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326 lines
9.6 KiB
C++
326 lines
9.6 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) 2011 Gael Guennebaud <g.gael@free.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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#include <Eigen/SparseCore>
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template<typename Solver, typename Rhs, typename DenseMat, typename DenseRhs>
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void check_sparse_solving(Solver& solver, const typename Solver::MatrixType& A, const Rhs& b, const DenseMat& dA, const DenseRhs& db)
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{
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typedef typename Solver::MatrixType Mat;
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typedef typename Mat::Scalar Scalar;
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DenseRhs refX = dA.lu().solve(db);
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Rhs x(b.rows(), b.cols());
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Rhs oldb = b;
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solver.compute(A);
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if (solver.info() != Success)
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{
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std::cerr << "sparse solver testing: factorization failed (check_sparse_solving)\n";
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exit(0);
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return;
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}
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x = solver.solve(b);
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if (solver.info() != Success)
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{
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std::cerr << "sparse solver testing: solving failed\n";
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return;
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}
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VERIFY(oldb.isApprox(b) && "sparse solver testing: the rhs should not be modified!");
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VERIFY(x.isApprox(refX,test_precision<Scalar>()));
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x.setZero();
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// test the analyze/factorize API
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solver.analyzePattern(A);
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solver.factorize(A);
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if (solver.info() != Success)
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{
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std::cerr << "sparse solver testing: factorization failed (check_sparse_solving)\n";
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exit(0);
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return;
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}
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x = solver.solve(b);
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if (solver.info() != Success)
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{
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std::cerr << "sparse solver testing: solving failed\n";
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return;
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}
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VERIFY(oldb.isApprox(b) && "sparse solver testing: the rhs should not be modified!");
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VERIFY(x.isApprox(refX,test_precision<Scalar>()));
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// test Block as the result and rhs:
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{
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DenseRhs x(db.rows(), db.cols());
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DenseRhs b(db), oldb(db);
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x.setZero();
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x.block(0,0,x.rows(),x.cols()) = solver.solve(b.block(0,0,b.rows(),b.cols()));
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VERIFY(oldb.isApprox(b) && "sparse solver testing: the rhs should not be modified!");
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VERIFY(x.isApprox(refX,test_precision<Scalar>()));
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}
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}
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template<typename Solver, typename Rhs>
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void check_sparse_solving_real_cases(Solver& solver, const typename Solver::MatrixType& A, const Rhs& b, const Rhs& refX)
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{
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typedef typename Solver::MatrixType Mat;
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typedef typename Mat::Scalar Scalar;
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typedef typename Mat::RealScalar RealScalar;
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Rhs x(b.rows(), b.cols());
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solver.compute(A);
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if (solver.info() != Success)
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{
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std::cerr << "sparse solver testing: factorization failed (check_sparse_solving_real_cases)\n";
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exit(0);
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return;
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}
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x = solver.solve(b);
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if (solver.info() != Success)
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{
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std::cerr << "sparse solver testing: solving failed\n";
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return;
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}
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RealScalar res_error;
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// Compute the norm of the relative error
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if(refX.size() != 0)
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res_error = (refX - x).norm()/refX.norm();
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else
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{
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// Compute the relative residual norm
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res_error = (b - A * x).norm()/b.norm();
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}
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if (res_error > test_precision<Scalar>() ){
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std::cerr << "Test " << g_test_stack.back() << " failed in "EI_PP_MAKE_STRING(__FILE__)
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<< " (" << EI_PP_MAKE_STRING(__LINE__) << ")" << std::endl << std::endl;
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abort();
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}
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}
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template<typename Solver, typename DenseMat>
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void check_sparse_determinant(Solver& solver, const typename Solver::MatrixType& A, const DenseMat& dA)
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{
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typedef typename Solver::MatrixType Mat;
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typedef typename Mat::Scalar Scalar;
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solver.compute(A);
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if (solver.info() != Success)
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{
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std::cerr << "sparse solver testing: factorization failed (check_sparse_determinant)\n";
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return;
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}
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Scalar refDet = dA.determinant();
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VERIFY_IS_APPROX(refDet,solver.determinant());
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}
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template<typename Solver, typename DenseMat>
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int generate_sparse_spd_problem(Solver& , typename Solver::MatrixType& A, typename Solver::MatrixType& halfA, DenseMat& dA, int maxSize = 300)
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{
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typedef typename Solver::MatrixType Mat;
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typedef typename Mat::Scalar Scalar;
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typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
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int size = internal::random<int>(1,maxSize);
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double density = (std::max)(8./(size*size), 0.01);
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Mat M(size, size);
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DenseMatrix dM(size, size);
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initSparse<Scalar>(density, dM, M, ForceNonZeroDiag);
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A = M * M.adjoint();
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dA = dM * dM.adjoint();
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halfA.resize(size,size);
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halfA.template selfadjointView<Solver::UpLo>().rankUpdate(M);
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return size;
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}
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#ifdef TEST_REAL_CASES
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template<typename Scalar>
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inline std::string get_matrixfolder()
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{
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std::string mat_folder = TEST_REAL_CASES;
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if( internal::is_same<Scalar, std::complex<float> >::value || internal::is_same<Scalar, std::complex<double> >::value )
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mat_folder = mat_folder + static_cast<std::string>("/complex/");
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else
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mat_folder = mat_folder + static_cast<std::string>("/real/");
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return mat_folder;
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}
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#endif
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template<typename Solver> void check_sparse_spd_solving(Solver& solver)
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{
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typedef typename Solver::MatrixType Mat;
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typedef typename Mat::Scalar Scalar;
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typedef SparseMatrix<Scalar,ColMajor> SpMat;
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typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
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typedef Matrix<Scalar,Dynamic,1> DenseVector;
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// generate the problem
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Mat A, halfA;
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DenseMatrix dA;
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for (int i = 0; i < g_repeat; i++) {
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int size = generate_sparse_spd_problem(solver, A, halfA, dA);
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// generate the right hand sides
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int rhsCols = internal::random<int>(1,16);
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double density = (std::max)(8./(size*rhsCols), 0.1);
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SpMat B(size,rhsCols);
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DenseVector b = DenseVector::Random(size);
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DenseMatrix dB(size,rhsCols);
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initSparse<Scalar>(density, dB, B, ForceNonZeroDiag);
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check_sparse_solving(solver, A, b, dA, b);
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check_sparse_solving(solver, halfA, b, dA, b);
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check_sparse_solving(solver, A, dB, dA, dB);
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check_sparse_solving(solver, halfA, dB, dA, dB);
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check_sparse_solving(solver, A, B, dA, dB);
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check_sparse_solving(solver, halfA, B, dA, dB);
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// check only once
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if(i==0)
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{
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b = DenseVector::Zero(size);
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check_sparse_solving(solver, A, b, dA, b);
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}
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}
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// First, get the folder
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#ifdef TEST_REAL_CASES
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if (internal::is_same<Scalar, float>::value
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|| internal::is_same<Scalar, std::complex<float> >::value)
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return ;
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std::string mat_folder = get_matrixfolder<Scalar>();
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MatrixMarketIterator<Scalar> it(mat_folder);
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for (; it; ++it)
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{
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if (it.sym() == SPD){
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Mat halfA;
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PermutationMatrix<Dynamic, Dynamic, Index> pnull;
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halfA.template selfadjointView<Solver::UpLo>() = it.matrix().template triangularView<Eigen::Lower>().twistedBy(pnull);
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std::cout<< " ==== SOLVING WITH MATRIX " << it.matname() << " ==== \n";
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check_sparse_solving_real_cases(solver, it.matrix(), it.rhs(), it.refX());
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check_sparse_solving_real_cases(solver, halfA, it.rhs(), it.refX());
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}
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}
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#endif
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}
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template<typename Solver> void check_sparse_spd_determinant(Solver& solver)
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{
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typedef typename Solver::MatrixType Mat;
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typedef typename Mat::Scalar Scalar;
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typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
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// generate the problem
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Mat A, halfA;
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DenseMatrix dA;
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generate_sparse_spd_problem(solver, A, halfA, dA, 30);
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for (int i = 0; i < g_repeat; i++) {
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check_sparse_determinant(solver, A, dA);
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check_sparse_determinant(solver, halfA, dA );
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}
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}
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template<typename Solver, typename DenseMat>
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int generate_sparse_square_problem(Solver&, typename Solver::MatrixType& A, DenseMat& dA, int maxSize = 300)
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{
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typedef typename Solver::MatrixType Mat;
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typedef typename Mat::Scalar Scalar;
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int size = internal::random<int>(1,maxSize);
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double density = (std::max)(8./(size*size), 0.01);
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A.resize(size,size);
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dA.resize(size,size);
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initSparse<Scalar>(density, dA, A, ForceNonZeroDiag);
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return size;
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}
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template<typename Solver> void check_sparse_square_solving(Solver& solver)
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{
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typedef typename Solver::MatrixType Mat;
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typedef typename Mat::Scalar Scalar;
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typedef SparseMatrix<Scalar,ColMajor> SpMat;
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typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
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typedef Matrix<Scalar,Dynamic,1> DenseVector;
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int rhsCols = internal::random<int>(1,16);
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Mat A;
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DenseMatrix dA;
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for (int i = 0; i < g_repeat; i++) {
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int size = generate_sparse_square_problem(solver, A, dA);
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A.makeCompressed();
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DenseVector b = DenseVector::Random(size);
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DenseMatrix dB(size,rhsCols);
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SpMat B(size,rhsCols);
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double density = (std::max)(8./(size*rhsCols), 0.1);
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initSparse<Scalar>(density, dB, B, ForceNonZeroDiag);
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B.makeCompressed();
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check_sparse_solving(solver, A, b, dA, b);
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check_sparse_solving(solver, A, dB, dA, dB);
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check_sparse_solving(solver, A, B, dA, dB);
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// check only once
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if(i==0)
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{
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b = DenseVector::Zero(size);
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check_sparse_solving(solver, A, b, dA, b);
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}
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}
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// First, get the folder
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#ifdef TEST_REAL_CASES
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if (internal::is_same<Scalar, float>::value
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|| internal::is_same<Scalar, std::complex<float> >::value)
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return ;
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std::string mat_folder = get_matrixfolder<Scalar>();
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MatrixMarketIterator<Scalar> it(mat_folder);
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for (; it; ++it)
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{
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std::cout<< " ==== SOLVING WITH MATRIX " << it.matname() << " ==== \n";
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check_sparse_solving_real_cases(solver, it.matrix(), it.rhs(), it.refX());
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}
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#endif
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}
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template<typename Solver> void check_sparse_square_determinant(Solver& solver)
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{
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typedef typename Solver::MatrixType Mat;
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typedef typename Mat::Scalar Scalar;
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typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
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// generate the problem
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Mat A;
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DenseMatrix dA;
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generate_sparse_square_problem(solver, A, dA, 30);
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A.makeCompressed();
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for (int i = 0; i < g_repeat; i++) {
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check_sparse_determinant(solver, A, dA);
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}
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}
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