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132 lines
4.5 KiB
132 lines
4.5 KiB
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#include "main.h"
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#include <Eigen/QR>
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template<typename MatrixType> void qr(const MatrixType& m)
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{
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typedef typename MatrixType::Index Index;
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Index rows = m.rows();
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Index cols = m.cols();
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typedef typename MatrixType::Scalar Scalar;
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typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType;
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MatrixType a = MatrixType::Random(rows,cols);
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HouseholderQR<MatrixType> qrOfA(a);
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MatrixQType q = qrOfA.householderQ();
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VERIFY_IS_UNITARY(q);
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MatrixType r = qrOfA.matrixQR().template triangularView<Upper>();
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VERIFY_IS_APPROX(a, qrOfA.householderQ() * r);
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}
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template<typename MatrixType, int Cols2> void qr_fixedsize()
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{
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enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };
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typedef typename MatrixType::Scalar Scalar;
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Matrix<Scalar,Rows,Cols> m1 = Matrix<Scalar,Rows,Cols>::Random();
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HouseholderQR<Matrix<Scalar,Rows,Cols> > qr(m1);
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Matrix<Scalar,Rows,Cols> r = qr.matrixQR();
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// FIXME need better way to construct trapezoid
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for(int i = 0; i < Rows; i++) for(int j = 0; j < Cols; j++) if(i>j) r(i,j) = Scalar(0);
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VERIFY_IS_APPROX(m1, qr.householderQ() * r);
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Matrix<Scalar,Cols,Cols2> m2 = Matrix<Scalar,Cols,Cols2>::Random(Cols,Cols2);
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Matrix<Scalar,Rows,Cols2> m3 = m1*m2;
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m2 = Matrix<Scalar,Cols,Cols2>::Random(Cols,Cols2);
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m2 = qr.solve(m3);
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VERIFY_IS_APPROX(m3, m1*m2);
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}
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template<typename MatrixType> void qr_invertible()
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{
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using std::log;
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using std::abs;
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using std::pow;
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using std::max;
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typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
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typedef typename MatrixType::Scalar Scalar;
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int size = internal::random<int>(10,50);
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MatrixType m1(size, size), m2(size, size), m3(size, size);
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m1 = MatrixType::Random(size,size);
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if (internal::is_same<RealScalar,float>::value)
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{
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// let's build a matrix more stable to inverse
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MatrixType a = MatrixType::Random(size,size*4);
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m1 += a * a.adjoint();
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}
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HouseholderQR<MatrixType> qr(m1);
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m3 = MatrixType::Random(size,size);
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m2 = qr.solve(m3);
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VERIFY_IS_APPROX(m3, m1*m2);
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// now construct a matrix with prescribed determinant
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m1.setZero();
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for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>();
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RealScalar absdet = abs(m1.diagonal().prod());
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m3 = qr.householderQ(); // get a unitary
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m1 = m3 * m1 * m3;
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qr.compute(m1);
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VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant());
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// This test is tricky if the determinant becomes too small.
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// Since we generate random numbers with magnitude rrange [0,1], the average determinant is 0.5^size
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VERIFY_IS_MUCH_SMALLER_THAN( abs(absdet-qr.absDeterminant()), (max)(RealScalar(pow(0.5,size)),(max)(abs(absdet),abs(qr.absDeterminant()))) );
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}
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template<typename MatrixType> void qr_verify_assert()
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{
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MatrixType tmp;
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HouseholderQR<MatrixType> qr;
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VERIFY_RAISES_ASSERT(qr.matrixQR())
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VERIFY_RAISES_ASSERT(qr.solve(tmp))
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VERIFY_RAISES_ASSERT(qr.householderQ())
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VERIFY_RAISES_ASSERT(qr.absDeterminant())
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VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
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}
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void test_qr()
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{
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for(int i = 0; i < g_repeat; i++) {
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CALL_SUBTEST_1( qr(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
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CALL_SUBTEST_2( qr(MatrixXcd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2),internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))) );
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CALL_SUBTEST_3(( qr_fixedsize<Matrix<float,3,4>, 2 >() ));
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CALL_SUBTEST_4(( qr_fixedsize<Matrix<double,6,2>, 4 >() ));
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CALL_SUBTEST_5(( qr_fixedsize<Matrix<double,2,5>, 7 >() ));
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CALL_SUBTEST_11( qr(Matrix<float,1,1>()) );
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}
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for(int i = 0; i < g_repeat; i++) {
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CALL_SUBTEST_1( qr_invertible<MatrixXf>() );
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CALL_SUBTEST_6( qr_invertible<MatrixXd>() );
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CALL_SUBTEST_7( qr_invertible<MatrixXcf>() );
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CALL_SUBTEST_8( qr_invertible<MatrixXcd>() );
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}
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CALL_SUBTEST_9(qr_verify_assert<Matrix3f>());
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CALL_SUBTEST_10(qr_verify_assert<Matrix3d>());
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CALL_SUBTEST_1(qr_verify_assert<MatrixXf>());
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CALL_SUBTEST_6(qr_verify_assert<MatrixXd>());
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CALL_SUBTEST_7(qr_verify_assert<MatrixXcf>());
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CALL_SUBTEST_8(qr_verify_assert<MatrixXcd>());
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// Test problem size constructors
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CALL_SUBTEST_12(HouseholderQR<MatrixXf>(10, 20));
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}
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