1namespace Eigen { 2 3/** \eigenManualPage CoeffwiseMathFunctions Catalog of coefficient-wise math functions 4 5 6<!-- <span style="font-size:300%; color:red; font-weight: 900;">!WORK IN PROGRESS!</span> --> 7 8This table presents a catalog of the coefficient-wise math functions supported by %Eigen. 9In this table, \c a, \c b, refer to Array objects or expressions, and \c m refers to a linear algebra Matrix/Vector object. Standard scalar types are abbreviated as follows: 10 - \c int: \c i32 11 - \c float: \c f 12 - \c double: \c d 13 - \c std::complex<float>: \c cf 14 - \c std::complex<double>: \c cd 15 16For each row, the first column list the equivalent calls for arrays, and matrices when supported. Of course, all functions are available for matrices by first casting it as an array: \c m.array(). 17 18The third column gives some hints in the underlying scalar implementation. In most cases, %Eigen does not implement itself the math function but relies on the STL for standard scalar types, or user-provided functions for custom scalar types. 19For instance, some simply calls the respective function of the STL while preserving <a href="http://en.cppreference.com/w/cpp/language/adl">argument-dependent lookup</a> for custom types. 20The following: 21\code 22using std::foo; 23foo(a[i]); 24\endcode 25means that the STL's function \c std::foo will be potentially called if it is compatible with the underlying scalar type. If not, then the user must ensure that an overload of the function foo is available for the given scalar type (usually defined in the same namespace as the given scalar type). 26This also means that, unless specified, if the function \c std::foo is available only in some recent c++ versions (e.g., c++11), then the respective %Eigen's function/method will be usable on standard types only if the compiler support the required c++ version. 27 28<table class="manual-hl"> 29<tr> 30<th>API</th><th>Description</th><th>Default scalar implementation</th><th>SIMD</th> 31</tr> 32<tr><td colspan="4"></td></tr> 33<tr><th colspan="4">Basic operations</th></tr> 34<tr> 35 <td class="code"> 36 \anchor cwisetable_abs 37 a.\link ArrayBase::abs abs\endlink(); \n 38 \link Eigen::abs abs\endlink(a); \n 39 m.\link MatrixBase::cwiseAbs cwiseAbs\endlink(); 40 </td> 41 <td>absolute value (\f$ |a_i| \f$) </td> 42 <td class="code"> 43 using <a href="http://en.cppreference.com/w/cpp/numeric/math/fabs">std::abs</a>; \n 44 abs(a[i]); 45 </td> 46 <td>SSE2, AVX (i32,f,d)</td> 47</tr> 48<tr> 49 <td class="code"> 50 \anchor cwisetable_inverse 51 a.\link ArrayBase::inverse inverse\endlink(); \n 52 \link Eigen::inverse inverse\endlink(a); \n 53 m.\link MatrixBase::cwiseInverse cwiseInverse\endlink(); 54 </td> 55 <td>inverse value (\f$ 1/a_i \f$) </td> 56 <td class="code"> 57 1/a[i]; 58 </td> 59 <td>All engines (f,d,fc,fd)</td> 60</tr> 61<tr> 62 <td class="code"> 63 \anchor cwisetable_conj 64 a.\link ArrayBase::conjugate conjugate\endlink(); \n 65 \link Eigen::conj conj\endlink(a); \n 66 m.\link MatrixBase::conjugate conjugate(); 67 </td> 68 <td><a href="https://en.wikipedia.org/wiki/Complex_conjugate">complex conjugate</a> (\f$ \bar{a_i} \f$),\n 69 no-op for real </td> 70 <td class="code"> 71 using <a href="http://en.cppreference.com/w/cpp/numeric/complex/conj">std::conj</a>; \n 72 conj(a[i]); 73 </td> 74 <td>All engines (fc,fd)</td> 75</tr> 76<tr> 77<th colspan="4">Exponential functions</th> 78</tr> 79<tr> 80 <td class="code"> 81 \anchor cwisetable_exp 82 a.\link ArrayBase::exp exp\endlink(); \n 83 \link Eigen::exp exp\endlink(a); 84 </td> 85 <td>\f$ e \f$ raised to the given power (\f$ e^{a_i} \f$) </td> 86 <td class="code"> 87 using <a href="http://en.cppreference.com/w/cpp/numeric/math/exp">std::exp</a>; \n 88 exp(a[i]); 89 </td> 90 <td>SSE2, AVX (f,d)</td> 91</tr> 92<tr> 93 <td class="code"> 94 \anchor cwisetable_log 95 a.\link ArrayBase::log log\endlink(); \n 96 \link Eigen::log log\endlink(a); 97 </td> 98 <td>natural (base \f$ e \f$) logarithm (\f$ \ln({a_i}) \f$)</td> 99 <td class="code"> 100 using <a href="http://en.cppreference.com/w/cpp/numeric/math/log">std::log</a>; \n 101 log(a[i]); 102 </td> 103 <td>SSE2, AVX (f)</td> 104</tr> 105<tr> 106 <td class="code"> 107 \anchor cwisetable_log1p 108 a.\link ArrayBase::log1p log1p\endlink(); \n 109 \link Eigen::log1p log1p\endlink(a); 110 </td> 111 <td>natural (base \f$ e \f$) logarithm of 1 plus \n the given number (\f$ \ln({1+a_i}) \f$)</td> 112 <td>built-in generic implementation based on \c log,\n 113 plus \c using <a href="http://en.cppreference.com/w/cpp/numeric/math/log1p">\c std::log1p </a>; \cpp11</td> 114 <td></td> 115</tr> 116<tr> 117 <td class="code"> 118 \anchor cwisetable_log10 119 a.\link ArrayBase::log10 log10\endlink(); \n 120 \link Eigen::log10 log10\endlink(a); 121 </td> 122 <td>base 10 logarithm (\f$ \log_{10}({a_i}) \f$)</td> 123 <td class="code"> 124 using <a href="http://en.cppreference.com/w/cpp/numeric/math/log10">std::log10</a>; \n 125 log10(a[i]); 126 </td> 127 <td></td> 128</tr> 129<tr> 130<th colspan="4">Power functions</th> 131</tr> 132<tr> 133 <td class="code"> 134 \anchor cwisetable_pow 135 a.\link ArrayBase::pow pow\endlink(b); \n 136 \link Eigen::pow pow\endlink(a,b); 137 </td> 138 <td>raises a number to the given power (\f$ a_i ^ {b_i} \f$) \n \c a and \c b can be either an array or scalar.</td> 139 <td class="code"> 140 using <a href="http://en.cppreference.com/w/cpp/numeric/math/pow">std::pow</a>; \n 141 pow(a[i],b[i]);\n 142 (plus builtin for integer types)</td> 143 <td></td> 144</tr> 145<tr> 146 <td class="code"> 147 \anchor cwisetable_sqrt 148 a.\link ArrayBase::sqrt sqrt\endlink(); \n 149 \link Eigen::sqrt sqrt\endlink(a);\n 150 m.\link MatrixBase::cwiseSqrt cwiseSqrt\endlink(); 151 </td> 152 <td>computes square root (\f$ \sqrt a_i \f$)</td> 153 <td class="code"> 154 using <a href="http://en.cppreference.com/w/cpp/numeric/math/sqrt">std::sqrt</a>; \n 155 sqrt(a[i]);</td> 156 <td>SSE2, AVX (f,d)</td> 157</tr> 158<tr> 159 <td class="code"> 160 \anchor cwisetable_rsqrt 161 a.\link ArrayBase::rsqrt rsqrt\endlink(); \n 162 \link Eigen::rsqrt rsqrt\endlink(a); 163 </td> 164 <td><a href="https://en.wikipedia.org/wiki/Fast_inverse_square_root">reciprocal square root</a> (\f$ 1/{\sqrt a_i} \f$)</td> 165 <td class="code"> 166 using <a href="http://en.cppreference.com/w/cpp/numeric/math/sqrt">std::sqrt</a>; \n 167 1/sqrt(a[i]); \n 168 </td> 169 <td>SSE2, AVX, AltiVec, ZVector (f,d)\n 170 (approx + 1 Newton iteration)</td> 171</tr> 172<tr> 173 <td class="code"> 174 \anchor cwisetable_square 175 a.\link ArrayBase::square square\endlink(); \n 176 \link Eigen::square square\endlink(a); 177 </td> 178 <td>computes square power (\f$ a_i^2 \f$)</td> 179 <td class="code"> 180 a[i]*a[i]</td> 181 <td>All (i32,f,d,cf,cd)</td> 182</tr> 183<tr> 184 <td class="code"> 185 \anchor cwisetable_cube 186 a.\link ArrayBase::cube cube\endlink(); \n 187 \link Eigen::cube cube\endlink(a); 188 </td> 189 <td>computes cubic power (\f$ a_i^3 \f$)</td> 190 <td class="code"> 191 a[i]*a[i]*a[i]</td> 192 <td>All (i32,f,d,cf,cd)</td> 193</tr> 194<tr> 195 <td class="code"> 196 \anchor cwisetable_abs2 197 a.\link ArrayBase::abs2 abs2\endlink(); \n 198 \link Eigen::abs2 abs2\endlink(a);\n 199 m.\link MatrixBase::cwiseAbs2 cwiseAbs2\endlink(); 200 </td> 201 <td>computes the squared absolute value (\f$ |a_i|^2 \f$)</td> 202 <td class="code"> 203 real: a[i]*a[i] \n 204 complex: real(a[i])*real(a[i]) \n 205 + imag(a[i])*imag(a[i])</td> 206 <td>All (i32,f,d)</td> 207</tr> 208<tr> 209<th colspan="4">Trigonometric functions</th> 210</tr> 211<tr> 212 <td class="code"> 213 \anchor cwisetable_sin 214 a.\link ArrayBase::sin sin\endlink(); \n 215 \link Eigen::sin sin\endlink(a); 216 </td> 217 <td>computes sine</td> 218 <td class="code"> 219 using <a href="http://en.cppreference.com/w/cpp/numeric/math/sin">std::sin</a>; \n 220 sin(a[i]);</td> 221 <td>SSE2, AVX (f)</td> 222</tr> 223<tr> 224 <td class="code"> 225 \anchor cwisetable_cos 226 a.\link ArrayBase::cos cos\endlink(); \n 227 \link Eigen::cos cos\endlink(a); 228 </td> 229 <td>computes cosine</td> 230 <td class="code"> 231 using <a href="http://en.cppreference.com/w/cpp/numeric/math/cos">std::cos</a>; \n 232 cos(a[i]);</td> 233 <td>SSE2, AVX (f)</td> 234</tr> 235<tr> 236 <td class="code"> 237 \anchor cwisetable_tan 238 a.\link ArrayBase::tan tan\endlink(); \n 239 \link Eigen::tan tan\endlink(a); 240 </td> 241 <td>computes tangent</td> 242 <td class="code"> 243 using <a href="http://en.cppreference.com/w/cpp/numeric/math/tan">std::tan</a>; \n 244 tan(a[i]);</td> 245 <td></td> 246</tr> 247<tr> 248 <td class="code"> 249 \anchor cwisetable_asin 250 a.\link ArrayBase::asin asin\endlink(); \n 251 \link Eigen::asin asin\endlink(a); 252 </td> 253 <td>computes arc sine (\f$ \sin^{-1} a_i \f$)</td> 254 <td class="code"> 255 using <a href="http://en.cppreference.com/w/cpp/numeric/math/asin">std::asin</a>; \n 256 asin(a[i]);</td> 257 <td></td> 258</tr> 259<tr> 260 <td class="code"> 261 \anchor cwisetable_acos 262 a.\link ArrayBase::acos acos\endlink(); \n 263 \link Eigen::acos acos\endlink(a); 264 </td> 265 <td>computes arc cosine (\f$ \cos^{-1} a_i \f$)</td> 266 <td class="code"> 267 using <a href="http://en.cppreference.com/w/cpp/numeric/math/acos">std::acos</a>; \n 268 acos(a[i]);</td> 269 <td></td> 270</tr> 271<tr> 272 <td class="code"> 273 \anchor cwisetable_atan 274 a.\link ArrayBase::atan tan\endlink(); \n 275 \link Eigen::atan atan\endlink(a); 276 </td> 277 <td>computes arc tangent (\f$ \tan^{-1} a_i \f$)</td> 278 <td class="code"> 279 using <a href="http://en.cppreference.com/w/cpp/numeric/math/atan">std::atan</a>; \n 280 atan(a[i]);</td> 281 <td></td> 282</tr> 283<tr> 284<th colspan="4">Hyperbolic functions</th> 285</tr> 286<tr> 287 <td class="code"> 288 \anchor cwisetable_sinh 289 a.\link ArrayBase::sinh sinh\endlink(); \n 290 \link Eigen::sinh sinh\endlink(a); 291 </td> 292 <td>computes hyperbolic sine</td> 293 <td class="code"> 294 using <a href="http://en.cppreference.com/w/cpp/numeric/math/sinh">std::sinh</a>; \n 295 sinh(a[i]);</td> 296 <td></td> 297</tr> 298<tr> 299 <td class="code"> 300 \anchor cwisetable_cosh 301 a.\link ArrayBase::cosh cohs\endlink(); \n 302 \link Eigen::cosh cosh\endlink(a); 303 </td> 304 <td>computes hyperbolic cosine</td> 305 <td class="code"> 306 using <a href="http://en.cppreference.com/w/cpp/numeric/math/cosh">std::cosh</a>; \n 307 cosh(a[i]);</td> 308 <td></td> 309</tr> 310<tr> 311 <td class="code"> 312 \anchor cwisetable_tanh 313 a.\link ArrayBase::tanh tanh\endlink(); \n 314 \link Eigen::tanh tanh\endlink(a); 315 </td> 316 <td>computes hyperbolic tangent</td> 317 <td class="code"> 318 using <a href="http://en.cppreference.com/w/cpp/numeric/math/tanh">std::tanh</a>; \n 319 tanh(a[i]);</td> 320 <td></td> 321</tr> 322<tr> 323<th colspan="4">Nearest integer floating point operations</th> 324</tr> 325<tr> 326 <td class="code"> 327 \anchor cwisetable_ceil 328 a.\link ArrayBase::ceil ceil\endlink(); \n 329 \link Eigen::ceil ceil\endlink(a); 330 </td> 331 <td>nearest integer not less than the given value</td> 332 <td class="code"> 333 using <a href="http://en.cppreference.com/w/cpp/numeric/math/ceil">std::ceil</a>; \n 334 ceil(a[i]);</td> 335 <td>SSE4,AVX,ZVector (f,d)</td> 336</tr> 337<tr> 338 <td class="code"> 339 \anchor cwisetable_floor 340 a.\link ArrayBase::floor floor\endlink(); \n 341 \link Eigen::floor floor\endlink(a); 342 </td> 343 <td>nearest integer not greater than the given value</td> 344 <td class="code"> 345 using <a href="http://en.cppreference.com/w/cpp/numeric/math/floor">std::floor</a>; \n 346 floor(a[i]);</td> 347 <td>SSE4,AVX,ZVector (f,d)</td> 348</tr> 349<tr> 350 <td class="code"> 351 \anchor cwisetable_round 352 a.\link ArrayBase::round round\endlink(); \n 353 \link Eigen::round round\endlink(a); 354 </td> 355 <td>nearest integer, \n rounding away from zero in halfway cases</td> 356 <td>built-in generic implementation \n based on \c floor and \c ceil,\n 357 plus \c using <a href="http://en.cppreference.com/w/cpp/numeric/math/round">\c std::round </a>; \cpp11</td> 358 <td>SSE4,AVX,ZVector (f,d)</td> 359</tr> 360<tr> 361<th colspan="4">Floating point manipulation functions</th> 362</tr> 363<tr> 364<th colspan="4">Classification and comparison</th> 365</tr> 366<tr> 367 <td class="code"> 368 \anchor cwisetable_isfinite 369 a.\link ArrayBase::isFinite isFinite\endlink(); \n 370 \link Eigen::isfinite isfinite\endlink(a); 371 </td> 372 <td>checks if the given number has finite value</td> 373 <td>built-in generic implementation,\n 374 plus \c using <a href="http://en.cppreference.com/w/cpp/numeric/math/isfinite">\c std::isfinite </a>; \cpp11</td> 375 <td></td> 376</tr> 377<tr> 378 <td class="code"> 379 \anchor cwisetable_isinf 380 a.\link ArrayBase::isInf isInf\endlink(); \n 381 \link Eigen::isinf isinf\endlink(a); 382 </td> 383 <td>checks if the given number is infinite</td> 384 <td>built-in generic implementation,\n 385 plus \c using <a href="http://en.cppreference.com/w/cpp/numeric/math/isinf">\c std::isinf </a>; \cpp11</td> 386 <td></td> 387</tr> 388<tr> 389 <td class="code"> 390 \anchor cwisetable_isnan 391 a.\link ArrayBase::isNaN isNaN\endlink(); \n 392 \link Eigen::isnan isnan\endlink(a); 393 </td> 394 <td>checks if the given number is not a number</td> 395 <td>built-in generic implementation,\n 396 plus \c using <a href="http://en.cppreference.com/w/cpp/numeric/math/isnan">\c std::isnan </a>; \cpp11</td> 397 <td></td> 398</tr> 399<tr> 400<th colspan="4">Error and gamma functions</th> 401</tr> 402<tr> <td colspan="4"> Require \c \#include \c <unsupported/Eigen/SpecialFunctions> </td></tr> 403<tr> 404 <td class="code"> 405 \anchor cwisetable_erf 406 a.\link ArrayBase::erf erf\endlink(); \n 407 \link Eigen::erf erf\endlink(a); 408 </td> 409 <td>error function</td> 410 <td class="code"> 411 using <a href="http://en.cppreference.com/w/cpp/numeric/math/erf">std::erf</a>; \cpp11 \n 412 erf(a[i]); 413 </td> 414 <td></td> 415</tr> 416<tr> 417 <td class="code"> 418 \anchor cwisetable_erfc 419 a.\link ArrayBase::erfc erfc\endlink(); \n 420 \link Eigen::erfc erfc\endlink(a); 421 </td> 422 <td>complementary error function</td> 423 <td class="code"> 424 using <a href="http://en.cppreference.com/w/cpp/numeric/math/erfc">std::erfc</a>; \cpp11 \n 425 erfc(a[i]); 426 </td> 427 <td></td> 428</tr> 429<tr> 430 <td class="code"> 431 \anchor cwisetable_lgamma 432 a.\link ArrayBase::lgamma lgamma\endlink(); \n 433 \link Eigen::lgamma lgamma\endlink(a); 434 </td> 435 <td>natural logarithm of the gamma function</td> 436 <td class="code"> 437 using <a href="http://en.cppreference.com/w/cpp/numeric/math/lgamma">std::lgamma</a>; \cpp11 \n 438 lgamma(a[i]); 439 </td> 440 <td></td> 441</tr> 442<tr> 443 <td class="code"> 444 \anchor cwisetable_digamma 445 a.\link ArrayBase::digamma digamma\endlink(); \n 446 \link Eigen::digamma digamma\endlink(a); 447 </td> 448 <td><a href="https://en.wikipedia.org/wiki/Digamma_function">logarithmic derivative of the gamma function</a></td> 449 <td> 450 built-in for float and double 451 </td> 452 <td></td> 453</tr> 454<tr> 455 <td class="code"> 456 \anchor cwisetable_igamma 457 \link Eigen::igamma igamma\endlink(a,x); 458 </td> 459 <td><a href="https://en.wikipedia.org/wiki/Incomplete_gamma_function">lower incomplete gamma integral</a> 460 \n \f$ \gamma(a_i,x_i)= \frac{1}{|a_i|} \int_{0}^{x_i}e^{\text{-}t} t^{a_i-1} \mathrm{d} t \f$</td> 461 <td> 462 built-in for float and double,\n but requires \cpp11 463 </td> 464 <td></td> 465</tr> 466<tr> 467 <td class="code"> 468 \anchor cwisetable_igammac 469 \link Eigen::igammac igammac\endlink(a,x); 470 </td> 471 <td><a href="https://en.wikipedia.org/wiki/Incomplete_gamma_function">upper incomplete gamma integral</a> 472 \n \f$ \Gamma(a_i,x_i) = \frac{1}{|a_i|} \int_{x_i}^{\infty}e^{\text{-}t} t^{a_i-1} \mathrm{d} t \f$</td> 473 <td> 474 built-in for float and double,\n but requires \cpp11 475 </td> 476 <td></td> 477</tr> 478<tr> 479<th colspan="4">Special functions</th> 480</tr> 481<tr> <td colspan="4"> Require \c \#include \c <unsupported/Eigen/SpecialFunctions> </td></tr> 482<tr> 483 <td class="code"> 484 \anchor cwisetable_polygamma 485 \link Eigen::polygamma polygamma\endlink(n,x); 486 </td> 487 <td><a href="https://en.wikipedia.org/wiki/Polygamma_function">n-th derivative of digamma at x</a></td> 488 <td> 489 built-in generic based on\n <a href="#cwisetable_lgamma">\c lgamma </a>, 490 <a href="#cwisetable_digamma"> \c digamma </a> 491 and <a href="#cwisetable_zeta">\c zeta </a>. 492 </td> 493 <td></td> 494</tr> 495<tr> 496 <td class="code"> 497 \anchor cwisetable_betainc 498 \link Eigen::betainc betainc\endlink(a,b,x); 499 </td> 500 <td><a href="https://en.wikipedia.org/wiki/Beta_function#Incomplete_beta_function">Incomplete beta function</a></td> 501 <td> 502 built-in for float and double,\n but requires \cpp11 503 </td> 504 <td></td> 505</tr> 506<tr> 507 <td class="code"> 508 \anchor cwisetable_zeta 509 \link Eigen::zeta zeta\endlink(a,b); 510 </td> 511 <td><a href="https://en.wikipedia.org/wiki/Hurwitz_zeta_function">Hurwitz zeta function</a> 512 \n \f$ \zeta(a_i,b_i)=\sum_{k=0}^{\infty}(b_i+k)^{\text{-}a_i} \f$</td> 513 <td> 514 built-in for float and double 515 </td> 516 <td></td> 517</tr> 518<tr><td colspan="4"></td></tr> 519</table> 520 521\n 522 523*/ 524 525} 526