template<typename Scalar> void test_spqr_scalar() { typedef SparseMatrix<Scalar,ColMajor> MatrixType; MatrixType A; Matrix<Scalar,Dynamic,Dynamic> dA; typedef Matrix<Scalar,Dynamic,1> DenseVector; DenseVector refX,x,b; SPQR<MatrixType> solver; generate_sparse_rectangular_problem(A,dA); int m = A.rows(); b = DenseVector::Random(m); solver.compute(A); if (solver.info() != Success) { std::cerr << "sparse QR factorization failed\n"; exit(0); return; } x = solver.solve(b); if (solver.info() != Success) { std::cerr << "sparse QR factorization failed\n"; exit(0); return; } //Compare with a dense solver refX = dA.colPivHouseholderQr().solve(b); VERIFY(x.isApprox(refX,test_precision<Scalar>())); }
template<typename Scalar> void test_sparseqr_scalar() { typedef SparseMatrix<Scalar,ColMajor> MatrixType; typedef Matrix<Scalar,Dynamic,Dynamic> DenseMat; typedef Matrix<Scalar,Dynamic,1> DenseVector; MatrixType A; DenseMat dA; DenseVector refX,x,b; SparseQR<MatrixType, COLAMDOrdering<int> > solver; generate_sparse_rectangular_problem(A,dA); b = dA * DenseVector::Random(A.cols()); solver.compute(A); if(internal::random<float>(0,1)>0.5f) solver.factorize(A); // this checks that calling analyzePattern is not needed if the pattern do not change. if (solver.info() != Success) { std::cerr << "sparse QR factorization failed\n"; exit(0); return; } x = solver.solve(b); if (solver.info() != Success) { std::cerr << "sparse QR factorization failed\n"; exit(0); return; } VERIFY_IS_APPROX(A * x, b); //Compare with a dense QR solver ColPivHouseholderQR<DenseMat> dqr(dA); refX = dqr.solve(b); VERIFY_IS_EQUAL(dqr.rank(), solver.rank()); if(solver.rank()==A.cols()) // full rank VERIFY_IS_APPROX(x, refX); // else // VERIFY((dA * refX - b).norm() * 2 > (A * x - b).norm() ); // Compute explicitly the matrix Q MatrixType Q, QtQ, idM; Q = solver.matrixQ(); //Check ||Q' * Q - I || QtQ = Q * Q.adjoint(); idM.resize(Q.rows(), Q.rows()); idM.setIdentity(); VERIFY(idM.isApprox(QtQ)); // Q to dense DenseMat dQ; dQ = solver.matrixQ(); VERIFY_IS_APPROX(Q, dQ); }