nifty_rg.py 72.7 KB
Newer Older
1
2
# NIFTY (Numerical Information Field Theory) has been developed at the
# Max-Planck-Institute for Astrophysics.
Marco Selig's avatar
Marco Selig committed
3
##
4
# Copyright (C) 2015 Max-Planck-Society
Marco Selig's avatar
Marco Selig committed
5
##
6
7
# Author: Marco Selig
# Project homepage: <http://www.mpa-garching.mpg.de/ift/nifty/>
Marco Selig's avatar
Marco Selig committed
8
##
9
10
11
12
# 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.
Marco Selig's avatar
Marco Selig committed
13
##
14
15
16
17
# 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.
Marco Selig's avatar
Marco Selig committed
18
##
19
20
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
Marco Selig's avatar
Marco Selig committed
21
22
23
24
25
26
27
28
29
30

"""
    ..                  __   ____   __
    ..                /__/ /   _/ /  /_
    ..      __ ___    __  /  /_  /   _/  __   __
    ..    /   _   | /  / /   _/ /  /   /  / /  /
    ..   /  / /  / /  / /  /   /  /_  /  /_/  /
    ..  /__/ /__/ /__/ /__/    \___/  \___   /  rg
    ..                               /______/

Marco Selig's avatar
Marco Selig committed
31
    NIFTY submodule for regular Cartesian grids.
Marco Selig's avatar
Marco Selig committed
32
33
34

"""
from __future__ import division
Ultimanet's avatar
Ultimanet committed
35

36
import itertools
Marco Selig's avatar
Marco Selig committed
37
import numpy as np
38
import os
39
from scipy.special import erf
Marco Selig's avatar
Marco Selig committed
40
41
42
import pylab as pl
from matplotlib.colors import LogNorm as ln
from matplotlib.ticker import LogFormatter as lf
Ultimanet's avatar
Ultimanet committed
43

44
45
from d2o import STRATEGIES as DISTRIBUTION_STRATEGIES

csongor's avatar
csongor committed
46
47
48
from nifty.nifty_core import point_space
from nifty.nifty_field import field

49
import nifty_fft
50
51
52
from nifty.config import about,\
                         nifty_configuration as gc,\
                         dependency_injector as gdi
Ultimanet's avatar
Ultimanet committed
53
from nifty.nifty_paradict import rg_space_paradict
54
55
from nifty.nifty_power_indices import rg_power_indices
from nifty.nifty_random import random
Ultima's avatar
Ultima committed
56
import nifty.nifty_utilities as utilities
57

Ultima's avatar
Ultima committed
58
MPI = gdi[gc['mpi_module']]
59
RG_DISTRIBUTION_STRATEGIES = DISTRIBUTION_STRATEGIES['global']
Ultimanet's avatar
Ultimanet committed
60

Marco Selig's avatar
Marco Selig committed
61

62
class rg_space(point_space):
Marco Selig's avatar
Marco Selig committed
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
    """
        ..      _____   _______
        ..    /   __/ /   _   /
        ..   /  /    /  /_/  /
        ..  /__/     \____  /  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.
110
        dtype : numpy.dtype
Marco Selig's avatar
Marco Selig committed
111
112
113
114
115
116
117
118
119
120
121
122
            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.
    """
123
    epsilon = 0.0001  # relative precision for comparisons
Marco Selig's avatar
Marco Selig committed
124

125
    def __init__(self, shape, zerocenter=False, complexity=0, distances=None,
csongor's avatar
csongor committed
126
                 harmonic=False, fft_module=gc['fft_module']):
Marco Selig's avatar
Marco Selig committed
127
128
129
130
131
132
133
134
135
136
137
138
        """
            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
Ultimanet's avatar
Ultimanet committed
139
                (default: False).
Marco Selig's avatar
Marco Selig committed
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
            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
        """
Ultima's avatar
Ultima committed
156
        self._cache_dict = {'check_codomain':{}}
157
        self.paradict = rg_space_paradict(shape=shape,
158
159
                                          complexity=complexity,
                                          zerocenter=zerocenter)
160
        # set dtype
161
        if self.paradict['complexity'] == 0:
162
            self.dtype = np.dtype('float64')
Marco Selig's avatar
Marco Selig committed
163
        else:
164
            self.dtype = np.dtype('complex128')
165

166
        # set volume/distances
167
168
169
170
171
        naxes = len(self.paradict['shape'])
        if distances is None:
            distances = 1 / np.array(self.paradict['shape'], dtype=np.float)
        elif np.isscalar(distances):
            distances = np.ones(naxes, dtype=np.float) * distances
Marco Selig's avatar
Marco Selig committed
172
        else:
173
174
175
176
            distances = np.array(distances, dtype=np.float)
            if np.size(distances) == 1:
                distances = distances * np.ones(naxes, dtype=np.float)
            if np.size(distances) != naxes:
177
                raise ValueError(about._errors.cstring(
178
179
180
                    "ERROR: size mismatch ( " + str(np.size(distances)) +
                    " <> " + str(naxes) + " )."))
        if np.any(distances <= 0):
181
            raise ValueError(about._errors.cstring(
182
                "ERROR: nonpositive distance(s)."))
Marco Selig's avatar
Marco Selig committed
183

184
        self.distances = tuple(distances)
185
186
187
        self.harmonic = bool(harmonic)
        self.discrete = False

188
189
        # Initializes the fast-fourier-transform machine, which will be used
        # to transform the space
Ultima's avatar
Ultima committed
190
        if not gc.validQ('fft_module', fft_module):
191
            about.warnings.cprint("WARNING: fft_module set to default.")
Ultima's avatar
Ultima committed
192
193
            fft_module = gc['fft_module']
        self.fft_machine = nifty_fft.fft_factory(fft_module)
194
195
196

        # Initialize the power_indices object which takes care of kindex,
        # pindex, rho and the pundex for a given set of parameters
csongor's avatar
csongor committed
197
198

        # TODO harmonic = True doesn't work yet
199
        if self.harmonic:
200
201
            self.power_indices = rg_power_indices(
                    shape=self.get_shape(),
202
                    dgrid=distances,
203
204
                    zerocentered=self.paradict['zerocenter'],
                    allowed_distribution_strategies=RG_DISTRIBUTION_STRATEGIES)
205

206
207
    @property
    def para(self):
208
        temp = np.array(self.paradict['shape'] +
209
210
                        [self.paradict['complexity']] +
                        self.paradict['zerocenter'], dtype=int)
211
        return temp
212

213
214
    @para.setter
    def para(self, x):
215
        self.paradict['shape'] = x[:(np.size(x) - 1) // 2]
216
217
        self.paradict['zerocenter'] = x[(np.size(x) + 1) // 2:]
        self.paradict['complexity'] = x[(np.size(x) - 1) // 2]
Ultimanet's avatar
Ultimanet committed
218

Ultima's avatar
Ultima committed
219
220
221
    def __hash__(self):
        result_hash = 0
        for (key, item) in vars(self).items():
Ultima's avatar
Ultima committed
222
            if key in ['_cache_dict', 'fft_machine', 'power_indices']:
Ultima's avatar
Ultima committed
223
224
225
226
                continue
            result_hash ^= item.__hash__() * hash(key)
        return result_hash

227
228
229
230
231
232
233
234
235
236
237
    # __identiftier__ returns an object which contains all information needed
    # to uniquely identify a space. It returns a (immutable) tuple which
    # therefore can be compared.
    # The rg_space version of __identifier__ filters out the vars-information
    # which is describing the rg_space's structure
    def _identifier(self):
        # Extract the identifying parts from the vars(self) dict.
        temp = [(ii[0],
                 ((lambda x: tuple(x) if
                  isinstance(x, np.ndarray) else x)(ii[1])))
                for ii in vars(self).iteritems()
Ultima's avatar
Ultima committed
238
                if ii[0] not in ['_cache_dict', 'fft_machine',
csongor's avatar
csongor committed
239
                                 'power_indices']]
240
241
        # Return the sorted identifiers as a tuple.
        return tuple(sorted(temp))
Ultimanet's avatar
Ultimanet committed
242

243
    def copy(self):
244
        return rg_space(shape=self.paradict['shape'],
245
246
                        complexity=self.paradict['complexity'],
                        zerocenter=self.paradict['zerocenter'],
247
                        distances=self.distances,
248
                        harmonic=self.harmonic,
csongor's avatar
csongor committed
249
                        fft_module=self.fft_machine.name)
250
251

    def get_shape(self):
252
        return tuple(self.paradict['shape'])
Marco Selig's avatar
Marco Selig committed
253

csongor's avatar
csongor committed
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
    def _complement_cast(self, x, axis=None, hermitianize=True):
        if axis is None:
            if x is not None and hermitianize and self.paradict['complexity']\
                    == 1 and not x.hermitian:
                about.warnings.cflush(
                     "WARNING: Data gets hermitianized. This operation is " +
                     "extremely expensive\n")
                x = utilities.hermitianize(x)
        else:
            # TODO hermitianize only on specific axis
            if x is not None and hermitianize and self.paradict['complexity']\
                    == 1 and not x.hermitian:
                about.warnings.cflush(
                     "WARNING: Data gets hermitianized. This operation is " +
                     "extremely expensive\n")
                x = utilities.hermitianize(x)
        return x
ultimanet's avatar
ultimanet committed
271

272
    def enforce_power(self, spec, size=None, kindex=None, codomain=None,
Ultima's avatar
Ultima committed
273
                      **kwargs):
Marco Selig's avatar
Marco Selig committed
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
        """
            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*
298
299
300
                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
301
                binning is done (default: None).
Marco Selig's avatar
Marco Selig committed
302
            nbin : integer, *optional*
303
                Number of used spectral bins; if given `log` is set to
304
305
                ``False``; iintegers below the minimum of 3 induce an automatic
                setting; by default no binning is done (default: None).
Marco Selig's avatar
Marco Selig committed
306
307
308
            binbounds : {list, array}, *optional*
                User specific inner boundaries of the bins, which are preferred
                over the above parameters; by default no binning is done
309
                (default: None).
Marco Selig's avatar
Marco Selig committed
310
        """
311
312
313
314
315
316
317

        # Setting up the local variables: kindex
        # The kindex is only necessary if spec is a function or if
        # the size is not set explicitly
        if kindex is None and (size is None or callable(spec)):
            # Determine which space should be used to get the kindex
            if self.harmonic:
318
319
                kindex_supply_space = self
            else:
320
321
                # Check if the given codomain is compatible with the space
                try:
322
323
324
                    assert(self.check_codomain(codomain))
                    kindex_supply_space = codomain
                except(AssertionError):
325
326
327
328
                    about.warnings.cprint("WARNING: Supplied codomain is " +
                                          "incompatible. Generating a " +
                                          "generic codomain. This can " +
                                          "be expensive!")
329
                    kindex_supply_space = self.get_codomain()
Ultima's avatar
Ultima committed
330

331
            kindex = kindex_supply_space.\
Ultima's avatar
Ultima committed
332
                power_indices.get_index_dict(**kwargs)['kindex']
333

334
335
336
        return self._enforce_power_helper(spec=spec,
                                          size=size,
                                          kindex=kindex)
337

Ultima's avatar
Ultima committed
338
    def _check_codomain(self, codomain):
Marco Selig's avatar
Marco Selig committed
339
        """
340
            Checks whether a given codomain is compatible to the space or not.
Marco Selig's avatar
Marco Selig committed
341
342
343

            Parameters
            ----------
344
345
            codomain : nifty.space
                Space to be checked for compatibility.
Marco Selig's avatar
Marco Selig committed
346
347
348

            Returns
            -------
349
350
            check : bool
                Whether or not the given codomain is compatible to the space.
Marco Selig's avatar
Marco Selig committed
351
        """
352
353
        if codomain is None:
            return False
354

355
        if not isinstance(codomain, rg_space):
356
357
            raise TypeError(about._errors.cstring(
                "ERROR: The given codomain must be a nifty rg_space."))
358

359
        # check number of number and size of axes
360
361
        if not np.all(np.array(self.paradict['shape']) ==
                      np.array(codomain.paradict['shape'])):
362
            return False
Ultima's avatar
Ultima committed
363

364
365
366
        # check harmonic flag
        if self.harmonic == codomain.harmonic:
            return False
Ultima's avatar
Ultima committed
367

368
369
370
371
        # check complexity-type
        # prepare the shorthands
        dcomp = self.paradict['complexity']
        cocomp = codomain.paradict['complexity']
Ultima's avatar
Ultima committed
372

373
374
375
376
377
378
379
380
381
382
383
384
385
386
        # Case 1: if the domain is copmleteley complex
        # -> the codomain must be complex, too
        if dcomp == 2:
            if cocomp != 2:
                return False
        # Case 2: domain is hermitian
        # -> codmomain can be real. If it is marked as hermitian or even
        # fully complex, a warning is raised
        elif dcomp == 1:
            if cocomp > 0:
                about.warnings.cprint("WARNING: Unrecommended codomain! " +
                                      "The domain is hermitian, hence the " +
                                      "codomain should be restricted to " +
                                      "real values!")
Ultima's avatar
Ultima committed
387

388
389
390
391
392
393
394
395
396
397
        # Case 3: domain is real
        # -> codmain should be hermitian
        elif dcomp == 0:
            if cocomp == 2:
                about.warnings.cprint("WARNING: Unrecommended codomain! " +
                                      "The domain is real, hence the " +
                                      "codomain should be restricted to " +
                                      "hermitian configurations!")
            elif cocomp == 0:
                return False
Ultima's avatar
Ultima committed
398

399
400
        # Check if the distances match, i.e. dist'=1/(num*dist)
        if not np.all(
401
                np.absolute(np.array(self.paradict['shape']) *
402
403
404
                            np.array(self.distances) *
                            np.array(codomain.distances) - 1) < self.epsilon):
            return False
Ultima's avatar
Ultima committed
405

406
        return True
407

408
    def get_codomain(self, cozerocenter=None, **kwargs):
Marco Selig's avatar
Marco Selig committed
409
        """
410
411
412
            Generates a compatible codomain to which transformations are
            reasonable, i.e.\  either a shifted grid or a Fourier conjugate
            grid.
Marco Selig's avatar
Marco Selig committed
413
414
415

            Parameters
            ----------
416
417
418
419
420
            coname : string, *optional*
                String specifying a desired codomain (default: None).
            cozerocenter : {bool, numpy.ndarray}, *optional*
                Whether or not the grid is zerocentered for each axis or not
                (default: None).
Marco Selig's avatar
Marco Selig committed
421
422
423

            Returns
            -------
424
425
            codomain : nifty.rg_space
                A compatible codomain.
Marco Selig's avatar
Marco Selig committed
426

427
428
429
430
431
432
            Notes
            -----
            Possible arguments for `coname` are ``'f'`` in which case the
            codomain arises from a Fourier transformation, ``'i'`` in which
            case it arises from an inverse Fourier transformation.If no
            `coname` is given, the Fourier conjugate grid is produced.
Marco Selig's avatar
Marco Selig committed
433
        """
434
435
436
437
438
439
440
441
        naxes = len(self.get_shape())
        # Parse the cozerocenter input
        if(cozerocenter is None):
            cozerocenter = self.paradict['zerocenter']
        # if the input is something scalar, cast it to a boolean
        elif(np.isscalar(cozerocenter)):
            cozerocenter = bool(cozerocenter)
        # if it is not a scalar...
Marco Selig's avatar
Marco Selig committed
442
        else:
443
444
445
446
447
448
449
450
451
452
453
            # ...cast it to a numpy array of booleans
            cozerocenter = np.array(cozerocenter, dtype=np.bool)
            # if it was a list of length 1, extract the boolean
            if(np.size(cozerocenter) == 1):
                cozerocenter = np.asscalar(cozerocenter)
            # if the length of the input does not match the number of
            # dimensions, raise an exception
            elif(np.size(cozerocenter) != naxes):
                raise ValueError(about._errors.cstring(
                    "ERROR: size mismatch ( " +
                    str(np.size(cozerocenter)) + " <> " + str(naxes) + " )."))
Marco Selig's avatar
Marco Selig committed
454

455
        # Set up the initialization variables
456
457
458
        shape = self.paradict['shape']
        distances = 1 / (np.array(self.paradict['shape']) *
                         np.array(self.distances))
459
        fft_module = self.fft_machine.name
460
        complexity = {0: 1, 1: 0, 2: 2}[self.paradict['complexity']]
461
        harmonic = bool(not self.harmonic)
Marco Selig's avatar
Marco Selig committed
462

463
        new_space = rg_space(shape,
464
465
                             zerocenter=cozerocenter,
                             complexity=complexity,
466
                             distances=distances,
467
                             harmonic=harmonic,
csongor's avatar
csongor committed
468
                             fft_module=fft_module)
469
        return new_space
Marco Selig's avatar
Marco Selig committed
470

471
    def get_random_values(self, **kwargs):
Marco Selig's avatar
Marco Selig committed
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
        """
            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}
490
491
                - "gau" (normal distribution with zero-mean and a given
                    standard
Marco Selig's avatar
Marco Selig committed
492
493
494
495
496
497
498
499
500
501
                    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).
502
503
            spec : {scalar, list, numpy.ndarray, nifty.field, function},
                *optional*
Marco Selig's avatar
Marco Selig committed
504
505
506
507
508
509
510
                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*
Ultimanet's avatar
Ultimanet committed
511
                A compatible codomain (default: None).
Marco Selig's avatar
Marco Selig committed
512
            log : bool, *optional*
513
514
                Flag specifying if the spectral binning is performed on
                    logarithmic
Marco Selig's avatar
Marco Selig committed
515
516
517
518
                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*
519
520
                Number of used spectral bins; if given `log` is set to
                    ``False``;
Marco Selig's avatar
Marco Selig committed
521
522
523
524
525
                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
526
                (default: None).
Ultimanet's avatar
Ultimanet committed
527
            vmin : float, *optional*
Marco Selig's avatar
Marco Selig committed
528
529
530
531
                Lower limit for a uniform distribution (default: 0).
            vmax : float, *optional*
                Upper limit for a uniform distribution (default: 1).
        """
532
        # Parse the keyword arguments
533
        arg = random.parse_arguments(self, **kwargs)
534

535
536
537
        if arg is None:
            return self.cast(0)

Ultima's avatar
Ultima committed
538
539
        # Should the output be hermitianized?
        hermitianizeQ = (self.paradict['complexity'] == 1)
Ultimanet's avatar
Ultimanet committed
540

541
        # Case 1: uniform distribution over {-1,+1}/{1,i,-1,-i}
Ultima's avatar
Ultima committed
542
543
        if arg['random'] == 'pm1' and not hermitianizeQ:
            sample = super(rg_space, self).get_random_values(**arg)
544

Ultima's avatar
Ultima committed
545
        elif arg['random'] == 'pm1' and hermitianizeQ:
546
            sample = self.get_random_values(random='uni', vmin=-1, vmax=1)
Ultima's avatar
Ultima committed
547

548
            if issubclass(sample.dtype.type, np.complexfloating):
Ultima's avatar
Ultima committed
549
550
551
552
553
                temp_data = sample.copy()
                sample[temp_data.real >= 0.5] = 1
                sample[(temp_data.real >= 0) * (temp_data.real < 0.5)] = -1
                sample[(temp_data.real < 0) * (temp_data.imag >= 0)] = 1j
                sample[(temp_data.real < 0) * (temp_data.imag < 0)] = -1j
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
                # Set the mirroring invariant points to real values
                product_list = []
                for s in self.get_shape():
                    # if the particular dimension has even length, set
                    # also the middle of the array to a real value
                    if s % 2 == 0:
                        product_list += [[0, s/2]]
                    else:
                        product_list += [[0]]

                for i in itertools.product(*product_list):
                    sample[i] = {1: 1,
                                 -1: -1,
                                 1j: 1,
                                 -1j: -1}[sample[i]]
Ultimanet's avatar
Ultimanet committed
569
            else:
Ultima's avatar
Ultima committed
570
571
                sample[sample >= 0] = 1
                sample[sample < 0] = -1
572

Ultima's avatar
Ultima committed
573
574
575
576
577
            try:
                sample.hermitian = True
            except(AttributeError):
                pass

578
        # Case 2: normal distribution with zero-mean and a given standard
579
        #         deviation or variance
Ultima's avatar
Ultima committed
580
581
        elif arg['random'] == 'gau':
            sample = super(rg_space, self).get_random_values(**arg)
582

583
            if hermitianizeQ:
Ultima's avatar
Ultima committed
584
                sample = utilities.hermitianize_gaussian(sample)
Ultimanet's avatar
Ultimanet committed
585

586
        # Case 3: uniform distribution
Ultima's avatar
Ultima committed
587
588
        elif arg['random'] == "uni" and not hermitianizeQ:
            sample = super(rg_space, self).get_random_values(**arg)
589

Ultima's avatar
Ultima committed
590
        elif arg['random'] == "uni" and hermitianizeQ:
591
592
593
594
595
            # For a hermitian uniform sample, generate a gaussian one
            # and then convert it to a uniform one
            sample = self.get_random_values(random='gau')
            # Use the cummulative of the gaussian, the error function in order
            # to transform it to a uniform distribution.
596
            if issubclass(sample.dtype.type, np.complexfloating):
Ultima's avatar
Ultima committed
597
                def temp_erf(x):
598
                    return erf(x.real) + 1j * erf(x.imag)
Ultimanet's avatar
Ultimanet committed
599
            else:
Ultima's avatar
Ultima committed
600
                def temp_erf(x):
601
                    return erf(x / np.sqrt(2))
Ultima's avatar
Ultima committed
602

603
            sample.apply_scalar_function(function=temp_erf, inplace=True)
604
605

            # Shift and stretch the uniform distribution into the given limits
606
            # sample = (sample + 1)/2 * (vmax-vmin) + vmin
Ultima's avatar
Ultima committed
607
608
            vmin = arg['vmin']
            vmax = arg['vmax']
609
610
            sample *= (vmax - vmin) / 2.
            sample += 1 / 2. * (vmax + vmin)
Marco Selig's avatar
Marco Selig committed
611

Ultima's avatar
Ultima committed
612
613
614
615
616
            try:
                sample.hermitian = True
            except(AttributeError):
                pass

Ultima's avatar
Ultima committed
617
618
619
620
        elif(arg['random'] == "syn"):
            spec = arg['spec']
            kpack = arg['kpack']
            harmonic_domain = arg['harmonic_domain']
Ultima's avatar
Ultima committed
621
622
623
624
625
            lnb_dict = {}
            for name in ('log', 'nbin', 'binbounds'):
                if arg[name] != 'default':
                    lnb_dict[name] = arg[name]

626
627
628
            # Check whether there is a kpack available or not.
            # kpack is only used for computing kdict and extracting kindex
            # If not, take kdict and kindex from the fourier_domain
629
            if kpack is None:
Ultimanet's avatar
Ultimanet committed
630
                power_indices =\
Ultima's avatar
Ultima committed
631
                    harmonic_domain.power_indices.get_index_dict(**lnb_dict)
632

Ultimanet's avatar
Ultimanet committed
633
634
635
636
637
638
                kindex = power_indices['kindex']
                kdict = power_indices['kdict']
                kpack = [power_indices['pindex'], power_indices['kindex']]
            else:
                kindex = kpack[1]
                kdict = harmonic_domain.power_indices.\
639
640
641
642
643
644
645
646
                    _compute_kdict_from_pindex_kindex(kpack[0], kpack[1])

            # draw the random samples
            # Case 1: self is a harmonic space
            if self.harmonic:
                # subcase 1: self is real
                # -> simply generate a random field in fourier space and
                # weight the entries accordingly to the powerspectrum
Ultimanet's avatar
Ultimanet committed
647
                if self.paradict['complexity'] == 0:
Ultima's avatar
Ultima committed
648
649
650
                    sample = self.get_random_values(random='gau',
                                                    mean=0,
                                                    std=1)
651
652
653
654
655
                # subcase 2: self is hermitian but probably complex
                # -> generate a real field (in position space) and transform
                # it to harmonic space -> field in harmonic space is
                # hermitian. Now weight the modes accordingly to the
                # powerspectrum.
Ultimanet's avatar
Ultimanet committed
656
657
                elif self.paradict['complexity'] == 1:
                    temp_codomain = self.get_codomain()
Ultima's avatar
Ultima committed
658
659
660
                    sample = temp_codomain.get_random_values(random='gau',
                                                             mean=0,
                                                             std=1)
661
662
663
664
665
666

                    # In order to get the normalisation right, the sqrt
                    # of self.dim must be divided out.
                    # Furthermore, the normalisation in the fft routine
                    # must be undone
                    # TODO: Insert explanation
667
                    sqrt_of_dim = np.sqrt(self.get_dim())
Ultimanet's avatar
Ultimanet committed
668
669
670
                    sample /= sqrt_of_dim
                    sample = temp_codomain.calc_weight(sample, power=-1)

671
                    # tronsform the random field to harmonic space
Ultimanet's avatar
Ultimanet committed
672
                    sample = temp_codomain.\
673
674
675
676
                        calc_transform(sample, codomain=self)

                    # ensure that the kdict and the harmonic_sample have the
                    # same distribution strategy
Ultima's avatar
Ultima committed
677
678
679
680
681
                    try:
                        assert(kdict.distribution_strategy ==
                               sample.distribution_strategy)
                    except AttributeError:
                        pass
682
683
684
685

                # subcase 3: self is fully complex
                # -> generate a complex random field in harmonic space and
                # weight the modes accordingly to the powerspectrum
Ultimanet's avatar
Ultimanet committed
686
                elif self.paradict['complexity'] == 2:
Ultima's avatar
Ultima committed
687
688
689
                    sample = self.get_random_values(random='gau',
                                                    mean=0,
                                                    std=1)
690

691
                # apply the powerspectrum renormalization
692
693
694
695
696
697
698
                # extract the local data from kdict
                local_kdict = kdict.get_local_data()
                rescaler = np.sqrt(
                    spec[np.searchsorted(kindex, local_kdict)])
                sample.apply_scalar_function(lambda x: x * rescaler,
                                             inplace=True)

699
            # Case 2: self is a position space
Ultimanet's avatar
Ultimanet committed
700
            else:
701
702
                # get a suitable codomain
                temp_codomain = self.get_codomain()
Ultimanet's avatar
Ultimanet committed
703

704
705
706
                # subcase 1: self is a real space.
                # -> generate a hermitian sample with the codomain in harmonic
                # space and make a fourier transformation.
Ultimanet's avatar
Ultimanet committed
707
                if self.paradict['complexity'] == 0:
708
                    # check that the codomain is hermitian
Ultimanet's avatar
Ultimanet committed
709
                    assert(temp_codomain.paradict['complexity'] == 1)
710
711
712
713

                # subcase 2: self is hermitian but probably complex
                # -> generate a real-valued random sample in fourier space
                # and transform it to real space
Ultimanet's avatar
Ultimanet committed
714
                elif self.paradict['complexity'] == 1:
715
716
                    # check that the codomain is real
                    assert(temp_codomain.paradict['complexity'] == 0)
Ultimanet's avatar
Ultimanet committed
717

718
719
720
721
722
723
                # subcase 3: self is fully complex
                # -> generate a complex-valued random sample in fourier space
                # and transform it to real space
                elif self.paradict['complexity'] == 2:
                    # check that the codomain is real
                    assert(temp_codomain.paradict['complexity'] == 2)
Ultimanet's avatar
Ultimanet committed
724

725
726
                # Get a hermitian/real/complex sample in harmonic space from
                # the codomain
Ultima's avatar
Ultima committed
727
728
729
730
731
                sample = temp_codomain.get_random_values(random='syn',
                                                         pindex=kpack[0],
                                                         kindex=kpack[1],
                                                         spec=spec,
                                                         codomain=self,
Ultima's avatar
Ultima committed
732
                                                         **lnb_dict)
733

734
                # Perform a fourier transform
Ultima's avatar
Ultima committed
735
                sample = temp_codomain.calc_transform(sample, codomain=self)
Ultimanet's avatar
Ultimanet committed
736
737

            if self.paradict['complexity'] == 1:
Ultima's avatar
Ultima committed
738
739
740
741
                try:
                    sample.hermitian = True
                except AttributeError:
                    pass
742

Ultimanet's avatar
Ultimanet committed
743
744
        else:
            raise KeyError(about._errors.cstring(
Ultima's avatar
Ultima committed
745
                "ERROR: unsupported random key '" + str(arg['random']) + "'."))
Marco Selig's avatar
Marco Selig committed
746

747
        return sample
Marco Selig's avatar
Marco Selig committed
748

749
    def calc_weight(self, x, axes=None, power=1):
Marco Selig's avatar
Marco Selig committed
750
751
752
753
754
755
756
757
758
        """
            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).
759
760
            axes : None, tuple
                Ignored in this case since it's a scalar operation.
Marco Selig's avatar
Marco Selig committed
761
762
763
764
765
766

            Returns
            -------
            y : numpy.ndarray
                Weighted array.
        """
767
768
        # weight
        x = x * self.get_weight(power=power)
Ultimanet's avatar
Ultimanet committed
769
        return x
Marco Selig's avatar
Marco Selig committed
770

771
    def get_weight(self, power=1):
772
        return np.prod(self.distances)**power
773

Jait Dixit's avatar
Jait Dixit committed
774
    def calc_transform(self, x, codomain=None, axes=None, **kwargs):
Marco Selig's avatar
Marco Selig committed
775
776
777
778
779
780
781
782
        """
            Computes the transform of a given array of field values.

            Parameters
            ----------
            x : numpy.ndarray
                Array to be transformed.
            codomain : nifty.rg_space, *optional*
783
                codomain space to which the transformation shall map
Marco Selig's avatar
Marco Selig committed
784
                (default: None).
785
            axes : None, tuple
Jait Dixit's avatar
Jait Dixit committed
786
                Axes in the array which should be transformed.
Marco Selig's avatar
Marco Selig committed
787
788
789
790
791
792

            Returns
            -------
            Tx : numpy.ndarray
                Transformed array
        """
793

794
        if codomain is None:
Ultimanet's avatar
Ultimanet committed
795
            codomain = self.get_codomain()
796
797

        # Check if the given codomain is suitable for the transformation
798
        if not self.check_codomain(codomain):
799
            raise ValueError(about._errors.cstring(
800
                "ERROR: unsupported codomain."))
801

802
        if codomain.harmonic:
803
            # correct for forward fft
804
            x = self.calc_weight(x, power=1)
805
806
807

        # Perform the transformation
        Tx = self.fft_machine.transform(val=x, domain=self, codomain=codomain,
Jait Dixit's avatar
Jait Dixit committed
808
                                        axes=axes, **kwargs)
809

810
        if not codomain.harmonic:
811
            # correct for inverse fft
Ultimanet's avatar
Ultimanet committed
812
813
            Tx = codomain.calc_weight(Tx, power=-1)

814
815
        return Tx

816
    def calc_smooth(self, x, sigma=0, codomain=None, axes=None):
Marco Selig's avatar
Marco Selig committed
817
818
819
820
821
822
823
824
825
826
827
828
        """
            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).
829
830
            axes: None, tuple
                Axes which should be smoothed
Marco Selig's avatar
Marco Selig committed
831
832
833
834
835
836
837

            Returns
            -------
            Gx : numpy.ndarray
                Smoothed array.
        """

838
        # Check sigma
Ultimanet's avatar
Ultimanet committed
839
        if sigma == 0:
Ultima's avatar
Ultima committed
840
            return self.unary_operation(x, op='copy')
Ultimanet's avatar
Ultimanet committed
841
842
843
        elif sigma == -1:
            about.infos.cprint(
                "INFO: Resetting sigma to sqrt(2)*max(dist).")
844
            sigma = np.sqrt(2) * np.max(self.distances)
845
        elif(sigma < 0):
Marco Selig's avatar
Marco Selig committed
846
            raise ValueError(about._errors.cstring("ERROR: invalid sigma."))
Ultimanet's avatar
Ultimanet committed
847

848
        # if a codomain was given...
849
        if codomain is not None:
850
            # ...check if it was suitable
Ultimanet's avatar
Ultimanet committed
851
852
            if not self.check_codomain(codomain):
                raise ValueError(about._errors.cstring(
853
854
                    "ERROR: the given codomain is not a compatible!"))
        else:
Ultimanet's avatar
Ultimanet committed
855
856
            codomain = self.get_codomain()

857
858
859
        x = self.calc_transform(x, codomain=codomain, axes=axes)
        x = codomain._calc_smooth_helper(x, sigma, axes=axes)
        x = codomain.calc_transform(x, codomain=self, axes=axes)
860
        return x
861

862
    def _calc_smooth_helper(self, x, sigma, axes=None):
863
        # multiply the gaussian kernel, etc...
864
865
        if axes is None:
            axes = range(len(x.shape))
866
867

        # if x is hermitian it remains hermitian during smoothing
csongor's avatar
csongor committed
868
869
        # TODO look at this later
        # if self.datamodel in RG_DISTRIBUTION_STRATEGIES:
870
        remember_hermitianQ = x.hermitian
Ultimanet's avatar
Ultimanet committed
871

872
873
874
875
        # Define the Gaussian kernel function
        gaussian = lambda x: np.exp(-2. * np.pi**2 * x**2 * sigma**2)

        # Define the variables in the dialect of the legacy smoothing.py
876
877
        nx = np.array(self.get_shape())
        dx = 1 / nx / self.distances
878
        # Multiply the data along each axis with suitable the gaussian kernel
Ultimanet's avatar
Ultimanet committed
879
        for i in range(len(nx)):
880
881
            # Prepare the exponent
            dk = 1. / nx[i] / dx[i]
Ultimanet's avatar
Ultimanet committed
882
            nk = nx[i]
883
            k = -0.5 * nk * dk + np.arange(nk) * dk
Ultimanet's avatar
Ultimanet committed
884
885
            if self.paradict['zerocenter'][i] == False:
                k = np.fft.fftshift(k)
886
            # compute the actual kernel vector
Ultimanet's avatar
Ultimanet committed
887
            gaussian_kernel_vector = gaussian(k)
888
            # blow up the vector to an array of shape (1,.,1,len(nk),1,.,1)
889
890
            blown_up_shape = [1, ] * len(x.shape)
            blown_up_shape[axes[i]] = len(gaussian_kernel_vector)
Ultimanet's avatar
Ultimanet committed
891
892
            gaussian_kernel_vector =\
                gaussian_kernel_vector.reshape(blown_up_shape)
893
894
            # apply the blown-up gaussian_kernel_vector
            x = x*gaussian_kernel_vector
895

896
        try:
897
            x.hermitian = remember_hermitianQ
898
899
        except AttributeError:
            pass
900

Ultimanet's avatar
Ultimanet committed
901
        return x
Marco Selig's avatar
Marco Selig committed
902

903
    def calc_power(self, x, **kwargs):
Marco Selig's avatar
Marco Selig committed
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
        """
            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).
            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*
928
929
                Flag specifying if the spectral binning is performed on
                logarithmic
Marco Selig's avatar
Marco Selig committed
930
931
932
933
                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*
934
935
                Number of used spectral bins; if given `log` is set to
                ``False``;
Marco Selig's avatar
Marco Selig committed
936
937
938
939
940
                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
941
                (default: None).
Marco Selig's avatar
Marco Selig committed
942
943

        """
Ultimanet's avatar
Ultimanet committed
944
945
        x = self.cast(x)

946
        # If self is a position space, delegate calc_power to its codomain.
947
        if not self.harmonic:
Marco Selig's avatar
Marco Selig committed
948
            try:
949
                codomain = kwargs['codomain']
Ultimanet's avatar
Ultimanet committed
950
951
            except(KeyError):
                codomain = self.get_codomain()
952

Ultimanet's avatar
Ultimanet committed
953
954
955
            y = self.calc_transform(x, codomain)
            kwargs.update({'codomain': self})
            return codomain.calc_power(y, **kwargs)
956
957
958
959
960

        # If some of the pindex, kindex or rho arrays are given explicitly,
        # favor them over those from the self.power_indices dictionary.
        # As the default value in kwargs.get(key, default) does NOT evaluate
        # lazy, a distinction of cases is necessary. Otherwise the
Ultima's avatar
Ultima committed
961
962
        # powerindices might be computed, although not needed
        if 'pindex' in kwargs and 'rho' in kwargs:
Ultimanet's avatar
Ultimanet committed
963
964
965
            pindex = kwargs.get('pindex')
            rho = kwargs.get('rho')
        else:
Ultima's avatar
Ultima committed
966
            power_indices = self.power_indices.get_index_dict(**kwargs)
Ultimanet's avatar
Ultimanet committed
967
968
            pindex = kwargs.get('pindex', power_indices['pindex'])
            rho = kwargs.get('rho', power_indices['rho'])
969

Ultimanet's avatar
Ultimanet committed
970
        fieldabs = abs(x)**2
971
        power_spectrum = np.zeros(rho.shape)
972

973
        power_spectrum = pindex.bincount(weights=fieldabs)
974
975

        # Divide out the degeneracy factor
Ultimanet's avatar
Ultimanet committed
976
977
        power_spectrum /= rho
        return power_spectrum
Marco Selig's avatar
Marco Selig committed
978

Ultima's avatar
Ultima committed
979
980
    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):
Marco Selig's avatar
Marco Selig committed
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
        """
            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).

        """
Ultima's avatar
Ultima committed
1048

Marco Selig's avatar
Marco Selig committed
1049
1050
1051
1052
1053
1054
1055
1056
1057
        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)
Ultima's avatar
Ultima committed
1058
1059
1060
1061
            try:
                x = x.get_full_data()
            except AttributeError:
                pass
Marco Selig's avatar
Marco Selig committed
1062

Ultima's avatar
Ultima committed
1063
1064
            fig = pl.figure(num=None,figsize=(6.4,4.8),dpi=None,
                            facecolor="none",edgecolor="none",frameon=False,FigureClass=pl.Figure)
Marco Selig's avatar
Marco Selig committed
1065
1066
1067
1068
1069
1070
1071
            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:
Ultima's avatar
Ultima committed
1072
1073
                    self.power_indices
                    kindex_supply_space = self
Marco Selig's avatar
Marco Selig committed
1074
                except:
Ultima's avatar
Ultima committed
1075
1076
1077
                    kindex_supply_space = self.get_codomain()

                xaxes = kindex_supply_space.power_indices.get_index_dict(
Ultima's avatar
Ultima committed
1078
                                                **kwargs)['kindex']
Ultima's avatar
Ultima committed
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088


#                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")
Marco Selig's avatar
Marco Selig committed
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126

            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 =