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/eigen2/eigen2_sparse_solvers.cpp b/test/eigen2/eigen2_sparse_solvers.cpp
new file mode 100644
index 0000000..3aef27a
--- /dev/null
+++ b/test/eigen2/eigen2_sparse_solvers.cpp
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+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Daniel Gomez Ferro <dgomezferro@gmail.com>
+//
+// 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.startFill();
+ for (int j=0 ; j<sparseMat.cols(); ++j)
+ for (int i=j ; i<sparseMat.rows(); ++i)
+ if (refMat(i,j)!=Scalar(0))
+ sparseMat.fill(i,j) = refMat(i,j);
+ sparseMat.endFill();
+}
+
+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
+ initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, &zeroCoords, &nonzeroCoords);
+ VERIFY_IS_APPROX(refMat2.template marked<LowerTriangular>().solveTriangular(vec2),
+ m2.template marked<LowerTriangular>().solveTriangular(vec3));
+
+ // lower - transpose
+ initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, &zeroCoords, &nonzeroCoords);
+ VERIFY_IS_APPROX(refMat2.template marked<LowerTriangular>().transpose().solveTriangular(vec2),
+ m2.template marked<LowerTriangular>().transpose().solveTriangular(vec3));
+
+ // upper
+ initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, &zeroCoords, &nonzeroCoords);
+ VERIFY_IS_APPROX(refMat2.template marked<UpperTriangular>().solveTriangular(vec2),
+ m2.template marked<UpperTriangular>().solveTriangular(vec3));
+
+ // upper - transpose
+ initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, &zeroCoords, &nonzeroCoords);
+ VERIFY_IS_APPROX(refMat2.template marked<UpperTriangular>().transpose().solveTriangular(vec2),
+ m2.template marked<UpperTriangular>().transpose().solveTriangular(vec3));
+ }
+
+ // test LLT
+ {
+ // TODO fix the issue with complex (see SparseLLT::solveInPlace)
+ SparseMatrix<Scalar> m2(rows, cols);
+ DenseMatrix refMat2(rows, cols);
+
+ DenseVector b = DenseVector::Random(cols);
+ DenseVector refX(cols), x(cols);
+
+ initSPD(density, refMat2, m2);
+
+ refMat2.llt().solve(b, &refX);
+ typedef SparseMatrix<Scalar,LowerTriangular|SelfAdjoint> SparseSelfAdjointMatrix;
+ if (!NumTraits<Scalar>::IsComplex)
+ {
+ x = b;
+ SparseLLT<SparseSelfAdjointMatrix> (m2).solveInPlace(x);
+ VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: default");
+ }
+ #ifdef EIGEN_CHOLMOD_SUPPORT
+ x = b;
+ SparseLLT<SparseSelfAdjointMatrix,Cholmod>(m2).solveInPlace(x);
+ VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: cholmod");
+ #endif
+ if (!NumTraits<Scalar>::IsComplex)
+ {
+ #ifdef EIGEN_TAUCS_SUPPORT
+ x = b;
+ SparseLLT<SparseSelfAdjointMatrix,Taucs>(m2,IncompleteFactorization).solveInPlace(x);
+ VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: taucs (IncompleteFactorization)");
+ x = b;
+ SparseLLT<SparseSelfAdjointMatrix,Taucs>(m2,SupernodalMultifrontal).solveInPlace(x);
+ VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: taucs (SupernodalMultifrontal)");
+ x = b;
+ SparseLLT<SparseSelfAdjointMatrix,Taucs>(m2,SupernodalLeftLooking).solveInPlace(x);
+ VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: taucs (SupernodalLeftLooking)");
+ #endif
+ }
+ }
+
+ // test LDLT
+ if (!NumTraits<Scalar>::IsComplex)
+ {
+ // TODO fix the issue with complex (see SparseLDLT::solveInPlace)
+ SparseMatrix<Scalar> m2(rows, cols);
+ DenseMatrix refMat2(rows, cols);
+
+ DenseVector b = DenseVector::Random(cols);
+ DenseVector refX(cols), x(cols);
+
+ //initSPD(density, refMat2, m2);
+ initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, 0, 0);
+ refMat2 += refMat2.adjoint();
+ refMat2.diagonal() *= 0.5;
+
+ refMat2.ldlt().solve(b, &refX);
+ typedef SparseMatrix<Scalar,UpperTriangular|SelfAdjoint> SparseSelfAdjointMatrix;
+ x = b;
+ SparseLDLT<SparseSelfAdjointMatrix> ldlt(m2);
+ if (ldlt.succeeded())
+ ldlt.solveInPlace(x);
+ VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LDLT: default");
+ }
+
+ // test LU
+ {
+ static int count = 0;
+ SparseMatrix<Scalar> m2(rows, cols);
+ DenseMatrix refMat2(rows, cols);
+
+ DenseVector b = DenseVector::Random(cols);
+ DenseVector refX(cols), x(cols);
+
+ initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag, &zeroCoords, &nonzeroCoords);
+
+ LU<DenseMatrix> refLu(refMat2);
+ refLu.solve(b, &refX);
+ #if defined(EIGEN_SUPERLU_SUPPORT) || defined(EIGEN_UMFPACK_SUPPORT)
+ Scalar refDet = refLu.determinant();
+ #endif
+ x.setZero();
+ // // SparseLU<SparseMatrix<Scalar> > (m2).solve(b,&x);
+ // // VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LU: default");
+ #ifdef EIGEN_SUPERLU_SUPPORT
+ {
+ x.setZero();
+ SparseLU<SparseMatrix<Scalar>,SuperLU> slu(m2);
+ if (slu.succeeded())
+ {
+ if (slu.solve(b,&x)) {
+ VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LU: SuperLU");
+ }
+ // std::cerr << refDet << " == " << slu.determinant() << "\n";
+ if (count==0) {
+ VERIFY_IS_APPROX(refDet,slu.determinant()); // FIXME det is not very stable for complex
+ }
+ }
+ }
+ #endif
+ #ifdef EIGEN_UMFPACK_SUPPORT
+ {
+ // check solve
+ x.setZero();
+ SparseLU<SparseMatrix<Scalar>,UmfPack> slu(m2);
+ if (slu.succeeded()) {
+ if (slu.solve(b,&x)) {
+ if (count==0) {
+ VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LU: umfpack"); // FIXME solve is not very stable for complex
+ }
+ }
+ VERIFY_IS_APPROX(refDet,slu.determinant());
+ // TODO check the extracted data
+ //std::cerr << slu.matrixL() << "\n";
+ }
+ }
+ #endif
+ count++;
+ }
+
+}
+
+void test_eigen2_sparse_solvers()
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( sparse_solvers<double>(8, 8) );
+ CALL_SUBTEST_2( sparse_solvers<std::complex<double> >(16, 16) );
+ CALL_SUBTEST_1( sparse_solvers<double>(101, 101) );
+ }
+}