1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. Eigen itself is part of the KDE project. 3 // 4 // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud (at) gmail.com> 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 12 template<typename MatrixType> void triangular(const MatrixType& m) 13 { 14 typedef typename MatrixType::Scalar Scalar; 15 typedef typename NumTraits<Scalar>::Real RealScalar; 16 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType; 17 18 RealScalar largerEps = 10*test_precision<RealScalar>(); 19 20 int rows = m.rows(); 21 int cols = m.cols(); 22 23 MatrixType m1 = MatrixType::Random(rows, cols), 24 m2 = MatrixType::Random(rows, cols), 25 m3(rows, cols), 26 m4(rows, cols), 27 r1(rows, cols), 28 r2(rows, cols), 29 mzero = MatrixType::Zero(rows, cols), 30 mones = MatrixType::Ones(rows, cols), 31 identity = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> 32 ::Identity(rows, rows), 33 square = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> 34 ::Random(rows, rows); 35 VectorType v1 = VectorType::Random(rows), 36 v2 = VectorType::Random(rows), 37 vzero = VectorType::Zero(rows); 38 39 MatrixType m1up = m1.template part<Eigen::UpperTriangular>(); 40 MatrixType m2up = m2.template part<Eigen::UpperTriangular>(); 41 42 if (rows*cols>1) 43 { 44 VERIFY(m1up.isUpperTriangular()); 45 VERIFY(m2up.transpose().isLowerTriangular()); 46 VERIFY(!m2.isLowerTriangular()); 47 } 48 49 // VERIFY_IS_APPROX(m1up.transpose() * m2, m1.upper().transpose().lower() * m2); 50 51 // test overloaded operator+= 52 r1.setZero(); 53 r2.setZero(); 54 r1.template part<Eigen::UpperTriangular>() += m1; 55 r2 += m1up; 56 VERIFY_IS_APPROX(r1,r2); 57 58 // test overloaded operator= 59 m1.setZero(); 60 m1.template part<Eigen::UpperTriangular>() = (m2.transpose() * m2).lazy(); 61 m3 = m2.transpose() * m2; 62 VERIFY_IS_APPROX(m3.template part<Eigen::LowerTriangular>().transpose(), m1); 63 64 // test overloaded operator= 65 m1.setZero(); 66 m1.template part<Eigen::LowerTriangular>() = (m2.transpose() * m2).lazy(); 67 VERIFY_IS_APPROX(m3.template part<Eigen::LowerTriangular>(), m1); 68 69 VERIFY_IS_APPROX(m3.template part<Diagonal>(), m3.diagonal().asDiagonal()); 70 71 m1 = MatrixType::Random(rows, cols); 72 for (int i=0; i<rows; ++i) 73 while (ei_abs2(m1(i,i))<1e-3) m1(i,i) = ei_random<Scalar>(); 74 75 Transpose<MatrixType> trm4(m4); 76 // test back and forward subsitution 77 m3 = m1.template part<Eigen::LowerTriangular>(); 78 VERIFY(m3.template marked<Eigen::LowerTriangular>().solveTriangular(m3).cwise().abs().isIdentity(test_precision<RealScalar>())); 79 VERIFY(m3.transpose().template marked<Eigen::UpperTriangular>() 80 .solveTriangular(m3.transpose()).cwise().abs().isIdentity(test_precision<RealScalar>())); 81 // check M * inv(L) using in place API 82 m4 = m3; 83 m3.transpose().template marked<Eigen::UpperTriangular>().solveTriangularInPlace(trm4); 84 VERIFY(m4.cwise().abs().isIdentity(test_precision<RealScalar>())); 85 86 m3 = m1.template part<Eigen::UpperTriangular>(); 87 VERIFY(m3.template marked<Eigen::UpperTriangular>().solveTriangular(m3).cwise().abs().isIdentity(test_precision<RealScalar>())); 88 VERIFY(m3.transpose().template marked<Eigen::LowerTriangular>() 89 .solveTriangular(m3.transpose()).cwise().abs().isIdentity(test_precision<RealScalar>())); 90 // check M * inv(U) using in place API 91 m4 = m3; 92 m3.transpose().template marked<Eigen::LowerTriangular>().solveTriangularInPlace(trm4); 93 VERIFY(m4.cwise().abs().isIdentity(test_precision<RealScalar>())); 94 95 m3 = m1.template part<Eigen::UpperTriangular>(); 96 VERIFY(m2.isApprox(m3 * (m3.template marked<Eigen::UpperTriangular>().solveTriangular(m2)), largerEps)); 97 m3 = m1.template part<Eigen::LowerTriangular>(); 98 VERIFY(m2.isApprox(m3 * (m3.template marked<Eigen::LowerTriangular>().solveTriangular(m2)), largerEps)); 99 100 VERIFY((m1.template part<Eigen::UpperTriangular>() * m2.template part<Eigen::UpperTriangular>()).isUpperTriangular()); 101 102 // test swap 103 m1.setOnes(); 104 m2.setZero(); 105 m2.template part<Eigen::UpperTriangular>().swap(m1); 106 m3.setZero(); 107 m3.template part<Eigen::UpperTriangular>().setOnes(); 108 VERIFY_IS_APPROX(m2,m3); 109 110 } 111 112 void selfadjoint() 113 { 114 Matrix2i m; 115 m << 1, 2, 116 3, 4; 117 118 Matrix2i m1 = Matrix2i::Zero(); 119 m1.part<SelfAdjoint>() = m; 120 Matrix2i ref1; 121 ref1 << 1, 2, 122 2, 4; 123 VERIFY(m1 == ref1); 124 125 Matrix2i m2 = Matrix2i::Zero(); 126 m2.part<SelfAdjoint>() = m.part<UpperTriangular>(); 127 Matrix2i ref2; 128 ref2 << 1, 2, 129 2, 4; 130 VERIFY(m2 == ref2); 131 132 Matrix2i m3 = Matrix2i::Zero(); 133 m3.part<SelfAdjoint>() = m.part<LowerTriangular>(); 134 Matrix2i ref3; 135 ref3 << 1, 0, 136 0, 4; 137 VERIFY(m3 == ref3); 138 139 // example inspired from bug 159 140 int array[] = {1, 2, 3, 4}; 141 Matrix2i::Map(array).part<SelfAdjoint>() = Matrix2i::Random().part<LowerTriangular>(); 142 143 std::cout << "hello\n" << array << std::endl; 144 } 145 146 void test_eigen2_triangular() 147 { 148 CALL_SUBTEST_8( selfadjoint() ); 149 for(int i = 0; i < g_repeat ; i++) { 150 CALL_SUBTEST_1( triangular(Matrix<float, 1, 1>()) ); 151 CALL_SUBTEST_2( triangular(Matrix<float, 2, 2>()) ); 152 CALL_SUBTEST_3( triangular(Matrix3d()) ); 153 CALL_SUBTEST_4( triangular(MatrixXcf(4, 4)) ); 154 CALL_SUBTEST_5( triangular(Matrix<std::complex<float>,8, 8>()) ); 155 CALL_SUBTEST_6( triangular(MatrixXd(17,17)) ); 156 CALL_SUBTEST_7( triangular(Matrix<float,Dynamic,Dynamic,RowMajor>(5, 5)) ); 157 } 158 } 159
