Squashed 'third_party/eigen/' content from commit 61d72f6
Change-Id: Iccc90fa0b55ab44037f018046d2fcffd90d9d025
git-subtree-dir: third_party/eigen
git-subtree-split: 61d72f6383cfa842868c53e30e087b0258177257
diff --git a/test/sparse_solver.h b/test/sparse_solver.h
new file mode 100644
index 0000000..59d77da
--- /dev/null
+++ b/test/sparse_solver.h
@@ -0,0 +1,362 @@
+// 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>()));
+ }
+}
+
+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;
+}
+
+template<typename Solver> void check_sparse_square_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;
+
+ 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);
+ }
+ }
+
+ // 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);
+ }
+}
+