// This file is part of Eigen, a lightweight C++ template library // for linear algebra. // // Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr> // Copyright (C) 2008 Daniel Gomez Ferro <dgomezferro@gmail.com> // Copyright (C) 2013 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@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> void sparse_basic(const SparseMatrixType& ref) { typedef typename SparseMatrixType::Index Index; typedef Matrix<Index,2,1> Vector2; const Index rows = ref.rows(); const Index cols = ref.cols(); typedef typename SparseMatrixType::Scalar Scalar; enum { Flags = SparseMatrixType::Flags }; double density = (std::max)(8./(rows*cols), 0.01); typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix; typedef Matrix<Scalar,Dynamic,1> DenseVector; typedef Matrix<Scalar,1,Dynamic> RowDenseVector; Scalar eps = 1e-6; Scalar s1 = internal::random<Scalar>(); { SparseMatrixType m(rows, cols); DenseMatrix refMat = DenseMatrix::Zero(rows, cols); DenseVector vec1 = DenseVector::Random(rows); std::vector<Vector2> zeroCoords; std::vector<Vector2> nonzeroCoords; initSparse<Scalar>(density, refMat, m, 0, &zeroCoords, &nonzeroCoords); if (zeroCoords.size()==0 || nonzeroCoords.size()==0) return; // test coeff and coeffRef for (int i=0; i<(int)zeroCoords.size(); ++i) { VERIFY_IS_MUCH_SMALLER_THAN( m.coeff(zeroCoords[i].x(),zeroCoords[i].y()), eps ); if(internal::is_same<SparseMatrixType,SparseMatrix<Scalar,Flags> >::value) VERIFY_RAISES_ASSERT( m.coeffRef(zeroCoords[0].x(),zeroCoords[0].y()) = 5 ); } VERIFY_IS_APPROX(m, refMat); m.coeffRef(nonzeroCoords[0].x(), nonzeroCoords[0].y()) = Scalar(5); refMat.coeffRef(nonzeroCoords[0].x(), nonzeroCoords[0].y()) = Scalar(5); VERIFY_IS_APPROX(m, refMat); // test InnerIterators and Block expressions for (int t=0; t<10; ++t) { int j = internal::random<int>(0,cols-1); int i = internal::random<int>(0,rows-1); int w = internal::random<int>(1,cols-j-1); int h = internal::random<int>(1,rows-i-1); VERIFY_IS_APPROX(m.block(i,j,h,w), refMat.block(i,j,h,w)); for(int c=0; c<w; c++) { VERIFY_IS_APPROX(m.block(i,j,h,w).col(c), refMat.block(i,j,h,w).col(c)); for(int r=0; r<h; r++) { VERIFY_IS_APPROX(m.block(i,j,h,w).col(c).coeff(r), refMat.block(i,j,h,w).col(c).coeff(r)); VERIFY_IS_APPROX(m.block(i,j,h,w).coeff(r,c), refMat.block(i,j,h,w).coeff(r,c)); } } for(int r=0; r<h; r++) { VERIFY_IS_APPROX(m.block(i,j,h,w).row(r), refMat.block(i,j,h,w).row(r)); for(int c=0; c<w; c++) { VERIFY_IS_APPROX(m.block(i,j,h,w).row(r).coeff(c), refMat.block(i,j,h,w).row(r).coeff(c)); VERIFY_IS_APPROX(m.block(i,j,h,w).coeff(r,c), refMat.block(i,j,h,w).coeff(r,c)); } } VERIFY_IS_APPROX(m.middleCols(j,w), refMat.middleCols(j,w)); VERIFY_IS_APPROX(m.middleRows(i,h), refMat.middleRows(i,h)); for(int r=0; r<h; r++) { VERIFY_IS_APPROX(m.middleCols(j,w).row(r), refMat.middleCols(j,w).row(r)); VERIFY_IS_APPROX(m.middleRows(i,h).row(r), refMat.middleRows(i,h).row(r)); for(int c=0; c<w; c++) { VERIFY_IS_APPROX(m.col(c).coeff(r), refMat.col(c).coeff(r)); VERIFY_IS_APPROX(m.row(r).coeff(c), refMat.row(r).coeff(c)); VERIFY_IS_APPROX(m.middleCols(j,w).coeff(r,c), refMat.middleCols(j,w).coeff(r,c)); VERIFY_IS_APPROX(m.middleRows(i,h).coeff(r,c), refMat.middleRows(i,h).coeff(r,c)); if(m.middleCols(j,w).coeff(r,c) != Scalar(0)) { VERIFY_IS_APPROX(m.middleCols(j,w).coeffRef(r,c), refMat.middleCols(j,w).coeff(r,c)); } if(m.middleRows(i,h).coeff(r,c) != Scalar(0)) { VERIFY_IS_APPROX(m.middleRows(i,h).coeff(r,c), refMat.middleRows(i,h).coeff(r,c)); } } } for(int c=0; c<w; c++) { VERIFY_IS_APPROX(m.middleCols(j,w).col(c), refMat.middleCols(j,w).col(c)); VERIFY_IS_APPROX(m.middleRows(i,h).col(c), refMat.middleRows(i,h).col(c)); } } for(int c=0; c<cols; c++) { VERIFY_IS_APPROX(m.col(c) + m.col(c), (m + m).col(c)); VERIFY_IS_APPROX(m.col(c) + m.col(c), refMat.col(c) + refMat.col(c)); } for(int r=0; r<rows; r++) { VERIFY_IS_APPROX(m.row(r) + m.row(r), (m + m).row(r)); VERIFY_IS_APPROX(m.row(r) + m.row(r), refMat.row(r) + refMat.row(r)); } // test assertion VERIFY_RAISES_ASSERT( m.coeffRef(-1,1) = 0 ); VERIFY_RAISES_ASSERT( m.coeffRef(0,m.cols()) = 0 ); } // test insert (inner random) { DenseMatrix m1(rows,cols); m1.setZero(); SparseMatrixType m2(rows,cols); if(internal::random<int>()%2) m2.reserve(VectorXi::Constant(m2.outerSize(), 2)); for (Index j=0; j<cols; ++j) { for (Index k=0; k<rows/2; ++k) { Index i = internal::random<Index>(0,rows-1); if (m1.coeff(i,j)==Scalar(0)) m2.insert(i,j) = m1(i,j) = internal::random<Scalar>(); } } m2.finalize(); VERIFY_IS_APPROX(m2,m1); } // test insert (fully random) { DenseMatrix m1(rows,cols); m1.setZero(); SparseMatrixType m2(rows,cols); if(internal::random<int>()%2) m2.reserve(VectorXi::Constant(m2.outerSize(), 2)); for (int k=0; k<rows*cols; ++k) { Index i = internal::random<Index>(0,rows-1); Index j = internal::random<Index>(0,cols-1); if ((m1.coeff(i,j)==Scalar(0)) && (internal::random<int>()%2)) m2.insert(i,j) = m1(i,j) = internal::random<Scalar>(); else { Scalar v = internal::random<Scalar>(); m2.coeffRef(i,j) += v; m1(i,j) += v; } } VERIFY_IS_APPROX(m2,m1); } // test insert (un-compressed) for(int mode=0;mode<4;++mode) { DenseMatrix m1(rows,cols); m1.setZero(); SparseMatrixType m2(rows,cols); VectorXi r(VectorXi::Constant(m2.outerSize(), ((mode%2)==0) ? m2.innerSize() : std::max<int>(1,m2.innerSize()/8))); m2.reserve(r); for (int k=0; k<rows*cols; ++k) { Index i = internal::random<Index>(0,rows-1); Index j = internal::random<Index>(0,cols-1); if (m1.coeff(i,j)==Scalar(0)) m2.insert(i,j) = m1(i,j) = internal::random<Scalar>(); if(mode==3) m2.reserve(r); } if(internal::random<int>()%2) m2.makeCompressed(); VERIFY_IS_APPROX(m2,m1); } // test innerVector() { DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows); SparseMatrixType m2(rows, rows); initSparse<Scalar>(density, refMat2, m2); Index j0 = internal::random<Index>(0,rows-1); Index j1 = internal::random<Index>(0,rows-1); if(SparseMatrixType::IsRowMajor) VERIFY_IS_APPROX(m2.innerVector(j0), refMat2.row(j0)); else VERIFY_IS_APPROX(m2.innerVector(j0), refMat2.col(j0)); if(SparseMatrixType::IsRowMajor) VERIFY_IS_APPROX(m2.innerVector(j0)+m2.innerVector(j1), refMat2.row(j0)+refMat2.row(j1)); else VERIFY_IS_APPROX(m2.innerVector(j0)+m2.innerVector(j1), refMat2.col(j0)+refMat2.col(j1)); SparseMatrixType m3(rows,rows); m3.reserve(VectorXi::Constant(rows,rows/2)); for(Index j=0; j<rows; ++j) for(Index k=0; k<j; ++k) m3.insertByOuterInner(j,k) = k+1; for(Index j=0; j<rows; ++j) { VERIFY(j==numext::real(m3.innerVector(j).nonZeros())); if(j>0) VERIFY(j==numext::real(m3.innerVector(j).lastCoeff())); } m3.makeCompressed(); for(Index j=0; j<rows; ++j) { VERIFY(j==numext::real(m3.innerVector(j).nonZeros())); if(j>0) VERIFY(j==numext::real(m3.innerVector(j).lastCoeff())); } //m2.innerVector(j0) = 2*m2.innerVector(j1); //refMat2.col(j0) = 2*refMat2.col(j1); //VERIFY_IS_APPROX(m2, refMat2); } // test innerVectors() { DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows); SparseMatrixType m2(rows, rows); initSparse<Scalar>(density, refMat2, m2); if(internal::random<float>(0,1)>0.5) m2.makeCompressed(); Index j0 = internal::random<Index>(0,rows-2); Index j1 = internal::random<Index>(0,rows-2); Index n0 = internal::random<Index>(1,rows-(std::max)(j0,j1)); if(SparseMatrixType::IsRowMajor) VERIFY_IS_APPROX(m2.innerVectors(j0,n0), refMat2.block(j0,0,n0,cols)); else VERIFY_IS_APPROX(m2.innerVectors(j0,n0), refMat2.block(0,j0,rows,n0)); if(SparseMatrixType::IsRowMajor) VERIFY_IS_APPROX(m2.innerVectors(j0,n0)+m2.innerVectors(j1,n0), refMat2.middleRows(j0,n0)+refMat2.middleRows(j1,n0)); else VERIFY_IS_APPROX(m2.innerVectors(j0,n0)+m2.innerVectors(j1,n0), refMat2.block(0,j0,rows,n0)+refMat2.block(0,j1,rows,n0)); VERIFY_IS_APPROX(m2, refMat2); m2.innerVectors(j0,n0) = m2.innerVectors(j0,n0) + m2.innerVectors(j1,n0); if(SparseMatrixType::IsRowMajor) refMat2.middleRows(j0,n0) = (refMat2.middleRows(j0,n0) + refMat2.middleRows(j1,n0)).eval(); else refMat2.middleCols(j0,n0) = (refMat2.middleCols(j0,n0) + refMat2.middleCols(j1,n0)).eval(); VERIFY_IS_APPROX(m2, refMat2); } // test basic computations { DenseMatrix refM1 = DenseMatrix::Zero(rows, rows); DenseMatrix refM2 = DenseMatrix::Zero(rows, rows); DenseMatrix refM3 = DenseMatrix::Zero(rows, rows); DenseMatrix refM4 = DenseMatrix::Zero(rows, rows); SparseMatrixType m1(rows, rows); SparseMatrixType m2(rows, rows); SparseMatrixType m3(rows, rows); SparseMatrixType m4(rows, rows); initSparse<Scalar>(density, refM1, m1); initSparse<Scalar>(density, refM2, m2); initSparse<Scalar>(density, refM3, m3); initSparse<Scalar>(density, refM4, m4); VERIFY_IS_APPROX(m1+m2, refM1+refM2); VERIFY_IS_APPROX(m1+m2+m3, refM1+refM2+refM3); VERIFY_IS_APPROX(m3.cwiseProduct(m1+m2), refM3.cwiseProduct(refM1+refM2)); VERIFY_IS_APPROX(m1*s1-m2, refM1*s1-refM2); VERIFY_IS_APPROX(m1*=s1, refM1*=s1); VERIFY_IS_APPROX(m1/=s1, refM1/=s1); VERIFY_IS_APPROX(m1+=m2, refM1+=refM2); VERIFY_IS_APPROX(m1-=m2, refM1-=refM2); if(SparseMatrixType::IsRowMajor) VERIFY_IS_APPROX(m1.innerVector(0).dot(refM2.row(0)), refM1.row(0).dot(refM2.row(0))); else VERIFY_IS_APPROX(m1.innerVector(0).dot(refM2.row(0)), refM1.col(0).dot(refM2.row(0))); VERIFY_IS_APPROX(m1.conjugate(), refM1.conjugate()); VERIFY_IS_APPROX(m1.real(), refM1.real()); refM4.setRandom(); // sparse cwise* dense VERIFY_IS_APPROX(m3.cwiseProduct(refM4), refM3.cwiseProduct(refM4)); // VERIFY_IS_APPROX(m3.cwise()/refM4, refM3.cwise()/refM4); // test aliasing VERIFY_IS_APPROX((m1 = -m1), (refM1 = -refM1)); VERIFY_IS_APPROX((m1 = m1.transpose()), (refM1 = refM1.transpose().eval())); VERIFY_IS_APPROX((m1 = -m1.transpose()), (refM1 = -refM1.transpose().eval())); VERIFY_IS_APPROX((m1 += -m1), (refM1 += -refM1)); } // test transpose { DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows); SparseMatrixType m2(rows, rows); initSparse<Scalar>(density, refMat2, m2); VERIFY_IS_APPROX(m2.transpose().eval(), refMat2.transpose().eval()); VERIFY_IS_APPROX(m2.transpose(), refMat2.transpose()); VERIFY_IS_APPROX(SparseMatrixType(m2.adjoint()), refMat2.adjoint()); } // test generic blocks { DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows); SparseMatrixType m2(rows, rows); initSparse<Scalar>(density, refMat2, m2); Index j0 = internal::random<Index>(0,rows-2); Index j1 = internal::random<Index>(0,rows-2); Index n0 = internal::random<Index>(1,rows-(std::max)(j0,j1)); if(SparseMatrixType::IsRowMajor) VERIFY_IS_APPROX(m2.block(j0,0,n0,cols), refMat2.block(j0,0,n0,cols)); else VERIFY_IS_APPROX(m2.block(0,j0,rows,n0), refMat2.block(0,j0,rows,n0)); if(SparseMatrixType::IsRowMajor) VERIFY_IS_APPROX(m2.block(j0,0,n0,cols)+m2.block(j1,0,n0,cols), refMat2.block(j0,0,n0,cols)+refMat2.block(j1,0,n0,cols)); else VERIFY_IS_APPROX(m2.block(0,j0,rows,n0)+m2.block(0,j1,rows,n0), refMat2.block(0,j0,rows,n0)+refMat2.block(0,j1,rows,n0)); Index i = internal::random<Index>(0,m2.outerSize()-1); if(SparseMatrixType::IsRowMajor) { m2.innerVector(i) = m2.innerVector(i) * s1; refMat2.row(i) = refMat2.row(i) * s1; VERIFY_IS_APPROX(m2,refMat2); } else { m2.innerVector(i) = m2.innerVector(i) * s1; refMat2.col(i) = refMat2.col(i) * s1; VERIFY_IS_APPROX(m2,refMat2); } VERIFY_IS_APPROX(DenseVector(m2.col(j0)), refMat2.col(j0)); VERIFY_IS_APPROX(m2.col(j0), refMat2.col(j0)); VERIFY_IS_APPROX(RowDenseVector(m2.row(j0)), refMat2.row(j0)); VERIFY_IS_APPROX(m2.row(j0), refMat2.row(j0)); VERIFY_IS_APPROX(m2.block(j0,j1,n0,n0), refMat2.block(j0,j1,n0,n0)); VERIFY_IS_APPROX((2*m2).block(j0,j1,n0,n0), (2*refMat2).block(j0,j1,n0,n0)); } // test prune { SparseMatrixType m2(rows, rows); DenseMatrix refM2(rows, rows); refM2.setZero(); int countFalseNonZero = 0; int countTrueNonZero = 0; for (Index j=0; j<m2.outerSize(); ++j) { m2.startVec(j); for (Index i=0; i<m2.innerSize(); ++i) { float x = internal::random<float>(0,1); if (x<0.1) { // do nothing } else if (x<0.5) { countFalseNonZero++; m2.insertBackByOuterInner(j,i) = Scalar(0); } else { countTrueNonZero++; m2.insertBackByOuterInner(j,i) = Scalar(1); if(SparseMatrixType::IsRowMajor) refM2(j,i) = Scalar(1); else refM2(i,j) = Scalar(1); } } } m2.finalize(); VERIFY(countFalseNonZero+countTrueNonZero == m2.nonZeros()); VERIFY_IS_APPROX(m2, refM2); m2.prune(Scalar(1)); VERIFY(countTrueNonZero==m2.nonZeros()); VERIFY_IS_APPROX(m2, refM2); } // test setFromTriplets { typedef Triplet<Scalar,Index> TripletType; std::vector<TripletType> triplets; int ntriplets = rows*cols; triplets.reserve(ntriplets); DenseMatrix refMat(rows,cols); refMat.setZero(); for(int i=0;i<ntriplets;++i) { Index r = internal::random<Index>(0,rows-1); Index c = internal::random<Index>(0,cols-1); Scalar v = internal::random<Scalar>(); triplets.push_back(TripletType(r,c,v)); refMat(r,c) += v; } SparseMatrixType m(rows,cols); m.setFromTriplets(triplets.begin(), triplets.end()); VERIFY_IS_APPROX(m, refMat); } // test triangularView { DenseMatrix refMat2(rows, rows), refMat3(rows, rows); SparseMatrixType m2(rows, rows), m3(rows, rows); initSparse<Scalar>(density, refMat2, m2); refMat3 = refMat2.template triangularView<Lower>(); m3 = m2.template triangularView<Lower>(); VERIFY_IS_APPROX(m3, refMat3); refMat3 = refMat2.template triangularView<Upper>(); m3 = m2.template triangularView<Upper>(); VERIFY_IS_APPROX(m3, refMat3); refMat3 = refMat2.template triangularView<UnitUpper>(); m3 = m2.template triangularView<UnitUpper>(); VERIFY_IS_APPROX(m3, refMat3); refMat3 = refMat2.template triangularView<UnitLower>(); m3 = m2.template triangularView<UnitLower>(); VERIFY_IS_APPROX(m3, refMat3); refMat3 = refMat2.template triangularView<StrictlyUpper>(); m3 = m2.template triangularView<StrictlyUpper>(); VERIFY_IS_APPROX(m3, refMat3); refMat3 = refMat2.template triangularView<StrictlyLower>(); m3 = m2.template triangularView<StrictlyLower>(); VERIFY_IS_APPROX(m3, refMat3); } // test selfadjointView if(!SparseMatrixType::IsRowMajor) { DenseMatrix refMat2(rows, rows), refMat3(rows, rows); SparseMatrixType m2(rows, rows), m3(rows, rows); initSparse<Scalar>(density, refMat2, m2); refMat3 = refMat2.template selfadjointView<Lower>(); m3 = m2.template selfadjointView<Lower>(); VERIFY_IS_APPROX(m3, refMat3); } // test sparseView { DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows); SparseMatrixType m2(rows, rows); initSparse<Scalar>(density, refMat2, m2); VERIFY_IS_APPROX(m2.eval(), refMat2.sparseView().eval()); } // test diagonal { DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows); SparseMatrixType m2(rows, rows); initSparse<Scalar>(density, refMat2, m2); VERIFY_IS_APPROX(m2.diagonal(), refMat2.diagonal().eval()); } // test conservative resize { std::vector< std::pair<Index,Index> > inc; inc.push_back(std::pair<Index,Index>(-3,-2)); inc.push_back(std::pair<Index,Index>(0,0)); inc.push_back(std::pair<Index,Index>(3,2)); inc.push_back(std::pair<Index,Index>(3,0)); inc.push_back(std::pair<Index,Index>(0,3)); for(size_t i = 0; i< inc.size(); i++) { Index incRows = inc[i].first; Index incCols = inc[i].second; SparseMatrixType m1(rows, cols); DenseMatrix refMat1 = DenseMatrix::Zero(rows, cols); initSparse<Scalar>(density, refMat1, m1); m1.conservativeResize(rows+incRows, cols+incCols); refMat1.conservativeResize(rows+incRows, cols+incCols); if (incRows > 0) refMat1.bottomRows(incRows).setZero(); if (incCols > 0) refMat1.rightCols(incCols).setZero(); VERIFY_IS_APPROX(m1, refMat1); // Insert new values if (incRows > 0) m1.insert(m1.rows()-1, 0) = refMat1(refMat1.rows()-1, 0) = 1; if (incCols > 0) m1.insert(0, m1.cols()-1) = refMat1(0, refMat1.cols()-1) = 1; VERIFY_IS_APPROX(m1, refMat1); } } // test Identity matrix { DenseMatrix refMat1 = DenseMatrix::Identity(rows, rows); SparseMatrixType m1(rows, rows); m1.setIdentity(); VERIFY_IS_APPROX(m1, refMat1); } } void test_sparse_basic() { for(int i = 0; i < g_repeat; i++) { int s = Eigen::internal::random<int>(1,50); EIGEN_UNUSED_VARIABLE(s); CALL_SUBTEST_1(( sparse_basic(SparseMatrix<double>(8, 8)) )); CALL_SUBTEST_2(( sparse_basic(SparseMatrix<std::complex<double>, ColMajor>(s, s)) )); CALL_SUBTEST_2(( sparse_basic(SparseMatrix<std::complex<double>, RowMajor>(s, s)) )); CALL_SUBTEST_1(( sparse_basic(SparseMatrix<double>(s, s)) )); CALL_SUBTEST_1(( sparse_basic(SparseMatrix<double,ColMajor,long int>(s, s)) )); CALL_SUBTEST_1(( sparse_basic(SparseMatrix<double,RowMajor,long int>(s, s)) )); CALL_SUBTEST_1(( sparse_basic(SparseMatrix<double,ColMajor,short int>(short(s), short(s))) )); CALL_SUBTEST_1(( sparse_basic(SparseMatrix<double,RowMajor,short int>(short(s), short(s))) )); } }