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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.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"
template<typename Scalar> void initSPD(double density, Matrix<Scalar,Dynamic,Dynamic>& refMat, SparseMatrix<Scalar>& sparseMat) { Matrix<Scalar,Dynamic,Dynamic> aux(refMat.rows(),refMat.cols()); initSparse(density,refMat,sparseMat); refMat = refMat * refMat.adjoint(); for (int k=0; k<2; ++k) { initSparse(density,aux,sparseMat,ForceNonZeroDiag); refMat += aux * aux.adjoint(); } sparseMat.setZero(); for (int j=0 ; j<sparseMat.cols(); ++j) for (int i=j ; i<sparseMat.rows(); ++i) if (refMat(i,j)!=Scalar(0)) sparseMat.insert(i,j) = refMat(i,j); sparseMat.finalize(); }
template<typename Scalar> void sparse_solvers(int rows, int cols) { double density = (std::max)(8./(rows*cols), 0.01); typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix; typedef Matrix<Scalar,Dynamic,1> DenseVector; // Scalar eps = 1e-6;
DenseVector vec1 = DenseVector::Random(rows);
std::vector<Vector2i> zeroCoords; std::vector<Vector2i> nonzeroCoords;
// test triangular solver
{ DenseVector vec2 = vec1, vec3 = vec1; SparseMatrix<Scalar> m2(rows, cols); DenseMatrix refMat2 = DenseMatrix::Zero(rows, cols);
// lower - dense
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, &zeroCoords, &nonzeroCoords); VERIFY_IS_APPROX(refMat2.template triangularView<Lower>().solve(vec2), m2.template triangularView<Lower>().solve(vec3));
// upper - dense
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, &zeroCoords, &nonzeroCoords); VERIFY_IS_APPROX(refMat2.template triangularView<Upper>().solve(vec2), m2.template triangularView<Upper>().solve(vec3)); VERIFY_IS_APPROX(refMat2.conjugate().template triangularView<Upper>().solve(vec2), m2.conjugate().template triangularView<Upper>().solve(vec3)); { SparseMatrix<Scalar> cm2(m2); //Index rows, Index cols, Index nnz, Index* outerIndexPtr, Index* innerIndexPtr, Scalar* valuePtr
MappedSparseMatrix<Scalar> mm2(rows, cols, cm2.nonZeros(), cm2.outerIndexPtr(), cm2.innerIndexPtr(), cm2.valuePtr()); VERIFY_IS_APPROX(refMat2.conjugate().template triangularView<Upper>().solve(vec2), mm2.conjugate().template triangularView<Upper>().solve(vec3)); }
// lower - transpose
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, &zeroCoords, &nonzeroCoords); VERIFY_IS_APPROX(refMat2.transpose().template triangularView<Upper>().solve(vec2), m2.transpose().template triangularView<Upper>().solve(vec3));
// upper - transpose
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, &zeroCoords, &nonzeroCoords); VERIFY_IS_APPROX(refMat2.transpose().template triangularView<Lower>().solve(vec2), m2.transpose().template triangularView<Lower>().solve(vec3));
SparseMatrix<Scalar> matB(rows, rows); DenseMatrix refMatB = DenseMatrix::Zero(rows, rows);
// lower - sparse
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular); initSparse<Scalar>(density, refMatB, matB); refMat2.template triangularView<Lower>().solveInPlace(refMatB); m2.template triangularView<Lower>().solveInPlace(matB); VERIFY_IS_APPROX(matB.toDense(), refMatB);
// upper - sparse
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular); initSparse<Scalar>(density, refMatB, matB); refMat2.template triangularView<Upper>().solveInPlace(refMatB); m2.template triangularView<Upper>().solveInPlace(matB); VERIFY_IS_APPROX(matB, refMatB);
// test deprecated API
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, &zeroCoords, &nonzeroCoords); VERIFY_IS_APPROX(refMat2.template triangularView<Lower>().solve(vec2), m2.template triangularView<Lower>().solve(vec3)); } }
void test_sparse_solvers() { for(int i = 0; i < g_repeat; i++) { CALL_SUBTEST_1(sparse_solvers<double>(8, 8) ); int s = internal::random<int>(1,300); CALL_SUBTEST_2(sparse_solvers<std::complex<double> >(s,s) ); CALL_SUBTEST_1(sparse_solvers<double>(s,s) ); } }
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