1 // This file is triangularView of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud (at) 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 12 13 14 template<typename MatrixType> void triangular_square(const MatrixType& m) 15 { 16 typedef typename MatrixType::Scalar Scalar; 17 typedef typename NumTraits<Scalar>::Real RealScalar; 18 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType; 19 20 RealScalar largerEps = 10*test_precision<RealScalar>(); 21 22 typename MatrixType::Index rows = m.rows(); 23 typename MatrixType::Index cols = m.cols(); 24 25 MatrixType m1 = MatrixType::Random(rows, cols), 26 m2 = MatrixType::Random(rows, cols), 27 m3(rows, cols), 28 m4(rows, cols), 29 r1(rows, cols), 30 r2(rows, cols); 31 VectorType v2 = VectorType::Random(rows); 32 33 MatrixType m1up = m1.template triangularView<Upper>(); 34 MatrixType m2up = m2.template triangularView<Upper>(); 35 36 if (rows*cols>1) 37 { 38 VERIFY(m1up.isUpperTriangular()); 39 VERIFY(m2up.transpose().isLowerTriangular()); 40 VERIFY(!m2.isLowerTriangular()); 41 } 42 43 // VERIFY_IS_APPROX(m1up.transpose() * m2, m1.upper().transpose().lower() * m2); 44 45 // test overloaded operator+= 46 r1.setZero(); 47 r2.setZero(); 48 r1.template triangularView<Upper>() += m1; 49 r2 += m1up; 50 VERIFY_IS_APPROX(r1,r2); 51 52 // test overloaded operator= 53 m1.setZero(); 54 m1.template triangularView<Upper>() = m2.transpose() + m2; 55 m3 = m2.transpose() + m2; 56 VERIFY_IS_APPROX(m3.template triangularView<Lower>().transpose().toDenseMatrix(), m1); 57 58 // test overloaded operator= 59 m1.setZero(); 60 m1.template triangularView<Lower>() = m2.transpose() + m2; 61 VERIFY_IS_APPROX(m3.template triangularView<Lower>().toDenseMatrix(), m1); 62 63 VERIFY_IS_APPROX(m3.template triangularView<Lower>().conjugate().toDenseMatrix(), 64 m3.conjugate().template triangularView<Lower>().toDenseMatrix()); 65 66 m1 = MatrixType::Random(rows, cols); 67 for (int i=0; i<rows; ++i) 68 while (internal::abs2(m1(i,i))<1e-1) m1(i,i) = internal::random<Scalar>(); 69 70 Transpose<MatrixType> trm4(m4); 71 // test back and forward subsitution with a vector as the rhs 72 m3 = m1.template triangularView<Upper>(); 73 VERIFY(v2.isApprox(m3.adjoint() * (m1.adjoint().template triangularView<Lower>().solve(v2)), largerEps)); 74 m3 = m1.template triangularView<Lower>(); 75 VERIFY(v2.isApprox(m3.transpose() * (m1.transpose().template triangularView<Upper>().solve(v2)), largerEps)); 76 m3 = m1.template triangularView<Upper>(); 77 VERIFY(v2.isApprox(m3 * (m1.template triangularView<Upper>().solve(v2)), largerEps)); 78 m3 = m1.template triangularView<Lower>(); 79 VERIFY(v2.isApprox(m3.conjugate() * (m1.conjugate().template triangularView<Lower>().solve(v2)), largerEps)); 80 81 // test back and forward subsitution with a matrix as the rhs 82 m3 = m1.template triangularView<Upper>(); 83 VERIFY(m2.isApprox(m3.adjoint() * (m1.adjoint().template triangularView<Lower>().solve(m2)), largerEps)); 84 m3 = m1.template triangularView<Lower>(); 85 VERIFY(m2.isApprox(m3.transpose() * (m1.transpose().template triangularView<Upper>().solve(m2)), largerEps)); 86 m3 = m1.template triangularView<Upper>(); 87 VERIFY(m2.isApprox(m3 * (m1.template triangularView<Upper>().solve(m2)), largerEps)); 88 m3 = m1.template triangularView<Lower>(); 89 VERIFY(m2.isApprox(m3.conjugate() * (m1.conjugate().template triangularView<Lower>().solve(m2)), largerEps)); 90 91 // check M * inv(L) using in place API 92 m4 = m3; 93 m1.transpose().template triangularView<Eigen::Upper>().solveInPlace(trm4); 94 VERIFY_IS_APPROX(m4 * m1.template triangularView<Eigen::Lower>(), m3); 95 96 // check M * inv(U) using in place API 97 m3 = m1.template triangularView<Upper>(); 98 m4 = m3; 99 m3.transpose().template triangularView<Eigen::Lower>().solveInPlace(trm4); 100 VERIFY_IS_APPROX(m4 * m1.template triangularView<Eigen::Upper>(), m3); 101 102 // check solve with unit diagonal 103 m3 = m1.template triangularView<UnitUpper>(); 104 VERIFY(m2.isApprox(m3 * (m1.template triangularView<UnitUpper>().solve(m2)), largerEps)); 105 106 // VERIFY(( m1.template triangularView<Upper>() 107 // * m2.template triangularView<Upper>()).isUpperTriangular()); 108 109 // test swap 110 m1.setOnes(); 111 m2.setZero(); 112 m2.template triangularView<Upper>().swap(m1); 113 m3.setZero(); 114 m3.template triangularView<Upper>().setOnes(); 115 VERIFY_IS_APPROX(m2,m3); 116 117 } 118 119 120 template<typename MatrixType> void triangular_rect(const MatrixType& m) 121 { 122 typedef const typename MatrixType::Index Index; 123 typedef typename MatrixType::Scalar Scalar; 124 typedef typename NumTraits<Scalar>::Real RealScalar; 125 enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime }; 126 typedef Matrix<Scalar, Rows, 1> VectorType; 127 typedef Matrix<Scalar, Rows, Rows> RMatrixType; 128 129 130 Index rows = m.rows(); 131 Index cols = m.cols(); 132 133 MatrixType m1 = MatrixType::Random(rows, cols), 134 m2 = MatrixType::Random(rows, cols), 135 m3(rows, cols), 136 m4(rows, cols), 137 r1(rows, cols), 138 r2(rows, cols); 139 140 MatrixType m1up = m1.template triangularView<Upper>(); 141 MatrixType m2up = m2.template triangularView<Upper>(); 142 143 if (rows>1 && cols>1) 144 { 145 VERIFY(m1up.isUpperTriangular()); 146 VERIFY(m2up.transpose().isLowerTriangular()); 147 VERIFY(!m2.isLowerTriangular()); 148 } 149 150 // test overloaded operator+= 151 r1.setZero(); 152 r2.setZero(); 153 r1.template triangularView<Upper>() += m1; 154 r2 += m1up; 155 VERIFY_IS_APPROX(r1,r2); 156 157 // test overloaded operator= 158 m1.setZero(); 159 m1.template triangularView<Upper>() = 3 * m2; 160 m3 = 3 * m2; 161 VERIFY_IS_APPROX(m3.template triangularView<Upper>().toDenseMatrix(), m1); 162 163 164 m1.setZero(); 165 m1.template triangularView<Lower>() = 3 * m2; 166 VERIFY_IS_APPROX(m3.template triangularView<Lower>().toDenseMatrix(), m1); 167 168 m1.setZero(); 169 m1.template triangularView<StrictlyUpper>() = 3 * m2; 170 VERIFY_IS_APPROX(m3.template triangularView<StrictlyUpper>().toDenseMatrix(), m1); 171 172 173 m1.setZero(); 174 m1.template triangularView<StrictlyLower>() = 3 * m2; 175 VERIFY_IS_APPROX(m3.template triangularView<StrictlyLower>().toDenseMatrix(), m1); 176 m1.setRandom(); 177 m2 = m1.template triangularView<Upper>(); 178 VERIFY(m2.isUpperTriangular()); 179 VERIFY(!m2.isLowerTriangular()); 180 m2 = m1.template triangularView<StrictlyUpper>(); 181 VERIFY(m2.isUpperTriangular()); 182 VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1))); 183 m2 = m1.template triangularView<UnitUpper>(); 184 VERIFY(m2.isUpperTriangular()); 185 m2.diagonal().array() -= Scalar(1); 186 VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1))); 187 m2 = m1.template triangularView<Lower>(); 188 VERIFY(m2.isLowerTriangular()); 189 VERIFY(!m2.isUpperTriangular()); 190 m2 = m1.template triangularView<StrictlyLower>(); 191 VERIFY(m2.isLowerTriangular()); 192 VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1))); 193 m2 = m1.template triangularView<UnitLower>(); 194 VERIFY(m2.isLowerTriangular()); 195 m2.diagonal().array() -= Scalar(1); 196 VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1))); 197 // test swap 198 m1.setOnes(); 199 m2.setZero(); 200 m2.template triangularView<Upper>().swap(m1); 201 m3.setZero(); 202 m3.template triangularView<Upper>().setOnes(); 203 VERIFY_IS_APPROX(m2,m3); 204 } 205 206 void bug_159() 207 { 208 Matrix3d m = Matrix3d::Random().triangularView<Lower>(); 209 EIGEN_UNUSED_VARIABLE(m) 210 } 211 212 void test_triangular() 213 { 214 int maxsize = (std::min)(EIGEN_TEST_MAX_SIZE,20); 215 for(int i = 0; i < g_repeat ; i++) 216 { 217 int r = internal::random<int>(2,maxsize); EIGEN_UNUSED_VARIABLE(r); 218 int c = internal::random<int>(2,maxsize); EIGEN_UNUSED_VARIABLE(c); 219 220 CALL_SUBTEST_1( triangular_square(Matrix<float, 1, 1>()) ); 221 CALL_SUBTEST_2( triangular_square(Matrix<float, 2, 2>()) ); 222 CALL_SUBTEST_3( triangular_square(Matrix3d()) ); 223 CALL_SUBTEST_4( triangular_square(Matrix<std::complex<float>,8, 8>()) ); 224 CALL_SUBTEST_5( triangular_square(MatrixXcd(r,r)) ); 225 CALL_SUBTEST_6( triangular_square(Matrix<float,Dynamic,Dynamic,RowMajor>(r, r)) ); 226 227 CALL_SUBTEST_7( triangular_rect(Matrix<float, 4, 5>()) ); 228 CALL_SUBTEST_8( triangular_rect(Matrix<double, 6, 2>()) ); 229 CALL_SUBTEST_9( triangular_rect(MatrixXcf(r, c)) ); 230 CALL_SUBTEST_5( triangular_rect(MatrixXcd(r, c)) ); 231 CALL_SUBTEST_6( triangular_rect(Matrix<float,Dynamic,Dynamic,RowMajor>(r, c)) ); 232 } 233 234 CALL_SUBTEST_1( bug_159() ); 235 } 236
