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Diffstat (limited to 'eigen/test/sparse_solver.h')
-rw-r--r-- | eigen/test/sparse_solver.h | 395 |
1 files changed, 395 insertions, 0 deletions
diff --git a/eigen/test/sparse_solver.h b/eigen/test/sparse_solver.h new file mode 100644 index 0000000..e1619d6 --- /dev/null +++ b/eigen/test/sparse_solver.h @@ -0,0 +1,395 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2011 Gael Guennebaud <g.gael@free.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" +#include <Eigen/SparseCore> + +template<typename Solver, typename Rhs, typename DenseMat, typename DenseRhs> +void check_sparse_solving(Solver& solver, const typename Solver::MatrixType& A, const Rhs& b, const DenseMat& dA, const DenseRhs& db) +{ + typedef typename Solver::MatrixType Mat; + typedef typename Mat::Scalar Scalar; + + DenseRhs refX = dA.lu().solve(db); + { + Rhs x(b.rows(), b.cols()); + Rhs oldb = b; + + solver.compute(A); + if (solver.info() != Success) + { + std::cerr << "sparse solver testing: factorization failed (check_sparse_solving)\n"; + exit(0); + return; + } + x = solver.solve(b); + if (solver.info() != Success) + { + std::cerr << "sparse solver testing: solving failed\n"; + return; + } + VERIFY(oldb.isApprox(b) && "sparse solver testing: the rhs should not be modified!"); + + VERIFY(x.isApprox(refX,test_precision<Scalar>())); + x.setZero(); + // test the analyze/factorize API + solver.analyzePattern(A); + solver.factorize(A); + if (solver.info() != Success) + { + std::cerr << "sparse solver testing: factorization failed (check_sparse_solving)\n"; + exit(0); + return; + } + x = solver.solve(b); + if (solver.info() != Success) + { + std::cerr << "sparse solver testing: solving failed\n"; + return; + } + VERIFY(oldb.isApprox(b) && "sparse solver testing: the rhs should not be modified!"); + + VERIFY(x.isApprox(refX,test_precision<Scalar>())); + } + + // test dense Block as the result and rhs: + { + DenseRhs x(db.rows(), db.cols()); + DenseRhs oldb(db); + x.setZero(); + x.block(0,0,x.rows(),x.cols()) = solver.solve(db.block(0,0,db.rows(),db.cols())); + VERIFY(oldb.isApprox(db) && "sparse solver testing: the rhs should not be modified!"); + VERIFY(x.isApprox(refX,test_precision<Scalar>())); + } + + // if not too large, do some extra check: + if(A.rows()<2000) + { + + // test expression as input + { + solver.compute(0.5*(A+A)); + Rhs x = solver.solve(b); + VERIFY(x.isApprox(refX,test_precision<Scalar>())); + + Solver solver2(0.5*(A+A)); + Rhs x2 = solver2.solve(b); + VERIFY(x2.isApprox(refX,test_precision<Scalar>())); + } + } +} + +template<typename Solver, typename Rhs> +void check_sparse_solving_real_cases(Solver& solver, const typename Solver::MatrixType& A, const Rhs& b, const Rhs& refX) +{ + typedef typename Solver::MatrixType Mat; + typedef typename Mat::Scalar Scalar; + typedef typename Mat::RealScalar RealScalar; + + Rhs x(b.rows(), b.cols()); + + solver.compute(A); + if (solver.info() != Success) + { + std::cerr << "sparse solver testing: factorization failed (check_sparse_solving_real_cases)\n"; + exit(0); + return; + } + x = solver.solve(b); + if (solver.info() != Success) + { + std::cerr << "sparse solver testing: solving failed\n"; + return; + } + + RealScalar res_error; + // Compute the norm of the relative error + if(refX.size() != 0) + res_error = (refX - x).norm()/refX.norm(); + else + { + // Compute the relative residual norm + res_error = (b - A * x).norm()/b.norm(); + } + if (res_error > test_precision<Scalar>() ){ + std::cerr << "Test " << g_test_stack.back() << " failed in "EI_PP_MAKE_STRING(__FILE__) + << " (" << EI_PP_MAKE_STRING(__LINE__) << ")" << std::endl << std::endl; + abort(); + } + +} +template<typename Solver, typename DenseMat> +void check_sparse_determinant(Solver& solver, const typename Solver::MatrixType& A, const DenseMat& dA) +{ + typedef typename Solver::MatrixType Mat; + typedef typename Mat::Scalar Scalar; + + solver.compute(A); + if (solver.info() != Success) + { + std::cerr << "sparse solver testing: factorization failed (check_sparse_determinant)\n"; + return; + } + + Scalar refDet = dA.determinant(); + VERIFY_IS_APPROX(refDet,solver.determinant()); +} +template<typename Solver, typename DenseMat> +void check_sparse_abs_determinant(Solver& solver, const typename Solver::MatrixType& A, const DenseMat& dA) +{ + using std::abs; + typedef typename Solver::MatrixType Mat; + typedef typename Mat::Scalar Scalar; + + solver.compute(A); + if (solver.info() != Success) + { + std::cerr << "sparse solver testing: factorization failed (check_sparse_abs_determinant)\n"; + return; + } + + Scalar refDet = abs(dA.determinant()); + VERIFY_IS_APPROX(refDet,solver.absDeterminant()); +} + +template<typename Solver, typename DenseMat> +int generate_sparse_spd_problem(Solver& , typename Solver::MatrixType& A, typename Solver::MatrixType& halfA, DenseMat& dA, int maxSize = 300) +{ + typedef typename Solver::MatrixType Mat; + typedef typename Mat::Scalar Scalar; + typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix; + + int size = internal::random<int>(1,maxSize); + double density = (std::max)(8./(size*size), 0.01); + + Mat M(size, size); + DenseMatrix dM(size, size); + + initSparse<Scalar>(density, dM, M, ForceNonZeroDiag); + + A = M * M.adjoint(); + dA = dM * dM.adjoint(); + + halfA.resize(size,size); + if(Solver::UpLo==(Lower|Upper)) + halfA = A; + else + halfA.template selfadjointView<Solver::UpLo>().rankUpdate(M); + + return size; +} + + +#ifdef TEST_REAL_CASES +template<typename Scalar> +inline std::string get_matrixfolder() +{ + std::string mat_folder = TEST_REAL_CASES; + if( internal::is_same<Scalar, std::complex<float> >::value || internal::is_same<Scalar, std::complex<double> >::value ) + mat_folder = mat_folder + static_cast<std::string>("/complex/"); + else + mat_folder = mat_folder + static_cast<std::string>("/real/"); + return mat_folder; +} +#endif + +template<typename Solver> void check_sparse_spd_solving(Solver& solver) +{ + typedef typename Solver::MatrixType Mat; + typedef typename Mat::Scalar Scalar; + typedef SparseMatrix<Scalar,ColMajor> SpMat; + typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix; + typedef Matrix<Scalar,Dynamic,1> DenseVector; + + // generate the problem + Mat A, halfA; + DenseMatrix dA; + for (int i = 0; i < g_repeat; i++) { + int size = generate_sparse_spd_problem(solver, A, halfA, dA); + + // generate the right hand sides + int rhsCols = internal::random<int>(1,16); + double density = (std::max)(8./(size*rhsCols), 0.1); + SpMat B(size,rhsCols); + DenseVector b = DenseVector::Random(size); + DenseMatrix dB(size,rhsCols); + initSparse<Scalar>(density, dB, B, ForceNonZeroDiag); + + check_sparse_solving(solver, A, b, dA, b); + check_sparse_solving(solver, halfA, b, dA, b); + check_sparse_solving(solver, A, dB, dA, dB); + check_sparse_solving(solver, halfA, dB, dA, dB); + check_sparse_solving(solver, A, B, dA, dB); + check_sparse_solving(solver, halfA, B, dA, dB); + + // check only once + if(i==0) + { + b = DenseVector::Zero(size); + check_sparse_solving(solver, A, b, dA, b); + } + } + + // First, get the folder +#ifdef TEST_REAL_CASES + if (internal::is_same<Scalar, float>::value + || internal::is_same<Scalar, std::complex<float> >::value) + return ; + + std::string mat_folder = get_matrixfolder<Scalar>(); + MatrixMarketIterator<Scalar> it(mat_folder); + for (; it; ++it) + { + if (it.sym() == SPD){ + Mat halfA; + PermutationMatrix<Dynamic, Dynamic, Index> pnull; + halfA.template selfadjointView<Solver::UpLo>() = it.matrix().template triangularView<Eigen::Lower>().twistedBy(pnull); + + std::cout<< " ==== SOLVING WITH MATRIX " << it.matname() << " ==== \n"; + check_sparse_solving_real_cases(solver, it.matrix(), it.rhs(), it.refX()); + check_sparse_solving_real_cases(solver, halfA, it.rhs(), it.refX()); + } + } +#endif +} + +template<typename Solver> void check_sparse_spd_determinant(Solver& solver) +{ + typedef typename Solver::MatrixType Mat; + typedef typename Mat::Scalar Scalar; + typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix; + + // generate the problem + Mat A, halfA; + DenseMatrix dA; + generate_sparse_spd_problem(solver, A, halfA, dA, 30); + + for (int i = 0; i < g_repeat; i++) { + check_sparse_determinant(solver, A, dA); + check_sparse_determinant(solver, halfA, dA ); + } +} + +template<typename Solver, typename DenseMat> +int generate_sparse_square_problem(Solver&, typename Solver::MatrixType& A, DenseMat& dA, int maxSize = 300) +{ + typedef typename Solver::MatrixType Mat; + typedef typename Mat::Scalar Scalar; + + int size = internal::random<int>(1,maxSize); + double density = (std::max)(8./(size*size), 0.01); + + A.resize(size,size); + dA.resize(size,size); + + initSparse<Scalar>(density, dA, A, ForceNonZeroDiag); + + return size; +} + + +struct prune_column { + int m_col; + prune_column(int col) : m_col(col) {} + template<class Scalar> + bool operator()(int, int col, const Scalar&) const { + return col != m_col; + } +}; + +template<typename Solver> void check_sparse_square_solving(Solver& solver, bool checkDeficient = false) +{ + typedef typename Solver::MatrixType Mat; + typedef typename Mat::Scalar Scalar; + typedef SparseMatrix<Scalar,ColMajor> SpMat; + typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix; + typedef Matrix<Scalar,Dynamic,1> DenseVector; + + int rhsCols = internal::random<int>(1,16); + + Mat A; + DenseMatrix dA; + for (int i = 0; i < g_repeat; i++) { + int size = generate_sparse_square_problem(solver, A, dA); + + A.makeCompressed(); + DenseVector b = DenseVector::Random(size); + DenseMatrix dB(size,rhsCols); + SpMat B(size,rhsCols); + double density = (std::max)(8./(size*rhsCols), 0.1); + initSparse<Scalar>(density, dB, B, ForceNonZeroDiag); + B.makeCompressed(); + check_sparse_solving(solver, A, b, dA, b); + check_sparse_solving(solver, A, dB, dA, dB); + check_sparse_solving(solver, A, B, dA, dB); + + // check only once + if(i==0) + { + b = DenseVector::Zero(size); + check_sparse_solving(solver, A, b, dA, b); + } + // regression test for Bug 792 (structurally rank deficient matrices): + if(checkDeficient && size>1) { + int col = internal::random<int>(0,size-1); + A.prune(prune_column(col)); + solver.compute(A); + VERIFY_IS_EQUAL(solver.info(), NumericalIssue); + } + } + + // First, get the folder +#ifdef TEST_REAL_CASES + if (internal::is_same<Scalar, float>::value + || internal::is_same<Scalar, std::complex<float> >::value) + return ; + + std::string mat_folder = get_matrixfolder<Scalar>(); + MatrixMarketIterator<Scalar> it(mat_folder); + for (; it; ++it) + { + std::cout<< " ==== SOLVING WITH MATRIX " << it.matname() << " ==== \n"; + check_sparse_solving_real_cases(solver, it.matrix(), it.rhs(), it.refX()); + } +#endif + +} + +template<typename Solver> void check_sparse_square_determinant(Solver& solver) +{ + typedef typename Solver::MatrixType Mat; + typedef typename Mat::Scalar Scalar; + typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix; + + // generate the problem + Mat A; + DenseMatrix dA; + generate_sparse_square_problem(solver, A, dA, 30); + A.makeCompressed(); + for (int i = 0; i < g_repeat; i++) { + check_sparse_determinant(solver, A, dA); + } +} + +template<typename Solver> void check_sparse_square_abs_determinant(Solver& solver) +{ + typedef typename Solver::MatrixType Mat; + typedef typename Mat::Scalar Scalar; + typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix; + + // generate the problem + Mat A; + DenseMatrix dA; + generate_sparse_square_problem(solver, A, dA, 30); + A.makeCompressed(); + for (int i = 0; i < g_repeat; i++) { + check_sparse_abs_determinant(solver, A, dA); + } +} + |