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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Desire Nuentsa Wakam <desire.nuentsa_wakam@inria.fr>
// Copyright (C) 2014 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
#include "sparse.h"
#include <Eigen/SparseQR>
template<typename MatrixType,typename DenseMat> int generate_sparse_rectangular_problem(MatrixType& A, DenseMat& dA, int maxRows = 300, int maxCols = 150) { eigen_assert(maxRows >= maxCols); typedef typename MatrixType::Scalar Scalar; int rows = internal::random<int>(1,maxRows); int cols = internal::random<int>(1,maxCols); double density = (std::max)(8./(rows*cols), 0.01); A.resize(rows,cols); dA.resize(rows,cols); initSparse<Scalar>(density, dA, A,ForceNonZeroDiag); A.makeCompressed(); int nop = internal::random<int>(0, internal::random<double>(0,1) > 0.5 ? cols/2 : 0); for(int k=0; k<nop; ++k) { int j0 = internal::random<int>(0,cols-1); int j1 = internal::random<int>(0,cols-1); Scalar s = internal::random<Scalar>(); A.col(j0) = s * A.col(j1); dA.col(j0) = s * dA.col(j1); } // if(rows<cols) {
// A.conservativeResize(cols,cols);
// dA.conservativeResize(cols,cols);
// dA.bottomRows(cols-rows).setZero();
// }
return rows; }
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)>0.5) 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); } void test_sparseqr() { for(int i=0; i<g_repeat; ++i) { CALL_SUBTEST_1(test_sparseqr_scalar<double>()); CALL_SUBTEST_2(test_sparseqr_scalar<std::complex<double> >()); } }
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