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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@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 "main.h"
#include <Eigen/QR>
template<typename MatrixType> void qr() { typedef typename MatrixType::Index Index;
Index rows = internal::random<Index>(20,200), cols = internal::random<int>(20,200), cols2 = internal::random<int>(20,200); Index rank = internal::random<Index>(1, (std::min)(rows, cols)-1);
typedef typename MatrixType::Scalar Scalar; typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType; MatrixType m1; createRandomPIMatrixOfRank(rank,rows,cols,m1); FullPivHouseholderQR<MatrixType> qr(m1); VERIFY_IS_EQUAL(rank, qr.rank()); VERIFY_IS_EQUAL(cols - qr.rank(), qr.dimensionOfKernel()); VERIFY(!qr.isInjective()); VERIFY(!qr.isInvertible()); VERIFY(!qr.isSurjective());
MatrixType r = qr.matrixQR(); MatrixQType q = qr.matrixQ(); VERIFY_IS_UNITARY(q); // FIXME need better way to construct trapezoid
for(int i = 0; i < rows; i++) for(int j = 0; j < cols; j++) if(i>j) r(i,j) = Scalar(0);
MatrixType c = qr.matrixQ() * r * qr.colsPermutation().inverse();
VERIFY_IS_APPROX(m1, c); // stress the ReturnByValue mechanism
MatrixType tmp; VERIFY_IS_APPROX(tmp.noalias() = qr.matrixQ() * r, (qr.matrixQ() * r).eval()); MatrixType m2 = MatrixType::Random(cols,cols2); MatrixType m3 = m1*m2; m2 = MatrixType::Random(cols,cols2); m2 = qr.solve(m3); VERIFY_IS_APPROX(m3, m1*m2); }
template<typename MatrixType> void qr_invertible() { using std::log; using std::abs; typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar; typedef typename MatrixType::Scalar Scalar;
int size = internal::random<int>(10,50);
MatrixType m1(size, size), m2(size, size), m3(size, size); m1 = MatrixType::Random(size,size);
if (internal::is_same<RealScalar,float>::value) { // let's build a matrix more stable to inverse
MatrixType a = MatrixType::Random(size,size*2); m1 += a * a.adjoint(); }
FullPivHouseholderQR<MatrixType> qr(m1); VERIFY(qr.isInjective()); VERIFY(qr.isInvertible()); VERIFY(qr.isSurjective());
m3 = MatrixType::Random(size,size); m2 = qr.solve(m3); VERIFY_IS_APPROX(m3, m1*m2);
// now construct a matrix with prescribed determinant
m1.setZero(); for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>(); RealScalar absdet = abs(m1.diagonal().prod()); m3 = qr.matrixQ(); // get a unitary
m1 = m3 * m1 * m3; qr.compute(m1); VERIFY_IS_APPROX(absdet, qr.absDeterminant()); VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant()); }
template<typename MatrixType> void qr_verify_assert() { MatrixType tmp;
FullPivHouseholderQR<MatrixType> qr; VERIFY_RAISES_ASSERT(qr.matrixQR()) VERIFY_RAISES_ASSERT(qr.solve(tmp)) VERIFY_RAISES_ASSERT(qr.matrixQ()) VERIFY_RAISES_ASSERT(qr.dimensionOfKernel()) VERIFY_RAISES_ASSERT(qr.isInjective()) VERIFY_RAISES_ASSERT(qr.isSurjective()) VERIFY_RAISES_ASSERT(qr.isInvertible()) VERIFY_RAISES_ASSERT(qr.inverse()) VERIFY_RAISES_ASSERT(qr.absDeterminant()) VERIFY_RAISES_ASSERT(qr.logAbsDeterminant()) }
void test_qr_fullpivoting() { for(int i = 0; i < 1; i++) { // FIXME : very weird bug here
// CALL_SUBTEST(qr(Matrix2f()) );
CALL_SUBTEST_1( qr<MatrixXf>() ); CALL_SUBTEST_2( qr<MatrixXd>() ); CALL_SUBTEST_3( qr<MatrixXcd>() ); }
for(int i = 0; i < g_repeat; i++) { CALL_SUBTEST_1( qr_invertible<MatrixXf>() ); CALL_SUBTEST_2( qr_invertible<MatrixXd>() ); CALL_SUBTEST_4( qr_invertible<MatrixXcf>() ); CALL_SUBTEST_3( qr_invertible<MatrixXcd>() ); }
CALL_SUBTEST_5(qr_verify_assert<Matrix3f>()); CALL_SUBTEST_6(qr_verify_assert<Matrix3d>()); CALL_SUBTEST_1(qr_verify_assert<MatrixXf>()); CALL_SUBTEST_2(qr_verify_assert<MatrixXd>()); CALL_SUBTEST_4(qr_verify_assert<MatrixXcf>()); CALL_SUBTEST_3(qr_verify_assert<MatrixXcd>());
// Test problem size constructors
CALL_SUBTEST_7(FullPivHouseholderQR<MatrixXf>(10, 20)); CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,10,20> >(10,20))); CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,10,20> >(Matrix<float,10,20>::Random()))); CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,20,10> >(20,10))); CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,20,10> >(Matrix<float,20,10>::Random()))); }
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