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qr_fullpivoting.cpp
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Sat, Feb 22, 00:18

qr_fullpivoting.cpp
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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>
#include "solverbase.h"
template<typename MatrixType> void qr()
{
STATIC_CHECK(( internal::is_same<typename FullPivHouseholderQR<MatrixType>::StorageIndex,int>::value ));
static const int Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime;
Index max_size = EIGEN_TEST_MAX_SIZE;
Index min_size = numext::maxi(1,EIGEN_TEST_MAX_SIZE/10);
Index rows = Rows == Dynamic ? internal::random<Index>(min_size,max_size) : Rows,
cols = Cols == Dynamic ? internal::random<Index>(min_size,max_size) : Cols,
cols2 = Cols == Dynamic ? internal::random<Index>(min_size,max_size) : Cols,
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());
check_solverbase<MatrixType, MatrixType>(m1, qr, rows, cols, cols2);
{
MatrixType m2, m3;
Index size = rows;
do {
m1 = MatrixType::Random(size,size);
qr.compute(m1);
} while(!qr.isInvertible());
MatrixType m1_inv = qr.inverse();
m3 = m1 * MatrixType::Random(size,cols2);
m2 = qr.solve(m3);
VERIFY_IS_APPROX(m2, m1_inv*m3);
}
}
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;
Index max_size = numext::mini(50,EIGEN_TEST_MAX_SIZE);
Index min_size = numext::maxi(1,EIGEN_TEST_MAX_SIZE/10);
Index size = internal::random<Index>(min_size,max_size);
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());
check_solverbase<MatrixType, MatrixType>(m1, qr, size, size, size);
// 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.transpose().solve(tmp))
VERIFY_RAISES_ASSERT(qr.adjoint().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())
}
EIGEN_DECLARE_TEST(qr_fullpivoting)
{
for(int i = 0; i < 1; i++) {
CALL_SUBTEST_5( qr<Matrix3f>() );
CALL_SUBTEST_6( qr<Matrix3d>() );
CALL_SUBTEST_8( 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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