nifty_rg.py 55.7 KB
 Marco Selig committed Jan 30, 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 26 27 28 29 30 ## NIFTY (Numerical Information Field Theory) has been developed at the ## Max-Planck-Institute for Astrophysics. ## ## Copyright (C) 2015 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 . """ .. __ ____ __ .. /__/ / _/ / /_ .. __ ___ __ / /_ / _/ __ __ .. / _ | / / / _/ / / / / / / .. / / / / / / / / / /_ / /_/ / .. /__/ /__/ /__/ /__/ \___/ \___ / rg .. /______/  Marco Selig committed Feb 03, 2015 31  NIFTY submodule for regular Cartesian grids.  Marco Selig committed Jan 30, 2015 32 33 34 35 36 37 38 39 40 41 42 43 44 45  """ from __future__ import division #from nifty import * import os import numpy as np import pylab as pl from matplotlib.colors import LogNorm as ln from matplotlib.ticker import LogFormatter as lf from nifty.nifty_core import about, \ random, \ space, \ field import nifty.smoothing as gs  Marco Selig committed Jan 30, 2015 46 import powerspectrum as gp  ultimanet committed Feb 05, 2015 47 '''  Marco Selig committed Jan 30, 2015 48 49 50 51 52 try: import gfft as gf except(ImportError): about.infos.cprint('INFO: "plain" gfft version 0.1.0') import gfft_rg as gf  ultimanet committed Feb 05, 2015 53 54 55 ''' import fft_rg  Marco Selig committed Jan 30, 2015 56 57 58 59 60 61 62 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 91 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  ##----------------------------------------------------------------------------- class rg_space(space): """ .. _____ _______ .. / __/ / _ / .. / / / /_/ / .. /__/ \____ / space class .. /______/ NIFTY subclass for spaces of regular Cartesian grids. Parameters ---------- num : {int, numpy.ndarray} Number of gridpoints or numbers of gridpoints along each axis. naxes : int, *optional* Number of axes (default: None). zerocenter : {bool, numpy.ndarray}, *optional* Whether the Fourier zero-mode is located in the center of the grid (or the center of each axis speparately) or not (default: True). hermitian : bool, *optional* Whether the fields living in the space follow hermitian symmetry or not (default: True). purelyreal : bool, *optional* Whether the field values are purely real (default: True). dist : {float, numpy.ndarray}, *optional* Distance between two grid points along each axis (default: None). fourier : bool, *optional* Whether the space represents a Fourier or a position grid (default: False). Notes ----- Only even numbers of grid points per axis are supported. The basis transformations between position x and Fourier mode k rely on (inverse) fast Fourier transformations using the :math:exp(2 \pi i k^\dagger x)-formulation. Attributes ---------- para : numpy.ndarray One-dimensional array containing information on the axes of the space in the following form: The first entries give the grid-points along each axis in reverse order; the next entry is 0 if the fields defined on the space are purely real-valued, 1 if they are hermitian and complex, and 2 if they are not hermitian, but complex-valued; the last entries hold the information on whether the axes are centered on zero or not, containing a one for each zero-centered axis and a zero for each other one, in reverse order. datatype : numpy.dtype Data type of the field values for a field defined on this space, either numpy.float64 or numpy.complex128. discrete : bool Whether or not the underlying space is discrete, always False for regular grids. vol : numpy.ndarray One-dimensional array containing the distances between two grid points along each axis, in reverse order. By default, the total length of each axis is assumed to be one. fourier : bool Whether or not the grid represents a Fourier basis. """ epsilon = 0.0001 ## relative precision for comparisons def __init__(self,num,naxes=None,zerocenter=True,hermitian=True,purelyreal=True,dist=None,fourier=False): """ Sets the attributes for an rg_space class instance. Parameters ---------- num : {int, numpy.ndarray} Number of gridpoints or numbers of gridpoints along each axis. naxes : int, *optional* Number of axes (default: None). zerocenter : {bool, numpy.ndarray}, *optional* Whether the Fourier zero-mode is located in the center of the grid (or the center of each axis speparately) or not (default: True). hermitian : bool, *optional* Whether the fields living in the space follow hermitian symmetry or not (default: True). purelyreal : bool, *optional* Whether the field values are purely real (default: True). dist : {float, numpy.ndarray}, *optional* Distance between two grid points along each axis (default: None). fourier : bool, *optional* Whether the space represents a Fourier or a position grid (default: False). Returns ------- None """ ## check parameters para = np.array([],dtype=np.int) if(np.isscalar(num)): num = np.array([num],dtype=np.int) else: num = np.array(num,dtype=np.int) if(np.any(num%2)): ## module restriction raise ValueError(about._errors.cstring("ERROR: unsupported odd number of grid points.")) if(naxes is None): naxes = np.size(num) elif(np.size(num)==1): num = num*np.ones(naxes,dtype=np.int,order='C') elif(np.size(num)!=naxes): raise ValueError(about._errors.cstring("ERROR: size mismatch ( "+str(np.size(num))+" <> "+str(naxes)+" ).")) para = np.append(para,num[::-1],axis=None) para = np.append(para,2-(bool(hermitian) or bool(purelyreal))-bool(purelyreal),axis=None) ## {0,1,2} if(np.isscalar(zerocenter)): zerocenter = bool(zerocenter)*np.ones(naxes,dtype=np.int,order='C') else: zerocenter = np.array(zerocenter,dtype=np.bool) if(np.size(zerocenter)==1): zerocenter = zerocenter*np.ones(naxes,dtype=np.int,order='C') elif(np.size(zerocenter)!=naxes): raise ValueError(about._errors.cstring("ERROR: size mismatch ( "+str(np.size(zerocenter))+" <> "+str(naxes)+" ).")) para = np.append(para,zerocenter[::-1]*-1,axis=None) ## -1 XOR 0 (centered XOR not) self.para = para ## set data type if(not self.para[naxes]): self.datatype = np.float64 else: self.datatype = np.complex128 self.discrete = False ## set volume if(dist is None): dist = 1/num.astype(self.datatype) elif(np.isscalar(dist)): dist = self.datatype(dist)*np.ones(naxes,dtype=self.datatype,order='C') else: dist = np.array(dist,dtype=self.datatype) if(np.size(dist)==1): dist = dist*np.ones(naxes,dtype=self.datatype,order='C') if(np.size(dist)!=naxes): raise ValueError(about._errors.cstring("ERROR: size mismatch ( "+str(np.size(dist))+" <> "+str(naxes)+" ).")) if(np.any(dist<=0)): raise ValueError(about._errors.cstring("ERROR: nonpositive distance(s).")) self.vol = np.real(dist)[::-1] self.fourier = bool(fourier)  ultimanet committed Feb 05, 2015 205 206  self.my_fft_object = fft_rg.fft_factory()  Marco Selig committed Jan 30, 2015 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816  ##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ def naxes(self): """ Returns the number of axes of the grid. Returns ------- naxes : int Number of axes of the regular grid. """ return (np.size(self.para)-1)//2 def zerocenter(self): """ Returns information on the centering of the axes. Returns ------- zerocenter : numpy.ndarray Whether the grid is centered on zero for each axis or not. """ return self.para[-(np.size(self.para)-1)//2:][::-1].astype(np.bool) def dist(self): """ Returns the distances between grid points along each axis. Returns ------- dist : np.ndarray Distances between two grid points on each axis. """ return self.vol[::-1] def dim(self,split=False): """ Computes the dimension of the space, i.e.\ the number of pixels. Parameters ---------- split : bool, *optional* Whether to return the dimension split up, i.e. the numbers of pixels along each axis, or their product (default: False). Returns ------- dim : {int, numpy.ndarray} Dimension(s) of the space. If split==True, a one-dimensional array with an entry for each axis is returned. """ ## dim = product(n) if(split): return self.para[:(np.size(self.para)-1)//2] else: return np.prod(self.para[:(np.size(self.para)-1)//2],axis=0,dtype=None,out=None) ##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ def dof(self): """ Computes the number of degrees of freedom of the space, i.e.\ the number of grid points multiplied with one or two, depending on complex-valuedness and hermitian symmetry of the fields. Returns ------- dof : int Number of degrees of freedom of the space. """ ## dof ~ dim if(self.para[(np.size(self.para)-1)//2]<2): return np.prod(self.para[:(np.size(self.para)-1)//2],axis=0,dtype=None,out=None) else: return 2*np.prod(self.para[:(np.size(self.para)-1)//2],axis=0,dtype=None,out=None) ##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ def enforce_power(self,spec,size=None,**kwargs): """ Provides a valid power spectrum array from a given object. Parameters ---------- spec : {float, list, numpy.ndarray, nifty.field, function} Fiducial power spectrum from which a valid power spectrum is to be calculated. Scalars are interpreted as constant power spectra. Returns ------- spec : numpy.ndarray Valid power spectrum. Other parameters ---------------- size : int, *optional* Number of bands the power spectrum shall have (default: None). kindex : numpy.ndarray, *optional* Scale of each band. codomain : nifty.space, *optional* A compatible codomain for power indexing (default: None). log : bool, *optional* Flag specifying if the spectral binning is performed on logarithmic scale or not; if set, the number of used bins is set automatically (if not given otherwise); by default no binning is done (default: None). nbin : integer, *optional* Number of used spectral bins; if given log is set to False; integers below the minimum of 3 induce an automatic setting; by default no binning is done (default: None). binbounds : {list, array}, *optional* User specific inner boundaries of the bins, which are preferred over the above parameters; by default no binning is done (default: None). vmin : {scalar, list, ndarray, field}, *optional* Lower limit of the uniform distribution if random == "uni" (default: 0). """ if(size is None)or(callable(spec)): ## explicit kindex kindex = kwargs.get("kindex",None) if(kindex is None): ## quick kindex if(self.fourier)and(not hasattr(self,"power_indices"))and(len(kwargs)==0): kindex = gp.nklength(gp.nkdict_fast(self.para[:(np.size(self.para)-1)//2],self.vol,fourier=True)) ## implicit kindex else: try: self.set_power_indices(**kwargs) except: codomain = kwargs.get("codomain",self.get_codomain()) codomain.set_power_indices(**kwargs) kindex = codomain.power_indices.get("kindex") else: kindex = self.power_indices.get("kindex") size = len(kindex) if(isinstance(spec,field)): spec = spec.val.astype(self.datatype) elif(callable(spec)): try: spec = np.array(spec(kindex),dtype=self.datatype) except: raise TypeError(about._errors.cstring("ERROR: invalid power spectra function.")) ## exception in spec(kindex) elif(np.isscalar(spec)): spec = np.array([spec],dtype=self.datatype) else: spec = np.array(spec,dtype=self.datatype) ## drop imaginary part spec = np.real(spec) ## check finiteness if(not np.all(np.isfinite(spec))): about.warnings.cprint("WARNING: infinite value(s).") ## check positivity (excluding null) if(np.any(spec<0)): raise ValueError(about._errors.cstring("ERROR: nonpositive value(s).")) elif(np.any(spec==0)): about.warnings.cprint("WARNING: nonpositive value(s).") ## extend if(np.size(spec)==1): spec = spec*np.ones(size,dtype=spec.dtype,order='C') ## size check elif(np.size(spec)size): about.warnings.cprint("WARNING: power spectrum cut to size ( == "+str(size)+" ).") spec = spec[:size] return spec ##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ def set_power_indices(self,**kwargs): """ Sets the (un)indexing objects for spectral indexing internally. Parameters ---------- log : bool Flag specifying if the binning is performed on logarithmic scale or not; if set, the number of used bins is set automatically (if not given otherwise); by default no binning is done (default: None). nbin : integer Number of used bins; if given log is set to False; integers below the minimum of 3 induce an automatic setting; by default no binning is done (default: None). binbounds : {list, array} User specific inner boundaries of the bins, which are preferred over the above parameters; by default no binning is done (default: None). Returns ------- None See Also -------- get_power_indices Raises ------ AttributeError If self.fourier == False. ValueError If the binning leaves one or more bins empty. """ if(not self.fourier): raise AttributeError(about._errors.cstring("ERROR: power spectra indexing ill-defined.")) ## check storage if(hasattr(self,"power_indices")): config = self.power_indices.get("config") ## check configuration redo = False if(config.get("log")!=kwargs.get("log",config.get("log"))): config["log"] = kwargs.get("log") redo = True if(config.get("nbin")!=kwargs.get("nbin",config.get("nbin"))): config["nbin"] = kwargs.get("nbin") redo = True if(np.any(config.get("binbounds")!=kwargs.get("binbounds",config.get("binbounds")))): config["binbounds"] = kwargs.get("binbounds") redo = True if(not redo): return None else: config = {"binbounds":kwargs.get("binbounds",None),"log":kwargs.get("log",None),"nbin":kwargs.get("nbin",None)} ## power indices about.infos.cflush("INFO: setting power indices ...") pindex,kindex,rho = gp.get_power_indices2(self.para[:(np.size(self.para)-1)//2],self.vol,self.para[-((np.size(self.para)-1)//2):].astype(np.bool),fourier=True) ## bin if ... if(config.get("log") is not None)or(config.get("nbin") is not None)or(config.get("binbounds") is not None): pindex,kindex,rho = gp.bin_power_indices(pindex,kindex,rho,**config) ## check binning if(np.any(rho==0)): raise ValueError(about._errors.cstring("ERROR: empty bin(s).")) ## binning too fine ## power undex pundex = np.unique(pindex,return_index=True,return_inverse=False)[1] ## storage self.power_indices = {"config":config,"kindex":kindex,"pindex":pindex,"pundex":pundex,"rho":rho} ## alphabetical about.infos.cprint(" done.") return None ##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ def enforce_values(self,x,extend=True): """ Computes valid field values from a given object, taking care of data types, shape, and symmetry. Parameters ---------- x : {float, numpy.ndarray, nifty.field} Object to be transformed into an array of valid field values. Returns ------- x : numpy.ndarray Array containing the valid field values. Other parameters ---------------- extend : bool, *optional* Whether a scalar is extented to a constant array or not (default: True). """ if(isinstance(x,field)): if(self==x.domain): if(self.datatype is not x.domain.datatype): raise TypeError(about._errors.cstring("ERROR: inequal data types ( '"+str(np.result_type(self.datatype))+"' <> '"+str(np.result_type(x.domain.datatype))+"' ).")) else: x = np.copy(x.val) else: raise ValueError(about._errors.cstring("ERROR: inequal domains.")) else: if(np.size(x)==1): if(extend): x = self.datatype(x)*np.ones(self.dim(split=True),dtype=self.datatype,order='C') else: if(np.isscalar(x)): x = np.array([x],dtype=self.datatype) else: x = np.array(x,dtype=self.datatype) else: x = self.enforce_shape(np.array(x,dtype=self.datatype)) ## hermitianize if ... if(about.hermitianize.status)and(np.size(x)!=1)and(self.para[(np.size(self.para)-1)//2]==1): x = gp.nhermitianize_fast(x,self.para[-((np.size(self.para)-1)//2):].astype(np.bool),special=False) ## check finiteness if(not np.all(np.isfinite(x))): about.warnings.cprint("WARNING: infinite value(s).") return x ##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ def get_random_values(self,**kwargs): """ Generates random field values according to the specifications given by the parameters, taking into account possible complex-valuedness and hermitian symmetry. Returns ------- x : numpy.ndarray Valid field values. Other parameters ---------------- random : string, *optional* Specifies the probability distribution from which the random numbers are to be drawn. Supported distributions are: - "pm1" (uniform distribution over {+1,-1} or {+1,+i,-1,-i} - "gau" (normal distribution with zero-mean and a given standard deviation or variance) - "syn" (synthesizes from a given power spectrum) - "uni" (uniform distribution over [vmin,vmax[) (default: None). dev : float, *optional* Standard deviation (default: 1). var : float, *optional* Variance, overriding dev if both are specified (default: 1). spec : {scalar, list, numpy.ndarray, nifty.field, function}, *optional* Power spectrum (default: 1). pindex : numpy.ndarray, *optional* Indexing array giving the power spectrum index of each band (default: None). kindex : numpy.ndarray, *optional* Scale of each band (default: None). codomain : nifty.rg_space, *optional* A compatible codomain with power indices (default: None). log : bool, *optional* Flag specifying if the spectral binning is performed on logarithmic scale or not; if set, the number of used bins is set automatically (if not given otherwise); by default no binning is done (default: None). nbin : integer, *optional* Number of used spectral bins; if given log is set to False; integers below the minimum of 3 induce an automatic setting; by default no binning is done (default: None). binbounds : {list, array}, *optional* User specific inner boundaries of the bins, which are preferred over the above parameters; by default no binning is done (default: None). vmin : {scalar, list, ndarray, field}, *optional* Lower limit of the uniform distribution if random == "uni" (default: 0). vmin : float, *optional* Lower limit for a uniform distribution (default: 0). vmax : float, *optional* Upper limit for a uniform distribution (default: 1). """ arg = random.arguments(self,**kwargs) if(arg is None): return np.zeros(self.dim(split=True),dtype=self.datatype,order='C') elif(arg[0]=="pm1"): if(about.hermitianize.status)and(self.para[(np.size(self.para)-1)//2]==1): return gp.random_hermitian_pm1(self.datatype,self.para[-((np.size(self.para)-1)//2):].astype(np.bool),self.dim(split=True)) ## special case else: x = random.pm1(datatype=self.datatype,shape=self.dim(split=True)) elif(arg[0]=="gau"): x = random.gau(datatype=self.datatype,shape=self.dim(split=True),mean=None,dev=arg[2],var=arg[3]) elif(arg[0]=="syn"): naxes = (np.size(self.para)-1)//2 x = gp.draw_vector_nd(self.para[:naxes],self.vol,arg[1],symtype=self.para[naxes],fourier=self.fourier,zerocentered=self.para[-naxes:].astype(np.bool),kpack=arg[2]) ## correct for 'ifft' if(not self.fourier): x = self.calc_weight(x,power=-1) return x elif(arg[0]=="uni"): x = random.uni(datatype=self.datatype,shape=self.dim(split=True),vmin=arg[1],vmax=arg[2]) else: raise KeyError(about._errors.cstring("ERROR: unsupported random key '"+str(arg[0])+"'.")) ## hermitianize if ... if(about.hermitianize.status)and(self.para[(np.size(self.para)-1)//2]==1): x = gp.nhermitianize_fast(x,self.para[-((np.size(self.para)-1)//2):].astype(np.bool),special=(arg[0] in ["gau","pm1"])) return x ##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ def check_codomain(self,codomain): """ Checks whether a given codomain is compatible to the space or not. Parameters ---------- codomain : nifty.space Space to be checked for compatibility. Returns ------- check : bool Whether or not the given codomain is compatible to the space. """ if(not isinstance(codomain,space)): raise TypeError(about._errors.cstring("ERROR: invalid input.")) elif(isinstance(codomain,rg_space)): ## naxes==naxes if((np.size(codomain.para)-1)//2==(np.size(self.para)-1)//2): naxes = (np.size(self.para)-1)//2 ## num'==num if(np.all(codomain.para[:naxes]==self.para[:naxes])): ## typ'==typ ==2 if(codomain.para[naxes]==self.para[naxes]==2): ## dist'~=1/(num*dist) if(np.all(np.absolute(self.para[:naxes]*self.vol*codomain.vol-1) "+str(naxes)+" ).")) if(coname is None): return rg_space(self.para[:naxes][::-1],naxes=naxes,zerocenter=cozerocenter,hermitian=bool(self.para[naxes]<2),purelyreal=bool(self.para[naxes]==1),dist=1/(self.para[:naxes]*self.vol)[::-1],fourier=bool(not self.fourier)) ## dist',fourier' = 1/(num*dist),NOT fourier elif(coname[0]=='f'): return rg_space(self.para[:naxes][::-1],naxes=naxes,zerocenter=cozerocenter,hermitian=bool(self.para[naxes]<2),purelyreal=bool(self.para[naxes]==1),dist=1/(self.para[:naxes]*self.vol)[::-1],fourier=True) ## dist',fourier' = 1/(num*dist),True elif(coname[0]=='i'): return rg_space(self.para[:naxes][::-1],naxes=naxes,zerocenter=cozerocenter,hermitian=bool(self.para[naxes]<2),purelyreal=bool(self.para[naxes]==1),dist=1/(self.para[:naxes]*self.vol)[::-1],fourier=False) ## dist',fourier' = 1/(num*dist),False else: return rg_space(self.para[:naxes][::-1],naxes=naxes,zerocenter=cozerocenter,hermitian=bool(self.para[naxes]<2),purelyreal=bool(not self.para[naxes]),dist=self.vol[::-1],fourier=self.fourier) ## dist',fourier' = dist,fourier ##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ def get_meta_volume(self,total=False): """ Calculates the meta volumes. The meta volumes are the volumes associated with each component of a field, taking into account field components that are not explicitly included in the array of field values but are determined by symmetry conditions. In the case of an :py:class:rg_space, the meta volumes are simply the pixel volumes. Parameters ---------- total : bool, *optional* Whether to return the total meta volume of the space or the individual ones of each pixel (default: False). Returns ------- mol : {numpy.ndarray, float} Meta volume of the pixels or the complete space. """ if(total): return self.dim(split=False)*np.prod(self.vol,axis=0,dtype=None,out=None) else: mol = np.ones(self.dim(split=True),dtype=self.vol.dtype,order='C') return self.calc_weight(mol,power=1) ##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ def calc_weight(self,x,power=1): """ Weights a given array with the pixel volumes to a given power. Parameters ---------- x : numpy.ndarray Array to be weighted. power : float, *optional* Power of the pixel volumes to be used (default: 1). Returns ------- y : numpy.ndarray Weighted array. """ x = self.enforce_shape(np.array(x,dtype=self.datatype)) ## weight return x*np.prod(self.vol,axis=0,dtype=None,out=None)**power ##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ def calc_dot(self,x,y): """ Computes the discrete inner product of two given arrays. Parameters ---------- x : numpy.ndarray First array y : numpy.ndarray Second array Returns ------- dot : scalar Inner product of the two arrays. """ x = self.enforce_shape(np.array(x,dtype=self.datatype)) y = self.enforce_shape(np.array(y,dtype=self.datatype)) ## inner product dot = np.dot(np.conjugate(x.flatten(order='C')),y.flatten(order='C'),out=None) if(np.isreal(dot)): return np.asscalar(np.real(dot)) elif(self.para[(np.size(self.para)-1)//2]!=2): ## check imaginary part if(np.absolute(dot.imag)>self.epsilon**2*np.absolute(dot.real)): about.warnings.cprint("WARNING: discarding considerable imaginary part.") return np.asscalar(np.real(dot)) else: return dot ##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ def calc_transform(self,x,codomain=None,**kwargs): """ Computes the transform of a given array of field values. Parameters ---------- x : numpy.ndarray Array to be transformed. codomain : nifty.rg_space, *optional* Target space to which the transformation shall map (default: None). Returns ------- Tx : numpy.ndarray Transformed array """ x = self.enforce_shape(np.array(x,dtype=self.datatype)) if(codomain is None): return x ## T == id ## mandatory(!) codomain check if(isinstance(codomain,rg_space))and(self.check_codomain(codomain)): naxes = (np.size(self.para)-1)//2 ## select machine if(np.all(np.absolute(self.para[:naxes]*self.vol*codomain.vol-1)self.epsilon**2*np.dot(Tx.real.flatten(order='C'),Tx.real.flatten(order='C'),out=None)): about.warnings.cprint("WARNING: discarding considerable imaginary part.") Tx = np.real(Tx) else: raise ValueError(about._errors.cstring("ERROR: unsupported transformation.")) return Tx.astype(codomain.datatype) ##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ def calc_smooth(self,x,sigma=0,**kwargs): """ Smoothes an array of field values by convolution with a Gaussian kernel. Parameters ---------- x : numpy.ndarray Array of field values to be smoothed. sigma : float, *optional* Standard deviation of the Gaussian kernel, specified in units of length in position space; for testing: a sigma of -1 will be reset to a reasonable value (default: 0). Returns ------- Gx : numpy.ndarray Smoothed array. """ x = self.enforce_shape(np.array(x,dtype=self.datatype)) naxes = (np.size(self.para)-1)//2 ## check sigma if(sigma==0): return x elif(sigma==-1): about.infos.cprint("INFO: invalid sigma reset.") if(self.fourier): sigma = 1.5/np.min(self.para[:naxes]*self.vol) ## sqrt(2)*max(dist) else: sigma = 1.5*np.max(self.vol) ## sqrt(2)*max(dist) elif(sigma<0): raise ValueError(about._errors.cstring("ERROR: invalid sigma.")) ## smooth Gx = gs.smooth_field(x,self.fourier,self.para[-naxes:].astype(np.bool).tolist(),bool(self.para[naxes]==1),self.vol,smooth_length=sigma) ## check complexity if(not self.para[naxes]): ## purely real ## check imaginary part if(np.any(Gx.imag!=0))and(np.dot(Gx.imag.flatten(order='C'),Gx.imag.flatten(order='C'),out=None)>self.epsilon**2*np.dot(Gx.real.flatten(order='C'),Gx.real.flatten(order='C'),out=None)): about.warnings.cprint("WARNING: discarding considerable imaginary part.") Gx = np.real(Gx) return Gx ##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ def calc_power(self,x,**kwargs): """ Computes the power of an array of field values. Parameters ---------- x : numpy.ndarray Array containing the field values of which the power is to be calculated. Returns ------- spec : numpy.ndarray Power contained in the input array. Other parameters ---------------- pindex : numpy.ndarray, *optional* Indexing array assigning the input array components to components of the power spectrum (default: None). kindex : numpy.ndarray, *optional* Scale corresponding to each band in the power spectrum (default: None). rho : numpy.ndarray, *optional* Number of degrees of freedom per band (default: None). codomain : nifty.space, *optional* A compatible codomain for power indexing (default: None). log : bool, *optional* Flag specifying if the spectral binning is performed on logarithmic scale or not; if set, the number of used bins is set automatically (if not given otherwise); by default no binning is done (default: None). nbin : integer, *optional* Number of used spectral bins; if given log is set to False; integers below the minimum of 3 induce an automatic setting; by default no binning is done (default: None). binbounds : {list, array}, *optional* User specific inner boundaries of the bins, which are preferred over the above parameters; by default no binning is done (default: None). vmin : {scalar, list, ndarray, field}, *optional* Lower limit of the uniform distribution if random == "uni" (default: 0). """ x = self.enforce_shape(np.array(x,dtype=self.datatype)) ## correct for 'fft' if(not self.fourier): x = self.calc_weight(x,power=1) ## explicit power indices pindex,kindex,rho = kwargs.get("pindex",None),kwargs.get("kindex",None),kwargs.get("rho",None) ## implicit power indices if(pindex is None)or(kindex is None)or(rho is None): try: self.set_power_indices(**kwargs) except: codomain = kwargs.get("codomain",self.get_codomain()) codomain.set_power_indices(**kwargs) pindex,kindex,rho = codomain.power_indices.get("pindex"),codomain.power_indices.get("kindex"),codomain.power_indices.get("rho") else: pindex,kindex,rho = self.power_indices.get("pindex"),self.power_indices.get("kindex"),self.power_indices.get("rho") ## power spectrum return gp.calc_ps_fast(x,self.para[:(np.size(self.para)-1)//2],self.vol,self.para[-((np.size(self.para)-1)//2):].astype(np.bool),fourier=self.fourier,pindex=pindex,kindex=kindex,rho=rho) ##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ def get_plot(self,x,title="",vmin=None,vmax=None,power=None,unit="",norm=None,cmap=None,cbar=True,other=None,legend=False,mono=True,**kwargs): """ Creates a plot of field values according to the specifications given by the parameters. Parameters ---------- x : numpy.ndarray Array containing the field values. Returns ------- None Other parameters ---------------- title : string, *optional* Title of the plot (default: ""). vmin : float, *optional* Minimum value to be displayed (default: min(x)). vmax : float, *optional* Maximum value to be displayed (default: max(x)). power : bool, *optional* Whether to plot the power contained in the field or the field values themselves (default: False). unit : string, *optional* Unit of the field values (default: ""). norm : string, *optional* Scaling of the field values before plotting (default: None). cmap : matplotlib.colors.LinearSegmentedColormap, *optional* Color map to be used for two-dimensional plots (default: None). cbar : bool, *optional* Whether to show the color bar or not (default: True). other : {single object, tuple of objects}, *optional* Object or tuple of objects to be added, where objects can be scalars, arrays, or fields (default: None). legend : bool, *optional* Whether to show the legend or not (default: False). mono : bool, *optional* Whether to plot the monopole or not (default: True). save : string, *optional* Valid file name where the figure is to be stored, by default the figure is not saved (default: False). error : {float, numpy.ndarray, nifty.field}, *optional* Object indicating some confidence interval to be plotted (default: None). kindex : numpy.ndarray, *optional* Scale corresponding to each band in the power spectrum (default: None). codomain : nifty.space, *optional* A compatible codomain for power indexing (default: None). log : bool, *optional* Flag specifying if the spectral binning is performed on logarithmic scale or not; if set, the number of used bins is set automatically (if not given otherwise); by default no binning is done (default: None). nbin : integer, *optional* Number of used spectral bins; if given log is set to False; integers below the minimum of 3 induce an automatic setting; by default no binning is done (default: None). binbounds : {list, array}, *optional* User specific inner boundaries of the bins, which are preferred over the above parameters; by default no binning is done (default: None). vmin : {scalar, list, ndarray, field}, *optional* Lower limit of the uniform distribution if random == "uni" (default: 0). """ if(not pl.isinteractive())and(not bool(kwargs.get("save",False))): about.warnings.cprint("WARNING: interactive mode off.") naxes = (np.size(self.para)-1)//2 if(power is None): power = bool(self.para[naxes]) if(power): x = self.calc_power(x,**kwargs) fig = pl.figure(num=None,figsize=(6.4,4.8),dpi=None,facecolor="none",edgecolor="none",frameon=False,FigureClass=pl.Figure) ax0 = fig.add_axes([0.12,0.12,0.82,0.76]) ## explicit kindex xaxes = kwargs.get("kindex",None) ## implicit kindex if(xaxes is None): try: self.set_power_indices(**kwargs) except: codomain = kwargs.get("codomain",self.get_codomain()) codomain.set_power_indices(**kwargs) xaxes = codomain.power_indices.get("kindex") else: xaxes = self.power_indices.get("kindex") if(norm is None)or(not isinstance(norm,int)): norm = naxes if(vmin is None): vmin = np.min(x[:mono].tolist()+(xaxes**norm*x)[1:].tolist(),axis=None,out=None) if(vmax is None): vmax = np.max(x[:mono].tolist()+(xaxes**norm*x)[1:].tolist(),axis=None,out=None) ax0.loglog(xaxes[1:],(xaxes**norm*x)[1:],color=[0.0,0.5,0.0],label="graph 0",linestyle='-',linewidth=2.0,zorder=1) if(mono): ax0.scatter(0.5*(xaxes[1]+xaxes[2]),x[0],s=20,color=[0.0,0.5,0.0],marker='o',cmap=None,norm=None,vmin=None,vmax=None,alpha=None,linewidths=None,verts=None,zorder=1) if(other is not None): if(isinstance(other,tuple)): other = list(other) for ii in xrange(len(other)): if(isinstance(other[ii],field)): other[ii] = other[ii].power(**kwargs) else: other[ii] = self.enforce_power(other[ii],size=np.size(xaxes),kindex=xaxes) elif(isinstance(other,field)): other = [other.power(**kwargs)] else: other = [self.enforce_power(other,size=np.size(xaxes),kindex=xaxes)] imax = max(1,len(other)-1) for ii in xrange(len(other)): ax0.loglog(xaxes[1:],(xaxes**norm*other[ii])[1:],color=[max(0.0,1.0-(2*ii/imax)**2),0.5*((2*ii-imax)/imax)**2,max(0.0,1.0-(2*(ii-imax)/imax)**2)],label="graph "+str(ii+1),linestyle='-',linewidth=1.0,zorder=-ii) if(mono): ax0.scatter(0.5*(xaxes[1]+xaxes[2]),other[ii][0],s=20,color=[max(0.0,1.0-(2*ii/imax)**2),0.5*((2*ii-imax)/imax)**2,max(0.0,1.0-(2*(ii-imax)/imax)**2)],marker='o',cmap=None,norm=None,vmin=None,vmax=None,alpha=None,linewidths=None,verts=None,zorder=-ii) if(legend): ax0.legend() ax0.set_xlim(xaxes[1],xaxes[-1]) ax0.set_xlabel(r"$|k|$") ax0.set_ylim(vmin,vmax) ax0.set_ylabel(r"$|k|^{%i} P_k$"%norm) ax0.set_title(title) else: x = self.enforce_shape(np.array(x)) if(naxes==1): fig = pl.figure(num=None,figsize=(6.4,4.8),dpi=None,facecolor="none",edgecolor="none",frameon=False,FigureClass=pl.Figure) ax0 = fig.add_axes([0.12,0.12,0.82,0.76]) xaxes = (np.arange(self.para[0],dtype=np.int)+self.para[2]*(self.para[0]//2))*self.vol if(vmin is None): if(np.iscomplexobj(x)): vmin = min(np.min(np.absolute(x),axis=None,out=None),np.min(np.real(x),axis=None,out=None),np.min(np.imag(x),axis=None,out=None)) else: vmin = np.min(x,axis=None,out=None) if(vmax is None): if(np.iscomplexobj(x)): vmax = max(np.max(np.absolute(x),axis=None,out=None),np.max(np.real(x),axis=None,out=None),np.max(np.imag(x),axis=None,out=None)) else: vmax = np.max(x,axis=None,out=None) if(norm=="log"): ax0graph = ax0.semilogy if(vmin<=0): raise ValueError(about._errors.cstring("ERROR: nonpositive value(s).")) else: ax0graph = ax0.plot if(np.iscomplexobj(x)): ax0graph(xaxes,np.absolute(x),color=[0.0,0.5,0.0],label="graph (absolute)",linestyle='-',linewidth=2.0,zorder=1) ax0graph(xaxes,np.real(x),color=[0.0,0.5,0.0],label="graph (real part)",linestyle="--",linewidth=1.0,zorder=0) ax0graph(xaxes,np.imag(x),color=[0.0,0.5,0.0],label="graph (imaginary part)",linestyle=':',linewidth=1.0,zorder=0) if(legend): ax0.legend() elif(other is not None): ax0graph(xaxes,x,color=[0.0,0.5,0.0],label="graph 0",linestyle='-',linewidth=2.0,zorder=1) if(isinstance(other,tuple)): other = [self.enforce_values(xx,extend=True) for xx in other] else: other = [self.enforce_values(other,extend=True)] imax = max(1,len(other)-1) for ii in xrange(len(other)): ax0graph(xaxes,other[ii],color=[max(0.0,1.0-(2*ii/imax)**2),0.5*((2*ii-imax)/imax)**2,max(0.0,1.0-(2*(ii-imax)/imax)**2)],label="graph "+str(ii+1),linestyle='-',linewidth=1.0,zorder=-ii) if("error" in kwargs): error = self.enforce_values(np.absolute(kwargs.get("error")),extend=True) ax0.fill_between(xaxes,x-error,x+error,color=[0.8,0.8,0.8],label="error 0",zorder=-len(other)) if(legend): ax0.legend() else: ax0graph(xaxes,x,color=[0.0,0.5,0.0],label="graph 0",linestyle='-',linewidth=2.0,zorder=1) if("error" in kwargs): error = self.enforce_values(np.absolute(kwargs.get("error")),extend=True) ax0.fill_between(xaxes,x-error,x+error,color=[0.8,0.8,0.8],label="error 0",zorder=0) ax0.set_xlim(xaxes[0],xaxes[-1]) ax0.set_xlabel("coordinate") ax0.set_ylim(vmin,vmax) if(unit): unit = " ["+unit+"]" ax0.set_ylabel("values"+unit) ax0.set_title(title) elif(naxes==2): if(np.iscomplexobj(x)): about.infos.cprint("INFO: absolute values and phases are plotted.") if(title): title += " " if(bool(kwargs.get("save",False))): save_ = os.path.splitext(os.path.basename(str(kwargs.get("save")))) kwargs.update(save=save_[0]+"_absolute"+save_[1]) self.get_plot(np.absolute(x),title=title+"(absolute)",vmin=vmin,vmax=vmax,power=False,unit=unit,norm=norm,cmap=cmap,cbar=cbar,other=None,legend=False,**kwargs) # self.get_plot(np.real(x),title=title+"(real part)",vmin=vmin,vmax=vmax,power=False,unit=unit,norm=norm,cmap=cmap,cbar=cbar,other=None,legend=False,**kwargs) # self.get_plot(np.imag(x),title=title+"(imaginary part)",vmin=vmin,vmax=vmax,power=False,unit=unit,norm=norm,cmap=cmap,cbar=cbar,other=None,legend=False,**kwargs) if(unit): unit = "rad" if(cmap is None): cmap = pl.cm.hsv_r if(bool(kwargs.get("save",False))): kwargs.update(save=save_[0]+"_phase"+save_[1]) self.get_plot(np.angle(x,deg=False),title=title+"(phase)",vmin=-3.1416,vmax=3.1416,power=False,unit=unit,norm=None,cmap=cmap,cbar=cbar,other=None,legend=False,**kwargs) ## values in [-pi,pi] return None ## leave method else: if(vmin is None): vmin = np.min(x,axis=None,out=None) if(vmax is None): vmax = np.max(x,axis=None,out=None) if(norm=="log")and(vmin<=0): raise ValueError(about._errors.cstring("ERROR: nonpositive value(s).")) s_ = np.array([self.para[1]*self.vol[1]/np.max(self.para[:naxes]*self.vol,axis=None,out=None),self.para[0]*self.vol[0]/np.max(self.para[:naxes]*self.vol,axis=None,out=None)*(1.0+0.159*bool(cbar))]) fig = pl.figure(num=None,figsize=(6.4*s_[0],6.4*s_[1]),dpi=None,facecolor="none",edgecolor="none",frameon=False,FigureClass=pl.Figure) ax0 = fig.add_axes([0.06/s_[0],0.06/s_[1],1.0-0.12/s_[0],1.0-0.12/s_[1]]) xaxes = (np.arange(self.para[1]+1,dtype=np.int)-0.5+self.para[4]*(self.para[1]//2))*self.vol[1] yaxes = (np.arange(self.para[0]+1,dtype=np.int)-0.5+self.para[3]*(self.para[0]//2))*self.vol[0] if(norm=="log"): n_ = ln(vmin=vmin,vmax=vmax) else: n_ = None sub = ax0.pcolormesh(xaxes,yaxes,x,cmap=cmap,norm=n_,vmin=vmin,vmax=vmax) ax0.set_xlim(xaxes[0],xaxes[-1]) ax0.set_xticks([0],minor=False) ax0.set_ylim(yaxes[0],yaxes[-1]) ax0.set_yticks([0],minor=False) ax0.set_aspect("equal") if(cbar): if(norm=="log"): f_ = lf(10,labelOnlyBase=False) b_ = sub.norm.inverse(np.linspace(0,1,sub.cmap.N+1)) v_ = np.linspace(sub.norm.vmin,sub.norm.vmax,sub.cmap.N) else: f_ = None b_ = None v_ = None cb0 = fig.colorbar(sub,ax=ax0,orientation="horizontal",fraction=0.1,pad=0.05,shrink=0.75,aspect=20,ticks=[vmin,vmax],format=f_,drawedges=False,boundaries=b_,values=v_) cb0.ax.text(0.5,-1.0,unit,fontdict=None,withdash=False,transform=cb0.ax.transAxes,horizontalalignment="center",verticalalignment="center") ax0.set_title(title) else: raise ValueError(about._errors.cstring("ERROR: unsupported number of axes ( "+str(naxes)+" > 2 ).")) if(bool(kwargs.get("save",False))): fig.savefig(str(kwargs.get("save")),dpi=None,facecolor="none",edgecolor="none",orientation="portrait",papertype=None,format=None,transparent=False,bbox_inches=None,pad_inches=0.1) pl.close(fig) else: fig.canvas.draw() ##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ def __repr__(self): return "" def __str__(self): naxes = (np.size(self.para)-1)//2 num = self.para[:naxes][::-1].tolist() zerocenter = self.para[-naxes:][::-1].astype(np.bool).tolist() dist = self.vol[::-1].tolist() return "nifty_rg.rg_space instance\n- num = "+str(num)+"\n- naxes = "+str(naxes)+"\n- hermitian = "+str(bool(self.para[naxes]<2))+"\n- purelyreal = "+str(bool(not self.para[naxes]))+"\n- zerocenter = "+str(zerocenter)+"\n- dist = "+str(dist)+"\n- fourier = "+str(self.fourier) ##-----------------------------------------------------------------------------