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509 lines
16 KiB
C++
509 lines
16 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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#include <sstream>
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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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typedef typename Mat::StorageIndex StorageIndex;
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DenseRhs refX = dA.householderQr().solve(db);
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{
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Rhs x(A.cols(), 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 << "ERROR | sparse solver testing, factorization failed (" << typeid(Solver).name() << ")\n";
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VERIFY(solver.info() == Success);
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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 << "WARNING | sparse solver testing: solving failed (" << typeid(Solver).name() << ")\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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VERIFY(solver.info() == Success && "factorization failed when using analyzePattern/factorize API");
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x = solver.solve(b);
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VERIFY(solver.info() == Success && "solving failed when using analyzePattern/factorize API");
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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 with Map
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MappedSparseMatrix<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()));
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solver.compute(Am);
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VERIFY(solver.info() == Success && "factorization failed when using Map");
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DenseRhs dx(refX);
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dx.setZero();
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Map<DenseRhs> xm(dx.data(), dx.rows(), dx.cols());
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Map<const DenseRhs> bm(db.data(), db.rows(), db.cols());
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xm = solver.solve(bm);
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VERIFY(solver.info() == Success && "solving failed when using Map");
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VERIFY(oldb.isApprox(bm) && "sparse solver testing: the rhs should not be modified!");
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VERIFY(xm.isApprox(refX,test_precision<Scalar>()));
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}
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// test initialization ctor
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{
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Rhs x(b.rows(), b.cols());
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Solver solver2(A);
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VERIFY(solver2.info() == Success);
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x = solver2.solve(b);
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VERIFY(x.isApprox(refX,test_precision<Scalar>()));
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}
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// test dense Block as the result and rhs:
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{
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DenseRhs x(refX.rows(), refX.cols());
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DenseRhs oldb(db);
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x.setZero();
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x.block(0,0,x.rows(),x.cols()) = solver.solve(db.block(0,0,db.rows(),db.cols()));
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VERIFY(oldb.isApprox(db) && "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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// test uncompressed inputs
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{
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Mat A2 = A;
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A2.reserve((ArrayXf::Random(A.outerSize())+2).template cast<typename Mat::StorageIndex>().eval());
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solver.compute(A2);
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Rhs x = solver.solve(b);
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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 typename Solver::MatrixType& fullA, 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(A.cols(), 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 << "ERROR | sparse solver testing, factorization failed (" << typeid(Solver).name() << ")\n";
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VERIFY(solver.info() == Success);
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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 << "WARNING | sparse solver testing, solving failed (" << typeid(Solver).name() << ")\n";
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return;
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}
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RealScalar res_error = (fullA*x-b).norm()/b.norm();
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VERIFY( (res_error <= test_precision<Scalar>() ) && "sparse solver failed without noticing it");
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if(refX.size() != 0 && (refX - x).norm()/refX.norm() > test_precision<Scalar>())
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{
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std::cerr << "WARNING | found solution is different from the provided reference one\n";
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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 << "WARNING | 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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void check_sparse_abs_determinant(Solver& solver, const typename Solver::MatrixType& A, const DenseMat& dA)
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{
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using std::abs;
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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 << "WARNING | sparse solver testing: factorization failed (check_sparse_abs_determinant)\n";
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return;
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}
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Scalar refDet = abs(dA.determinant());
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VERIFY_IS_APPROX(refDet,solver.absDeterminant());
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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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if(Solver::UpLo==(Lower|Upper))
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halfA = A;
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else
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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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std::string sym_to_string(int sym)
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{
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if(sym==Symmetric) return "Symmetric ";
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if(sym==SPD) return "SPD ";
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return "";
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}
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template<typename Derived>
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std::string solver_stats(const IterativeSolverBase<Derived> &solver)
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{
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std::stringstream ss;
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ss << solver.iterations() << " iters, error: " << solver.error();
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return ss.str();
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}
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template<typename Derived>
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std::string solver_stats(const SparseSolverBase<Derived> &/*solver*/)
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{
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return "";
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}
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#endif
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template<typename Solver> void check_sparse_spd_solving(Solver& solver, int maxSize = 300, int maxRealWorldSize = 100000)
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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::StorageIndex StorageIndex;
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typedef SparseMatrix<Scalar,ColMajor, StorageIndex> 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, maxSize);
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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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CALL_SUBTEST( check_sparse_solving(solver, A, b, dA, b) );
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CALL_SUBTEST( check_sparse_solving(solver, halfA, b, dA, b) );
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CALL_SUBTEST( check_sparse_solving(solver, A, dB, dA, dB) );
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CALL_SUBTEST( check_sparse_solving(solver, halfA, dB, dA, dB) );
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CALL_SUBTEST( check_sparse_solving(solver, A, B, dA, dB) );
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CALL_SUBTEST( 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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// Test real problems with double precision only
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if (internal::is_same<typename NumTraits<Scalar>::Real, double>::value)
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{
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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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A = it.matrix();
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if(A.diagonal().size() <= maxRealWorldSize)
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{
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DenseVector b = it.rhs();
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DenseVector refX = it.refX();
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PermutationMatrix<Dynamic, Dynamic, StorageIndex> pnull;
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halfA.resize(A.rows(), A.cols());
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if(Solver::UpLo == (Lower|Upper))
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halfA = A;
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else
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halfA.template selfadjointView<Solver::UpLo>() = A.template triangularView<Eigen::Lower>().twistedBy(pnull);
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std::cout << "INFO | Testing " << sym_to_string(it.sym()) << "sparse problem " << it.matname()
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<< " (" << A.rows() << "x" << A.cols() << ") using " << typeid(Solver).name() << "..." << std::endl;
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CALL_SUBTEST( check_sparse_solving_real_cases(solver, A, b, A, refX) );
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std::string stats = solver_stats(solver);
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if(stats.size()>0)
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std::cout << "INFO | " << stats << std::endl;
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CALL_SUBTEST( check_sparse_solving_real_cases(solver, halfA, b, A, refX) );
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}
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else
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{
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std::cout << "INFO | Skip sparse problem \"" << it.matname() << "\" (too large)" << std::endl;
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}
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}
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}
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}
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#else
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EIGEN_UNUSED_VARIABLE(maxRealWorldSize);
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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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Index generate_sparse_square_problem(Solver&, typename Solver::MatrixType& A, DenseMat& dA, int maxSize = 300, int options = ForceNonZeroDiag)
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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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Index 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, options);
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return size;
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}
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struct prune_column {
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Index m_col;
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prune_column(Index col) : m_col(col) {}
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template<class Scalar>
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bool operator()(Index, Index col, const Scalar&) const {
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return col != m_col;
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}
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};
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template<typename Solver> void check_sparse_square_solving(Solver& solver, int maxSize = 300, int maxRealWorldSize = 100000, bool checkDeficient = false)
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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, typename Mat::StorageIndex> 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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Index size = generate_sparse_square_problem(solver, A, dA, maxSize);
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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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CALL_SUBTEST(check_sparse_solving(solver, A, b, dA, b));
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CALL_SUBTEST(check_sparse_solving(solver, A, dB, dA, dB));
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CALL_SUBTEST(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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// regression test for Bug 792 (structurally rank deficient matrices):
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if(checkDeficient && size>1) {
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Index col = internal::random<int>(0,int(size-1));
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A.prune(prune_column(col));
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solver.compute(A);
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VERIFY_IS_EQUAL(solver.info(), NumericalIssue);
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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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// Test real problems with double precision only
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if (internal::is_same<typename NumTraits<Scalar>::Real, double>::value)
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{
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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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A = it.matrix();
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if(A.diagonal().size() <= maxRealWorldSize)
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{
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DenseVector b = it.rhs();
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DenseVector refX = it.refX();
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std::cout << "INFO | Testing " << sym_to_string(it.sym()) << "sparse problem " << it.matname()
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<< " (" << A.rows() << "x" << A.cols() << ") using " << typeid(Solver).name() << "..." << std::endl;
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CALL_SUBTEST(check_sparse_solving_real_cases(solver, A, b, A, refX));
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std::string stats = solver_stats(solver);
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if(stats.size()>0)
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std::cout << "INFO | " << stats << std::endl;
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}
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else
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{
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std::cout << "INFO | SKIP sparse problem \"" << it.matname() << "\" (too large)" << std::endl;
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}
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}
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}
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#else
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EIGEN_UNUSED_VARIABLE(maxRealWorldSize);
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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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for (int i = 0; i < g_repeat; i++) {
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// generate the problem
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Mat A;
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DenseMatrix dA;
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int size = internal::random<int>(1,30);
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dA.setRandom(size,size);
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dA = (dA.array().abs()<0.3).select(0,dA);
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dA.diagonal() = (dA.diagonal().array()==0).select(1,dA.diagonal());
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A = dA.sparseView();
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A.makeCompressed();
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check_sparse_determinant(solver, A, dA);
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}
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}
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template<typename Solver> void check_sparse_square_abs_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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for (int i = 0; i < g_repeat; i++) {
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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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check_sparse_abs_determinant(solver, A, dA);
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}
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}
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template<typename Solver, typename DenseMat>
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void generate_sparse_leastsquare_problem(Solver&, typename Solver::MatrixType& A, DenseMat& dA, int maxSize = 300, int options = ForceNonZeroDiag)
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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 rows = internal::random<int>(1,maxSize);
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int cols = internal::random<int>(1,rows);
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double density = (std::max)(8./(rows*cols), 0.01);
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A.resize(rows,cols);
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dA.resize(rows,cols);
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initSparse<Scalar>(density, dA, A, options);
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}
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template<typename Solver> void check_sparse_leastsquare_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, typename Mat::StorageIndex> 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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generate_sparse_leastsquare_problem(solver, A, dA);
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A.makeCompressed();
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DenseVector b = DenseVector::Random(A.rows());
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DenseMatrix dB(A.rows(),rhsCols);
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SpMat B(A.rows(),rhsCols);
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double density = (std::max)(8./(A.rows()*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(A.rows());
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check_sparse_solving(solver, A, b, dA, b);
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}
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}
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}
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