Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 1 | // This file is part of Eigen, a lightweight C++ template library |
| 2 | // for linear algebra. |
| 3 | // |
| 4 | // Copyright (C) 2012 Desire Nuentsa Wakam <desire.nuentsa_wakam@inria.fr> |
| 5 | // Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr> |
| 6 | // |
| 7 | // This Source Code Form is subject to the terms of the Mozilla |
| 8 | // Public License v. 2.0. If a copy of the MPL was not distributed |
| 9 | #include "sparse.h" |
| 10 | #include <Eigen/SparseQR> |
| 11 | |
| 12 | template<typename MatrixType,typename DenseMat> |
| 13 | int generate_sparse_rectangular_problem(MatrixType& A, DenseMat& dA, int maxRows = 300, int maxCols = 150) |
| 14 | { |
| 15 | eigen_assert(maxRows >= maxCols); |
| 16 | typedef typename MatrixType::Scalar Scalar; |
| 17 | int rows = internal::random<int>(1,maxRows); |
| 18 | int cols = internal::random<int>(1,maxCols); |
| 19 | double density = (std::max)(8./(rows*cols), 0.01); |
| 20 | |
| 21 | A.resize(rows,cols); |
| 22 | dA.resize(rows,cols); |
| 23 | initSparse<Scalar>(density, dA, A,ForceNonZeroDiag); |
| 24 | A.makeCompressed(); |
| 25 | int nop = internal::random<int>(0, internal::random<double>(0,1) > 0.5 ? cols/2 : 0); |
| 26 | for(int k=0; k<nop; ++k) |
| 27 | { |
| 28 | int j0 = internal::random<int>(0,cols-1); |
| 29 | int j1 = internal::random<int>(0,cols-1); |
| 30 | Scalar s = internal::random<Scalar>(); |
| 31 | A.col(j0) = s * A.col(j1); |
| 32 | dA.col(j0) = s * dA.col(j1); |
| 33 | } |
| 34 | |
| 35 | // if(rows<cols) { |
| 36 | // A.conservativeResize(cols,cols); |
| 37 | // dA.conservativeResize(cols,cols); |
| 38 | // dA.bottomRows(cols-rows).setZero(); |
| 39 | // } |
| 40 | |
| 41 | return rows; |
| 42 | } |
| 43 | |
| 44 | template<typename Scalar> void test_sparseqr_scalar() |
| 45 | { |
| 46 | typedef SparseMatrix<Scalar,ColMajor> MatrixType; |
| 47 | typedef Matrix<Scalar,Dynamic,Dynamic> DenseMat; |
| 48 | typedef Matrix<Scalar,Dynamic,1> DenseVector; |
| 49 | MatrixType A; |
| 50 | DenseMat dA; |
| 51 | DenseVector refX,x,b; |
| 52 | SparseQR<MatrixType, COLAMDOrdering<int> > solver; |
| 53 | generate_sparse_rectangular_problem(A,dA); |
| 54 | |
| 55 | b = dA * DenseVector::Random(A.cols()); |
| 56 | solver.compute(A); |
| 57 | if (solver.info() != Success) |
| 58 | { |
| 59 | std::cerr << "sparse QR factorization failed\n"; |
| 60 | exit(0); |
| 61 | return; |
| 62 | } |
| 63 | x = solver.solve(b); |
| 64 | if (solver.info() != Success) |
| 65 | { |
| 66 | std::cerr << "sparse QR factorization failed\n"; |
| 67 | exit(0); |
| 68 | return; |
| 69 | } |
| 70 | |
| 71 | VERIFY_IS_APPROX(A * x, b); |
| 72 | |
| 73 | //Compare with a dense QR solver |
| 74 | ColPivHouseholderQR<DenseMat> dqr(dA); |
| 75 | refX = dqr.solve(b); |
| 76 | |
| 77 | VERIFY_IS_EQUAL(dqr.rank(), solver.rank()); |
| 78 | if(solver.rank()==A.cols()) // full rank |
| 79 | VERIFY_IS_APPROX(x, refX); |
| 80 | // else |
| 81 | // VERIFY((dA * refX - b).norm() * 2 > (A * x - b).norm() ); |
| 82 | |
| 83 | // Compute explicitly the matrix Q |
| 84 | MatrixType Q, QtQ, idM; |
| 85 | Q = solver.matrixQ(); |
| 86 | //Check ||Q' * Q - I || |
| 87 | QtQ = Q * Q.adjoint(); |
| 88 | idM.resize(Q.rows(), Q.rows()); idM.setIdentity(); |
| 89 | VERIFY(idM.isApprox(QtQ)); |
| 90 | } |
| 91 | void test_sparseqr() |
| 92 | { |
| 93 | for(int i=0; i<g_repeat; ++i) |
| 94 | { |
| 95 | CALL_SUBTEST_1(test_sparseqr_scalar<double>()); |
| 96 | CALL_SUBTEST_2(test_sparseqr_scalar<std::complex<double> >()); |
| 97 | } |
| 98 | } |
| 99 | |