<Cplx>() * dC1.transpose() );
VERIFY_IS_APPROX( sC2 = (sC1 * sR1.transpose()).pruned(), dC3 = dC1 * dR1.template cast<Cplx>().transpose() );
VERIFY_IS_APPROX( sC2 = (sR1.transpose() * sC1.transpose()).pruned(), dC3 = dR1.template cast<Cplx>().transpose() * dC1.transpose() );
VERIFY_IS_APPROX( sC2 = (sC1.transpose() * sR1.transpose()).pruned(), dC3 = dC1.transpose() * dR1.template cast<Cplx>().transpose() );
VERIFY_IS_APPROX( sCR = (sR1 * sC1).pruned(), dC3 = dR1.template cast<Cplx>() * dC1 );
VERIFY_IS_APPROX( sCR = (sC1 * sR1).pruned(), dC3 = dC1 * dR1.template cast<Cplx>() );
VERIFY_IS_APPROX( sCR = (sR1.transpose() * sC1).pruned(), dC3 = dR1.template cast<Cplx>().transpose() * dC1 );
VERIFY_IS_APPROX( sCR = (sC1.transpose() * sR1).pruned(), dC3 = dC1.transpose() * dR1.template cast<Cplx>() );
VERIFY_IS_APPROX( sCR = (sR1 * sC1.transpose()).pruned(), dC3 = dR1.template cast<Cplx>() * dC1.transpose() );
VERIFY_IS_APPROX( sCR = (sC1 * sR1.transpose()).pruned(), dC3 = dC1 * dR1.template cast<Cplx>().transpose() );
VERIFY_IS_APPROX( sCR = (sR1.transpose() * sC1.transpose()).pruned(), dC3 = dR1.template cast<Cplx>().transpose() * dC1.transpose() );
VERIFY_IS_APPROX( sCR = (sC1.transpose() * sR1.transpose()).pruned(), dC3 = dC1.transpose() * dR1.template cast<Cplx>().transpose() );
VERIFY_IS_APPROX( dC2 = (sR1 * sC1), dC3 = dR1.template cast<Cplx>() * dC1 );
VERIFY_IS_APPROX( dC2 = (sC1 * sR1), dC3 = dC1 * dR1.template cast<Cplx>() );
VERIFY_IS_APPROX( dC2 = (sR1.transpose() * sC1), dC3 = dR1.template cast<Cplx>().transpose() * dC1 );
VERIFY_IS_APPROX( dC2 = (sC1.transpose() * sR1), dC3 = dC1.transpose() * dR1.template cast<Cplx>() );
VERIFY_IS_APPROX( dC2 = (sR1 * sC1.transpose()), dC3 = dR1.template cast<Cplx>() * dC1.transpose() );
VERIFY_IS_APPROX( dC2 = (sC1 * sR1.transpose()), dC3 = dC1 * dR1.template cast<Cplx>().transpose() );
VERIFY_IS_APPROX( dC2 = (sR1.transpose() * sC1.transpose()), dC3 = dR1.template cast<Cplx>().transpose() * dC1.transpose() );
VERIFY_IS_APPROX( dC2 = (sC1.transpose() * sR1.transpose()), dC3 = dC1.transpose() * dR1.template cast<Cplx>().transpose() );
VERIFY_IS_APPROX( dC2 = dR1 * sC1, dC3 = dR1.template cast<Cplx>() * sC1 );
VERIFY_IS_APPROX( dC2 = sR1 * dC1, dC3 = sR1.template cast<Cplx>() * dC1 );
VERIFY_IS_APPROX( dC2 = dC1 * sR1, dC3 = dC1 * sR1.template cast<Cplx>() );
VERIFY_IS_APPROX( dC2 = sC1 * dR1, dC3 = sC1 * dR1.template cast<Cplx>() );
VERIFY_IS_APPROX( dC2 = dR1.row(0) * sC1, dC3 = dR1.template cast<Cplx>().row(0) * sC1 );
VERIFY_IS_APPROX( dC2 = sR1 * dC1.col(0), dC3 = sR1.template cast<Cplx>() * dC1.col(0) );
VERIFY_IS_APPROX( dC2 = dC1.row(0) * sR1, dC3 = dC1.row(0) * sR1.template cast<Cplx>() );
VERIFY_IS_APPROX( dC2 = sC1 * dR1.col(0), dC3 = sC1 * dR1.template cast<Cplx>().col(0) );
}
EIGEN_DECLARE_TEST(sparse_product)
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( (sparse_product<SparseMatrix<double,ColMajor> >()) );
CALL_SUBTEST_1( (sparse_product<SparseMatrix<double,RowMajor> >()) );
CALL_SUBTEST_1( (bug_942<double>()) );
CALL_SUBTEST_2( (sparse_product<SparseMatrix<std::complex<double>, ColMajor > >()) );
CALL_SUBTEST_2( (sparse_product<SparseMatrix<std::complex<double>, RowMajor > >()) );
CALL_SUBTEST_3( (sparse_product<SparseMatrix<float,ColMajor,long int> >()) );
CALL_SUBTEST_4( (sparse_product_regression_test<SparseMatrix<double,RowMajor>, Matrix<double, Dynamic, Dynamic, RowMajor> >()) );
CALL_SUBTEST_5( (test_mixing_types<float>()) );
}
}
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