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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/.
#include "sparse.h"
template<typename SparseMatrixType, typename DenseMatrix, bool IsRowMajor=SparseMatrixType::IsRowMajor> struct test_outer;
template<typename SparseMatrixType, typename DenseMatrix> struct test_outer<SparseMatrixType,DenseMatrix,false> { static void run(SparseMatrixType& m2, SparseMatrixType& m4, DenseMatrix& refMat2, DenseMatrix& refMat4) { typedef typename SparseMatrixType::Index Index; Index c = internal::random<Index>(0,m2.cols()-1); Index c1 = internal::random<Index>(0,m2.cols()-1); VERIFY_IS_APPROX(m4=m2.col(c)*refMat2.col(c1).transpose(), refMat4=refMat2.col(c)*refMat2.col(c1).transpose()); VERIFY_IS_APPROX(m4=refMat2.col(c1)*m2.col(c).transpose(), refMat4=refMat2.col(c1)*refMat2.col(c).transpose()); }};
template<typename SparseMatrixType, typename DenseMatrix> struct test_outer<SparseMatrixType,DenseMatrix,true> { static void run(SparseMatrixType& m2, SparseMatrixType& m4, DenseMatrix& refMat2, DenseMatrix& refMat4) { typedef typename SparseMatrixType::Index Index; Index r = internal::random<Index>(0,m2.rows()-1); Index c1 = internal::random<Index>(0,m2.cols()-1); VERIFY_IS_APPROX(m4=m2.row(r).transpose()*refMat2.col(c1).transpose(), refMat4=refMat2.row(r).transpose()*refMat2.col(c1).transpose()); VERIFY_IS_APPROX(m4=refMat2.col(c1)*m2.row(r), refMat4=refMat2.col(c1)*refMat2.row(r)); }};
// (m2,m4,refMat2,refMat4,dv1);
// VERIFY_IS_APPROX(m4=m2.innerVector(c)*dv1.transpose(), refMat4=refMat2.colVector(c)*dv1.transpose());
// VERIFY_IS_APPROX(m4=dv1*mcm.col(c).transpose(), refMat4=dv1*refMat2.col(c).transpose());
template<typename SparseMatrixType> void sparse_product(){ typedef typename SparseMatrixType::Index Index; 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), 0.1); typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix; typedef Matrix<Scalar,Dynamic,1> DenseVector; typedef Matrix<Scalar,1,Dynamic> RowDenseVector; typedef SparseVector<Scalar,0,Index> ColSpVector; typedef SparseVector<Scalar,RowMajor,Index> 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*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());
// test aliasing
m4 = m2; refMat4 = refMat2; VERIFY_IS_APPROX(m4=m4*m3, refMat4=refMat4*refMat3);
// sparse * dense
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+refMat3), refMat4=refMat2*(refMat3+refMat3)); VERIFY_IS_APPROX(dm4=m2t.transpose()*(refMat3+refMat5)*0.5, refMat4=refMat2t.transpose()*(refMat3+refMat5)*0.5);
// dense * sparse
VERIFY_IS_APPROX(dm4=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
test_outer<SparseMatrixType,DenseMatrix>::run(m2,m4,refMat2,refMat4);
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=rv0*m3, dcv1=drv0*refMat3); VERIFY_IS_APPROX(rv1=rv0*m3, drv1=drv0*refMat3); VERIFY_IS_APPROX(cv1=m3*cv0, dcv1=refMat3*dcv0); VERIFY_IS_APPROX(cv1=m3t.adjoint()*cv0, dcv1=refMat3t.adjoint()*dcv0); 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); 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()); // 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 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); SparseMatrixType mUp(rows, rows); SparseMatrixType mLo(rows, rows); SparseMatrixType mS(rows, rows); 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() *= 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);
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); // sparse selfadjointView * sparse
SparseMatrixType mSres(rows,rows); VERIFY_IS_APPROX(mSres = mLo.template selfadjointView<Lower>()*mS, refX = refLo.template selfadjointView<Lower>()*refS); // sparse * sparse selfadjointview
VERIFY_IS_APPROX(mSres = mS * mLo.template selfadjointView<Lower>(), refX = refS * refLo.template selfadjointView<Lower>()); } }
// 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 );}
void 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_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> >()) ); }}
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