1 // This file is part 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 template<typename ArrayType> void array(const ArrayType& m) 13 { 14 typedef typename ArrayType::Index Index; 15 typedef typename ArrayType::Scalar Scalar; 16 typedef Array<Scalar, ArrayType::RowsAtCompileTime, 1> ColVectorType; 17 typedef Array<Scalar, 1, ArrayType::ColsAtCompileTime> RowVectorType; 18 19 Index rows = m.rows(); 20 Index cols = m.cols(); 21 22 ArrayType m1 = ArrayType::Random(rows, cols), 23 m2 = ArrayType::Random(rows, cols), 24 m3(rows, cols); 25 26 ColVectorType cv1 = ColVectorType::Random(rows); 27 RowVectorType rv1 = RowVectorType::Random(cols); 28 29 Scalar s1 = internal::random<Scalar>(), 30 s2 = internal::random<Scalar>(); 31 32 // scalar addition 33 VERIFY_IS_APPROX(m1 + s1, s1 + m1); 34 VERIFY_IS_APPROX(m1 + s1, ArrayType::Constant(rows,cols,s1) + m1); 35 VERIFY_IS_APPROX(s1 - m1, (-m1)+s1 ); 36 VERIFY_IS_APPROX(m1 - s1, m1 - ArrayType::Constant(rows,cols,s1)); 37 VERIFY_IS_APPROX(s1 - m1, ArrayType::Constant(rows,cols,s1) - m1); 38 VERIFY_IS_APPROX((m1*Scalar(2)) - s2, (m1+m1) - ArrayType::Constant(rows,cols,s2) ); 39 m3 = m1; 40 m3 += s2; 41 VERIFY_IS_APPROX(m3, m1 + s2); 42 m3 = m1; 43 m3 -= s1; 44 VERIFY_IS_APPROX(m3, m1 - s1); 45 46 // scalar operators via Maps 47 m3 = m1; 48 ArrayType::Map(m1.data(), m1.rows(), m1.cols()) -= ArrayType::Map(m2.data(), m2.rows(), m2.cols()); 49 VERIFY_IS_APPROX(m1, m3 - m2); 50 51 m3 = m1; 52 ArrayType::Map(m1.data(), m1.rows(), m1.cols()) += ArrayType::Map(m2.data(), m2.rows(), m2.cols()); 53 VERIFY_IS_APPROX(m1, m3 + m2); 54 55 m3 = m1; 56 ArrayType::Map(m1.data(), m1.rows(), m1.cols()) *= ArrayType::Map(m2.data(), m2.rows(), m2.cols()); 57 VERIFY_IS_APPROX(m1, m3 * m2); 58 59 m3 = m1; 60 m2 = ArrayType::Random(rows,cols); 61 m2 = (m2==0).select(1,m2); 62 ArrayType::Map(m1.data(), m1.rows(), m1.cols()) /= ArrayType::Map(m2.data(), m2.rows(), m2.cols()); 63 VERIFY_IS_APPROX(m1, m3 / m2); 64 65 // reductions 66 VERIFY_IS_APPROX(m1.abs().colwise().sum().sum(), m1.abs().sum()); 67 VERIFY_IS_APPROX(m1.abs().rowwise().sum().sum(), m1.abs().sum()); 68 using std::abs; 69 VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.colwise().sum().sum() - m1.sum()), m1.abs().sum()); 70 VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.rowwise().sum().sum() - m1.sum()), m1.abs().sum()); 71 if (!internal::isMuchSmallerThan(abs(m1.sum() - (m1+m2).sum()), m1.abs().sum(), test_precision<Scalar>())) 72 VERIFY_IS_NOT_APPROX(((m1+m2).rowwise().sum()).sum(), m1.sum()); 73 VERIFY_IS_APPROX(m1.colwise().sum(), m1.colwise().redux(internal::scalar_sum_op<Scalar>())); 74 75 // vector-wise ops 76 m3 = m1; 77 VERIFY_IS_APPROX(m3.colwise() += cv1, m1.colwise() + cv1); 78 m3 = m1; 79 VERIFY_IS_APPROX(m3.colwise() -= cv1, m1.colwise() - cv1); 80 m3 = m1; 81 VERIFY_IS_APPROX(m3.rowwise() += rv1, m1.rowwise() + rv1); 82 m3 = m1; 83 VERIFY_IS_APPROX(m3.rowwise() -= rv1, m1.rowwise() - rv1); 84 } 85 86 template<typename ArrayType> void comparisons(const ArrayType& m) 87 { 88 using std::abs; 89 typedef typename ArrayType::Index Index; 90 typedef typename ArrayType::Scalar Scalar; 91 typedef typename NumTraits<Scalar>::Real RealScalar; 92 93 Index rows = m.rows(); 94 Index cols = m.cols(); 95 96 Index r = internal::random<Index>(0, rows-1), 97 c = internal::random<Index>(0, cols-1); 98 99 ArrayType m1 = ArrayType::Random(rows, cols), 100 m2 = ArrayType::Random(rows, cols), 101 m3(rows, cols); 102 103 VERIFY(((m1 + Scalar(1)) > m1).all()); 104 VERIFY(((m1 - Scalar(1)) < m1).all()); 105 if (rows*cols>1) 106 { 107 m3 = m1; 108 m3(r,c) += 1; 109 VERIFY(! (m1 < m3).all() ); 110 VERIFY(! (m1 > m3).all() ); 111 } 112 113 // comparisons to scalar 114 VERIFY( (m1 != (m1(r,c)+1) ).any() ); 115 VERIFY( (m1 > (m1(r,c)-1) ).any() ); 116 VERIFY( (m1 < (m1(r,c)+1) ).any() ); 117 VERIFY( (m1 == m1(r,c) ).any() ); 118 119 // test Select 120 VERIFY_IS_APPROX( (m1<m2).select(m1,m2), m1.cwiseMin(m2) ); 121 VERIFY_IS_APPROX( (m1>m2).select(m1,m2), m1.cwiseMax(m2) ); 122 Scalar mid = (m1.cwiseAbs().minCoeff() + m1.cwiseAbs().maxCoeff())/Scalar(2); 123 for (int j=0; j<cols; ++j) 124 for (int i=0; i<rows; ++i) 125 m3(i,j) = abs(m1(i,j))<mid ? 0 : m1(i,j); 126 VERIFY_IS_APPROX( (m1.abs()<ArrayType::Constant(rows,cols,mid)) 127 .select(ArrayType::Zero(rows,cols),m1), m3); 128 // shorter versions: 129 VERIFY_IS_APPROX( (m1.abs()<ArrayType::Constant(rows,cols,mid)) 130 .select(0,m1), m3); 131 VERIFY_IS_APPROX( (m1.abs()>=ArrayType::Constant(rows,cols,mid)) 132 .select(m1,0), m3); 133 // even shorter version: 134 VERIFY_IS_APPROX( (m1.abs()<mid).select(0,m1), m3); 135 136 // count 137 VERIFY(((m1.abs()+1)>RealScalar(0.1)).count() == rows*cols); 138 139 // and/or 140 VERIFY( (m1<RealScalar(0) && m1>RealScalar(0)).count() == 0); 141 VERIFY( (m1<RealScalar(0) || m1>=RealScalar(0)).count() == rows*cols); 142 RealScalar a = m1.abs().mean(); 143 VERIFY( (m1<-a || m1>a).count() == (m1.abs()>a).count()); 144 145 typedef Array<typename ArrayType::Index, Dynamic, 1> ArrayOfIndices; 146 147 // TODO allows colwise/rowwise for array 148 VERIFY_IS_APPROX(((m1.abs()+1)>RealScalar(0.1)).colwise().count(), ArrayOfIndices::Constant(cols,rows).transpose()); 149 VERIFY_IS_APPROX(((m1.abs()+1)>RealScalar(0.1)).rowwise().count(), ArrayOfIndices::Constant(rows, cols)); 150 } 151 152 template<typename ArrayType> void array_real(const ArrayType& m) 153 { 154 using std::abs; 155 using std::sqrt; 156 typedef typename ArrayType::Index Index; 157 typedef typename ArrayType::Scalar Scalar; 158 typedef typename NumTraits<Scalar>::Real RealScalar; 159 160 Index rows = m.rows(); 161 Index cols = m.cols(); 162 163 ArrayType m1 = ArrayType::Random(rows, cols), 164 m2 = ArrayType::Random(rows, cols), 165 m3(rows, cols); 166 167 Scalar s1 = internal::random<Scalar>(); 168 169 // these tests are mostly to check possible compilation issues. 170 VERIFY_IS_APPROX(m1.sin(), sin(m1)); 171 VERIFY_IS_APPROX(m1.cos(), cos(m1)); 172 VERIFY_IS_APPROX(m1.asin(), asin(m1)); 173 VERIFY_IS_APPROX(m1.acos(), acos(m1)); 174 VERIFY_IS_APPROX(m1.tan(), tan(m1)); 175 176 VERIFY_IS_APPROX(cos(m1+RealScalar(3)*m2), cos((m1+RealScalar(3)*m2).eval())); 177 178 VERIFY_IS_APPROX(m1.abs().sqrt(), sqrt(abs(m1))); 179 VERIFY_IS_APPROX(m1.abs(), sqrt(numext::abs2(m1))); 180 181 VERIFY_IS_APPROX(numext::abs2(numext::real(m1)) + numext::abs2(numext::imag(m1)), numext::abs2(m1)); 182 VERIFY_IS_APPROX(numext::abs2(real(m1)) + numext::abs2(imag(m1)), numext::abs2(m1)); 183 if(!NumTraits<Scalar>::IsComplex) 184 VERIFY_IS_APPROX(numext::real(m1), m1); 185 186 // shift argument of logarithm so that it is not zero 187 Scalar smallNumber = NumTraits<Scalar>::dummy_precision(); 188 VERIFY_IS_APPROX((m1.abs() + smallNumber).log() , log(abs(m1) + smallNumber)); 189 190 VERIFY_IS_APPROX(m1.exp() * m2.exp(), exp(m1+m2)); 191 VERIFY_IS_APPROX(m1.exp(), exp(m1)); 192 VERIFY_IS_APPROX(m1.exp() / m2.exp(),(m1-m2).exp()); 193 194 VERIFY_IS_APPROX(m1.pow(2), m1.square()); 195 VERIFY_IS_APPROX(pow(m1,2), m1.square()); 196 197 ArrayType exponents = ArrayType::Constant(rows, cols, RealScalar(2)); 198 VERIFY_IS_APPROX(Eigen::pow(m1,exponents), m1.square()); 199 200 m3 = m1.abs(); 201 VERIFY_IS_APPROX(m3.pow(RealScalar(0.5)), m3.sqrt()); 202 VERIFY_IS_APPROX(pow(m3,RealScalar(0.5)), m3.sqrt()); 203 204 // scalar by array division 205 const RealScalar tiny = sqrt(std::numeric_limits<RealScalar>::epsilon()); 206 s1 += Scalar(tiny); 207 m1 += ArrayType::Constant(rows,cols,Scalar(tiny)); 208 VERIFY_IS_APPROX(s1/m1, s1 * m1.inverse()); 209 210 // check inplace transpose 211 m3 = m1; 212 m3.transposeInPlace(); 213 VERIFY_IS_APPROX(m3,m1.transpose()); 214 m3.transposeInPlace(); 215 VERIFY_IS_APPROX(m3,m1); 216 } 217 218 template<typename ArrayType> void array_complex(const ArrayType& m) 219 { 220 typedef typename ArrayType::Index Index; 221 222 Index rows = m.rows(); 223 Index cols = m.cols(); 224 225 ArrayType m1 = ArrayType::Random(rows, cols), 226 m2(rows, cols); 227 228 for (Index i = 0; i < m.rows(); ++i) 229 for (Index j = 0; j < m.cols(); ++j) 230 m2(i,j) = sqrt(m1(i,j)); 231 232 VERIFY_IS_APPROX(m1.sqrt(), m2); 233 VERIFY_IS_APPROX(m1.sqrt(), Eigen::sqrt(m1)); 234 } 235 236 template<typename ArrayType> void min_max(const ArrayType& m) 237 { 238 typedef typename ArrayType::Index Index; 239 typedef typename ArrayType::Scalar Scalar; 240 241 Index rows = m.rows(); 242 Index cols = m.cols(); 243 244 ArrayType m1 = ArrayType::Random(rows, cols); 245 246 // min/max with array 247 Scalar maxM1 = m1.maxCoeff(); 248 Scalar minM1 = m1.minCoeff(); 249 250 VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, minM1), (m1.min)(ArrayType::Constant(rows,cols, minM1))); 251 VERIFY_IS_APPROX(m1, (m1.min)(ArrayType::Constant(rows,cols, maxM1))); 252 253 VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, maxM1), (m1.max)(ArrayType::Constant(rows,cols, maxM1))); 254 VERIFY_IS_APPROX(m1, (m1.max)(ArrayType::Constant(rows,cols, minM1))); 255 256 // min/max with scalar input 257 VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, minM1), (m1.min)( minM1)); 258 VERIFY_IS_APPROX(m1, (m1.min)( maxM1)); 259 260 VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, maxM1), (m1.max)( maxM1)); 261 VERIFY_IS_APPROX(m1, (m1.max)( minM1)); 262 263 } 264 265 void test_array() 266 { 267 for(int i = 0; i < g_repeat; i++) { 268 CALL_SUBTEST_1( array(Array<float, 1, 1>()) ); 269 CALL_SUBTEST_2( array(Array22f()) ); 270 CALL_SUBTEST_3( array(Array44d()) ); 271 CALL_SUBTEST_4( array(ArrayXXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 272 CALL_SUBTEST_5( array(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 273 CALL_SUBTEST_6( array(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 274 } 275 for(int i = 0; i < g_repeat; i++) { 276 CALL_SUBTEST_1( comparisons(Array<float, 1, 1>()) ); 277 CALL_SUBTEST_2( comparisons(Array22f()) ); 278 CALL_SUBTEST_3( comparisons(Array44d()) ); 279 CALL_SUBTEST_5( comparisons(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 280 CALL_SUBTEST_6( comparisons(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 281 } 282 for(int i = 0; i < g_repeat; i++) { 283 CALL_SUBTEST_1( min_max(Array<float, 1, 1>()) ); 284 CALL_SUBTEST_2( min_max(Array22f()) ); 285 CALL_SUBTEST_3( min_max(Array44d()) ); 286 CALL_SUBTEST_5( min_max(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 287 CALL_SUBTEST_6( min_max(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 288 } 289 for(int i = 0; i < g_repeat; i++) { 290 CALL_SUBTEST_1( array_real(Array<float, 1, 1>()) ); 291 CALL_SUBTEST_2( array_real(Array22f()) ); 292 CALL_SUBTEST_3( array_real(Array44d()) ); 293 CALL_SUBTEST_5( array_real(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 294 } 295 for(int i = 0; i < g_repeat; i++) { 296 CALL_SUBTEST_4( array_complex(ArrayXXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 297 } 298 299 VERIFY((internal::is_same< internal::global_math_functions_filtering_base<int>::type, int >::value)); 300 VERIFY((internal::is_same< internal::global_math_functions_filtering_base<float>::type, float >::value)); 301 VERIFY((internal::is_same< internal::global_math_functions_filtering_base<Array2i>::type, ArrayBase<Array2i> >::value)); 302 typedef CwiseUnaryOp<internal::scalar_sum_op<double>, ArrayXd > Xpr; 303 VERIFY((internal::is_same< internal::global_math_functions_filtering_base<Xpr>::type, 304 ArrayBase<Xpr> 305 >::value)); 306 } 307
