[136] | 1 | // This file is part of Eigen, a lightweight C++ template library
|
---|
| 2 | // for linear algebra.
|
---|
| 3 | //
|
---|
| 4 | // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
|
---|
| 5 | //
|
---|
| 6 | // This Source Code Form is subject to the terms of the Mozilla
|
---|
| 7 | // Public License v. 2.0. If a copy of the MPL was not distributed
|
---|
| 8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
---|
| 9 |
|
---|
| 10 | #include "main.h"
|
---|
| 11 | #include <Eigen/QR>
|
---|
| 12 |
|
---|
| 13 | template<typename MatrixType> void qr(const MatrixType& m)
|
---|
| 14 | {
|
---|
| 15 | typedef typename MatrixType::Index Index;
|
---|
| 16 |
|
---|
| 17 | Index rows = m.rows();
|
---|
| 18 | Index cols = m.cols();
|
---|
| 19 |
|
---|
| 20 | typedef typename MatrixType::Scalar Scalar;
|
---|
| 21 | typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType;
|
---|
| 22 |
|
---|
| 23 | MatrixType a = MatrixType::Random(rows,cols);
|
---|
| 24 | HouseholderQR<MatrixType> qrOfA(a);
|
---|
| 25 |
|
---|
| 26 | MatrixQType q = qrOfA.householderQ();
|
---|
| 27 | VERIFY_IS_UNITARY(q);
|
---|
| 28 |
|
---|
| 29 | MatrixType r = qrOfA.matrixQR().template triangularView<Upper>();
|
---|
| 30 | VERIFY_IS_APPROX(a, qrOfA.householderQ() * r);
|
---|
| 31 | }
|
---|
| 32 |
|
---|
| 33 | template<typename MatrixType, int Cols2> void qr_fixedsize()
|
---|
| 34 | {
|
---|
| 35 | enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };
|
---|
| 36 | typedef typename MatrixType::Scalar Scalar;
|
---|
| 37 | Matrix<Scalar,Rows,Cols> m1 = Matrix<Scalar,Rows,Cols>::Random();
|
---|
| 38 | HouseholderQR<Matrix<Scalar,Rows,Cols> > qr(m1);
|
---|
| 39 |
|
---|
| 40 | Matrix<Scalar,Rows,Cols> r = qr.matrixQR();
|
---|
| 41 | // FIXME need better way to construct trapezoid
|
---|
| 42 | for(int i = 0; i < Rows; i++) for(int j = 0; j < Cols; j++) if(i>j) r(i,j) = Scalar(0);
|
---|
| 43 |
|
---|
| 44 | VERIFY_IS_APPROX(m1, qr.householderQ() * r);
|
---|
| 45 |
|
---|
| 46 | Matrix<Scalar,Cols,Cols2> m2 = Matrix<Scalar,Cols,Cols2>::Random(Cols,Cols2);
|
---|
| 47 | Matrix<Scalar,Rows,Cols2> m3 = m1*m2;
|
---|
| 48 | m2 = Matrix<Scalar,Cols,Cols2>::Random(Cols,Cols2);
|
---|
| 49 | m2 = qr.solve(m3);
|
---|
| 50 | VERIFY_IS_APPROX(m3, m1*m2);
|
---|
| 51 | }
|
---|
| 52 |
|
---|
| 53 | template<typename MatrixType> void qr_invertible()
|
---|
| 54 | {
|
---|
| 55 | using std::log;
|
---|
| 56 | using std::abs;
|
---|
| 57 | typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
|
---|
| 58 | typedef typename MatrixType::Scalar Scalar;
|
---|
| 59 |
|
---|
| 60 | int size = internal::random<int>(10,50);
|
---|
| 61 |
|
---|
| 62 | MatrixType m1(size, size), m2(size, size), m3(size, size);
|
---|
| 63 | m1 = MatrixType::Random(size,size);
|
---|
| 64 |
|
---|
| 65 | if (internal::is_same<RealScalar,float>::value)
|
---|
| 66 | {
|
---|
| 67 | // let's build a matrix more stable to inverse
|
---|
| 68 | MatrixType a = MatrixType::Random(size,size*2);
|
---|
| 69 | m1 += a * a.adjoint();
|
---|
| 70 | }
|
---|
| 71 |
|
---|
| 72 | HouseholderQR<MatrixType> qr(m1);
|
---|
| 73 | m3 = MatrixType::Random(size,size);
|
---|
| 74 | m2 = qr.solve(m3);
|
---|
| 75 | VERIFY_IS_APPROX(m3, m1*m2);
|
---|
| 76 |
|
---|
| 77 | // now construct a matrix with prescribed determinant
|
---|
| 78 | m1.setZero();
|
---|
| 79 | for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>();
|
---|
| 80 | RealScalar absdet = abs(m1.diagonal().prod());
|
---|
| 81 | m3 = qr.householderQ(); // get a unitary
|
---|
| 82 | m1 = m3 * m1 * m3;
|
---|
| 83 | qr.compute(m1);
|
---|
| 84 | VERIFY_IS_APPROX(absdet, qr.absDeterminant());
|
---|
| 85 | VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant());
|
---|
| 86 | }
|
---|
| 87 |
|
---|
| 88 | template<typename MatrixType> void qr_verify_assert()
|
---|
| 89 | {
|
---|
| 90 | MatrixType tmp;
|
---|
| 91 |
|
---|
| 92 | HouseholderQR<MatrixType> qr;
|
---|
| 93 | VERIFY_RAISES_ASSERT(qr.matrixQR())
|
---|
| 94 | VERIFY_RAISES_ASSERT(qr.solve(tmp))
|
---|
| 95 | VERIFY_RAISES_ASSERT(qr.householderQ())
|
---|
| 96 | VERIFY_RAISES_ASSERT(qr.absDeterminant())
|
---|
| 97 | VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
|
---|
| 98 | }
|
---|
| 99 |
|
---|
| 100 | void test_qr()
|
---|
| 101 | {
|
---|
| 102 | for(int i = 0; i < g_repeat; i++) {
|
---|
| 103 | CALL_SUBTEST_1( qr(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
|
---|
| 104 | CALL_SUBTEST_2( qr(MatrixXcd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2),internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))) );
|
---|
| 105 | CALL_SUBTEST_3(( qr_fixedsize<Matrix<float,3,4>, 2 >() ));
|
---|
| 106 | CALL_SUBTEST_4(( qr_fixedsize<Matrix<double,6,2>, 4 >() ));
|
---|
| 107 | CALL_SUBTEST_5(( qr_fixedsize<Matrix<double,2,5>, 7 >() ));
|
---|
| 108 | CALL_SUBTEST_11( qr(Matrix<float,1,1>()) );
|
---|
| 109 | }
|
---|
| 110 |
|
---|
| 111 | for(int i = 0; i < g_repeat; i++) {
|
---|
| 112 | CALL_SUBTEST_1( qr_invertible<MatrixXf>() );
|
---|
| 113 | CALL_SUBTEST_6( qr_invertible<MatrixXd>() );
|
---|
| 114 | CALL_SUBTEST_7( qr_invertible<MatrixXcf>() );
|
---|
| 115 | CALL_SUBTEST_8( qr_invertible<MatrixXcd>() );
|
---|
| 116 | }
|
---|
| 117 |
|
---|
| 118 | CALL_SUBTEST_9(qr_verify_assert<Matrix3f>());
|
---|
| 119 | CALL_SUBTEST_10(qr_verify_assert<Matrix3d>());
|
---|
| 120 | CALL_SUBTEST_1(qr_verify_assert<MatrixXf>());
|
---|
| 121 | CALL_SUBTEST_6(qr_verify_assert<MatrixXd>());
|
---|
| 122 | CALL_SUBTEST_7(qr_verify_assert<MatrixXcf>());
|
---|
| 123 | CALL_SUBTEST_8(qr_verify_assert<MatrixXcd>());
|
---|
| 124 |
|
---|
| 125 | // Test problem size constructors
|
---|
| 126 | CALL_SUBTEST_12(HouseholderQR<MatrixXf>(10, 20));
|
---|
| 127 | }
|
---|