[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) 2008-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
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| 5 | //
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| 6 | // This Source Code Form is subject to the terms of the Mozilla
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| 7 | // Public License v. 2.0. If a copy of the MPL was not distributed
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| 8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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| 9 |
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| 10 | #include "main.h"
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| 11 | #include <Eigen/LU>
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| 12 | using namespace std;
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| 13 |
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| 14 | template<typename MatrixType> void lu_non_invertible()
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| 15 | {
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| 16 | typedef typename MatrixType::Index Index;
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| 17 | typedef typename MatrixType::RealScalar RealScalar;
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| 18 | /* this test covers the following files:
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| 19 | LU.h
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| 20 | */
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| 21 | Index rows, cols, cols2;
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| 22 | if(MatrixType::RowsAtCompileTime==Dynamic)
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| 23 | {
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| 24 | rows = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE);
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| 25 | }
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| 26 | else
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| 27 | {
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| 28 | rows = MatrixType::RowsAtCompileTime;
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| 29 | }
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| 30 | if(MatrixType::ColsAtCompileTime==Dynamic)
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| 31 | {
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| 32 | cols = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE);
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| 33 | cols2 = internal::random<int>(2,EIGEN_TEST_MAX_SIZE);
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| 34 | }
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| 35 | else
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| 36 | {
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| 37 | cols2 = cols = MatrixType::ColsAtCompileTime;
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| 38 | }
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| 39 |
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| 40 | enum {
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| 41 | RowsAtCompileTime = MatrixType::RowsAtCompileTime,
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| 42 | ColsAtCompileTime = MatrixType::ColsAtCompileTime
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| 43 | };
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| 44 | typedef typename internal::kernel_retval_base<FullPivLU<MatrixType> >::ReturnType KernelMatrixType;
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| 45 | typedef typename internal::image_retval_base<FullPivLU<MatrixType> >::ReturnType ImageMatrixType;
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| 46 | typedef Matrix<typename MatrixType::Scalar, ColsAtCompileTime, ColsAtCompileTime>
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| 47 | CMatrixType;
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| 48 | typedef Matrix<typename MatrixType::Scalar, RowsAtCompileTime, RowsAtCompileTime>
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| 49 | RMatrixType;
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| 50 |
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| 51 | Index rank = internal::random<Index>(1, (std::min)(rows, cols)-1);
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| 52 |
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| 53 | // The image of the zero matrix should consist of a single (zero) column vector
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| 54 | VERIFY((MatrixType::Zero(rows,cols).fullPivLu().image(MatrixType::Zero(rows,cols)).cols() == 1));
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| 55 |
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| 56 | MatrixType m1(rows, cols), m3(rows, cols2);
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| 57 | CMatrixType m2(cols, cols2);
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| 58 | createRandomPIMatrixOfRank(rank, rows, cols, m1);
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| 59 |
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| 60 | FullPivLU<MatrixType> lu;
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| 61 |
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| 62 | // The special value 0.01 below works well in tests. Keep in mind that we're only computing the rank
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| 63 | // of singular values are either 0 or 1.
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| 64 | // So it's not clear at all that the epsilon should play any role there.
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| 65 | lu.setThreshold(RealScalar(0.01));
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| 66 | lu.compute(m1);
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| 67 |
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| 68 | MatrixType u(rows,cols);
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| 69 | u = lu.matrixLU().template triangularView<Upper>();
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| 70 | RMatrixType l = RMatrixType::Identity(rows,rows);
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| 71 | l.block(0,0,rows,(std::min)(rows,cols)).template triangularView<StrictlyLower>()
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| 72 | = lu.matrixLU().block(0,0,rows,(std::min)(rows,cols));
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| 73 |
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| 74 | VERIFY_IS_APPROX(lu.permutationP() * m1 * lu.permutationQ(), l*u);
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| 75 |
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| 76 | KernelMatrixType m1kernel = lu.kernel();
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| 77 | ImageMatrixType m1image = lu.image(m1);
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| 78 |
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| 79 | VERIFY_IS_APPROX(m1, lu.reconstructedMatrix());
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| 80 | VERIFY(rank == lu.rank());
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| 81 | VERIFY(cols - lu.rank() == lu.dimensionOfKernel());
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| 82 | VERIFY(!lu.isInjective());
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| 83 | VERIFY(!lu.isInvertible());
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| 84 | VERIFY(!lu.isSurjective());
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| 85 | VERIFY((m1 * m1kernel).isMuchSmallerThan(m1));
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| 86 | VERIFY(m1image.fullPivLu().rank() == rank);
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| 87 | VERIFY_IS_APPROX(m1 * m1.adjoint() * m1image, m1image);
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| 88 |
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| 89 | m2 = CMatrixType::Random(cols,cols2);
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| 90 | m3 = m1*m2;
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| 91 | m2 = CMatrixType::Random(cols,cols2);
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| 92 | // test that the code, which does resize(), may be applied to an xpr
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| 93 | m2.block(0,0,m2.rows(),m2.cols()) = lu.solve(m3);
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| 94 | VERIFY_IS_APPROX(m3, m1*m2);
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| 95 | }
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| 96 |
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| 97 | template<typename MatrixType> void lu_invertible()
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| 98 | {
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| 99 | /* this test covers the following files:
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| 100 | LU.h
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| 101 | */
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| 102 | typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
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| 103 | DenseIndex size = MatrixType::RowsAtCompileTime;
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| 104 | if( size==Dynamic)
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| 105 | size = internal::random<DenseIndex>(1,EIGEN_TEST_MAX_SIZE);
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| 106 |
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| 107 | MatrixType m1(size, size), m2(size, size), m3(size, size);
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| 108 | FullPivLU<MatrixType> lu;
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| 109 | lu.setThreshold(RealScalar(0.01));
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| 110 | do {
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| 111 | m1 = MatrixType::Random(size,size);
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| 112 | lu.compute(m1);
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| 113 | } while(!lu.isInvertible());
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| 114 |
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| 115 | VERIFY_IS_APPROX(m1, lu.reconstructedMatrix());
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| 116 | VERIFY(0 == lu.dimensionOfKernel());
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| 117 | VERIFY(lu.kernel().cols() == 1); // the kernel() should consist of a single (zero) column vector
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| 118 | VERIFY(size == lu.rank());
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| 119 | VERIFY(lu.isInjective());
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| 120 | VERIFY(lu.isSurjective());
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| 121 | VERIFY(lu.isInvertible());
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| 122 | VERIFY(lu.image(m1).fullPivLu().isInvertible());
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| 123 | m3 = MatrixType::Random(size,size);
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| 124 | m2 = lu.solve(m3);
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| 125 | VERIFY_IS_APPROX(m3, m1*m2);
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| 126 | VERIFY_IS_APPROX(m2, lu.inverse()*m3);
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| 127 |
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| 128 | // Regression test for Bug 302
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| 129 | MatrixType m4 = MatrixType::Random(size,size);
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| 130 | VERIFY_IS_APPROX(lu.solve(m3*m4), lu.solve(m3)*m4);
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| 131 | }
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| 132 |
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| 133 | template<typename MatrixType> void lu_partial_piv()
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| 134 | {
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| 135 | /* this test covers the following files:
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| 136 | PartialPivLU.h
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| 137 | */
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| 138 | typedef typename MatrixType::Index Index;
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| 139 | Index rows = internal::random<Index>(1,4);
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| 140 | Index cols = rows;
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| 141 |
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| 142 | MatrixType m1(cols, rows);
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| 143 | m1.setRandom();
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| 144 | PartialPivLU<MatrixType> plu(m1);
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| 145 |
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| 146 | VERIFY_IS_APPROX(m1, plu.reconstructedMatrix());
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| 147 | }
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| 148 |
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| 149 | template<typename MatrixType> void lu_verify_assert()
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| 150 | {
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| 151 | MatrixType tmp;
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| 152 |
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| 153 | FullPivLU<MatrixType> lu;
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| 154 | VERIFY_RAISES_ASSERT(lu.matrixLU())
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| 155 | VERIFY_RAISES_ASSERT(lu.permutationP())
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| 156 | VERIFY_RAISES_ASSERT(lu.permutationQ())
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| 157 | VERIFY_RAISES_ASSERT(lu.kernel())
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| 158 | VERIFY_RAISES_ASSERT(lu.image(tmp))
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| 159 | VERIFY_RAISES_ASSERT(lu.solve(tmp))
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| 160 | VERIFY_RAISES_ASSERT(lu.determinant())
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| 161 | VERIFY_RAISES_ASSERT(lu.rank())
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| 162 | VERIFY_RAISES_ASSERT(lu.dimensionOfKernel())
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| 163 | VERIFY_RAISES_ASSERT(lu.isInjective())
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| 164 | VERIFY_RAISES_ASSERT(lu.isSurjective())
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| 165 | VERIFY_RAISES_ASSERT(lu.isInvertible())
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| 166 | VERIFY_RAISES_ASSERT(lu.inverse())
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| 167 |
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| 168 | PartialPivLU<MatrixType> plu;
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| 169 | VERIFY_RAISES_ASSERT(plu.matrixLU())
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| 170 | VERIFY_RAISES_ASSERT(plu.permutationP())
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| 171 | VERIFY_RAISES_ASSERT(plu.solve(tmp))
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| 172 | VERIFY_RAISES_ASSERT(plu.determinant())
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| 173 | VERIFY_RAISES_ASSERT(plu.inverse())
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| 174 | }
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| 175 |
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| 176 | void test_lu()
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| 177 | {
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| 178 | for(int i = 0; i < g_repeat; i++) {
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| 179 | CALL_SUBTEST_1( lu_non_invertible<Matrix3f>() );
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| 180 | CALL_SUBTEST_1( lu_invertible<Matrix3f>() );
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| 181 | CALL_SUBTEST_1( lu_verify_assert<Matrix3f>() );
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| 182 |
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| 183 | CALL_SUBTEST_2( (lu_non_invertible<Matrix<double, 4, 6> >()) );
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| 184 | CALL_SUBTEST_2( (lu_verify_assert<Matrix<double, 4, 6> >()) );
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| 185 |
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| 186 | CALL_SUBTEST_3( lu_non_invertible<MatrixXf>() );
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| 187 | CALL_SUBTEST_3( lu_invertible<MatrixXf>() );
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| 188 | CALL_SUBTEST_3( lu_verify_assert<MatrixXf>() );
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| 189 |
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| 190 | CALL_SUBTEST_4( lu_non_invertible<MatrixXd>() );
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| 191 | CALL_SUBTEST_4( lu_invertible<MatrixXd>() );
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| 192 | CALL_SUBTEST_4( lu_partial_piv<MatrixXd>() );
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| 193 | CALL_SUBTEST_4( lu_verify_assert<MatrixXd>() );
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| 194 |
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| 195 | CALL_SUBTEST_5( lu_non_invertible<MatrixXcf>() );
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| 196 | CALL_SUBTEST_5( lu_invertible<MatrixXcf>() );
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| 197 | CALL_SUBTEST_5( lu_verify_assert<MatrixXcf>() );
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| 198 |
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| 199 | CALL_SUBTEST_6( lu_non_invertible<MatrixXcd>() );
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| 200 | CALL_SUBTEST_6( lu_invertible<MatrixXcd>() );
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| 201 | CALL_SUBTEST_6( lu_partial_piv<MatrixXcd>() );
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| 202 | CALL_SUBTEST_6( lu_verify_assert<MatrixXcd>() );
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| 203 |
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| 204 | CALL_SUBTEST_7(( lu_non_invertible<Matrix<float,Dynamic,16> >() ));
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| 205 |
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| 206 | // Test problem size constructors
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| 207 | CALL_SUBTEST_9( PartialPivLU<MatrixXf>(10) );
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| 208 | CALL_SUBTEST_9( FullPivLU<MatrixXf>(10, 20); );
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| 209 | }
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| 210 | }
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