nifty_simple_math.py 10.9 KB
 Ultimanet committed Jun 11, 2015 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 ``````## NIFTY (Numerical Information Field Theory) has been developed at the ## Max-Planck-Institute for Astrophysics. ## ## Copyright (C) 2013 Max-Planck-Society ## ## Author: Marco Selig ## Project homepage: ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. ## See the GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ##----------------------------------------------------------------------------- import numpy as np #from nifty.nifty_core import field `````` Ultima committed Sep 10, 2015 26 ``````from keepers import about `````` Ultimanet committed Jun 11, 2015 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 `````` def _math_helper(x, function): try: return x.apply_scalar_function(function) except(AttributeError): return function(np.array(x)) def cos(x): """ Returns the cos of a given object. Parameters ---------- x : {scalar, list, array, field} Input argument. Returns ------- cosx : {scalar, array, field} Cosine of `x` to the specified base. See Also -------- sin tan Examples -------- >>> cos([-1,1]) array([ 0.54030231, 0.54030231]) >>> cos(field(point_space(2), val=[10, 100])).val array([ 0.54030231, 0.54030231]) """ return _math_helper(x, np.cos) `````` Ultima committed Sep 10, 2015 62 `````` `````` Ultimanet committed Jun 11, 2015 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 ``````def sin(x): """ Returns the sine of a given object. Parameters ---------- x : {scalar, list, array, field} Input argument. Returns ------- sinx : {scalar, array, field} Sine of `x` to the specified base. See Also -------- cos tan Examples -------- >>> sin([-1,1]) array([-0.84147098, 0.84147098]) >>> sin(field(point_space(2), val=[-1, 1])).val array([-0.84147098, 0.84147098]) """ return _math_helper(x, np.sin) `````` Ultima committed Sep 10, 2015 91 `````` `````` Ultimanet committed Jun 11, 2015 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 ``````def cosh(x): """ Returns the hyperbolic cosine of a given object. Parameters ---------- x : {scalar, list, array, field} Input argument. Returns ------- coshx : {scalar, array, field} cosh of `x` to the specified base. See Also -------- sinh tanh Examples -------- >>> cosh([-1,1]) array([ 1.54308063, 1.54308063]) >>> cosh(field(point_space(2), val=[-1, 1])).val array([ 1.54308063, 1.54308063]) """ return _math_helper(x, np.cosh) def sinh(x): """ Returns the hyperbolic sine of a given object. Parameters ---------- x : {scalar, list, array, field} Input argument. Returns ------- sinhx : {scalar, array, field} sinh of `x` to the specified base. See Also -------- cosh tanh Examples -------- >>> sinh([-1,1]) array([-1.17520119, 1.17520119]) >>> sinh(field(point_space(2), val=[-1, 1])).val array([-1.17520119, 1.17520119]) """ return _math_helper(x, np.sinh) def tan(x): """ Returns the tangent of a given object. Parameters ---------- x : {scalar, list, array, field} Input argument. Returns ------- tanx : {scalar, array, field} Tangent of `x` to the specified base. See Also -------- cos sin Examples -------- >>> tan([10,100]) array([ 0.64836083, -0.58721392]) >>> tan(field(point_space(2), val=[10, 100])).val array([ 0.64836083, -0.58721392]) """ return _math_helper(x, np.tan) def tanh(x): """ Returns the hyperbolic tangent of a given object. Parameters ---------- x : {scalar, list, array, field} Input argument. Returns ------- tanhx : {scalar, array, field} tanh of `x` to the specified base. See Also -------- cosh sinh Examples -------- >>> tanh([-1,1]) array([-0.76159416, 0.76159416]) >>> tanh(field(point_space(2), val=[-1, 1])).val array([-0.76159416, 0.76159416]) """ return _math_helper(x, np.tanh) def arccos(x): """ Returns the arccosine of a given object. Parameters ---------- x : {scalar, list, array, field} Input argument. Returns ------- arccosx : {scalar, array, field} arccos of `x` to the specified base. See Also -------- arcsin arctan Examples -------- >>> arccos([-1,1]) array([ 3.14159265, 0. ]) >>> arccos(field(point_space(2), val=[-1, 1])).val array([ 3.14159265, 0. ]) """ return _math_helper(x, np.arccos) def arcsin(x): """ Returns the arcsine of a given object. Parameters ---------- x : {scalar, list, array, field} Input argument. Returns ------- arcsinx : {scalar, array, field} Logarithm of `x` to the specified base. See Also -------- arccos arctan Examples -------- >>> arcsin([-1,1]) array([-1.57079633, 1.57079633]) >>> arcsin(field(point_space(2), val=[-1, 1])).val array([-1.57079633, 1.57079633]) """ return _math_helper(x, np.arcsin) def arccosh(x): """ Returns the hyperbolic arccos of a given object. Parameters ---------- x : {scalar, list, array, field} Input argument. Returns ------- arccoshx : {scalar, array, field} arccos of `x` to the specified base. See Also -------- arcsinh arctanh Examples -------- >>> arcosh([1,10]) array([ 0. , 2.99322285]) >>> arccosh(field(point_space(2), val=[1, 10])).val array([ 0. , 2.99322285]) """ return _math_helper(x, np.arccosh) def arcsinh(x): """ Returns the hypberbolic sin of a given object. Parameters ---------- x : {scalar, list, array, field} Input argument. Returns ------- arcsinhx : {scalar, array, field} arcsinh of `x` to the specified base. See Also -------- arccosh arctanh Examples -------- >>> arcsinh([1,10]) array([ 0.88137359, 2.99822295]) >>> arcsinh(field(point_space(2), val=[1, 10])).val array([ 0.88137359, 2.99822295]) """ return _math_helper(x, np.arcsinh) def arctan(x): """ Returns the arctan of a given object. Parameters ---------- x : {scalar, list, array, field} Input argument. Returns ------- arctanx : {scalar, array, field} arctan of `x` to the specified base. See Also -------- arccos arcsin Examples -------- >>> arctan([1,10]) array([ 0.78539816, 1.47112767]) >>> arctan(field(point_space(2), val=[1, 10])).val array([ 0.78539816, 1.47112767]) """ return _math_helper(x, np.arctan) def arctanh(x): """ Returns the hyperbolic arc tangent of a given object. Parameters ---------- x : {scalar, list, array, field} Input argument. Returns ------- arctanhx : {scalar, array, field} arctanh of `x` to the specified base. See Also -------- arccosh arcsinh Examples -------- >>> arctanh([0,0.5]) array([ 0. , 0.54930614]) >>> arctanh(field(point_space(2), val=[0, 0.5])).val array([ 0. , 0.54930614]) """ return _math_helper(x, np.arctanh) def sqrt(x): """ Returns the square root of a given object. Parameters ---------- x : {scalar, list, array, field} Input argument. Returns ------- sqrtx : {scalar, array, field} Square root of `x`. Examples -------- >>> sqrt([10,100]) array([ 10. , 31.6227766]) >>> sqrt(field(point_space(2), val=[10, 100])).val array([ 10. , 31.6227766]) """ return _math_helper(x, np.sqrt) def exp(x): """ Returns the exponential of a given object. Parameters ---------- x : {scalar, list, array, field} Input argument. Returns ------- expx : {scalar, array, field} Exponential of `x` to the specified base. See Also -------- log Examples -------- >>> exp([10,100]) array([ 2.20264658e+04, 2.68811714e+43]) >>> exp(field(point_space(2), val=[10, 100])).val array([ 2.20264658e+04, 2.68811714e+43]) """ return _math_helper(x, np.exp) def log(x,base=None): """ Returns the logarithm with respect to a specified base. Parameters ---------- x : {scalar, list, array, field} Input argument. base : {scalar, list, array, field}, *optional* Base of the logarithm (default: Euler's number). Returns ------- logx : {scalar, array, field} Logarithm of `x` to the specified base. See Also -------- exp Examples -------- >>> log([100, 1000], base=10) array([ 2., 3.]) >>> log(field(point_space(2), val=[100, 1000]), base=10).val array([ 2., 3.]) """ if(base is None): return _math_helper(x, np.log) base = np.array(base) if(np.all(base>0)): return _math_helper(x, np.log)/np.log(base) else: raise ValueError(about._errors.cstring("ERROR: invalid input basis.")) def conjugate(x): """ Computes the complex conjugate of a given object. Parameters ---------- x : {ndarray, field} The object to be complex conjugated. Returns ------- conjx : {ndarray,field} The complex conjugated object. `````` Ultima committed Sep 10, 2015 483 `````` """ `````` Ultimanet committed Jun 11, 2015 484 485 `````` return _math_helper(x, np.conjugate) `````` Ultima committed Jul 21, 2015 486 `````` `````` Ultima committed Sep 10, 2015 487 488 `````` `````` Ultimanet committed Jun 11, 2015 489 490 `````` ##---------------------------------``````