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265 lines
12 KiB
C++
265 lines
12 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#include "sparse.h"
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template<typename SparseMatrixType> void sparse_product()
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{
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typedef typename SparseMatrixType::Index Index;
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Index n = 100;
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const Index rows = internal::random<Index>(1,n);
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const Index cols = internal::random<Index>(1,n);
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const Index depth = internal::random<Index>(1,n);
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typedef typename SparseMatrixType::Scalar Scalar;
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enum { Flags = SparseMatrixType::Flags };
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double density = (std::max)(8./(rows*cols), 0.1);
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typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
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typedef Matrix<Scalar,Dynamic,1> DenseVector;
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typedef Matrix<Scalar,1,Dynamic> RowDenseVector;
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typedef SparseVector<Scalar,0,Index> ColSpVector;
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typedef SparseVector<Scalar,RowMajor,Index> RowSpVector;
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Scalar s1 = internal::random<Scalar>();
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Scalar s2 = internal::random<Scalar>();
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// test matrix-matrix product
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{
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DenseMatrix refMat2 = DenseMatrix::Zero(rows, depth);
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DenseMatrix refMat2t = DenseMatrix::Zero(depth, rows);
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DenseMatrix refMat3 = DenseMatrix::Zero(depth, cols);
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DenseMatrix refMat3t = DenseMatrix::Zero(cols, depth);
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DenseMatrix refMat4 = DenseMatrix::Zero(rows, cols);
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DenseMatrix refMat4t = DenseMatrix::Zero(cols, rows);
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DenseMatrix refMat5 = DenseMatrix::Random(depth, cols);
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DenseMatrix refMat6 = DenseMatrix::Random(rows, rows);
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DenseMatrix dm4 = DenseMatrix::Zero(rows, rows);
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// DenseVector dv1 = DenseVector::Random(rows);
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SparseMatrixType m2 (rows, depth);
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SparseMatrixType m2t(depth, rows);
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SparseMatrixType m3 (depth, cols);
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SparseMatrixType m3t(cols, depth);
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SparseMatrixType m4 (rows, cols);
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SparseMatrixType m4t(cols, rows);
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SparseMatrixType m6(rows, rows);
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initSparse(density, refMat2, m2);
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initSparse(density, refMat2t, m2t);
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initSparse(density, refMat3, m3);
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initSparse(density, refMat3t, m3t);
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initSparse(density, refMat4, m4);
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initSparse(density, refMat4t, m4t);
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initSparse(density, refMat6, m6);
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// int c = internal::random<int>(0,depth-1);
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// sparse * sparse
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VERIFY_IS_APPROX(m4=m2*m3, refMat4=refMat2*refMat3);
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VERIFY_IS_APPROX(m4=m2t.transpose()*m3, refMat4=refMat2t.transpose()*refMat3);
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VERIFY_IS_APPROX(m4=m2t.transpose()*m3t.transpose(), refMat4=refMat2t.transpose()*refMat3t.transpose());
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VERIFY_IS_APPROX(m4=m2*m3t.transpose(), refMat4=refMat2*refMat3t.transpose());
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VERIFY_IS_APPROX(m4 = m2*m3/s1, refMat4 = refMat2*refMat3/s1);
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VERIFY_IS_APPROX(m4 = m2*m3*s1, refMat4 = refMat2*refMat3*s1);
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VERIFY_IS_APPROX(m4 = s2*m2*m3*s1, refMat4 = s2*refMat2*refMat3*s1);
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VERIFY_IS_APPROX(m4=(m2*m3).pruned(0), refMat4=refMat2*refMat3);
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VERIFY_IS_APPROX(m4=(m2t.transpose()*m3).pruned(0), refMat4=refMat2t.transpose()*refMat3);
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VERIFY_IS_APPROX(m4=(m2t.transpose()*m3t.transpose()).pruned(0), refMat4=refMat2t.transpose()*refMat3t.transpose());
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VERIFY_IS_APPROX(m4=(m2*m3t.transpose()).pruned(0), refMat4=refMat2*refMat3t.transpose());
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// test aliasing
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m4 = m2; refMat4 = refMat2;
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VERIFY_IS_APPROX(m4=m4*m3, refMat4=refMat4*refMat3);
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// sparse * dense
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VERIFY_IS_APPROX(dm4=m2*refMat3, refMat4=refMat2*refMat3);
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VERIFY_IS_APPROX(dm4=m2*refMat3t.transpose(), refMat4=refMat2*refMat3t.transpose());
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VERIFY_IS_APPROX(dm4=m2t.transpose()*refMat3, refMat4=refMat2t.transpose()*refMat3);
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VERIFY_IS_APPROX(dm4=m2t.transpose()*refMat3t.transpose(), refMat4=refMat2t.transpose()*refMat3t.transpose());
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VERIFY_IS_APPROX(dm4=m2*(refMat3+refMat3), refMat4=refMat2*(refMat3+refMat3));
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VERIFY_IS_APPROX(dm4=m2t.transpose()*(refMat3+refMat5)*0.5, refMat4=refMat2t.transpose()*(refMat3+refMat5)*0.5);
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// dense * sparse
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VERIFY_IS_APPROX(dm4=refMat2*m3, refMat4=refMat2*refMat3);
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VERIFY_IS_APPROX(dm4=refMat2*m3t.transpose(), refMat4=refMat2*refMat3t.transpose());
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VERIFY_IS_APPROX(dm4=refMat2t.transpose()*m3, refMat4=refMat2t.transpose()*refMat3);
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VERIFY_IS_APPROX(dm4=refMat2t.transpose()*m3t.transpose(), refMat4=refMat2t.transpose()*refMat3t.transpose());
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// sparse * dense and dense * sparse outer product
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{
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Index c = internal::random<Index>(0,depth-1);
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Index r = internal::random<Index>(0,rows-1);
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Index c1 = internal::random<Index>(0,cols-1);
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Index r1 = internal::random<Index>(0,depth-1);
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DenseMatrix dm5 = DenseMatrix::Random(depth, cols);
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VERIFY_IS_APPROX( m4=m2.col(c)*dm5.col(c1).transpose(), refMat4=refMat2.col(c)*dm5.col(c1).transpose());
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VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
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VERIFY_IS_APPROX( m4=m2.middleCols(c,1)*dm5.col(c1).transpose(), refMat4=refMat2.col(c)*dm5.col(c1).transpose());
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VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
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VERIFY_IS_APPROX(dm4=m2.col(c)*dm5.col(c1).transpose(), refMat4=refMat2.col(c)*dm5.col(c1).transpose());
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VERIFY_IS_APPROX(m4=dm5.col(c1)*m2.col(c).transpose(), refMat4=dm5.col(c1)*refMat2.col(c).transpose());
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VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
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VERIFY_IS_APPROX(m4=dm5.col(c1)*m2.middleCols(c,1).transpose(), refMat4=dm5.col(c1)*refMat2.col(c).transpose());
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VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
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VERIFY_IS_APPROX(dm4=dm5.col(c1)*m2.col(c).transpose(), refMat4=dm5.col(c1)*refMat2.col(c).transpose());
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VERIFY_IS_APPROX( m4=dm5.row(r1).transpose()*m2.col(c).transpose(), refMat4=dm5.row(r1).transpose()*refMat2.col(c).transpose());
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VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
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VERIFY_IS_APPROX(dm4=dm5.row(r1).transpose()*m2.col(c).transpose(), refMat4=dm5.row(r1).transpose()*refMat2.col(c).transpose());
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VERIFY_IS_APPROX( m4=m2.row(r).transpose()*dm5.col(c1).transpose(), refMat4=refMat2.row(r).transpose()*dm5.col(c1).transpose());
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VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
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VERIFY_IS_APPROX( m4=m2.middleRows(r,1).transpose()*dm5.col(c1).transpose(), refMat4=refMat2.row(r).transpose()*dm5.col(c1).transpose());
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VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
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VERIFY_IS_APPROX(dm4=m2.row(r).transpose()*dm5.col(c1).transpose(), refMat4=refMat2.row(r).transpose()*dm5.col(c1).transpose());
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VERIFY_IS_APPROX( m4=dm5.col(c1)*m2.row(r), refMat4=dm5.col(c1)*refMat2.row(r));
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VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
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VERIFY_IS_APPROX( m4=dm5.col(c1)*m2.middleRows(r,1), refMat4=dm5.col(c1)*refMat2.row(r));
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VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
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VERIFY_IS_APPROX(dm4=dm5.col(c1)*m2.row(r), refMat4=dm5.col(c1)*refMat2.row(r));
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VERIFY_IS_APPROX( m4=dm5.row(r1).transpose()*m2.row(r), refMat4=dm5.row(r1).transpose()*refMat2.row(r));
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VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
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VERIFY_IS_APPROX(dm4=dm5.row(r1).transpose()*m2.row(r), refMat4=dm5.row(r1).transpose()*refMat2.row(r));
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}
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VERIFY_IS_APPROX(m6=m6*m6, refMat6=refMat6*refMat6);
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// sparse matrix * sparse vector
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ColSpVector cv0(cols), cv1;
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DenseVector dcv0(cols), dcv1;
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initSparse(2*density,dcv0, cv0);
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RowSpVector rv0(depth), rv1;
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RowDenseVector drv0(depth), drv1(rv1);
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initSparse(2*density,drv0, rv0);
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VERIFY_IS_APPROX(cv1=rv0*m3, dcv1=drv0*refMat3);
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VERIFY_IS_APPROX(rv1=rv0*m3, drv1=drv0*refMat3);
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VERIFY_IS_APPROX(cv1=m3*cv0, dcv1=refMat3*dcv0);
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VERIFY_IS_APPROX(cv1=m3t.adjoint()*cv0, dcv1=refMat3t.adjoint()*dcv0);
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VERIFY_IS_APPROX(rv1=m3*cv0, drv1=refMat3*dcv0);
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}
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// test matrix - diagonal product
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{
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DenseMatrix refM2 = DenseMatrix::Zero(rows, cols);
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DenseMatrix refM3 = DenseMatrix::Zero(rows, cols);
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DenseMatrix d3 = DenseMatrix::Zero(rows, cols);
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DiagonalMatrix<Scalar,Dynamic> d1(DenseVector::Random(cols));
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DiagonalMatrix<Scalar,Dynamic> d2(DenseVector::Random(rows));
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SparseMatrixType m2(rows, cols);
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SparseMatrixType m3(rows, cols);
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initSparse<Scalar>(density, refM2, m2);
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initSparse<Scalar>(density, refM3, m3);
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VERIFY_IS_APPROX(m3=m2*d1, refM3=refM2*d1);
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VERIFY_IS_APPROX(m3=m2.transpose()*d2, refM3=refM2.transpose()*d2);
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VERIFY_IS_APPROX(m3=d2*m2, refM3=d2*refM2);
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VERIFY_IS_APPROX(m3=d1*m2.transpose(), refM3=d1*refM2.transpose());
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// also check with a SparseWrapper:
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DenseVector v1 = DenseVector::Random(cols);
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DenseVector v2 = DenseVector::Random(rows);
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VERIFY_IS_APPROX(m3=m2*v1.asDiagonal(), refM3=refM2*v1.asDiagonal());
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VERIFY_IS_APPROX(m3=m2.transpose()*v2.asDiagonal(), refM3=refM2.transpose()*v2.asDiagonal());
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VERIFY_IS_APPROX(m3=v2.asDiagonal()*m2, refM3=v2.asDiagonal()*refM2);
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VERIFY_IS_APPROX(m3=v1.asDiagonal()*m2.transpose(), refM3=v1.asDiagonal()*refM2.transpose());
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VERIFY_IS_APPROX(m3=v2.asDiagonal()*m2*v1.asDiagonal(), refM3=v2.asDiagonal()*refM2*v1.asDiagonal());
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// evaluate to a dense matrix to check the .row() and .col() iterator functions
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VERIFY_IS_APPROX(d3=m2*d1, refM3=refM2*d1);
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VERIFY_IS_APPROX(d3=m2.transpose()*d2, refM3=refM2.transpose()*d2);
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VERIFY_IS_APPROX(d3=d2*m2, refM3=d2*refM2);
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VERIFY_IS_APPROX(d3=d1*m2.transpose(), refM3=d1*refM2.transpose());
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}
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// test self adjoint products
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{
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DenseMatrix b = DenseMatrix::Random(rows, rows);
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DenseMatrix x = DenseMatrix::Random(rows, rows);
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DenseMatrix refX = DenseMatrix::Random(rows, rows);
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DenseMatrix refUp = DenseMatrix::Zero(rows, rows);
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DenseMatrix refLo = DenseMatrix::Zero(rows, rows);
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DenseMatrix refS = DenseMatrix::Zero(rows, rows);
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SparseMatrixType mUp(rows, rows);
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SparseMatrixType mLo(rows, rows);
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SparseMatrixType mS(rows, rows);
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do {
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initSparse<Scalar>(density, refUp, mUp, ForceRealDiag|/*ForceNonZeroDiag|*/MakeUpperTriangular);
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} while (refUp.isZero());
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refLo = refUp.adjoint();
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mLo = mUp.adjoint();
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refS = refUp + refLo;
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refS.diagonal() *= 0.5;
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mS = mUp + mLo;
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// TODO be able to address the diagonal....
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for (int k=0; k<mS.outerSize(); ++k)
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for (typename SparseMatrixType::InnerIterator it(mS,k); it; ++it)
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if (it.index() == k)
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it.valueRef() *= 0.5;
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VERIFY_IS_APPROX(refS.adjoint(), refS);
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VERIFY_IS_APPROX(mS.adjoint(), mS);
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VERIFY_IS_APPROX(mS, refS);
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VERIFY_IS_APPROX(x=mS*b, refX=refS*b);
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VERIFY_IS_APPROX(x=mUp.template selfadjointView<Upper>()*b, refX=refS*b);
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VERIFY_IS_APPROX(x=mLo.template selfadjointView<Lower>()*b, refX=refS*b);
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VERIFY_IS_APPROX(x=mS.template selfadjointView<Upper|Lower>()*b, refX=refS*b);
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// sparse selfadjointView * sparse
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SparseMatrixType mSres(rows,rows);
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VERIFY_IS_APPROX(mSres = mLo.template selfadjointView<Lower>()*mS,
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refX = refLo.template selfadjointView<Lower>()*refS);
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// sparse * sparse selfadjointview
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VERIFY_IS_APPROX(mSres = mS * mLo.template selfadjointView<Lower>(),
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refX = refS * refLo.template selfadjointView<Lower>());
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}
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}
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// New test for Bug in SparseTimeDenseProduct
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template<typename SparseMatrixType, typename DenseMatrixType> void sparse_product_regression_test()
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{
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// This code does not compile with afflicted versions of the bug
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SparseMatrixType sm1(3,2);
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DenseMatrixType m2(2,2);
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sm1.setZero();
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m2.setZero();
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DenseMatrixType m3 = sm1*m2;
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// This code produces a segfault with afflicted versions of another SparseTimeDenseProduct
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// bug
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SparseMatrixType sm2(20000,2);
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sm2.setZero();
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DenseMatrixType m4(sm2*m2);
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VERIFY_IS_APPROX( m4(0,0), 0.0 );
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}
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void test_sparse_product()
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{
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for(int i = 0; i < g_repeat; i++) {
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CALL_SUBTEST_1( (sparse_product<SparseMatrix<double,ColMajor> >()) );
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CALL_SUBTEST_1( (sparse_product<SparseMatrix<double,RowMajor> >()) );
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CALL_SUBTEST_2( (sparse_product<SparseMatrix<std::complex<double>, ColMajor > >()) );
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CALL_SUBTEST_2( (sparse_product<SparseMatrix<std::complex<double>, RowMajor > >()) );
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CALL_SUBTEST_3( (sparse_product<SparseMatrix<float,ColMajor,long int> >()) );
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CALL_SUBTEST_4( (sparse_product_regression_test<SparseMatrix<double,RowMajor>, Matrix<double, Dynamic, Dynamic, RowMajor> >()) );
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}
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}
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