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132 lines
4.2 KiB
132 lines
4.2 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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// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
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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()
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{
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typedef typename MatrixType::Index Index;
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Index rows = internal::random<Index>(20,200), cols = internal::random<int>(20,200), cols2 = internal::random<int>(20,200);
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Index rank = internal::random<Index>(1, (std::min)(rows, cols)-1);
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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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typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType;
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MatrixType m1;
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createRandomPIMatrixOfRank(rank,rows,cols,m1);
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FullPivHouseholderQR<MatrixType> qr(m1);
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VERIFY(rank == qr.rank());
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VERIFY(cols - qr.rank() == qr.dimensionOfKernel());
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VERIFY(!qr.isInjective());
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VERIFY(!qr.isInvertible());
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VERIFY(!qr.isSurjective());
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MatrixType r = qr.matrixQR();
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MatrixQType q = qr.matrixQ();
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VERIFY_IS_UNITARY(q);
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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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MatrixType c = qr.matrixQ() * r * qr.colsPermutation().inverse();
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VERIFY_IS_APPROX(m1, c);
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MatrixType m2 = MatrixType::Random(cols,cols2);
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MatrixType m3 = m1*m2;
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m2 = MatrixType::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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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*2);
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m1 += a * a.adjoint();
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}
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FullPivHouseholderQR<MatrixType> qr(m1);
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VERIFY(qr.isInjective());
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VERIFY(qr.isInvertible());
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VERIFY(qr.isSurjective());
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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 = internal::abs(m1.diagonal().prod());
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m3 = qr.matrixQ(); // 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(absdet, qr.absDeterminant());
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VERIFY_IS_APPROX(internal::log(absdet), qr.logAbsDeterminant());
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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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FullPivHouseholderQR<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.matrixQ())
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VERIFY_RAISES_ASSERT(qr.dimensionOfKernel())
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VERIFY_RAISES_ASSERT(qr.isInjective())
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VERIFY_RAISES_ASSERT(qr.isSurjective())
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VERIFY_RAISES_ASSERT(qr.isInvertible())
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VERIFY_RAISES_ASSERT(qr.inverse())
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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_fullpivoting()
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{
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for(int i = 0; i < 1; i++) {
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// FIXME : very weird bug here
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// CALL_SUBTEST(qr(Matrix2f()) );
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CALL_SUBTEST_1( qr<MatrixXf>() );
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CALL_SUBTEST_2( qr<MatrixXd>() );
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CALL_SUBTEST_3( qr<MatrixXcd>() );
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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_2( qr_invertible<MatrixXd>() );
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CALL_SUBTEST_4( qr_invertible<MatrixXcf>() );
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CALL_SUBTEST_3( qr_invertible<MatrixXcd>() );
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}
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CALL_SUBTEST_5(qr_verify_assert<Matrix3f>());
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CALL_SUBTEST_6(qr_verify_assert<Matrix3d>());
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CALL_SUBTEST_1(qr_verify_assert<MatrixXf>());
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CALL_SUBTEST_2(qr_verify_assert<MatrixXd>());
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CALL_SUBTEST_4(qr_verify_assert<MatrixXcf>());
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CALL_SUBTEST_3(qr_verify_assert<MatrixXcd>());
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// Test problem size constructors
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CALL_SUBTEST_7(FullPivHouseholderQR<MatrixXf>(10, 20));
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}
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