space.py 14.4 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) 2013 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
31
32
33
34
35
36
37
38
39
40
41
42
43
44

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

    .. The NIFTY project homepage is http://www.mpa-garching.mpg.de/ift/nifty/

    NIFTY [#]_, "Numerical Information Field Theory", is a versatile
    library designed to enable the development of signal inference algorithms
    that operate regardless of the underlying spatial grid and its resolution.
    Its object-oriented framework is written in Python, although it accesses
    libraries written in Cython, C++, and C for efficiency.

    NIFTY offers a toolkit that abstracts discretized representations of
    continuous spaces, fields in these spaces, and operators acting on fields
    into classes. Thereby, the correct normalization of operations on fields is
    taken care of automatically without concerning the user. This allows for an
    abstract formulation and programming of inference algorithms, including
    those derived within information field theory. Thus, NIFTY permits its user
Marco Selig's avatar
Marco Selig committed
45
    to rapidly prototype algorithms in 1D and then apply the developed code in
Marco Selig's avatar
Marco Selig committed
46
47
48
49
50
    higher-dimensional settings of real world problems. The set of spaces on
    which NIFTY operates comprises point sets, n-dimensional regular grids,
    spherical spaces, their harmonic counterparts, and product spaces
    constructed as combinations of those.

51
52
53
54
55
56
57
    References
    ----------
    .. [#] Selig et al., "NIFTY -- Numerical Information Field Theory --
        a versatile Python library for signal inference",
        `A&A, vol. 554, id. A26 <http://dx.doi.org/10.1051/0004-6361/201321236>`_,
        2013; `arXiv:1301.4499 <http://www.arxiv.org/abs/1301.4499>`_

Marco Selig's avatar
Marco Selig committed
58
59
60
61
62
63
    Class & Feature Overview
    ------------------------
    The NIFTY library features three main classes: **spaces** that represent
    certain grids, **fields** that are defined on spaces, and **operators**
    that apply to fields.

64
65
    .. Overview of all (core) classes:
    ..
Marco Selig's avatar
Marco Selig committed
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
    .. - switch
    .. - notification
    .. - _about
    .. - random
    .. - space
    ..     - point_space
    ..     - rg_space
    ..     - lm_space
    ..     - gl_space
    ..     - hp_space
    ..     - nested_space
    .. - field
    .. - operator
    ..     - diagonal_operator
    ..         - power_operator
    ..     - projection_operator
    ..     - vecvec_operator
    ..     - response_operator
    .. - probing
    ..     - trace_probing
    ..     - diagonal_probing

88
89
    Overview of the main classes and functions:

Marco Selig's avatar
Marco Selig committed
90
91
    .. automodule:: nifty

92
93
94
95
96
97
98
99
100
101
102
103
104
105
    - :py:class:`space`
        - :py:class:`point_space`
        - :py:class:`rg_space`
        - :py:class:`lm_space`
        - :py:class:`gl_space`
        - :py:class:`hp_space`
        - :py:class:`nested_space`
    - :py:class:`field`
    - :py:class:`operator`
        - :py:class:`diagonal_operator`
            - :py:class:`power_operator`
        - :py:class:`projection_operator`
        - :py:class:`vecvec_operator`
        - :py:class:`response_operator`
Marco Selig's avatar
Marco Selig committed
106

107
        .. currentmodule:: nifty.nifty_tools
Marco Selig's avatar
Marco Selig committed
108

109
110
        - :py:class:`invertible_operator`
        - :py:class:`propagator_operator`
Marco Selig's avatar
Marco Selig committed
111

112
        .. currentmodule:: nifty.nifty_explicit
Marco Selig's avatar
Marco Selig committed
113

114
        - :py:class:`explicit_operator`
Marco Selig's avatar
Marco Selig committed
115

116
    .. automodule:: nifty
Marco Selig's avatar
Marco Selig committed
117

118
119
120
    - :py:class:`probing`
        - :py:class:`trace_probing`
        - :py:class:`diagonal_probing`
Marco Selig's avatar
Marco Selig committed
121

122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
        .. currentmodule:: nifty.nifty_explicit

        - :py:class:`explicit_probing`

    .. currentmodule:: nifty.nifty_tools

    - :py:class:`conjugate_gradient`
    - :py:class:`steepest_descent`

    .. currentmodule:: nifty.nifty_explicit

    - :py:func:`explicify`

    .. currentmodule:: nifty.nifty_power

    - :py:func:`weight_power`,
      :py:func:`smooth_power`,
      :py:func:`infer_power`,
      :py:func:`interpolate_power`
Marco Selig's avatar
Marco Selig committed
141
142
143
144

"""
from __future__ import division
import numpy as np
Marco Selig's avatar
Marco Selig committed
145
import pylab as pl
146

csongor's avatar
csongor committed
147
from nifty.config import about
theos's avatar
theos committed
148
from space_paradict import SpaceParadict
Marco Selig's avatar
Marco Selig committed
149

Ultimanet's avatar
Ultimanet committed
150

theos's avatar
theos committed
151
class Space(object):
Marco Selig's avatar
Marco Selig committed
152
    """
Ultimanet's avatar
Ultimanet committed
153
154
155
156
157
158
159
        ..                            __             __
        ..                          /__/           /  /_
        ..      ______    ______    __   __ ___   /   _/
        ..    /   _   | /   _   | /  / /   _   | /  /
        ..   /  /_/  / /  /_/  / /  / /  / /  / /  /_
        ..  /   ____/  \______/ /__/ /__/ /__/  \___/  space class
        .. /__/
Marco Selig's avatar
Marco Selig committed
160

Ultimanet's avatar
Ultimanet committed
161
        NIFTY subclass for unstructured spaces.
Marco Selig's avatar
Marco Selig committed
162

Ultimanet's avatar
Ultimanet committed
163
164
        Unstructured spaces are lists of values without any geometrical
        information.
Marco Selig's avatar
Marco Selig committed
165
166
167

        Parameters
        ----------
Ultimanet's avatar
Ultimanet committed
168
169
        num : int
            Number of points.
170
        dtype : numpy.dtype, *optional*
Ultimanet's avatar
Ultimanet committed
171
            Data type of the field values (default: None).
Marco Selig's avatar
Marco Selig committed
172

Ultimanet's avatar
Ultimanet committed
173
        Attributes
Marco Selig's avatar
Marco Selig committed
174
        ----------
Ultimanet's avatar
Ultimanet committed
175
176
        para : numpy.ndarray
            Array containing the number of points.
177
        dtype : numpy.dtype
Ultimanet's avatar
Ultimanet committed
178
179
180
181
182
183
            Data type of the field values.
        discrete : bool
            Parameter captioning the fact that a :py:class:`point_space` is
            always discrete.
        vol : numpy.ndarray
            Pixel volume of the :py:class:`point_space`, which is always 1.
Marco Selig's avatar
Marco Selig committed
184
    """
185

186
    def __init__(self, dtype=np.dtype('float'), **kwargs):
Ultimanet's avatar
Ultimanet committed
187
188
        """
            Sets the attributes for a point_space class instance.
Marco Selig's avatar
Marco Selig committed
189

Ultimanet's avatar
Ultimanet committed
190
191
192
193
            Parameters
            ----------
            num : int
                Number of points.
194
            dtype : numpy.dtype, *optional*
Ultimanet's avatar
Ultimanet committed
195
                Data type of the field values (default: numpy.float64).
Marco Selig's avatar
Marco Selig committed
196

Ultimanet's avatar
Ultimanet committed
197
198
199
200
            Returns
            -------
            None.
        """
theos's avatar
theos committed
201
        self.paradict = SpaceParadict(**kwargs)
202

203
204
        # parse dtype
        dtype = np.dtype(dtype)
Ultima's avatar
Ultima committed
205
        self.dtype = dtype
theos's avatar
theos committed
206
        self._harmonic = None
207

theos's avatar
theos committed
208
209
210
    @property
    def harmonic(self):
        return self._harmonic
211

Ultima's avatar
Ultima committed
212
213
214
215
    def __hash__(self):
        # Extract the identifying parts from the vars(self) dict.
        result_hash = 0
        for (key, item) in vars(self).items():
216
            if key in []:
Ultima's avatar
Ultima committed
217
                continue
theos's avatar
theos committed
218
            result_hash ^= item.__hash__() ^ int(hash(key)/117)
Ultima's avatar
Ultima committed
219
220
        return result_hash

theos's avatar
theos committed
221
222
223
224
225
    def __eq__(self, x):
        if isinstance(x, type(self)):
            return hash(self) == hash(x)
        else:
            return False
226

227
    def copy(self):
theos's avatar
theos committed
228
        return self.__class__(dtype=self.dtype, **self.paradict.parameters)
229

230
231
    @property
    def shape(self):
232
233
        raise NotImplementedError(about._errors.cstring(
            "ERROR: There is no generic shape for the Space base class."))
Marco Selig's avatar
Marco Selig committed
234

235
236
    @property
    def dim(self):
237
238
        raise NotImplementedError(about._errors.cstring(
            "ERROR: There is no generic dim for the Space base class."))
Marco Selig's avatar
Marco Selig committed
239

240
241
    @property
    def dof(self):
Ultimanet's avatar
Ultimanet committed
242
243
244
245
        """
            Computes the number of degrees of freedom of the space, i.e./  the
            number of points for real-valued fields and twice that number for
            complex-valued fields.
Marco Selig's avatar
Marco Selig committed
246

Ultimanet's avatar
Ultimanet committed
247
248
249
250
251
            Returns
            -------
            dof : int
                Number of degrees of freedom of the space.
        """
252
253
254
        dof = self.dim
        if issubclass(self.dtype.type, np.complexfloating):
            dof = dof * 2
Ultima's avatar
Ultima committed
255
        return dof
256

257
    @property
258
    def total_volume(self):
theos's avatar
theos committed
259
260
        raise NotImplementedError(about._errors.cstring(
            "ERROR: There is no generic volume for the Space base class."))
261

262
    def complement_cast(self, x, axes=None):
263
264
        return x

265
    def weight(self, x, power=1, axes=None):
Marco Selig's avatar
Marco Selig committed
266
        """
Ultimanet's avatar
Ultimanet committed
267
268
            Weights a given array of field values with the pixel volumes (not
            the meta volumes) to a given power.
Marco Selig's avatar
Marco Selig committed
269
270
271

            Parameters
            ----------
Ultimanet's avatar
Ultimanet committed
272
273
274
275
            x : numpy.ndarray
                Array to be weighted.
            power : float, *optional*
                Power of the pixel volumes to be used (default: 1).
Marco Selig's avatar
Marco Selig committed
276
277

            Returns
Ultimanet's avatar
Ultimanet committed
278
279
280
            -------
            y : numpy.ndarray
                Weighted array.
Marco Selig's avatar
Marco Selig committed
281
        """
282
        raise NotImplementedError
Ultima's avatar
Ultima committed
283

284
    def dot_contraction(self, x, axes):
Ultimanet's avatar
Ultimanet committed
285
286
287
        """
            Computes the discrete inner product of two given arrays of field
            values.
Marco Selig's avatar
Marco Selig committed
288

Ultimanet's avatar
Ultimanet committed
289
290
291
292
293
294
            Parameters
            ----------
            x : numpy.ndarray
                First array
            y : numpy.ndarray
                Second array
Marco Selig's avatar
Marco Selig committed
295

Ultimanet's avatar
Ultimanet committed
296
297
298
299
300
            Returns
            -------
            dot : scalar
                Inner product of the two arrays.
        """
301
        return x.sum(axis=axes)
302

303
304
305
    def compute_k_array(self, distribution_strategy):
        raise NotImplementedError(about._errors.cstring(
            "ERROR: There is no generic k_array for Space base class."))
306

307
    def smooth(self, x, **kwargs):
308
        raise AttributeError(about._errors.cstring(
309
            "ERROR: There is no generic smoothing for Space base class."))
310
311
312

    def get_plot(self, x, title="", vmin=None, vmax=None, unit=None,
                 norm=None, other=None, legend=False, save=None, **kwargs):
Marco Selig's avatar
Marco Selig committed
313
        """
314
315
            Creates a plot of field values according to the specifications
            given by the parameters.
Marco Selig's avatar
Marco Selig committed
316
317
318

            Parameters
            ----------
Ultimanet's avatar
Ultimanet committed
319
            x : numpy.ndarray
320
                Array containing the field values.
Marco Selig's avatar
Marco Selig committed
321
322
323

            Returns
            -------
324
            None
325

Ultimanet's avatar
Ultimanet committed
326
            Other parameters
327
            ----------------
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
            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)``).
            unit : string, *optional*
                Unit of the field values (default: "").
            norm : string, *optional*
                Scaling of the field values before plotting (default: None).
            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).
            save : string, *optional*
                Valid file name where the figure is to be stored, by default
                the figure is not saved (default: False).

Ultimanet's avatar
Ultimanet committed
347
        """
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
        if not pl.isinteractive() and save is not None:
            about.warnings.cprint("WARNING: interactive mode off.")

        x = self.cast(x)

        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.dtype('int'))

364
        if (norm == "log") and (vmin <= 0):
365
366
367
368
369
370
371
372
            raise ValueError(about._errors.cstring(
                "ERROR: nonpositive value(s)."))

        if issubclass(self.dtype.type, np.complexfloating):
            if vmin is None:
                vmin = min(x.real.min(), x.imag.min(), abs(x).min())
            if vmax is None:
                vmax = min(x.real.max(), x.imag.max(), abs(x).max())
Ultimanet's avatar
Ultimanet committed
373
        else:
374
375
376
377
            if vmin is None:
                vmin = x.min()
            if vmax is None:
                vmax = x.max()
Ultimanet's avatar
Ultimanet committed
378

379
380
381
        ax0.set_xlim(xaxes[0], xaxes[-1])
        ax0.set_xlabel("index")
        ax0.set_ylim(vmin, vmax)
382

383
384
        if(norm == "log"):
            ax0.set_yscale('log')
Marco Selig's avatar
Marco Selig committed
385

386
387
388
389
390
391
392
393
394
395
396
397
398
399
        if issubclass(self.dtype.type, np.complexfloating):
            ax0.scatter(xaxes, self.unary_operation(x, op='abs'),
                        color=[0.0, 0.5, 0.0], marker='o',
                        label="graph (absolute)", facecolor="none", zorder=1)
            ax0.scatter(xaxes, self.unary_operation(x, op='real'),
                        color=[0.0, 0.5, 0.0], marker='s',
                        label="graph (real part)", facecolor="none", zorder=1)
            ax0.scatter(xaxes, self.unary_operation(x, op='imag'),
                        color=[0.0, 0.5, 0.0], marker='D',
                        label="graph (imaginary part)", facecolor="none",
                        zorder=1)
        else:
            ax0.scatter(xaxes, x, color=[0.0, 0.5, 0.0], marker='o',
                        label="graph 0", zorder=1)
Marco Selig's avatar
Marco Selig committed
400

401
402
403
404
405
406
407
408
409
410
411
412
        if other is not None:
            if not isinstance(other, tuple):
                other = (other, )
            imax = max(1, len(other) - 1)
            for ii in xrange(len(other)):
                ax0.scatter(xaxes, self.dtype(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)],
                            marker='o', label="'other' graph " + str(ii),
                            zorder=-ii)
Ultimanet's avatar
Ultimanet committed
413

414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
        if legend:
            ax0.legend()

        if unit is not None:
            unit = " [" + unit + "]"
        else:
            unit = ""

        ax0.set_ylabel("values" + unit)
        ax0.set_title(title)

        if save is not None:
            fig.savefig(str(save), dpi=None,
                        facecolor="none", edgecolor="none")
            pl.close(fig)
        else:
            fig.canvas.draw()
Marco Selig's avatar
Marco Selig committed
431

432
    def __repr__(self):
Ultima's avatar
Ultima committed
433
434
        string = ""
        string += str(type(self)) + "\n"
Ultima's avatar
Ultima committed
435
        string += "paradict: " + str(self.paradict) + "\n"
436
437
        string += "dtype: " + str(self.dtype) + "\n"
        string += "harmonic: " + str(self.harmonic) + "\n"
Ultima's avatar
Ultima committed
438
        return string