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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>
//
// 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(const MatrixType& m)
{
typedef typename MatrixType::Index Index;
Index rows = m.rows();
Index cols = m.cols();
typedef typename MatrixType::Scalar Scalar;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType;
MatrixType a = MatrixType::Random(rows,cols);
HouseholderQR<MatrixType> qrOfA(a);
MatrixQType q = qrOfA.householderQ();
VERIFY_IS_UNITARY(q);
MatrixType r = qrOfA.matrixQR().template triangularView<Upper>();
VERIFY_IS_APPROX(a, qrOfA.householderQ() * r);
}
template<typename MatrixType, int Cols2> void qr_fixedsize()
{
enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };
typedef typename MatrixType::Scalar Scalar;
Matrix<Scalar,Rows,Cols> m1 = Matrix<Scalar,Rows,Cols>::Random();
HouseholderQR<Matrix<Scalar,Rows,Cols> > qr(m1);
Matrix<Scalar,Rows,Cols> r = qr.matrixQR();
// 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);
VERIFY_IS_APPROX(m1, qr.householderQ() * r);
Matrix<Scalar,Cols,Cols2> m2 = Matrix<Scalar,Cols,Cols2>::Random(Cols,Cols2);
Matrix<Scalar,Rows,Cols2> m3 = m1*m2;
m2 = Matrix<Scalar,Cols,Cols2>::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;
using std::pow;
using std::max;
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*4);
m1 += a * a.adjoint();
}
HouseholderQR<MatrixType> qr(m1);
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.householderQ(); // get a unitary
m1 = m3 * m1 * m3;
qr.compute(m1);
VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant());
// This test is tricky if the determinant becomes too small.
// Since we generate random numbers with magnitude rrange [0,1], the average determinant is 0.5^size
VERIFY_IS_MUCH_SMALLER_THAN( abs(absdet-qr.absDeterminant()), (max)(RealScalar(pow(0.5,size)),(max)(abs(absdet),abs(qr.absDeterminant()))) );
}
template<typename MatrixType> void qr_verify_assert()
{
MatrixType tmp;
HouseholderQR<MatrixType> qr;
VERIFY_RAISES_ASSERT(qr.matrixQR())
VERIFY_RAISES_ASSERT(qr.solve(tmp))
VERIFY_RAISES_ASSERT(qr.householderQ())
VERIFY_RAISES_ASSERT(qr.absDeterminant())
VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
}
void test_qr()
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( qr(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
CALL_SUBTEST_2( qr(MatrixXcd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2),internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))) );
CALL_SUBTEST_3(( qr_fixedsize<Matrix<float,3,4>, 2 >() ));
CALL_SUBTEST_4(( qr_fixedsize<Matrix<double,6,2>, 4 >() ));
CALL_SUBTEST_5(( qr_fixedsize<Matrix<double,2,5>, 7 >() ));
CALL_SUBTEST_11( qr(Matrix<float,1,1>()) );
}
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( qr_invertible<MatrixXf>() );
CALL_SUBTEST_6( qr_invertible<MatrixXd>() );
CALL_SUBTEST_7( qr_invertible<MatrixXcf>() );
CALL_SUBTEST_8( qr_invertible<MatrixXcd>() );
}
CALL_SUBTEST_9(qr_verify_assert<Matrix3f>());
CALL_SUBTEST_10(qr_verify_assert<Matrix3d>());
CALL_SUBTEST_1(qr_verify_assert<MatrixXf>());
CALL_SUBTEST_6(qr_verify_assert<MatrixXd>());
CALL_SUBTEST_7(qr_verify_assert<MatrixXcf>());
CALL_SUBTEST_8(qr_verify_assert<MatrixXcd>());
// Test problem size constructors
CALL_SUBTEST_12(HouseholderQR<MatrixXf>(10, 20));
}
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