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							337 lines
						
					
					
						
							17 KiB
						
					
					
				
								// 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::StorageIndex StorageIndex;
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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), 0.2);
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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,StorageIndex> ColSpVector;
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								  typedef SparseVector<Scalar,RowMajor,StorageIndex> 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+m2)*m3, refMat4 = (refMat2+refMat2)*refMat3);
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								    VERIFY_IS_APPROX(m4 = m2*m3.leftCols(cols/2), refMat4 = refMat2*refMat3.leftCols(cols/2));
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								    VERIFY_IS_APPROX(m4 = m2*(m3+m3).leftCols(cols/2), refMat4 = refMat2*(refMat3+refMat3).leftCols(cols/2));
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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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								    // dense ?= sparse * sparse
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								    VERIFY_IS_APPROX(dm4 =m2*m3, refMat4 =refMat2*refMat3);
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								    VERIFY_IS_APPROX(dm4+=m2*m3, refMat4+=refMat2*refMat3);
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								    VERIFY_IS_APPROX(dm4-=m2*m3, refMat4-=refMat2*refMat3);
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								    VERIFY_IS_APPROX(dm4 =m2t.transpose()*m3, refMat4 =refMat2t.transpose()*refMat3);
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								    VERIFY_IS_APPROX(dm4+=m2t.transpose()*m3, refMat4+=refMat2t.transpose()*refMat3);
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								    VERIFY_IS_APPROX(dm4-=m2t.transpose()*m3, refMat4-=refMat2t.transpose()*refMat3);
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								    VERIFY_IS_APPROX(dm4 =m2t.transpose()*m3t.transpose(), refMat4 =refMat2t.transpose()*refMat3t.transpose());
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								    VERIFY_IS_APPROX(dm4+=m2t.transpose()*m3t.transpose(), refMat4+=refMat2t.transpose()*refMat3t.transpose());
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								    VERIFY_IS_APPROX(dm4-=m2t.transpose()*m3t.transpose(), refMat4-=refMat2t.transpose()*refMat3t.transpose());
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								    VERIFY_IS_APPROX(dm4 =m2*m3t.transpose(), refMat4 =refMat2*refMat3t.transpose());
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								    VERIFY_IS_APPROX(dm4+=m2*m3t.transpose(), refMat4+=refMat2*refMat3t.transpose());
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								    VERIFY_IS_APPROX(dm4-=m2*m3t.transpose(), refMat4-=refMat2*refMat3t.transpose());
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								    VERIFY_IS_APPROX(dm4 = m2*m3*s1, refMat4 = refMat2*refMat3*s1);
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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 matrix
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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, refMat4=refMat2*refMat3);
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								    VERIFY_IS_APPROX(dm4=dm4+m2*refMat3, refMat4=refMat4+refMat2*refMat3);
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								    VERIFY_IS_APPROX(dm4+=m2*refMat3, refMat4+=refMat2*refMat3);
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								    VERIFY_IS_APPROX(dm4-=m2*refMat3, refMat4-=refMat2*refMat3);
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								    VERIFY_IS_APPROX(dm4.noalias()+=m2*refMat3, refMat4+=refMat2*refMat3);
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								    VERIFY_IS_APPROX(dm4.noalias()-=m2*refMat3, refMat4-=refMat2*refMat3);
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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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								    // sparse * dense vector
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								    VERIFY_IS_APPROX(dm4.col(0)=m2*refMat3.col(0), refMat4.col(0)=refMat2*refMat3.col(0));
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								    VERIFY_IS_APPROX(dm4.col(0)=m2*refMat3t.transpose().col(0), refMat4.col(0)=refMat2*refMat3t.transpose().col(0));
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								    VERIFY_IS_APPROX(dm4.col(0)=m2t.transpose()*refMat3.col(0), refMat4.col(0)=refMat2t.transpose()*refMat3.col(0));
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								    VERIFY_IS_APPROX(dm4.col(0)=m2t.transpose()*refMat3t.transpose().col(0), refMat4.col(0)=refMat2t.transpose()*refMat3t.transpose().col(0));
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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=dm4+refMat2*m3, refMat4=refMat4+refMat2*refMat3);
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								    VERIFY_IS_APPROX(dm4+=refMat2*m3, refMat4+=refMat2*refMat3);
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								    VERIFY_IS_APPROX(dm4-=refMat2*m3, refMat4-=refMat2*refMat3);
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								    VERIFY_IS_APPROX(dm4.noalias()+=refMat2*m3, refMat4+=refMat2*refMat3);
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								    VERIFY_IS_APPROX(dm4.noalias()-=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=m3*cv0, dcv1=refMat3*dcv0);    
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								    VERIFY_IS_APPROX(rv1=rv0*m3, drv1=drv0*refMat3);
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								    VERIFY_IS_APPROX(cv1=m3t.adjoint()*cv0, dcv1=refMat3t.adjoint()*dcv0);
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								    VERIFY_IS_APPROX(cv1=rv0*m3, dcv1=drv0*refMat3);
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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);
							 | 
						|
								    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() *= 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);
							 | 
						|
								    
							 | 
						|
								    // 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 );
							 | 
						|
								}
							 | 
						|
								
							 | 
						|
								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_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> >()) );
							 | 
						|
								  }
							 | 
						|
								}
							 |