hp_space.py 14.5 KB
Newer Older
csongor's avatar
csongor committed
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
31
32
33
34
35
36
37
38
39
40
# 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: <http://www.mpa-garching.mpg.de/ift/nifty/>
#
# 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 <http://www.gnu.org/licenses/>.

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

    NIFTY submodule for grids on the two-sphere.

"""
from __future__ import division

import numpy as np
import pylab as pl

from d2o import STRATEGIES as DISTRIBUTION_STRATEGIES

41
from nifty.spaces.lm_space import LMSpace
42

43
from nifty.spaces.space import Space
csongor's avatar
csongor committed
44

Jait Dixit's avatar
Jait Dixit committed
45
from nifty.config import about, nifty_configuration as gc,\
csongor's avatar
csongor committed
46
                         dependency_injector as gdi
theos's avatar
theos committed
47
from hp_space_paradict import HPSpaceParadict
csongor's avatar
csongor committed
48
49
50
51
52
53
from nifty.nifty_random import random

hp = gdi.get('healpy')

HP_DISTRIBUTION_STRATEGIES = DISTRIBUTION_STRATEGIES['global']

54
55

class HPSpace(Space):
csongor's avatar
csongor committed
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
    """
        ..        __
        ..      /  /
        ..     /  /___    ______
        ..    /   _   | /   _   |
        ..   /  / /  / /  /_/  /
        ..  /__/ /__/ /   ____/  space class
        ..           /__/

        NIFTY subclass for HEALPix discretizations of the two-sphere [#]_.

        Parameters
        ----------
        nside : int
            Resolution parameter for the HEALPix discretization, resulting in
            ``12*nside**2`` pixels.

        See Also
        --------
        gl_space : A class for the Gauss-Legendre discretization of the
            sphere [#]_.
        lm_space : A class for spherical harmonic components.

        Notes
        -----
        Only powers of two are allowed for `nside`.

        References
        ----------
        .. [#] K.M. Gorski et al., 2005, "HEALPix: A Framework for
               High-Resolution Discretization and Fast Analysis of Data
               Distributed on the Sphere", *ApJ* 622..759G.
        .. [#] M. Reinecke and D. Sverre Seljebotn, 2013, "Libsharp - spherical
               harmonic transforms revisited";
               `arXiv:1303.4945 <http://www.arxiv.org/abs/1303.4945>`_

        Attributes
        ----------
        para : numpy.ndarray
            Array containing the number `nside`.
        dtype : numpy.dtype
            Data type of the field values, which is always numpy.float64.
        discrete : bool
            Whether or not the underlying space is discrete, always ``False``
            for spherical spaces.
        vol : numpy.ndarray
            An array with one element containing the pixel size.
    """

    def __init__(self, nside):
        """
            Sets the attributes for a hp_space class instance.

            Parameters
            ----------
            nside : int
                Resolution parameter for the HEALPix discretization, resulting
                in ``12*nside**2`` pixels.

            Returns
            -------
            None

            Raises
            ------
            ImportError
                If the healpy module is not available.
            ValueError
                If input `nside` is invaild.

        """
        # check imports
        if not gc['use_healpy']:
Jait Dixit's avatar
Jait Dixit committed
129
            raise ImportError("ERROR: healpy not available.")
csongor's avatar
csongor committed
130

Jait Dixit's avatar
Jait Dixit committed
131
132
        # let the abstract Space class initialize dtype
        super(HPSpace, self).__init__(dtype=np.dtype('float64'))
csongor's avatar
csongor committed
133

Jait Dixit's avatar
Jait Dixit committed
134
135
136
137
138
139
        self.paradict = HPSpaceParadict(nside=nside,
                                        distances=np.float(
                                            4 * np.pi / (12 * nside ** 2))
                                        )
        # HPSpace is never harmonic
        self._harmonic = False
csongor's avatar
csongor committed
140
141

    def copy(self):
142
        return HPSpace(nside=self.paradict['nside'])
csongor's avatar
csongor committed
143
144
145

    @property
    def shape(self):
Jait Dixit's avatar
Jait Dixit committed
146
        return (np.int(12 * self.paradict['nside'] ** 2),)
csongor's avatar
csongor committed
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

    @property
    def meta_volume(self):
        """
            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.

            Parameters
            ----------
            total : bool, *optional*
                Whether to return the total meta volume of the space or the
                individual ones of each field component (default: False).

            Returns
            -------
            mol : {numpy.ndarray, float}
                Meta volume of the field components or the complete space.

            Notes
            -----
            For HEALpix discretizations, the meta volumes are the pixel sizes.
        """
        return np.float(4 * np.pi)

    @property
    def meta_volume_split(self):
Jait Dixit's avatar
Jait Dixit committed
177
        pass
csongor's avatar
csongor committed
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212

    # TODO: Extend to binning/log
    def enforce_power(self, spec, size=None, kindex=None):
        if kindex is None:
            kindex_size = self.paradict['nside'] * 3
            kindex = np.arange(kindex_size,
                               dtype=np.array(self.distances).dtype)
        return self._enforce_power_helper(spec=spec,
                                          size=size,
                                          kindex=kindex)

    def calc_power(self, x, niter=0, **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
            ----------------
            iter : int, *optional*
                Number of iterations performed in the HEALPix basis
                transformation.
        """
        x = self.cast(x)

        nside = self.paradict['nside']
Jait Dixit's avatar
Jait Dixit committed
213
        lmax = 3 * nside - 1
csongor's avatar
csongor committed
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
        mmax = lmax

        # if self.datamodel != 'not':
        #     about.warnings.cprint(
        #         "WARNING: Field data is consolidated to all nodes for "
        #         "external smoothalm method!")

        np_x = x.get_full_data()

        # power spectrum
        return hp.anafast(np_x, map2=None, nspec=None, lmax=lmax, mmax=mmax,
                          iter=niter, alm=False, pol=True, use_weights=False,
                          datapath=None)

    def get_plot(self, x, title="", vmin=None, vmax=None, power=False, 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).
            iter : int, *optional*
                Number of iterations performed in the HEALPix basis
                transformation.
        """
277
278
        from nifty.field import Field

csongor's avatar
csongor committed
279
280
281
282
283
        try:
            x = x.get_full_data()
        except AttributeError:
            pass

Jait Dixit's avatar
Jait Dixit committed
284
        if (not pl.isinteractive()) and (not bool(kwargs.get("save", False))):
csongor's avatar
csongor committed
285
286
            about.warnings.cprint("WARNING: interactive mode off.")

Jait Dixit's avatar
Jait Dixit committed
287
        if (power):
csongor's avatar
csongor committed
288
289
            x = self.calc_power(x, **kwargs)

Jait Dixit's avatar
Jait Dixit committed
290
291
292
293
            fig = pl.figure(num=None, figsize=(6.4, 4.8), dpi=None,
                            facecolor="none",
                            edgecolor="none", frameon=False,
                            FigureClass=pl.Figure)
csongor's avatar
csongor committed
294
295
296
            ax0 = fig.add_axes([0.12, 0.12, 0.82, 0.76])

            xaxes = np.arange(3 * self.para[0], dtype=np.int)
Jait Dixit's avatar
Jait Dixit committed
297
            if (vmin is None):
csongor's avatar
csongor committed
298
                vmin = np.min(x[:mono].tolist(
Jait Dixit's avatar
Jait Dixit committed
299
300
301
                ) + (xaxes * (2 * xaxes + 1) * x)[1:].tolist(), axis=None,
                              out=None)
            if (vmax is None):
csongor's avatar
csongor committed
302
                vmax = np.max(x[:mono].tolist(
Jait Dixit's avatar
Jait Dixit committed
303
304
                ) + (xaxes * (2 * xaxes + 1) * x)[1:].tolist(), axis=None,
                              out=None)
csongor's avatar
csongor committed
305
            ax0.loglog(xaxes[1:], (xaxes * (2 * xaxes + 1) * x)[1:], color=[0.0,
Jait Dixit's avatar
Jait Dixit committed
306
307
308
309
310
311
312
313
314
315
316
                                                                            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)):
csongor's avatar
csongor committed
317
318
                    other = list(other)
                    for ii in xrange(len(other)):
Jait Dixit's avatar
Jait Dixit committed
319
                        if (isinstance(other[ii], Field)):
csongor's avatar
csongor committed
320
321
322
                            other[ii] = other[ii].power(**kwargs)
                        else:
                            other[ii] = self.enforce_power(other[ii])
Jait Dixit's avatar
Jait Dixit committed
323
                elif (isinstance(other, Field)):
csongor's avatar
csongor committed
324
325
326
327
328
                    other = [other.power(**kwargs)]
                else:
                    other = [self.enforce_power(other)]
                imax = max(1, len(other) - 1)
                for ii in xrange(len(other)):
Jait Dixit's avatar
Jait Dixit committed
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
                    ax0.loglog(xaxes[1:],
                               (xaxes * (2 * xaxes + 1) * 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):
csongor's avatar
csongor committed
349
350
351
352
353
354
355
356
357
                    ax0.legend()

            ax0.set_xlim(xaxes[1], xaxes[-1])
            ax0.set_xlabel(r"$\ell$")
            ax0.set_ylim(vmin, vmax)
            ax0.set_ylabel(r"$\ell(2\ell+1) C_\ell$")
            ax0.set_title(title)

        else:
Jait Dixit's avatar
Jait Dixit committed
358
359
360
            if (norm == "log"):
                if (vmin is not None):
                    if (vmin <= 0):
csongor's avatar
csongor committed
361
362
                        raise ValueError(about._errors.cstring(
                            "ERROR: nonpositive value(s)."))
Jait Dixit's avatar
Jait Dixit committed
363
                elif (np.min(x, axis=None, out=None) <= 0):
csongor's avatar
csongor committed
364
365
                    raise ValueError(about._errors.cstring(
                        "ERROR: nonpositive value(s)."))
Jait Dixit's avatar
Jait Dixit committed
366
            if (cmap is None):
csongor's avatar
csongor committed
367
368
                cmap = pl.cm.jet  # default
            cmap.set_under(color='k', alpha=0.0)  # transparent box
Jait Dixit's avatar
Jait Dixit committed
369
370
371
372
373
374
            hp.mollview(x, fig=None, rot=None, coord=None, unit=unit, xsize=800,
                        title=title, nest=False, min=vmin, max=vmax,
                        flip="astro", remove_dip=False,
                        remove_mono=False, gal_cut=0, format="%g", format2="%g",
                        cbar=cbar, cmap=cmap, notext=False, norm=norm,
                        hold=False, margins=None, sub=None)
csongor's avatar
csongor committed
375
376
            fig = pl.gcf()

Jait Dixit's avatar
Jait Dixit committed
377
378
379
380
381
        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)
csongor's avatar
csongor committed
382
383
384
            pl.close(fig)
        else:
            fig.canvas.draw()