[136] | 1 | // This file is part of Eigen, a lightweight C++ template library
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| 2 | // for linear algebra. Eigen itself is part of the KDE project.
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| 3 | //
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| 4 | // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@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 |
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| 12 | template<typename MatrixType> void triangular(const MatrixType& m)
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| 13 | {
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| 14 | typedef typename MatrixType::Scalar Scalar;
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| 15 | typedef typename NumTraits<Scalar>::Real RealScalar;
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| 16 |
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| 17 | RealScalar largerEps = 10*test_precision<RealScalar>();
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| 18 |
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| 19 | int rows = m.rows();
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| 20 | int cols = m.cols();
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| 21 |
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| 22 | MatrixType m1 = MatrixType::Random(rows, cols),
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| 23 | m2 = MatrixType::Random(rows, cols),
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| 24 | m3(rows, cols),
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| 25 | m4(rows, cols),
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| 26 | r1(rows, cols),
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| 27 | r2(rows, cols);
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| 28 |
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| 29 | MatrixType m1up = m1.template part<Eigen::UpperTriangular>();
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| 30 | MatrixType m2up = m2.template part<Eigen::UpperTriangular>();
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| 31 |
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| 32 | if (rows*cols>1)
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| 33 | {
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| 34 | VERIFY(m1up.isUpperTriangular());
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| 35 | VERIFY(m2up.transpose().isLowerTriangular());
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| 36 | VERIFY(!m2.isLowerTriangular());
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| 37 | }
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| 38 |
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| 39 | // VERIFY_IS_APPROX(m1up.transpose() * m2, m1.upper().transpose().lower() * m2);
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| 40 |
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| 41 | // test overloaded operator+=
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| 42 | r1.setZero();
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| 43 | r2.setZero();
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| 44 | r1.template part<Eigen::UpperTriangular>() += m1;
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| 45 | r2 += m1up;
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| 46 | VERIFY_IS_APPROX(r1,r2);
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| 47 |
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| 48 | // test overloaded operator=
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| 49 | m1.setZero();
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| 50 | m1.template part<Eigen::UpperTriangular>() = (m2.transpose() * m2).lazy();
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| 51 | m3 = m2.transpose() * m2;
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| 52 | VERIFY_IS_APPROX(m3.template part<Eigen::LowerTriangular>().transpose(), m1);
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| 53 |
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| 54 | // test overloaded operator=
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| 55 | m1.setZero();
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| 56 | m1.template part<Eigen::LowerTriangular>() = (m2.transpose() * m2).lazy();
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| 57 | VERIFY_IS_APPROX(m3.template part<Eigen::LowerTriangular>(), m1);
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| 58 |
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| 59 | VERIFY_IS_APPROX(m3.template part<Diagonal>(), m3.diagonal().asDiagonal());
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| 60 |
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| 61 | m1 = MatrixType::Random(rows, cols);
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| 62 | for (int i=0; i<rows; ++i)
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| 63 | while (ei_abs2(m1(i,i))<1e-3) m1(i,i) = ei_random<Scalar>();
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| 64 |
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| 65 | Transpose<MatrixType> trm4(m4);
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| 66 | // test back and forward subsitution
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| 67 | m3 = m1.template part<Eigen::LowerTriangular>();
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| 68 | VERIFY(m3.template marked<Eigen::LowerTriangular>().solveTriangular(m3).cwise().abs().isIdentity(test_precision<RealScalar>()));
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| 69 | VERIFY(m3.transpose().template marked<Eigen::UpperTriangular>()
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| 70 | .solveTriangular(m3.transpose()).cwise().abs().isIdentity(test_precision<RealScalar>()));
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| 71 | // check M * inv(L) using in place API
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| 72 | m4 = m3;
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| 73 | m3.transpose().template marked<Eigen::UpperTriangular>().solveTriangularInPlace(trm4);
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| 74 | VERIFY(m4.cwise().abs().isIdentity(test_precision<RealScalar>()));
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| 75 |
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| 76 | m3 = m1.template part<Eigen::UpperTriangular>();
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| 77 | VERIFY(m3.template marked<Eigen::UpperTriangular>().solveTriangular(m3).cwise().abs().isIdentity(test_precision<RealScalar>()));
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| 78 | VERIFY(m3.transpose().template marked<Eigen::LowerTriangular>()
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| 79 | .solveTriangular(m3.transpose()).cwise().abs().isIdentity(test_precision<RealScalar>()));
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| 80 | // check M * inv(U) using in place API
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| 81 | m4 = m3;
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| 82 | m3.transpose().template marked<Eigen::LowerTriangular>().solveTriangularInPlace(trm4);
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| 83 | VERIFY(m4.cwise().abs().isIdentity(test_precision<RealScalar>()));
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| 84 |
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| 85 | m3 = m1.template part<Eigen::UpperTriangular>();
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| 86 | VERIFY(m2.isApprox(m3 * (m3.template marked<Eigen::UpperTriangular>().solveTriangular(m2)), largerEps));
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| 87 | m3 = m1.template part<Eigen::LowerTriangular>();
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| 88 | VERIFY(m2.isApprox(m3 * (m3.template marked<Eigen::LowerTriangular>().solveTriangular(m2)), largerEps));
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| 89 |
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| 90 | VERIFY((m1.template part<Eigen::UpperTriangular>() * m2.template part<Eigen::UpperTriangular>()).isUpperTriangular());
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| 91 |
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| 92 | // test swap
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| 93 | m1.setOnes();
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| 94 | m2.setZero();
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| 95 | m2.template part<Eigen::UpperTriangular>().swap(m1);
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| 96 | m3.setZero();
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| 97 | m3.template part<Eigen::UpperTriangular>().setOnes();
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| 98 | VERIFY_IS_APPROX(m2,m3);
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| 99 |
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| 100 | }
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| 101 |
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| 102 | void selfadjoint()
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| 103 | {
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| 104 | Matrix2i m;
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| 105 | m << 1, 2,
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| 106 | 3, 4;
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| 107 |
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| 108 | Matrix2i m1 = Matrix2i::Zero();
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| 109 | m1.part<SelfAdjoint>() = m;
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| 110 | Matrix2i ref1;
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| 111 | ref1 << 1, 2,
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| 112 | 2, 4;
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| 113 | VERIFY(m1 == ref1);
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| 114 |
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| 115 | Matrix2i m2 = Matrix2i::Zero();
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| 116 | m2.part<SelfAdjoint>() = m.part<UpperTriangular>();
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| 117 | Matrix2i ref2;
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| 118 | ref2 << 1, 2,
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| 119 | 2, 4;
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| 120 | VERIFY(m2 == ref2);
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| 121 |
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| 122 | Matrix2i m3 = Matrix2i::Zero();
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| 123 | m3.part<SelfAdjoint>() = m.part<LowerTriangular>();
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| 124 | Matrix2i ref3;
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| 125 | ref3 << 1, 0,
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| 126 | 0, 4;
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| 127 | VERIFY(m3 == ref3);
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| 128 |
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| 129 | // example inspired from bug 159
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| 130 | int array[] = {1, 2, 3, 4};
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| 131 | Matrix2i::Map(array).part<SelfAdjoint>() = Matrix2i::Random().part<LowerTriangular>();
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| 132 |
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| 133 | std::cout << "hello\n" << array << std::endl;
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| 134 | }
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| 135 |
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| 136 | void test_eigen2_triangular()
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| 137 | {
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| 138 | CALL_SUBTEST_8( selfadjoint() );
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| 139 | for(int i = 0; i < g_repeat ; i++) {
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| 140 | CALL_SUBTEST_1( triangular(Matrix<float, 1, 1>()) );
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| 141 | CALL_SUBTEST_2( triangular(Matrix<float, 2, 2>()) );
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| 142 | CALL_SUBTEST_3( triangular(Matrix3d()) );
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| 143 | CALL_SUBTEST_4( triangular(MatrixXcf(4, 4)) );
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| 144 | CALL_SUBTEST_5( triangular(Matrix<std::complex<float>,8, 8>()) );
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| 145 | CALL_SUBTEST_6( triangular(MatrixXd(17,17)) );
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| 146 | CALL_SUBTEST_7( triangular(Matrix<float,Dynamic,Dynamic,RowMajor>(5, 5)) );
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| 147 | }
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| 148 | }
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