| 1 | // This file is triangularView 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 Gael Guennebaud <gael.guennebaud@inria.fr>
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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 |
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| 12 |
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| 13 |
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| 14 | template<typename MatrixType> void triangular_square(const MatrixType& m)
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| 15 | {
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| 16 | typedef typename MatrixType::Scalar Scalar;
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| 17 | typedef typename NumTraits<Scalar>::Real RealScalar;
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| 18 | typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
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| 19 |
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| 20 | RealScalar largerEps = 10*test_precision<RealScalar>();
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| 21 |
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| 22 | typename MatrixType::Index rows = m.rows();
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| 23 | typename MatrixType::Index cols = m.cols();
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| 24 |
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| 25 | MatrixType m1 = MatrixType::Random(rows, cols),
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| 26 | m2 = MatrixType::Random(rows, cols),
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| 27 | m3(rows, cols),
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| 28 | m4(rows, cols),
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| 29 | r1(rows, cols),
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| 30 | r2(rows, cols);
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| 31 | VectorType v2 = VectorType::Random(rows);
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| 32 |
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| 33 | MatrixType m1up = m1.template triangularView<Upper>();
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| 34 | MatrixType m2up = m2.template triangularView<Upper>();
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| 35 |
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| 36 | if (rows*cols>1)
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| 37 | {
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| 38 | VERIFY(m1up.isUpperTriangular());
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| 39 | VERIFY(m2up.transpose().isLowerTriangular());
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| 40 | VERIFY(!m2.isLowerTriangular());
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| 41 | }
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| 42 |
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| 43 | // VERIFY_IS_APPROX(m1up.transpose() * m2, m1.upper().transpose().lower() * m2);
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| 44 |
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| 45 | // test overloaded operator+=
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| 46 | r1.setZero();
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| 47 | r2.setZero();
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| 48 | r1.template triangularView<Upper>() += m1;
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| 49 | r2 += m1up;
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| 50 | VERIFY_IS_APPROX(r1,r2);
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| 51 |
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| 52 | // test overloaded operator=
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| 53 | m1.setZero();
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| 54 | m1.template triangularView<Upper>() = m2.transpose() + m2;
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| 55 | m3 = m2.transpose() + m2;
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| 56 | VERIFY_IS_APPROX(m3.template triangularView<Lower>().transpose().toDenseMatrix(), m1);
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| 57 |
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| 58 | // test overloaded operator=
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| 59 | m1.setZero();
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| 60 | m1.template triangularView<Lower>() = m2.transpose() + m2;
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| 61 | VERIFY_IS_APPROX(m3.template triangularView<Lower>().toDenseMatrix(), m1);
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| 62 |
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| 63 | VERIFY_IS_APPROX(m3.template triangularView<Lower>().conjugate().toDenseMatrix(),
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| 64 | m3.conjugate().template triangularView<Lower>().toDenseMatrix());
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| 65 |
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| 66 | m1 = MatrixType::Random(rows, cols);
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| 67 | for (int i=0; i<rows; ++i)
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| 68 | while (numext::abs2(m1(i,i))<1e-1) m1(i,i) = internal::random<Scalar>();
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| 69 |
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| 70 | Transpose<MatrixType> trm4(m4);
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| 71 | // test back and forward subsitution with a vector as the rhs
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| 72 | m3 = m1.template triangularView<Upper>();
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| 73 | VERIFY(v2.isApprox(m3.adjoint() * (m1.adjoint().template triangularView<Lower>().solve(v2)), largerEps));
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| 74 | m3 = m1.template triangularView<Lower>();
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| 75 | VERIFY(v2.isApprox(m3.transpose() * (m1.transpose().template triangularView<Upper>().solve(v2)), largerEps));
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| 76 | m3 = m1.template triangularView<Upper>();
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| 77 | VERIFY(v2.isApprox(m3 * (m1.template triangularView<Upper>().solve(v2)), largerEps));
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| 78 | m3 = m1.template triangularView<Lower>();
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| 79 | VERIFY(v2.isApprox(m3.conjugate() * (m1.conjugate().template triangularView<Lower>().solve(v2)), largerEps));
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| 80 |
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| 81 | // test back and forward subsitution with a matrix as the rhs
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| 82 | m3 = m1.template triangularView<Upper>();
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| 83 | VERIFY(m2.isApprox(m3.adjoint() * (m1.adjoint().template triangularView<Lower>().solve(m2)), largerEps));
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| 84 | m3 = m1.template triangularView<Lower>();
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| 85 | VERIFY(m2.isApprox(m3.transpose() * (m1.transpose().template triangularView<Upper>().solve(m2)), largerEps));
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| 86 | m3 = m1.template triangularView<Upper>();
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| 87 | VERIFY(m2.isApprox(m3 * (m1.template triangularView<Upper>().solve(m2)), largerEps));
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| 88 | m3 = m1.template triangularView<Lower>();
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| 89 | VERIFY(m2.isApprox(m3.conjugate() * (m1.conjugate().template triangularView<Lower>().solve(m2)), largerEps));
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| 90 |
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| 91 | // check M * inv(L) using in place API
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| 92 | m4 = m3;
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| 93 | m1.transpose().template triangularView<Eigen::Upper>().solveInPlace(trm4);
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| 94 | VERIFY_IS_APPROX(m4 * m1.template triangularView<Eigen::Lower>(), m3);
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| 95 |
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| 96 | // check M * inv(U) using in place API
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| 97 | m3 = m1.template triangularView<Upper>();
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| 98 | m4 = m3;
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| 99 | m3.transpose().template triangularView<Eigen::Lower>().solveInPlace(trm4);
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| 100 | VERIFY_IS_APPROX(m4 * m1.template triangularView<Eigen::Upper>(), m3);
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| 101 |
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| 102 | // check solve with unit diagonal
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| 103 | m3 = m1.template triangularView<UnitUpper>();
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| 104 | VERIFY(m2.isApprox(m3 * (m1.template triangularView<UnitUpper>().solve(m2)), largerEps));
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| 105 |
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| 106 | // VERIFY(( m1.template triangularView<Upper>()
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| 107 | // * m2.template triangularView<Upper>()).isUpperTriangular());
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| 108 |
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| 109 | // test swap
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| 110 | m1.setOnes();
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| 111 | m2.setZero();
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| 112 | m2.template triangularView<Upper>().swap(m1);
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| 113 | m3.setZero();
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| 114 | m3.template triangularView<Upper>().setOnes();
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| 115 | VERIFY_IS_APPROX(m2,m3);
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| 116 |
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| 117 | }
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| 118 |
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| 119 |
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| 120 | template<typename MatrixType> void triangular_rect(const MatrixType& m)
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| 121 | {
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| 122 | typedef const typename MatrixType::Index Index;
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| 123 | typedef typename MatrixType::Scalar Scalar;
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| 124 | typedef typename NumTraits<Scalar>::Real RealScalar;
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| 125 | enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };
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| 126 |
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| 127 | Index rows = m.rows();
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| 128 | Index cols = m.cols();
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| 129 |
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| 130 | MatrixType m1 = MatrixType::Random(rows, cols),
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| 131 | m2 = MatrixType::Random(rows, cols),
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| 132 | m3(rows, cols),
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| 133 | m4(rows, cols),
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| 134 | r1(rows, cols),
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| 135 | r2(rows, cols);
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| 136 |
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| 137 | MatrixType m1up = m1.template triangularView<Upper>();
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| 138 | MatrixType m2up = m2.template triangularView<Upper>();
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| 139 |
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| 140 | if (rows>1 && cols>1)
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| 141 | {
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| 142 | VERIFY(m1up.isUpperTriangular());
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| 143 | VERIFY(m2up.transpose().isLowerTriangular());
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| 144 | VERIFY(!m2.isLowerTriangular());
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| 145 | }
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| 146 |
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| 147 | // test overloaded operator+=
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| 148 | r1.setZero();
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| 149 | r2.setZero();
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| 150 | r1.template triangularView<Upper>() += m1;
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| 151 | r2 += m1up;
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| 152 | VERIFY_IS_APPROX(r1,r2);
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| 153 |
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| 154 | // test overloaded operator=
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| 155 | m1.setZero();
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| 156 | m1.template triangularView<Upper>() = 3 * m2;
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| 157 | m3 = 3 * m2;
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| 158 | VERIFY_IS_APPROX(m3.template triangularView<Upper>().toDenseMatrix(), m1);
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| 159 |
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| 160 |
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| 161 | m1.setZero();
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| 162 | m1.template triangularView<Lower>() = 3 * m2;
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| 163 | VERIFY_IS_APPROX(m3.template triangularView<Lower>().toDenseMatrix(), m1);
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| 164 |
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| 165 | m1.setZero();
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| 166 | m1.template triangularView<StrictlyUpper>() = 3 * m2;
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| 167 | VERIFY_IS_APPROX(m3.template triangularView<StrictlyUpper>().toDenseMatrix(), m1);
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| 168 |
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| 169 |
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| 170 | m1.setZero();
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| 171 | m1.template triangularView<StrictlyLower>() = 3 * m2;
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| 172 | VERIFY_IS_APPROX(m3.template triangularView<StrictlyLower>().toDenseMatrix(), m1);
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| 173 | m1.setRandom();
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| 174 | m2 = m1.template triangularView<Upper>();
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| 175 | VERIFY(m2.isUpperTriangular());
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| 176 | VERIFY(!m2.isLowerTriangular());
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| 177 | m2 = m1.template triangularView<StrictlyUpper>();
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| 178 | VERIFY(m2.isUpperTriangular());
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| 179 | VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
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| 180 | m2 = m1.template triangularView<UnitUpper>();
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| 181 | VERIFY(m2.isUpperTriangular());
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| 182 | m2.diagonal().array() -= Scalar(1);
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| 183 | VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
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| 184 | m2 = m1.template triangularView<Lower>();
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| 185 | VERIFY(m2.isLowerTriangular());
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| 186 | VERIFY(!m2.isUpperTriangular());
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| 187 | m2 = m1.template triangularView<StrictlyLower>();
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| 188 | VERIFY(m2.isLowerTriangular());
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| 189 | VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
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| 190 | m2 = m1.template triangularView<UnitLower>();
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| 191 | VERIFY(m2.isLowerTriangular());
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| 192 | m2.diagonal().array() -= Scalar(1);
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| 193 | VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
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| 194 | // test swap
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| 195 | m1.setOnes();
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| 196 | m2.setZero();
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| 197 | m2.template triangularView<Upper>().swap(m1);
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| 198 | m3.setZero();
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| 199 | m3.template triangularView<Upper>().setOnes();
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| 200 | VERIFY_IS_APPROX(m2,m3);
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| 201 | }
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| 202 |
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| 203 | void bug_159()
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| 204 | {
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| 205 | Matrix3d m = Matrix3d::Random().triangularView<Lower>();
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| 206 | EIGEN_UNUSED_VARIABLE(m)
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| 207 | }
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| 208 |
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| 209 | void test_triangular()
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| 210 | {
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| 211 | int maxsize = (std::min)(EIGEN_TEST_MAX_SIZE,20);
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| 212 | for(int i = 0; i < g_repeat ; i++)
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| 213 | {
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| 214 | int r = internal::random<int>(2,maxsize); TEST_SET_BUT_UNUSED_VARIABLE(r)
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| 215 | int c = internal::random<int>(2,maxsize); TEST_SET_BUT_UNUSED_VARIABLE(c)
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| 216 |
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| 217 | CALL_SUBTEST_1( triangular_square(Matrix<float, 1, 1>()) );
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| 218 | CALL_SUBTEST_2( triangular_square(Matrix<float, 2, 2>()) );
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| 219 | CALL_SUBTEST_3( triangular_square(Matrix3d()) );
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| 220 | CALL_SUBTEST_4( triangular_square(Matrix<std::complex<float>,8, 8>()) );
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| 221 | CALL_SUBTEST_5( triangular_square(MatrixXcd(r,r)) );
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| 222 | CALL_SUBTEST_6( triangular_square(Matrix<float,Dynamic,Dynamic,RowMajor>(r, r)) );
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| 223 |
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| 224 | CALL_SUBTEST_7( triangular_rect(Matrix<float, 4, 5>()) );
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| 225 | CALL_SUBTEST_8( triangular_rect(Matrix<double, 6, 2>()) );
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| 226 | CALL_SUBTEST_9( triangular_rect(MatrixXcf(r, c)) );
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| 227 | CALL_SUBTEST_5( triangular_rect(MatrixXcd(r, c)) );
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| 228 | CALL_SUBTEST_6( triangular_rect(Matrix<float,Dynamic,Dynamic,RowMajor>(r, c)) );
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| 229 | }
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| 230 |
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| 231 | CALL_SUBTEST_1( bug_159() );
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| 232 | }
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