| // 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/. | |
| // SPDX-License-Identifier: MPL-2.0 | |
| #ifndef EIGEN_TEST_SPARSE_SOLVER_H | |
| #define EIGEN_TEST_SPARSE_SOLVER_H | |
| #include "sparse.h" | |
| #include <Eigen/SparseCore> | |
| #include <Eigen/SparseLU> | |
| #include <sstream> | |
| template <typename Solver, typename Rhs, typename Guess, typename Result> | |
| void solve_with_guess(IterativeSolverBase<Solver>& solver, const MatrixBase<Rhs>& b, const Guess& g, Result& x) { | |
| if (internal::random<bool>()) { | |
| // With a temporary through evaluator<SolveWithGuess> | |
| x = solver.derived().solveWithGuess(b, g) + Result::Zero(x.rows(), x.cols()); | |
| } else { | |
| // direct evaluation within x through Assignment<Result,SolveWithGuess> | |
| x = solver.derived().solveWithGuess(b.derived(), g); | |
| } | |
| } | |
| template <typename Solver, typename Rhs, typename Guess, typename Result> | |
| void solve_with_guess(SparseSolverBase<Solver>& solver, const MatrixBase<Rhs>& b, const Guess&, Result& x) { | |
| if (internal::random<bool>()) | |
| x = solver.derived().solve(b) + Result::Zero(x.rows(), x.cols()); | |
| else | |
| x = solver.derived().solve(b); | |
| } | |
| template <typename Solver, typename Rhs, typename Guess, typename Result> | |
| void solve_with_guess(SparseSolverBase<Solver>& solver, const SparseMatrixBase<Rhs>& b, const Guess&, Result& x) { | |
| x = solver.derived().solve(b); | |
| } | |
| 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; | |
| typedef typename Mat::StorageIndex StorageIndex; | |
| DenseRhs refX = dA.householderQr().solve(db); | |
| { | |
| Rhs x(A.cols(), b.cols()); | |
| Rhs oldb = b; | |
| solver.compute(A); | |
| if (solver.info() != Success) { | |
| std::cerr << "ERROR | sparse solver testing, factorization failed (" << typeid(Solver).name() << ")\n"; | |
| VERIFY(solver.info() == Success); | |
| } | |
| x = solver.solve(b); | |
| if (solver.info() != Success) { | |
| std::cerr << "WARNING: sparse solver testing: solving failed (" << typeid(Solver).name() << ")\n"; | |
| // dump call stack: | |
| g_test_level++; | |
| VERIFY(solver.info() == Success); | |
| g_test_level--; | |
| return; | |
| } | |
| VERIFY(oldb.isApprox(b) && "sparse solver testing: the rhs should not be modified!"); | |
| VERIFY(x.isApprox(refX, test_precision<Scalar>())); | |
| x.setZero(); | |
| solve_with_guess(solver, b, x, x); | |
| VERIFY(solver.info() == Success && "solving failed when using solve_with_guess API"); | |
| 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); | |
| VERIFY(solver.info() == Success && "factorization failed when using analyzePattern/factorize API"); | |
| x = solver.solve(b); | |
| VERIFY(solver.info() == Success && "solving failed when using analyzePattern/factorize API"); | |
| VERIFY(oldb.isApprox(b) && "sparse solver testing: the rhs should not be modified!"); | |
| VERIFY(x.isApprox(refX, test_precision<Scalar>())); | |
| x.setZero(); | |
| // test with Map | |
| Map<SparseMatrix<Scalar, Mat::Options, StorageIndex>> Am( | |
| A.rows(), A.cols(), A.nonZeros(), const_cast<StorageIndex*>(A.outerIndexPtr()), | |
| const_cast<StorageIndex*>(A.innerIndexPtr()), const_cast<Scalar*>(A.valuePtr())); | |
| solver.compute(Am); | |
| VERIFY(solver.info() == Success && "factorization failed when using Map"); | |
| DenseRhs dx(refX); | |
| dx.setZero(); | |
| Map<DenseRhs> xm(dx.data(), dx.rows(), dx.cols()); | |
| Map<const DenseRhs> bm(db.data(), db.rows(), db.cols()); | |
| xm = solver.solve(bm); | |
| VERIFY(solver.info() == Success && "solving failed when using Map"); | |
| VERIFY(oldb.isApprox(bm) && "sparse solver testing: the rhs should not be modified!"); | |
| VERIFY(xm.isApprox(refX, test_precision<Scalar>())); | |
| // Test with a Map and non-unit stride. | |
| Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> out(2 * xm.rows(), 2 * xm.cols()); | |
| out.setZero(); | |
| // The outer stride spans DenseRhs's outer dimension, so it must be taken from outerStride() | |
| // rather than from rows(): the two differ when DenseRhs is row major. | |
| Eigen::Map<DenseRhs, 0, Stride<Eigen::Dynamic, 2>> outm(out.data(), xm.rows(), xm.cols(), | |
| Stride<Eigen::Dynamic, 2>(2 * xm.outerStride(), 2)); | |
| outm = solver.solve(bm); | |
| VERIFY(outm.isApprox(refX, test_precision<Scalar>())); | |
| } | |
| // if not too large, do some extra check: | |
| if (A.rows() < 2000) { | |
| // test initialization ctor | |
| { | |
| Rhs x(b.rows(), b.cols()); | |
| Solver solver2(A); | |
| VERIFY(solver2.info() == Success); | |
| x = solver2.solve(b); | |
| VERIFY(x.isApprox(refX, test_precision<Scalar>())); | |
| } | |
| // test dense Block as the result and rhs: | |
| { | |
| DenseRhs x(refX.rows(), refX.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>())); | |
| } | |
| // test uncompressed inputs | |
| { | |
| Mat A2 = A; | |
| A2.reserve((ArrayXf::Random(A.outerSize()) + 2).template cast<typename Mat::StorageIndex>().eval()); | |
| solver.compute(A2); | |
| Rhs x = solver.solve(b); | |
| VERIFY(x.isApprox(refX, test_precision<Scalar>())); | |
| } | |
| // 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>())); | |
| } | |
| } | |
| } | |
| #endif // EIGEN_TEST_SPARSE_SOLVER_H | |
| // specialization of generic check_sparse_solving for SuperLU in order to also test adjoint and transpose solves | |
| template <typename Scalar, typename Rhs, typename DenseMat, typename DenseRhs> | |
| void check_sparse_solving(Eigen::SparseLU<Eigen::SparseMatrix<Scalar>>& solver, | |
| const typename Eigen::SparseMatrix<Scalar>& A, const Rhs& b, const DenseMat& dA, | |
| const DenseRhs& db) { | |
| typedef typename Eigen::SparseMatrix<Scalar> Mat; | |
| typedef typename Mat::StorageIndex StorageIndex; | |
| typedef typename Eigen::SparseLU<Eigen::SparseMatrix<Scalar>> Solver; | |
| // reference solutions computed by dense QR solver | |
| DenseRhs refX1 = dA.householderQr().solve(db); // solution of A x = db | |
| DenseRhs refX2 = dA.transpose().householderQr().solve(db); // solution of A^T * x = db (use transposed matrix A^T) | |
| DenseRhs refX3 = dA.adjoint().householderQr().solve(db); // solution of A^* * x = db (use adjoint matrix A^*) | |
| { | |
| Rhs x1(A.cols(), b.cols()); | |
| Rhs x2(A.cols(), b.cols()); | |
| Rhs x3(A.cols(), b.cols()); | |
| Rhs oldb = b; | |
| solver.compute(A); | |
| if (solver.info() != Success) { | |
| std::cerr << "ERROR | sparse solver testing, factorization failed (" << typeid(Solver).name() << ")\n"; | |
| VERIFY(solver.info() == Success); | |
| } | |
| x1 = solver.solve(b); | |
| if (solver.info() != Success) { | |
| std::cerr << "WARNING | sparse solver testing: solving failed (" << typeid(Solver).name() << ")\n"; | |
| return; | |
| } | |
| VERIFY(oldb.isApprox(b, 0.0) && "sparse solver testing: the rhs should not be modified!"); | |
| VERIFY(x1.isApprox(refX1, test_precision<Scalar>())); | |
| // test solve with transposed | |
| x2 = solver.transpose().solve(b); | |
| VERIFY(oldb.isApprox(b) && "sparse solver testing: the rhs should not be modified!"); | |
| VERIFY(x2.isApprox(refX2, test_precision<Scalar>())); | |
| // test solve with adjoint | |
| // solver.template _solve_impl_transposed<true>(b, x3); | |
| x3 = solver.adjoint().solve(b); | |
| VERIFY(oldb.isApprox(b, 0.0) && "sparse solver testing: the rhs should not be modified!"); | |
| VERIFY(x3.isApprox(refX3, test_precision<Scalar>())); | |
| x1.setZero(); | |
| solve_with_guess(solver, b, x1, x1); | |
| VERIFY(solver.info() == Success && "solving failed when using analyzePattern/factorize API"); | |
| VERIFY(oldb.isApprox(b, 0.0) && "sparse solver testing: the rhs should not be modified!"); | |
| VERIFY(x1.isApprox(refX1, test_precision<Scalar>())); | |
| x1.setZero(); | |
| x2.setZero(); | |
| x3.setZero(); | |
| // test the analyze/factorize API | |
| solver.analyzePattern(A); | |
| solver.factorize(A); | |
| VERIFY(solver.info() == Success && "factorization failed when using analyzePattern/factorize API"); | |
| x1 = solver.solve(b); | |
| x2 = solver.transpose().solve(b); | |
| x3 = solver.adjoint().solve(b); | |
| VERIFY(solver.info() == Success && "solving failed when using analyzePattern/factorize API"); | |
| VERIFY(oldb.isApprox(b, 0.0) && "sparse solver testing: the rhs should not be modified!"); | |
| VERIFY(x1.isApprox(refX1, test_precision<Scalar>())); | |
| VERIFY(x2.isApprox(refX2, test_precision<Scalar>())); | |
| VERIFY(x3.isApprox(refX3, test_precision<Scalar>())); | |
| x1.setZero(); | |
| // test with Map | |
| Map<SparseMatrix<Scalar, Mat::Options, StorageIndex>> Am( | |
| A.rows(), A.cols(), A.nonZeros(), const_cast<StorageIndex*>(A.outerIndexPtr()), | |
| const_cast<StorageIndex*>(A.innerIndexPtr()), const_cast<Scalar*>(A.valuePtr())); | |
| solver.compute(Am); | |
| VERIFY(solver.info() == Success && "factorization failed when using Map"); | |
| DenseRhs dx(refX1); | |
| dx.setZero(); | |
| Map<DenseRhs> xm(dx.data(), dx.rows(), dx.cols()); | |
| Map<const DenseRhs> bm(db.data(), db.rows(), db.cols()); | |
| xm = solver.solve(bm); | |
| VERIFY(solver.info() == Success && "solving failed when using Map"); | |
| VERIFY(oldb.isApprox(bm, 0.0) && "sparse solver testing: the rhs should not be modified!"); | |
| VERIFY(xm.isApprox(refX1, test_precision<Scalar>())); | |
| } | |
| // if not too large, do some extra check: | |
| if (A.rows() < 2000) { | |
| // test initialization ctor | |
| { | |
| Rhs x(b.rows(), b.cols()); | |
| Solver solver2(A); | |
| VERIFY(solver2.info() == Success); | |
| x = solver2.solve(b); | |
| VERIFY(x.isApprox(refX1, test_precision<Scalar>())); | |
| } | |
| // test dense Block as the result and rhs: | |
| { | |
| DenseRhs x(refX1.rows(), refX1.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, 0.0) && "sparse solver testing: the rhs should not be modified!"); | |
| VERIFY(x.isApprox(refX1, test_precision<Scalar>())); | |
| } | |
| // test uncompressed inputs | |
| { | |
| Mat A2 = A; | |
| A2.reserve((ArrayXf::Random(A.outerSize()) + 2).template cast<typename Mat::StorageIndex>().eval()); | |
| solver.compute(A2); | |
| Rhs x = solver.solve(b); | |
| VERIFY(x.isApprox(refX1, test_precision<Scalar>())); | |
| } | |
| // test expression as input | |
| { | |
| solver.compute(0.5 * (A + A)); | |
| Rhs x = solver.solve(b); | |
| VERIFY(x.isApprox(refX1, test_precision<Scalar>())); | |
| Solver solver2(0.5 * (A + A)); | |
| Rhs x2 = solver2.solve(b); | |
| VERIFY(x2.isApprox(refX1, 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 typename Solver::MatrixType& fullA, const Rhs& refX) { | |
| typedef typename Solver::MatrixType Mat; | |
| typedef typename Mat::Scalar Scalar; | |
| typedef typename Mat::RealScalar RealScalar; | |
| Rhs x(A.cols(), b.cols()); | |
| solver.compute(A); | |
| if (solver.info() != Success) { | |
| std::cerr << "ERROR | sparse solver testing, factorization failed (" << typeid(Solver).name() << ")\n"; | |
| VERIFY(solver.info() == Success); | |
| } | |
| x = solver.solve(b); | |
| if (solver.info() != Success) { | |
| std::cerr << "WARNING | sparse solver testing, solving failed (" << typeid(Solver).name() << ")\n"; | |
| return; | |
| } | |
| RealScalar res_error = (fullA * x - b).norm() / b.norm(); | |
| VERIFY((res_error <= test_precision<Scalar>()) && "sparse solver failed without noticing it"); | |
| if (refX.size() != 0 && (refX - x).norm() / refX.norm() > test_precision<Scalar>()) { | |
| std::cerr << "WARNING | found solution is different from the provided reference one\n"; | |
| } | |
| } | |
| 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 << "WARNING | 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 << "WARNING | 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> | |
| void check_sparse_log_abs_determinant(Solver& solver, const typename Solver::MatrixType& A, const DenseMat& dA) { | |
| typedef typename Solver::MatrixType Mat; | |
| typedef typename Mat::Scalar Scalar; | |
| typedef typename NumTraits<Scalar>::Real RealScalar; | |
| solver.compute(A); | |
| if (solver.info() != Success) { | |
| std::cerr << "WARNING | sparse solver testing: factorization failed (check_sparse_log_abs_determinant)\n"; | |
| return; | |
| } | |
| Scalar refDet = dA.determinant(); | |
| RealScalar refAbsDet = numext::abs(refDet); | |
| VERIFY_IS_APPROX(refAbsDet, solver.absDeterminant()); | |
| VERIFY_IS_APPROX(numext::sign(refDet), solver.signDeterminant()); | |
| // log|det| crosses zero, so the meaningful bound here is absolute once |log|det|| drops below one. | |
| RealScalar refLogAbsDet = numext::log(refAbsDet); | |
| VERIFY_IS_MUCH_SMALLER_THAN(solver.logAbsDeterminant() - refLogAbsDet, | |
| numext::maxi(RealScalar(1), numext::abs(refLogAbsDet))); | |
| } | |
| 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. / static_cast<double>(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 (std::is_same<Scalar, std::complex<float>>::value || std::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; | |
| } | |
| std::string sym_to_string(int sym) { | |
| if (sym == Symmetric) return "Symmetric "; | |
| if (sym == SPD) return "SPD "; | |
| return ""; | |
| } | |
| template <typename Derived> | |
| std::string solver_stats(const IterativeSolverBase<Derived>& solver) { | |
| std::stringstream ss; | |
| ss << solver.iterations() << " iters, error: " << solver.error(); | |
| return ss.str(); | |
| } | |
| template <typename Derived> | |
| std::string solver_stats(const SparseSolverBase<Derived>& /*solver*/) { | |
| return ""; | |
| } | |
| #endif | |
| template <typename Solver> | |
| void check_sparse_spd_solving(Solver& solver, int maxSize = (std::min)(300, EIGEN_TEST_MAX_SIZE), | |
| int maxRealWorldSize = 100000) { | |
| typedef typename Solver::MatrixType Mat; | |
| typedef typename Mat::Scalar Scalar; | |
| typedef typename Mat::StorageIndex StorageIndex; | |
| typedef SparseMatrix<Scalar, ColMajor, StorageIndex> SpMat; | |
| typedef SparseVector<Scalar, 0, StorageIndex> SpVec; | |
| 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, maxSize); | |
| // generate the right hand sides | |
| int rhsCols = internal::random<int>(1, 16); | |
| double density = (std::max)(8. / static_cast<double>(size * rhsCols), 0.1); | |
| SpMat B(size, rhsCols); | |
| DenseVector b = DenseVector::Random(size); | |
| DenseMatrix dB(size, rhsCols); | |
| initSparse<Scalar>(density, dB, B, ForceNonZeroDiag); | |
| SpVec c = B.col(0); | |
| DenseVector dc = dB.col(0); | |
| CALL_SUBTEST(check_sparse_solving(solver, A, b, dA, b)); | |
| CALL_SUBTEST(check_sparse_solving(solver, halfA, b, dA, b)); | |
| CALL_SUBTEST(check_sparse_solving(solver, A, dB, dA, dB)); | |
| CALL_SUBTEST(check_sparse_solving(solver, halfA, dB, dA, dB)); | |
| CALL_SUBTEST(check_sparse_solving(solver, A, B, dA, dB)); | |
| CALL_SUBTEST(check_sparse_solving(solver, halfA, B, dA, dB)); | |
| CALL_SUBTEST(check_sparse_solving(solver, A, c, dA, dc)); | |
| CALL_SUBTEST(check_sparse_solving(solver, halfA, c, dA, dc)); | |
| // 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 | |
| // Test real problems with double precision only | |
| if (std::is_same<typename NumTraits<Scalar>::Real, double>::value) { | |
| std::string mat_folder = get_matrixfolder<Scalar>(); | |
| MatrixMarketIterator<Scalar> it(mat_folder); | |
| for (; it; ++it) { | |
| if (it.sym() == SPD) { | |
| A = it.matrix(); | |
| if (A.diagonal().size() <= maxRealWorldSize) { | |
| DenseVector b = it.rhs(); | |
| DenseVector refX = it.refX(); | |
| PermutationMatrix<Dynamic, Dynamic, StorageIndex> pnull; | |
| halfA.resize(A.rows(), A.cols()); | |
| if (Solver::UpLo == (Lower | Upper)) | |
| halfA = A; | |
| else | |
| halfA.template selfadjointView<Solver::UpLo>() = A.template triangularView<Eigen::Lower>().twistedBy(pnull); | |
| std::cout << "INFO | Testing " << sym_to_string(it.sym()) << "sparse problem " << it.matname() << " (" | |
| << A.rows() << "x" << A.cols() << ") using " << typeid(Solver).name() << "..." << std::endl; | |
| CALL_SUBTEST(check_sparse_solving_real_cases(solver, A, b, A, refX)); | |
| std::string stats = solver_stats(solver); | |
| if (stats.size() > 0) std::cout << "INFO | " << stats << std::endl; | |
| CALL_SUBTEST(check_sparse_solving_real_cases(solver, halfA, b, A, refX)); | |
| } else { | |
| std::cout << "INFO | Skip sparse problem \"" << it.matname() << "\" (too large)" << std::endl; | |
| } | |
| } | |
| } | |
| } | |
| #else | |
| EIGEN_UNUSED_VARIABLE(maxRealWorldSize); | |
| #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); | |
| check_sparse_determinant(solver, A, dA); | |
| check_sparse_determinant(solver, halfA, dA); | |
| } | |
| template <typename Solver> | |
| void check_sparse_spd_log_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, halfA; | |
| DenseMatrix dA; | |
| generate_sparse_spd_problem(solver, A, halfA, dA, 30); | |
| check_sparse_log_abs_determinant(solver, A, dA); | |
| check_sparse_log_abs_determinant(solver, halfA, dA); | |
| } | |
| template <typename Solver, typename DenseMat> | |
| int generate_sparse_nonhermitian_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. / static_cast<double>(size * size), 0.01); | |
| Mat M(size, size); | |
| DenseMatrix dM(size, size); | |
| initSparse<Scalar>(density, dM, M, ForceNonZeroDiag); | |
| A = M * M.transpose(); | |
| dA = dM * dM.transpose(); | |
| halfA.resize(size, size); | |
| if (Solver::UpLo == (Lower | Upper)) | |
| halfA = A; | |
| else | |
| halfA = A.template triangularView<Solver::UpLo>(); | |
| return size; | |
| } | |
| template <typename Solver> | |
| void check_sparse_nonhermitian_solving(Solver& solver, int maxSize = (std::min)(300, EIGEN_TEST_MAX_SIZE), | |
| int maxRealWorldSize = 100000) { | |
| typedef typename Solver::MatrixType Mat; | |
| typedef typename Mat::Scalar Scalar; | |
| typedef typename Mat::StorageIndex StorageIndex; | |
| typedef SparseMatrix<Scalar, ColMajor, StorageIndex> SpMat; | |
| typedef SparseVector<Scalar, 0, StorageIndex> SpVec; | |
| 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_nonhermitian_problem(solver, A, halfA, dA, maxSize); | |
| // generate the right hand sides | |
| int rhsCols = internal::random<int>(1, 16); | |
| double density = (std::max)(8. / static_cast<double>(size * rhsCols), 0.1); | |
| SpMat B(size, rhsCols); | |
| DenseVector b = DenseVector::Random(size); | |
| DenseMatrix dB(size, rhsCols); | |
| initSparse<Scalar>(density, dB, B, ForceNonZeroDiag); | |
| SpVec c = B.col(0); | |
| DenseVector dc = dB.col(0); | |
| CALL_SUBTEST(check_sparse_solving(solver, A, b, dA, b)); | |
| CALL_SUBTEST(check_sparse_solving(solver, halfA, b, dA, b)); | |
| CALL_SUBTEST(check_sparse_solving(solver, A, dB, dA, dB)); | |
| CALL_SUBTEST(check_sparse_solving(solver, halfA, dB, dA, dB)); | |
| CALL_SUBTEST(check_sparse_solving(solver, A, B, dA, dB)); | |
| CALL_SUBTEST(check_sparse_solving(solver, halfA, B, dA, dB)); | |
| CALL_SUBTEST(check_sparse_solving(solver, A, c, dA, dc)); | |
| CALL_SUBTEST(check_sparse_solving(solver, halfA, c, dA, dc)); | |
| // check only once | |
| if (i == 0) { | |
| b = DenseVector::Zero(size); | |
| check_sparse_solving(solver, A, b, dA, b); | |
| } | |
| } | |
| EIGEN_UNUSED_VARIABLE(maxRealWorldSize); | |
| } | |
| template <typename Solver> | |
| void check_sparse_nonhermitian_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_nonhermitian_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> | |
| void check_sparse_nonhermitian_log_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, halfA; | |
| DenseMatrix dA; | |
| generate_sparse_nonhermitian_problem(solver, A, halfA, dA, 30); | |
| for (int i = 0; i < g_repeat; i++) { | |
| check_sparse_log_abs_determinant(solver, A, dA); | |
| check_sparse_log_abs_determinant(solver, halfA, dA); | |
| } | |
| } | |
| template <typename Solver> | |
| void check_sparse_zero_matrix(Solver& solver) { | |
| typedef typename Solver::MatrixType Mat; | |
| Mat A(1, 1); | |
| solver.compute(A); | |
| VERIFY_IS_EQUAL(solver.info(), NumericalIssue); | |
| } | |
| template <typename Solver, typename DenseMat> | |
| Index generate_sparse_square_problem(Solver&, typename Solver::MatrixType& A, DenseMat& dA, int maxSize = 300, | |
| int options = ForceNonZeroDiag) { | |
| typedef typename Solver::MatrixType Mat; | |
| typedef typename Mat::Scalar Scalar; | |
| Index size = internal::random<int>(1, maxSize); | |
| double density = (std::max)(8. / static_cast<double>(size * size), 0.01); | |
| A.resize(size, size); | |
| dA.resize(size, size); | |
| initSparse<Scalar>(density, dA, A, options); | |
| return size; | |
| } | |
| struct prune_column { | |
| Index m_col; | |
| prune_column(Index col) : m_col(col) {} | |
| template <class Scalar> | |
| bool operator()(Index, Index col, const Scalar&) const { | |
| return col != m_col; | |
| } | |
| }; | |
| template <typename Solver> | |
| void check_sparse_square_solving(Solver& solver, int maxSize = 300, int maxRealWorldSize = 100000, | |
| bool checkDeficient = false) { | |
| typedef typename Solver::MatrixType Mat; | |
| typedef typename Mat::Scalar Scalar; | |
| typedef SparseMatrix<Scalar, ColMajor, typename Mat::StorageIndex> SpMat; | |
| typedef SparseVector<Scalar, 0, typename Mat::StorageIndex> SpVec; | |
| 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++) { | |
| Index size = generate_sparse_square_problem(solver, A, dA, maxSize); | |
| A.makeCompressed(); | |
| DenseVector b = DenseVector::Random(size); | |
| DenseMatrix dB(size, rhsCols); | |
| SpMat B(size, rhsCols); | |
| double density = (std::max)(8. / double(size * rhsCols), 0.1); | |
| initSparse<Scalar>(density, dB, B, ForceNonZeroDiag); | |
| B.makeCompressed(); | |
| SpVec c = B.col(0); | |
| DenseVector dc = dB.col(0); | |
| CALL_SUBTEST(check_sparse_solving(solver, A, b, dA, b)); | |
| CALL_SUBTEST(check_sparse_solving(solver, A, dB, dA, dB)); | |
| CALL_SUBTEST(check_sparse_solving(solver, A, B, dA, dB)); | |
| CALL_SUBTEST(check_sparse_solving(solver, A, c, dA, dc)); | |
| // check only once | |
| if (i == 0) { | |
| CALL_SUBTEST(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) { | |
| Index col = internal::random<int>(0, int(size - 1)); | |
| A.prune(prune_column(col)); | |
| solver.compute(A); | |
| VERIFY_IS_EQUAL(solver.info(), NumericalIssue); | |
| } | |
| } | |
| // First, get the folder | |
| #ifdef TEST_REAL_CASES | |
| // Test real problems with double precision only | |
| if (std::is_same<typename NumTraits<Scalar>::Real, double>::value) { | |
| std::string mat_folder = get_matrixfolder<Scalar>(); | |
| MatrixMarketIterator<Scalar> it(mat_folder); | |
| for (; it; ++it) { | |
| A = it.matrix(); | |
| if (A.diagonal().size() <= maxRealWorldSize) { | |
| DenseVector b = it.rhs(); | |
| DenseVector refX = it.refX(); | |
| std::cout << "INFO | Testing " << sym_to_string(it.sym()) << "sparse problem " << it.matname() << " (" | |
| << A.rows() << "x" << A.cols() << ") using " << typeid(Solver).name() << "..." << std::endl; | |
| CALL_SUBTEST(check_sparse_solving_real_cases(solver, A, b, A, refX)); | |
| std::string stats = solver_stats(solver); | |
| if (stats.size() > 0) std::cout << "INFO | " << stats << std::endl; | |
| } else { | |
| std::cout << "INFO | SKIP sparse problem \"" << it.matname() << "\" (too large)" << std::endl; | |
| } | |
| } | |
| } | |
| #else | |
| EIGEN_UNUSED_VARIABLE(maxRealWorldSize); | |
| #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; | |
| for (int i = 0; i < g_repeat; i++) { | |
| // generate the problem | |
| Mat A; | |
| DenseMatrix dA; | |
| int size = internal::random<int>(1, 30); | |
| dA.setRandom(size, size); | |
| dA = (dA.array().abs() < 0.3).select(0, dA); | |
| dA.diagonal() = (dA.diagonal().array() == 0).select(1, dA.diagonal()); | |
| A = dA.sparseView(); | |
| A.makeCompressed(); | |
| 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; | |
| for (int i = 0; i < g_repeat; i++) { | |
| // generate the problem | |
| Mat A; | |
| DenseMatrix dA; | |
| generate_sparse_square_problem(solver, A, dA, 30); | |
| A.makeCompressed(); | |
| check_sparse_abs_determinant(solver, A, dA); | |
| } | |
| } | |
| template <typename Solver, typename DenseMat> | |
| void generate_sparse_leastsquare_problem(Solver&, typename Solver::MatrixType& A, DenseMat& dA, int maxSize = 300, | |
| int options = ForceNonZeroDiag) { | |
| typedef typename Solver::MatrixType Mat; | |
| typedef typename Mat::Scalar Scalar; | |
| int rows = internal::random<int>(1, maxSize); | |
| int cols = internal::random<int>(1, rows); | |
| double density = (std::max)(8. / (rows * cols), 0.01); | |
| A.resize(rows, cols); | |
| dA.resize(rows, cols); | |
| initSparse<Scalar>(density, dA, A, options); | |
| } | |
| template <typename Solver> | |
| void check_sparse_leastsquare_solving(Solver& solver) { | |
| typedef typename Solver::MatrixType Mat; | |
| typedef typename Mat::Scalar Scalar; | |
| typedef SparseMatrix<Scalar, ColMajor, typename Mat::StorageIndex> 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++) { | |
| generate_sparse_leastsquare_problem(solver, A, dA); | |
| A.makeCompressed(); | |
| DenseVector b = DenseVector::Random(A.rows()); | |
| DenseMatrix dB(A.rows(), rhsCols); | |
| SpMat B(A.rows(), rhsCols); | |
| double density = (std::max)(8. / (A.rows() * 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(A.rows()); | |
| check_sparse_solving(solver, A, b, dA, b); | |
| } | |
| } | |
| } |