template<typename Scalar> void sparse_lu(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; DenseVector vec1 = DenseVector::Random(rows); std::vector<Vector2i> zeroCoords; std::vector<Vector2i> nonzeroCoords; 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); FullPivLU<DenseMatrix> refLu(refMat2); refX = refLu.solve(b); #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_UMFPACK_SUPPORT { // check solve x.setZero(); SparseLU<SparseMatrix<Scalar>,UmfPack> lu(m2); VERIFY(lu.succeeded() && "umfpack LU decomposition failed"); VERIFY(lu.solve(b,&x) && "umfpack LU solving failed"); VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LU: umfpack"); VERIFY_IS_APPROX(refDet,lu.determinant()); // TODO check the extracted data //std::cerr << slu.matrixL() << "\n"; } #endif #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 (slu.solve(b, &x, SvTranspose)) { VERIFY(b.isApprox(m2.transpose() * x, test_precision<Scalar>())); } if (slu.solve(b, &x, SvAdjoint)) { VERIFY(b.isApprox(m2.adjoint() * x, test_precision<Scalar>())); } if (!NumTraits<Scalar>::IsComplex) { VERIFY_IS_APPROX(refDet,slu.determinant()); // FIXME det is not very stable for complex } } } #endif }