[136] | 1 | // This file is part of Eigen, a lightweight C++ template library
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| 2 | // for linear algebra.
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| 3 | //
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| 4 | // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
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| 5 | // Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
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| 6 | //
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| 7 | // This Source Code Form is subject to the terms of the Mozilla
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| 8 | // Public License v. 2.0. If a copy of the MPL was not distributed
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| 9 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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| 10 |
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| 11 | #include "main.h"
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| 12 | #include <Eigen/QR>
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| 13 |
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| 14 | template<typename MatrixType> void qr()
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| 15 | {
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| 16 | typedef typename MatrixType::Index Index;
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| 17 |
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| 18 | Index rows = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE), cols = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE), cols2 = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE);
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| 19 | Index rank = internal::random<Index>(1, (std::min)(rows, cols)-1);
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| 20 |
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| 21 | typedef typename MatrixType::Scalar Scalar;
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| 22 | typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType;
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| 23 | MatrixType m1;
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| 24 | createRandomPIMatrixOfRank(rank,rows,cols,m1);
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| 25 | ColPivHouseholderQR<MatrixType> qr(m1);
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| 26 | VERIFY(rank == qr.rank());
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| 27 | VERIFY(cols - qr.rank() == qr.dimensionOfKernel());
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| 28 | VERIFY(!qr.isInjective());
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| 29 | VERIFY(!qr.isInvertible());
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| 30 | VERIFY(!qr.isSurjective());
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| 31 |
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| 32 | MatrixQType q = qr.householderQ();
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| 33 | VERIFY_IS_UNITARY(q);
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| 34 |
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| 35 | MatrixType r = qr.matrixQR().template triangularView<Upper>();
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| 36 | MatrixType c = q * r * qr.colsPermutation().inverse();
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| 37 | VERIFY_IS_APPROX(m1, c);
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| 38 |
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| 39 | MatrixType m2 = MatrixType::Random(cols,cols2);
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| 40 | MatrixType m3 = m1*m2;
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| 41 | m2 = MatrixType::Random(cols,cols2);
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| 42 | m2 = qr.solve(m3);
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| 43 | VERIFY_IS_APPROX(m3, m1*m2);
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| 44 | }
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| 45 |
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| 46 | template<typename MatrixType, int Cols2> void qr_fixedsize()
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| 47 | {
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| 48 | enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };
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| 49 | typedef typename MatrixType::Scalar Scalar;
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| 50 | int rank = internal::random<int>(1, (std::min)(int(Rows), int(Cols))-1);
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| 51 | Matrix<Scalar,Rows,Cols> m1;
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| 52 | createRandomPIMatrixOfRank(rank,Rows,Cols,m1);
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| 53 | ColPivHouseholderQR<Matrix<Scalar,Rows,Cols> > qr(m1);
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| 54 | VERIFY(rank == qr.rank());
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| 55 | VERIFY(Cols - qr.rank() == qr.dimensionOfKernel());
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| 56 | VERIFY(qr.isInjective() == (rank == Rows));
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| 57 | VERIFY(qr.isSurjective() == (rank == Cols));
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| 58 | VERIFY(qr.isInvertible() == (qr.isInjective() && qr.isSurjective()));
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| 59 |
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| 60 | Matrix<Scalar,Rows,Cols> r = qr.matrixQR().template triangularView<Upper>();
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| 61 | Matrix<Scalar,Rows,Cols> c = qr.householderQ() * r * qr.colsPermutation().inverse();
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| 62 | VERIFY_IS_APPROX(m1, c);
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| 63 |
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| 64 | Matrix<Scalar,Cols,Cols2> m2 = Matrix<Scalar,Cols,Cols2>::Random(Cols,Cols2);
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| 65 | Matrix<Scalar,Rows,Cols2> m3 = m1*m2;
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| 66 | m2 = Matrix<Scalar,Cols,Cols2>::Random(Cols,Cols2);
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| 67 | m2 = qr.solve(m3);
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| 68 | VERIFY_IS_APPROX(m3, m1*m2);
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| 69 | }
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| 70 |
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| 71 | template<typename MatrixType> void qr_invertible()
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| 72 | {
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| 73 | using std::log;
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| 74 | using std::abs;
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| 75 | typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
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| 76 | typedef typename MatrixType::Scalar Scalar;
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| 77 |
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| 78 | int size = internal::random<int>(10,50);
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| 79 |
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| 80 | MatrixType m1(size, size), m2(size, size), m3(size, size);
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| 81 | m1 = MatrixType::Random(size,size);
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| 82 |
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| 83 | if (internal::is_same<RealScalar,float>::value)
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| 84 | {
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| 85 | // let's build a matrix more stable to inverse
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| 86 | MatrixType a = MatrixType::Random(size,size*2);
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| 87 | m1 += a * a.adjoint();
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| 88 | }
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| 89 |
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| 90 | ColPivHouseholderQR<MatrixType> qr(m1);
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| 91 | m3 = MatrixType::Random(size,size);
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| 92 | m2 = qr.solve(m3);
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| 93 | //VERIFY_IS_APPROX(m3, m1*m2);
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| 94 |
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| 95 | // now construct a matrix with prescribed determinant
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| 96 | m1.setZero();
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| 97 | for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>();
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| 98 | RealScalar absdet = abs(m1.diagonal().prod());
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| 99 | m3 = qr.householderQ(); // get a unitary
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| 100 | m1 = m3 * m1 * m3;
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| 101 | qr.compute(m1);
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| 102 | VERIFY_IS_APPROX(absdet, qr.absDeterminant());
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| 103 | VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant());
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| 104 | }
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| 105 |
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| 106 | template<typename MatrixType> void qr_verify_assert()
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| 107 | {
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| 108 | MatrixType tmp;
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| 109 |
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| 110 | ColPivHouseholderQR<MatrixType> qr;
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| 111 | VERIFY_RAISES_ASSERT(qr.matrixQR())
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| 112 | VERIFY_RAISES_ASSERT(qr.solve(tmp))
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| 113 | VERIFY_RAISES_ASSERT(qr.householderQ())
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| 114 | VERIFY_RAISES_ASSERT(qr.dimensionOfKernel())
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| 115 | VERIFY_RAISES_ASSERT(qr.isInjective())
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| 116 | VERIFY_RAISES_ASSERT(qr.isSurjective())
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| 117 | VERIFY_RAISES_ASSERT(qr.isInvertible())
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| 118 | VERIFY_RAISES_ASSERT(qr.inverse())
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| 119 | VERIFY_RAISES_ASSERT(qr.absDeterminant())
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| 120 | VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
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| 121 | }
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| 122 |
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| 123 | void test_qr_colpivoting()
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| 124 | {
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| 125 | for(int i = 0; i < g_repeat; i++) {
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| 126 | CALL_SUBTEST_1( qr<MatrixXf>() );
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| 127 | CALL_SUBTEST_2( qr<MatrixXd>() );
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| 128 | CALL_SUBTEST_3( qr<MatrixXcd>() );
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| 129 | CALL_SUBTEST_4(( qr_fixedsize<Matrix<float,3,5>, 4 >() ));
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| 130 | CALL_SUBTEST_5(( qr_fixedsize<Matrix<double,6,2>, 3 >() ));
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| 131 | CALL_SUBTEST_5(( qr_fixedsize<Matrix<double,1,1>, 1 >() ));
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| 132 | }
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| 133 |
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| 134 | for(int i = 0; i < g_repeat; i++) {
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| 135 | CALL_SUBTEST_1( qr_invertible<MatrixXf>() );
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| 136 | CALL_SUBTEST_2( qr_invertible<MatrixXd>() );
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| 137 | CALL_SUBTEST_6( qr_invertible<MatrixXcf>() );
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| 138 | CALL_SUBTEST_3( qr_invertible<MatrixXcd>() );
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| 139 | }
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| 140 |
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| 141 | CALL_SUBTEST_7(qr_verify_assert<Matrix3f>());
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| 142 | CALL_SUBTEST_8(qr_verify_assert<Matrix3d>());
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| 143 | CALL_SUBTEST_1(qr_verify_assert<MatrixXf>());
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| 144 | CALL_SUBTEST_2(qr_verify_assert<MatrixXd>());
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| 145 | CALL_SUBTEST_6(qr_verify_assert<MatrixXcf>());
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| 146 | CALL_SUBTEST_3(qr_verify_assert<MatrixXcd>());
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| 147 |
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| 148 | // Test problem size constructors
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| 149 | CALL_SUBTEST_9(ColPivHouseholderQR<MatrixXf>(10, 20));
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| 150 | }
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