array_cwise.cpp (27758B)
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@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 // Test the corner cases of pow(x, y) for real types. 14 template<typename Scalar> 15 void pow_test() { 16 const Scalar zero = Scalar(0); 17 const Scalar eps = Eigen::NumTraits<Scalar>::epsilon(); 18 const Scalar one = Scalar(1); 19 const Scalar two = Scalar(2); 20 const Scalar three = Scalar(3); 21 const Scalar sqrt_half = Scalar(std::sqrt(0.5)); 22 const Scalar sqrt2 = Scalar(std::sqrt(2)); 23 const Scalar inf = Eigen::NumTraits<Scalar>::infinity(); 24 const Scalar nan = Eigen::NumTraits<Scalar>::quiet_NaN(); 25 const Scalar denorm_min = std::numeric_limits<Scalar>::denorm_min(); 26 const Scalar min = (std::numeric_limits<Scalar>::min)(); 27 const Scalar max = (std::numeric_limits<Scalar>::max)(); 28 const Scalar max_exp = (static_cast<Scalar>(int(Eigen::NumTraits<Scalar>::max_exponent())) * Scalar(EIGEN_LN2)) / eps; 29 30 const static Scalar abs_vals[] = {zero, 31 denorm_min, 32 min, 33 eps, 34 sqrt_half, 35 one, 36 sqrt2, 37 two, 38 three, 39 max_exp, 40 max, 41 inf, 42 nan}; 43 const int abs_cases = 13; 44 const int num_cases = 2*abs_cases * 2*abs_cases; 45 // Repeat the same value to make sure we hit the vectorized path. 46 const int num_repeats = 32; 47 Array<Scalar, Dynamic, Dynamic> x(num_repeats, num_cases); 48 Array<Scalar, Dynamic, Dynamic> y(num_repeats, num_cases); 49 int count = 0; 50 for (int i = 0; i < abs_cases; ++i) { 51 const Scalar abs_x = abs_vals[i]; 52 for (int sign_x = 0; sign_x < 2; ++sign_x) { 53 Scalar x_case = sign_x == 0 ? -abs_x : abs_x; 54 for (int j = 0; j < abs_cases; ++j) { 55 const Scalar abs_y = abs_vals[j]; 56 for (int sign_y = 0; sign_y < 2; ++sign_y) { 57 Scalar y_case = sign_y == 0 ? -abs_y : abs_y; 58 for (int repeat = 0; repeat < num_repeats; ++repeat) { 59 x(repeat, count) = x_case; 60 y(repeat, count) = y_case; 61 } 62 ++count; 63 } 64 } 65 } 66 } 67 68 Array<Scalar, Dynamic, Dynamic> actual = x.pow(y); 69 const Scalar tol = test_precision<Scalar>(); 70 bool all_pass = true; 71 for (int i = 0; i < 1; ++i) { 72 for (int j = 0; j < num_cases; ++j) { 73 Scalar e = static_cast<Scalar>(std::pow(x(i,j), y(i,j))); 74 Scalar a = actual(i, j); 75 bool fail = !(a==e) && !internal::isApprox(a, e, tol) && !((numext::isnan)(a) && (numext::isnan)(e)); 76 all_pass &= !fail; 77 if (fail) { 78 std::cout << "pow(" << x(i,j) << "," << y(i,j) << ") = " << a << " != " << e << std::endl; 79 } 80 } 81 } 82 VERIFY(all_pass); 83 } 84 85 template<typename ArrayType> void array(const ArrayType& m) 86 { 87 typedef typename ArrayType::Scalar Scalar; 88 typedef typename ArrayType::RealScalar RealScalar; 89 typedef Array<Scalar, ArrayType::RowsAtCompileTime, 1> ColVectorType; 90 typedef Array<Scalar, 1, ArrayType::ColsAtCompileTime> RowVectorType; 91 92 Index rows = m.rows(); 93 Index cols = m.cols(); 94 95 ArrayType m1 = ArrayType::Random(rows, cols), 96 m2 = ArrayType::Random(rows, cols), 97 m3(rows, cols); 98 ArrayType m4 = m1; // copy constructor 99 VERIFY_IS_APPROX(m1, m4); 100 101 ColVectorType cv1 = ColVectorType::Random(rows); 102 RowVectorType rv1 = RowVectorType::Random(cols); 103 104 Scalar s1 = internal::random<Scalar>(), 105 s2 = internal::random<Scalar>(); 106 107 // scalar addition 108 VERIFY_IS_APPROX(m1 + s1, s1 + m1); 109 VERIFY_IS_APPROX(m1 + s1, ArrayType::Constant(rows,cols,s1) + m1); 110 VERIFY_IS_APPROX(s1 - m1, (-m1)+s1 ); 111 VERIFY_IS_APPROX(m1 - s1, m1 - ArrayType::Constant(rows,cols,s1)); 112 VERIFY_IS_APPROX(s1 - m1, ArrayType::Constant(rows,cols,s1) - m1); 113 VERIFY_IS_APPROX((m1*Scalar(2)) - s2, (m1+m1) - ArrayType::Constant(rows,cols,s2) ); 114 m3 = m1; 115 m3 += s2; 116 VERIFY_IS_APPROX(m3, m1 + s2); 117 m3 = m1; 118 m3 -= s1; 119 VERIFY_IS_APPROX(m3, m1 - s1); 120 121 // scalar operators via Maps 122 m3 = m1; 123 ArrayType::Map(m1.data(), m1.rows(), m1.cols()) -= ArrayType::Map(m2.data(), m2.rows(), m2.cols()); 124 VERIFY_IS_APPROX(m1, m3 - m2); 125 126 m3 = m1; 127 ArrayType::Map(m1.data(), m1.rows(), m1.cols()) += ArrayType::Map(m2.data(), m2.rows(), m2.cols()); 128 VERIFY_IS_APPROX(m1, m3 + m2); 129 130 m3 = m1; 131 ArrayType::Map(m1.data(), m1.rows(), m1.cols()) *= ArrayType::Map(m2.data(), m2.rows(), m2.cols()); 132 VERIFY_IS_APPROX(m1, m3 * m2); 133 134 m3 = m1; 135 m2 = ArrayType::Random(rows,cols); 136 m2 = (m2==0).select(1,m2); 137 ArrayType::Map(m1.data(), m1.rows(), m1.cols()) /= ArrayType::Map(m2.data(), m2.rows(), m2.cols()); 138 VERIFY_IS_APPROX(m1, m3 / m2); 139 140 // reductions 141 VERIFY_IS_APPROX(m1.abs().colwise().sum().sum(), m1.abs().sum()); 142 VERIFY_IS_APPROX(m1.abs().rowwise().sum().sum(), m1.abs().sum()); 143 using std::abs; 144 VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.colwise().sum().sum() - m1.sum()), m1.abs().sum()); 145 VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.rowwise().sum().sum() - m1.sum()), m1.abs().sum()); 146 if (!internal::isMuchSmallerThan(abs(m1.sum() - (m1+m2).sum()), m1.abs().sum(), test_precision<Scalar>())) 147 VERIFY_IS_NOT_APPROX(((m1+m2).rowwise().sum()).sum(), m1.sum()); 148 VERIFY_IS_APPROX(m1.colwise().sum(), m1.colwise().redux(internal::scalar_sum_op<Scalar,Scalar>())); 149 150 // vector-wise ops 151 m3 = m1; 152 VERIFY_IS_APPROX(m3.colwise() += cv1, m1.colwise() + cv1); 153 m3 = m1; 154 VERIFY_IS_APPROX(m3.colwise() -= cv1, m1.colwise() - cv1); 155 m3 = m1; 156 VERIFY_IS_APPROX(m3.rowwise() += rv1, m1.rowwise() + rv1); 157 m3 = m1; 158 VERIFY_IS_APPROX(m3.rowwise() -= rv1, m1.rowwise() - rv1); 159 160 // Conversion from scalar 161 VERIFY_IS_APPROX((m3 = s1), ArrayType::Constant(rows,cols,s1)); 162 VERIFY_IS_APPROX((m3 = 1), ArrayType::Constant(rows,cols,1)); 163 VERIFY_IS_APPROX((m3.topLeftCorner(rows,cols) = 1), ArrayType::Constant(rows,cols,1)); 164 typedef Array<Scalar, 165 ArrayType::RowsAtCompileTime==Dynamic?2:ArrayType::RowsAtCompileTime, 166 ArrayType::ColsAtCompileTime==Dynamic?2:ArrayType::ColsAtCompileTime, 167 ArrayType::Options> FixedArrayType; 168 { 169 FixedArrayType f1(s1); 170 VERIFY_IS_APPROX(f1, FixedArrayType::Constant(s1)); 171 FixedArrayType f2(numext::real(s1)); 172 VERIFY_IS_APPROX(f2, FixedArrayType::Constant(numext::real(s1))); 173 FixedArrayType f3((int)100*numext::real(s1)); 174 VERIFY_IS_APPROX(f3, FixedArrayType::Constant((int)100*numext::real(s1))); 175 f1.setRandom(); 176 FixedArrayType f4(f1.data()); 177 VERIFY_IS_APPROX(f4, f1); 178 } 179 #if EIGEN_HAS_CXX11 180 { 181 FixedArrayType f1{s1}; 182 VERIFY_IS_APPROX(f1, FixedArrayType::Constant(s1)); 183 FixedArrayType f2{numext::real(s1)}; 184 VERIFY_IS_APPROX(f2, FixedArrayType::Constant(numext::real(s1))); 185 FixedArrayType f3{(int)100*numext::real(s1)}; 186 VERIFY_IS_APPROX(f3, FixedArrayType::Constant((int)100*numext::real(s1))); 187 f1.setRandom(); 188 FixedArrayType f4{f1.data()}; 189 VERIFY_IS_APPROX(f4, f1); 190 } 191 #endif 192 193 // pow 194 VERIFY_IS_APPROX(m1.pow(2), m1.square()); 195 VERIFY_IS_APPROX(pow(m1,2), m1.square()); 196 VERIFY_IS_APPROX(m1.pow(3), m1.cube()); 197 VERIFY_IS_APPROX(pow(m1,3), m1.cube()); 198 VERIFY_IS_APPROX((-m1).pow(3), -m1.cube()); 199 VERIFY_IS_APPROX(pow(2*m1,3), 8*m1.cube()); 200 ArrayType exponents = ArrayType::Constant(rows, cols, RealScalar(2)); 201 VERIFY_IS_APPROX(Eigen::pow(m1,exponents), m1.square()); 202 VERIFY_IS_APPROX(m1.pow(exponents), m1.square()); 203 VERIFY_IS_APPROX(Eigen::pow(2*m1,exponents), 4*m1.square()); 204 VERIFY_IS_APPROX((2*m1).pow(exponents), 4*m1.square()); 205 VERIFY_IS_APPROX(Eigen::pow(m1,2*exponents), m1.square().square()); 206 VERIFY_IS_APPROX(m1.pow(2*exponents), m1.square().square()); 207 VERIFY_IS_APPROX(Eigen::pow(m1(0,0), exponents), ArrayType::Constant(rows,cols,m1(0,0)*m1(0,0))); 208 209 // Check possible conflicts with 1D ctor 210 typedef Array<Scalar, Dynamic, 1> OneDArrayType; 211 { 212 OneDArrayType o1(rows); 213 VERIFY(o1.size()==rows); 214 OneDArrayType o2(static_cast<int>(rows)); 215 VERIFY(o2.size()==rows); 216 } 217 #if EIGEN_HAS_CXX11 218 { 219 OneDArrayType o1{rows}; 220 VERIFY(o1.size()==rows); 221 OneDArrayType o4{int(rows)}; 222 VERIFY(o4.size()==rows); 223 } 224 #endif 225 // Check possible conflicts with 2D ctor 226 typedef Array<Scalar, Dynamic, Dynamic> TwoDArrayType; 227 typedef Array<Scalar, 2, 1> ArrayType2; 228 { 229 TwoDArrayType o1(rows,cols); 230 VERIFY(o1.rows()==rows); 231 VERIFY(o1.cols()==cols); 232 TwoDArrayType o2(static_cast<int>(rows),static_cast<int>(cols)); 233 VERIFY(o2.rows()==rows); 234 VERIFY(o2.cols()==cols); 235 236 ArrayType2 o3(rows,cols); 237 VERIFY(o3(0)==Scalar(rows) && o3(1)==Scalar(cols)); 238 ArrayType2 o4(static_cast<int>(rows),static_cast<int>(cols)); 239 VERIFY(o4(0)==Scalar(rows) && o4(1)==Scalar(cols)); 240 } 241 #if EIGEN_HAS_CXX11 242 { 243 TwoDArrayType o1{rows,cols}; 244 VERIFY(o1.rows()==rows); 245 VERIFY(o1.cols()==cols); 246 TwoDArrayType o2{int(rows),int(cols)}; 247 VERIFY(o2.rows()==rows); 248 VERIFY(o2.cols()==cols); 249 250 ArrayType2 o3{rows,cols}; 251 VERIFY(o3(0)==Scalar(rows) && o3(1)==Scalar(cols)); 252 ArrayType2 o4{int(rows),int(cols)}; 253 VERIFY(o4(0)==Scalar(rows) && o4(1)==Scalar(cols)); 254 } 255 #endif 256 } 257 258 template<typename ArrayType> void comparisons(const ArrayType& m) 259 { 260 using std::abs; 261 typedef typename ArrayType::Scalar Scalar; 262 typedef typename NumTraits<Scalar>::Real RealScalar; 263 264 Index rows = m.rows(); 265 Index cols = m.cols(); 266 267 Index r = internal::random<Index>(0, rows-1), 268 c = internal::random<Index>(0, cols-1); 269 270 ArrayType m1 = ArrayType::Random(rows, cols), 271 m2 = ArrayType::Random(rows, cols), 272 m3(rows, cols), 273 m4 = m1; 274 275 m4 = (m4.abs()==Scalar(0)).select(1,m4); 276 277 VERIFY(((m1 + Scalar(1)) > m1).all()); 278 VERIFY(((m1 - Scalar(1)) < m1).all()); 279 if (rows*cols>1) 280 { 281 m3 = m1; 282 m3(r,c) += 1; 283 VERIFY(! (m1 < m3).all() ); 284 VERIFY(! (m1 > m3).all() ); 285 } 286 VERIFY(!(m1 > m2 && m1 < m2).any()); 287 VERIFY((m1 <= m2 || m1 >= m2).all()); 288 289 // comparisons array to scalar 290 VERIFY( (m1 != (m1(r,c)+1) ).any() ); 291 VERIFY( (m1 > (m1(r,c)-1) ).any() ); 292 VERIFY( (m1 < (m1(r,c)+1) ).any() ); 293 VERIFY( (m1 == m1(r,c) ).any() ); 294 295 // comparisons scalar to array 296 VERIFY( ( (m1(r,c)+1) != m1).any() ); 297 VERIFY( ( (m1(r,c)-1) < m1).any() ); 298 VERIFY( ( (m1(r,c)+1) > m1).any() ); 299 VERIFY( ( m1(r,c) == m1).any() ); 300 301 // test Select 302 VERIFY_IS_APPROX( (m1<m2).select(m1,m2), m1.cwiseMin(m2) ); 303 VERIFY_IS_APPROX( (m1>m2).select(m1,m2), m1.cwiseMax(m2) ); 304 Scalar mid = (m1.cwiseAbs().minCoeff() + m1.cwiseAbs().maxCoeff())/Scalar(2); 305 for (int j=0; j<cols; ++j) 306 for (int i=0; i<rows; ++i) 307 m3(i,j) = abs(m1(i,j))<mid ? 0 : m1(i,j); 308 VERIFY_IS_APPROX( (m1.abs()<ArrayType::Constant(rows,cols,mid)) 309 .select(ArrayType::Zero(rows,cols),m1), m3); 310 // shorter versions: 311 VERIFY_IS_APPROX( (m1.abs()<ArrayType::Constant(rows,cols,mid)) 312 .select(0,m1), m3); 313 VERIFY_IS_APPROX( (m1.abs()>=ArrayType::Constant(rows,cols,mid)) 314 .select(m1,0), m3); 315 // even shorter version: 316 VERIFY_IS_APPROX( (m1.abs()<mid).select(0,m1), m3); 317 318 // count 319 VERIFY(((m1.abs()+1)>RealScalar(0.1)).count() == rows*cols); 320 321 // and/or 322 VERIFY( (m1<RealScalar(0) && m1>RealScalar(0)).count() == 0); 323 VERIFY( (m1<RealScalar(0) || m1>=RealScalar(0)).count() == rows*cols); 324 RealScalar a = m1.abs().mean(); 325 VERIFY( (m1<-a || m1>a).count() == (m1.abs()>a).count()); 326 327 typedef Array<Index, Dynamic, 1> ArrayOfIndices; 328 329 // TODO allows colwise/rowwise for array 330 VERIFY_IS_APPROX(((m1.abs()+1)>RealScalar(0.1)).colwise().count(), ArrayOfIndices::Constant(cols,rows).transpose()); 331 VERIFY_IS_APPROX(((m1.abs()+1)>RealScalar(0.1)).rowwise().count(), ArrayOfIndices::Constant(rows, cols)); 332 } 333 334 template<typename ArrayType> void array_real(const ArrayType& m) 335 { 336 using std::abs; 337 using std::sqrt; 338 typedef typename ArrayType::Scalar Scalar; 339 typedef typename NumTraits<Scalar>::Real RealScalar; 340 341 Index rows = m.rows(); 342 Index cols = m.cols(); 343 344 ArrayType m1 = ArrayType::Random(rows, cols), 345 m2 = ArrayType::Random(rows, cols), 346 m3(rows, cols), 347 m4 = m1; 348 349 m4 = (m4.abs()==Scalar(0)).select(Scalar(1),m4); 350 351 Scalar s1 = internal::random<Scalar>(); 352 353 // these tests are mostly to check possible compilation issues with free-functions. 354 VERIFY_IS_APPROX(m1.sin(), sin(m1)); 355 VERIFY_IS_APPROX(m1.cos(), cos(m1)); 356 VERIFY_IS_APPROX(m1.tan(), tan(m1)); 357 VERIFY_IS_APPROX(m1.asin(), asin(m1)); 358 VERIFY_IS_APPROX(m1.acos(), acos(m1)); 359 VERIFY_IS_APPROX(m1.atan(), atan(m1)); 360 VERIFY_IS_APPROX(m1.sinh(), sinh(m1)); 361 VERIFY_IS_APPROX(m1.cosh(), cosh(m1)); 362 VERIFY_IS_APPROX(m1.tanh(), tanh(m1)); 363 #if EIGEN_HAS_CXX11_MATH 364 VERIFY_IS_APPROX(m1.tanh().atanh(), atanh(tanh(m1))); 365 VERIFY_IS_APPROX(m1.sinh().asinh(), asinh(sinh(m1))); 366 VERIFY_IS_APPROX(m1.cosh().acosh(), acosh(cosh(m1))); 367 #endif 368 VERIFY_IS_APPROX(m1.logistic(), logistic(m1)); 369 370 VERIFY_IS_APPROX(m1.arg(), arg(m1)); 371 VERIFY_IS_APPROX(m1.round(), round(m1)); 372 VERIFY_IS_APPROX(m1.rint(), rint(m1)); 373 VERIFY_IS_APPROX(m1.floor(), floor(m1)); 374 VERIFY_IS_APPROX(m1.ceil(), ceil(m1)); 375 VERIFY((m1.isNaN() == (Eigen::isnan)(m1)).all()); 376 VERIFY((m1.isInf() == (Eigen::isinf)(m1)).all()); 377 VERIFY((m1.isFinite() == (Eigen::isfinite)(m1)).all()); 378 VERIFY_IS_APPROX(m4.inverse(), inverse(m4)); 379 VERIFY_IS_APPROX(m1.abs(), abs(m1)); 380 VERIFY_IS_APPROX(m1.abs2(), abs2(m1)); 381 VERIFY_IS_APPROX(m1.square(), square(m1)); 382 VERIFY_IS_APPROX(m1.cube(), cube(m1)); 383 VERIFY_IS_APPROX(cos(m1+RealScalar(3)*m2), cos((m1+RealScalar(3)*m2).eval())); 384 VERIFY_IS_APPROX(m1.sign(), sign(m1)); 385 VERIFY((m1.sqrt().sign().isNaN() == (Eigen::isnan)(sign(sqrt(m1)))).all()); 386 387 // avoid inf and NaNs so verification doesn't fail 388 m3 = m4.abs(); 389 VERIFY_IS_APPROX(m3.sqrt(), sqrt(abs(m3))); 390 VERIFY_IS_APPROX(m3.rsqrt(), Scalar(1)/sqrt(abs(m3))); 391 VERIFY_IS_APPROX(rsqrt(m3), Scalar(1)/sqrt(abs(m3))); 392 VERIFY_IS_APPROX(m3.log(), log(m3)); 393 VERIFY_IS_APPROX(m3.log1p(), log1p(m3)); 394 VERIFY_IS_APPROX(m3.log10(), log10(m3)); 395 VERIFY_IS_APPROX(m3.log2(), log2(m3)); 396 397 398 VERIFY((!(m1>m2) == (m1<=m2)).all()); 399 400 VERIFY_IS_APPROX(sin(m1.asin()), m1); 401 VERIFY_IS_APPROX(cos(m1.acos()), m1); 402 VERIFY_IS_APPROX(tan(m1.atan()), m1); 403 VERIFY_IS_APPROX(sinh(m1), Scalar(0.5)*(exp(m1)-exp(-m1))); 404 VERIFY_IS_APPROX(cosh(m1), Scalar(0.5)*(exp(m1)+exp(-m1))); 405 VERIFY_IS_APPROX(tanh(m1), (Scalar(0.5)*(exp(m1)-exp(-m1)))/(Scalar(0.5)*(exp(m1)+exp(-m1)))); 406 VERIFY_IS_APPROX(logistic(m1), (Scalar(1)/(Scalar(1)+exp(-m1)))); 407 VERIFY_IS_APPROX(arg(m1), ((m1<Scalar(0)).template cast<Scalar>())*Scalar(std::acos(Scalar(-1)))); 408 VERIFY((round(m1) <= ceil(m1) && round(m1) >= floor(m1)).all()); 409 VERIFY((rint(m1) <= ceil(m1) && rint(m1) >= floor(m1)).all()); 410 VERIFY(((ceil(m1) - round(m1)) <= Scalar(0.5) || (round(m1) - floor(m1)) <= Scalar(0.5)).all()); 411 VERIFY(((ceil(m1) - round(m1)) <= Scalar(1.0) && (round(m1) - floor(m1)) <= Scalar(1.0)).all()); 412 VERIFY(((ceil(m1) - rint(m1)) <= Scalar(0.5) || (rint(m1) - floor(m1)) <= Scalar(0.5)).all()); 413 VERIFY(((ceil(m1) - rint(m1)) <= Scalar(1.0) && (rint(m1) - floor(m1)) <= Scalar(1.0)).all()); 414 VERIFY((Eigen::isnan)((m1*Scalar(0))/Scalar(0)).all()); 415 VERIFY((Eigen::isinf)(m4/Scalar(0)).all()); 416 VERIFY(((Eigen::isfinite)(m1) && (!(Eigen::isfinite)(m1*Scalar(0)/Scalar(0))) && (!(Eigen::isfinite)(m4/Scalar(0)))).all()); 417 VERIFY_IS_APPROX(inverse(inverse(m4)),m4); 418 VERIFY((abs(m1) == m1 || abs(m1) == -m1).all()); 419 VERIFY_IS_APPROX(m3, sqrt(abs2(m3))); 420 VERIFY_IS_APPROX(m1.absolute_difference(m2), (m1 > m2).select(m1 - m2, m2 - m1)); 421 VERIFY_IS_APPROX( m1.sign(), -(-m1).sign() ); 422 VERIFY_IS_APPROX( m1*m1.sign(),m1.abs()); 423 VERIFY_IS_APPROX(m1.sign() * m1.abs(), m1); 424 425 VERIFY_IS_APPROX(numext::abs2(numext::real(m1)) + numext::abs2(numext::imag(m1)), numext::abs2(m1)); 426 VERIFY_IS_APPROX(numext::abs2(Eigen::real(m1)) + numext::abs2(Eigen::imag(m1)), numext::abs2(m1)); 427 if(!NumTraits<Scalar>::IsComplex) 428 VERIFY_IS_APPROX(numext::real(m1), m1); 429 430 // shift argument of logarithm so that it is not zero 431 Scalar smallNumber = NumTraits<Scalar>::dummy_precision(); 432 VERIFY_IS_APPROX((m3 + smallNumber).log() , log(abs(m3) + smallNumber)); 433 VERIFY_IS_APPROX((m3 + smallNumber + Scalar(1)).log() , log1p(abs(m3) + smallNumber)); 434 435 VERIFY_IS_APPROX(m1.exp() * m2.exp(), exp(m1+m2)); 436 VERIFY_IS_APPROX(m1.exp(), exp(m1)); 437 VERIFY_IS_APPROX(m1.exp() / m2.exp(),(m1-m2).exp()); 438 439 VERIFY_IS_APPROX(m1.expm1(), expm1(m1)); 440 VERIFY_IS_APPROX((m3 + smallNumber).exp() - Scalar(1), expm1(abs(m3) + smallNumber)); 441 442 VERIFY_IS_APPROX(m3.pow(RealScalar(0.5)), m3.sqrt()); 443 VERIFY_IS_APPROX(pow(m3,RealScalar(0.5)), m3.sqrt()); 444 445 VERIFY_IS_APPROX(m3.pow(RealScalar(-0.5)), m3.rsqrt()); 446 VERIFY_IS_APPROX(pow(m3,RealScalar(-0.5)), m3.rsqrt()); 447 448 // Avoid inf and NaN. 449 m3 = (m1.square()<NumTraits<Scalar>::epsilon()).select(Scalar(1),m3); 450 VERIFY_IS_APPROX(m3.pow(RealScalar(-2)), m3.square().inverse()); 451 pow_test<Scalar>(); 452 453 VERIFY_IS_APPROX(log10(m3), log(m3)/numext::log(Scalar(10))); 454 VERIFY_IS_APPROX(log2(m3), log(m3)/numext::log(Scalar(2))); 455 456 // scalar by array division 457 const RealScalar tiny = sqrt(std::numeric_limits<RealScalar>::epsilon()); 458 s1 += Scalar(tiny); 459 m1 += ArrayType::Constant(rows,cols,Scalar(tiny)); 460 VERIFY_IS_APPROX(s1/m1, s1 * m1.inverse()); 461 462 // check inplace transpose 463 m3 = m1; 464 m3.transposeInPlace(); 465 VERIFY_IS_APPROX(m3, m1.transpose()); 466 m3.transposeInPlace(); 467 VERIFY_IS_APPROX(m3, m1); 468 } 469 470 template<typename ArrayType> void array_complex(const ArrayType& m) 471 { 472 typedef typename ArrayType::Scalar Scalar; 473 typedef typename NumTraits<Scalar>::Real RealScalar; 474 475 Index rows = m.rows(); 476 Index cols = m.cols(); 477 478 ArrayType m1 = ArrayType::Random(rows, cols), 479 m2(rows, cols), 480 m4 = m1; 481 482 m4.real() = (m4.real().abs()==RealScalar(0)).select(RealScalar(1),m4.real()); 483 m4.imag() = (m4.imag().abs()==RealScalar(0)).select(RealScalar(1),m4.imag()); 484 485 Array<RealScalar, -1, -1> m3(rows, cols); 486 487 for (Index i = 0; i < m.rows(); ++i) 488 for (Index j = 0; j < m.cols(); ++j) 489 m2(i,j) = sqrt(m1(i,j)); 490 491 // these tests are mostly to check possible compilation issues with free-functions. 492 VERIFY_IS_APPROX(m1.sin(), sin(m1)); 493 VERIFY_IS_APPROX(m1.cos(), cos(m1)); 494 VERIFY_IS_APPROX(m1.tan(), tan(m1)); 495 VERIFY_IS_APPROX(m1.sinh(), sinh(m1)); 496 VERIFY_IS_APPROX(m1.cosh(), cosh(m1)); 497 VERIFY_IS_APPROX(m1.tanh(), tanh(m1)); 498 VERIFY_IS_APPROX(m1.logistic(), logistic(m1)); 499 VERIFY_IS_APPROX(m1.arg(), arg(m1)); 500 VERIFY((m1.isNaN() == (Eigen::isnan)(m1)).all()); 501 VERIFY((m1.isInf() == (Eigen::isinf)(m1)).all()); 502 VERIFY((m1.isFinite() == (Eigen::isfinite)(m1)).all()); 503 VERIFY_IS_APPROX(m4.inverse(), inverse(m4)); 504 VERIFY_IS_APPROX(m1.log(), log(m1)); 505 VERIFY_IS_APPROX(m1.log10(), log10(m1)); 506 VERIFY_IS_APPROX(m1.log2(), log2(m1)); 507 VERIFY_IS_APPROX(m1.abs(), abs(m1)); 508 VERIFY_IS_APPROX(m1.abs2(), abs2(m1)); 509 VERIFY_IS_APPROX(m1.sqrt(), sqrt(m1)); 510 VERIFY_IS_APPROX(m1.square(), square(m1)); 511 VERIFY_IS_APPROX(m1.cube(), cube(m1)); 512 VERIFY_IS_APPROX(cos(m1+RealScalar(3)*m2), cos((m1+RealScalar(3)*m2).eval())); 513 VERIFY_IS_APPROX(m1.sign(), sign(m1)); 514 515 516 VERIFY_IS_APPROX(m1.exp() * m2.exp(), exp(m1+m2)); 517 VERIFY_IS_APPROX(m1.exp(), exp(m1)); 518 VERIFY_IS_APPROX(m1.exp() / m2.exp(),(m1-m2).exp()); 519 520 VERIFY_IS_APPROX(m1.expm1(), expm1(m1)); 521 VERIFY_IS_APPROX(expm1(m1), exp(m1) - 1.); 522 // Check for larger magnitude complex numbers that expm1 matches exp - 1. 523 VERIFY_IS_APPROX(expm1(10. * m1), exp(10. * m1) - 1.); 524 525 VERIFY_IS_APPROX(sinh(m1), 0.5*(exp(m1)-exp(-m1))); 526 VERIFY_IS_APPROX(cosh(m1), 0.5*(exp(m1)+exp(-m1))); 527 VERIFY_IS_APPROX(tanh(m1), (0.5*(exp(m1)-exp(-m1)))/(0.5*(exp(m1)+exp(-m1)))); 528 VERIFY_IS_APPROX(logistic(m1), (1.0/(1.0 + exp(-m1)))); 529 530 for (Index i = 0; i < m.rows(); ++i) 531 for (Index j = 0; j < m.cols(); ++j) 532 m3(i,j) = std::atan2(m1(i,j).imag(), m1(i,j).real()); 533 VERIFY_IS_APPROX(arg(m1), m3); 534 535 std::complex<RealScalar> zero(0.0,0.0); 536 VERIFY((Eigen::isnan)(m1*zero/zero).all()); 537 #if EIGEN_COMP_MSVC 538 // msvc complex division is not robust 539 VERIFY((Eigen::isinf)(m4/RealScalar(0)).all()); 540 #else 541 #if EIGEN_COMP_CLANG 542 // clang's complex division is notoriously broken too 543 if((numext::isinf)(m4(0,0)/RealScalar(0))) { 544 #endif 545 VERIFY((Eigen::isinf)(m4/zero).all()); 546 #if EIGEN_COMP_CLANG 547 } 548 else 549 { 550 VERIFY((Eigen::isinf)(m4.real()/zero.real()).all()); 551 } 552 #endif 553 #endif // MSVC 554 555 VERIFY(((Eigen::isfinite)(m1) && (!(Eigen::isfinite)(m1*zero/zero)) && (!(Eigen::isfinite)(m1/zero))).all()); 556 557 VERIFY_IS_APPROX(inverse(inverse(m4)),m4); 558 VERIFY_IS_APPROX(conj(m1.conjugate()), m1); 559 VERIFY_IS_APPROX(abs(m1), sqrt(square(m1.real())+square(m1.imag()))); 560 VERIFY_IS_APPROX(abs(m1), sqrt(abs2(m1))); 561 VERIFY_IS_APPROX(log10(m1), log(m1)/log(10)); 562 VERIFY_IS_APPROX(log2(m1), log(m1)/log(2)); 563 564 VERIFY_IS_APPROX( m1.sign(), -(-m1).sign() ); 565 VERIFY_IS_APPROX( m1.sign() * m1.abs(), m1); 566 567 // scalar by array division 568 Scalar s1 = internal::random<Scalar>(); 569 const RealScalar tiny = std::sqrt(std::numeric_limits<RealScalar>::epsilon()); 570 s1 += Scalar(tiny); 571 m1 += ArrayType::Constant(rows,cols,Scalar(tiny)); 572 VERIFY_IS_APPROX(s1/m1, s1 * m1.inverse()); 573 574 // check inplace transpose 575 m2 = m1; 576 m2.transposeInPlace(); 577 VERIFY_IS_APPROX(m2, m1.transpose()); 578 m2.transposeInPlace(); 579 VERIFY_IS_APPROX(m2, m1); 580 // Check vectorized inplace transpose. 581 ArrayType m5 = ArrayType::Random(131, 131); 582 ArrayType m6 = m5; 583 m6.transposeInPlace(); 584 VERIFY_IS_APPROX(m6, m5.transpose()); 585 } 586 587 template<typename ArrayType> void min_max(const ArrayType& m) 588 { 589 typedef typename ArrayType::Scalar Scalar; 590 591 Index rows = m.rows(); 592 Index cols = m.cols(); 593 594 ArrayType m1 = ArrayType::Random(rows, cols); 595 596 // min/max with array 597 Scalar maxM1 = m1.maxCoeff(); 598 Scalar minM1 = m1.minCoeff(); 599 600 VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, minM1), (m1.min)(ArrayType::Constant(rows,cols, minM1))); 601 VERIFY_IS_APPROX(m1, (m1.min)(ArrayType::Constant(rows,cols, maxM1))); 602 603 VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, maxM1), (m1.max)(ArrayType::Constant(rows,cols, maxM1))); 604 VERIFY_IS_APPROX(m1, (m1.max)(ArrayType::Constant(rows,cols, minM1))); 605 606 // min/max with scalar input 607 VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, minM1), (m1.min)( minM1)); 608 VERIFY_IS_APPROX(m1, (m1.min)( maxM1)); 609 610 VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, maxM1), (m1.max)( maxM1)); 611 VERIFY_IS_APPROX(m1, (m1.max)( minM1)); 612 613 614 // min/max with various NaN propagation options. 615 if (m1.size() > 1 && !NumTraits<Scalar>::IsInteger) { 616 m1(0,0) = NumTraits<Scalar>::quiet_NaN(); 617 maxM1 = m1.template maxCoeff<PropagateNaN>(); 618 minM1 = m1.template minCoeff<PropagateNaN>(); 619 VERIFY((numext::isnan)(maxM1)); 620 VERIFY((numext::isnan)(minM1)); 621 622 maxM1 = m1.template maxCoeff<PropagateNumbers>(); 623 minM1 = m1.template minCoeff<PropagateNumbers>(); 624 VERIFY(!(numext::isnan)(maxM1)); 625 VERIFY(!(numext::isnan)(minM1)); 626 } 627 } 628 629 template<int N> 630 struct shift_left { 631 template<typename Scalar> 632 Scalar operator()(const Scalar& v) const { 633 return v << N; 634 } 635 }; 636 637 template<int N> 638 struct arithmetic_shift_right { 639 template<typename Scalar> 640 Scalar operator()(const Scalar& v) const { 641 return v >> N; 642 } 643 }; 644 645 template<typename ArrayType> void array_integer(const ArrayType& m) 646 { 647 Index rows = m.rows(); 648 Index cols = m.cols(); 649 650 ArrayType m1 = ArrayType::Random(rows, cols), 651 m2(rows, cols); 652 653 m2 = m1.template shiftLeft<2>(); 654 VERIFY( (m2 == m1.unaryExpr(shift_left<2>())).all() ); 655 m2 = m1.template shiftLeft<9>(); 656 VERIFY( (m2 == m1.unaryExpr(shift_left<9>())).all() ); 657 658 m2 = m1.template shiftRight<2>(); 659 VERIFY( (m2 == m1.unaryExpr(arithmetic_shift_right<2>())).all() ); 660 m2 = m1.template shiftRight<9>(); 661 VERIFY( (m2 == m1.unaryExpr(arithmetic_shift_right<9>())).all() ); 662 } 663 664 EIGEN_DECLARE_TEST(array_cwise) 665 { 666 for(int i = 0; i < g_repeat; i++) { 667 CALL_SUBTEST_1( array(Array<float, 1, 1>()) ); 668 CALL_SUBTEST_2( array(Array22f()) ); 669 CALL_SUBTEST_3( array(Array44d()) ); 670 CALL_SUBTEST_4( array(ArrayXXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 671 CALL_SUBTEST_5( array(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 672 CALL_SUBTEST_6( array(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 673 CALL_SUBTEST_6( array(Array<Index,Dynamic,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 674 CALL_SUBTEST_6( array_integer(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 675 CALL_SUBTEST_6( array_integer(Array<Index,Dynamic,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 676 } 677 for(int i = 0; i < g_repeat; i++) { 678 CALL_SUBTEST_1( comparisons(Array<float, 1, 1>()) ); 679 CALL_SUBTEST_2( comparisons(Array22f()) ); 680 CALL_SUBTEST_3( comparisons(Array44d()) ); 681 CALL_SUBTEST_5( comparisons(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 682 CALL_SUBTEST_6( comparisons(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 683 } 684 for(int i = 0; i < g_repeat; i++) { 685 CALL_SUBTEST_1( min_max(Array<float, 1, 1>()) ); 686 CALL_SUBTEST_2( min_max(Array22f()) ); 687 CALL_SUBTEST_3( min_max(Array44d()) ); 688 CALL_SUBTEST_5( min_max(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 689 CALL_SUBTEST_6( min_max(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 690 } 691 for(int i = 0; i < g_repeat; i++) { 692 CALL_SUBTEST_1( array_real(Array<float, 1, 1>()) ); 693 CALL_SUBTEST_2( array_real(Array22f()) ); 694 CALL_SUBTEST_3( array_real(Array44d()) ); 695 CALL_SUBTEST_5( array_real(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 696 CALL_SUBTEST_7( array_real(Array<Eigen::half, 32, 32>()) ); 697 CALL_SUBTEST_8( array_real(Array<Eigen::bfloat16, 32, 32>()) ); 698 } 699 for(int i = 0; i < g_repeat; i++) { 700 CALL_SUBTEST_4( array_complex(ArrayXXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 701 } 702 703 VERIFY((internal::is_same< internal::global_math_functions_filtering_base<int>::type, int >::value)); 704 VERIFY((internal::is_same< internal::global_math_functions_filtering_base<float>::type, float >::value)); 705 VERIFY((internal::is_same< internal::global_math_functions_filtering_base<Array2i>::type, ArrayBase<Array2i> >::value)); 706 typedef CwiseUnaryOp<internal::scalar_abs_op<double>, ArrayXd > Xpr; 707 VERIFY((internal::is_same< internal::global_math_functions_filtering_base<Xpr>::type, 708 ArrayBase<Xpr> 709 >::value)); 710 }