rg_space.py 11.8 KB
Newer Older
1
2
3
4
5
# NIFTy
# Copyright (C) 2017  Theo Steininger
#
# Author: Theo Steininger
#
6
7
8
9
# 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.
10
#
11
12
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
13
14
15
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
16
# You should have received a copy of the GNU General Public License
17
# along with this program.  If not, see <http://www.gnu.org/licenses/>.
Marco Selig's avatar
Marco Selig committed
18
19
20
21
22
23
24
25
26
27

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

Marco Selig's avatar
Marco Selig committed
28
    NIFTY submodule for regular Cartesian grids.
Marco Selig's avatar
Marco Selig committed
29
30
31

"""
from __future__ import division
Ultimanet's avatar
Ultimanet committed
32

Marco Selig's avatar
Marco Selig committed
33
import numpy as np
Ultimanet's avatar
Ultimanet committed
34

35
36
from d2o import distributed_data_object,\
                STRATEGIES as DISTRIBUTION_STRATEGIES
37

38
from nifty.spaces.space import Space
csongor's avatar
csongor committed
39

Marco Selig's avatar
Marco Selig committed
40

Theo Steininger's avatar
Theo Steininger committed
41
class RGSpace(Space):
Marco Selig's avatar
Marco Selig committed
42
43
44
45
46
47
48
49
50
51
52
    """
        ..      _____   _______
        ..    /   __/ /   _   /
        ..   /  /    /  /_/  /
        ..  /__/     \____  /  space class
        ..          /______/

        NIFTY subclass for spaces of regular Cartesian grids.

            Parameters
            ----------
Martin Reinecke's avatar
Martin Reinecke committed
53
            shape : {int, numpy.ndarray}
54
                Number of grid points or numbers of gridpoints along each axis.
Marco Selig's avatar
Marco Selig committed
55
            zerocenter : {bool, numpy.ndarray}, *optional*
Theo Steininger's avatar
Theo Steininger committed
56
57
58
            Whether x==0 (or k==0, respectively) is located in the center of
            the grid (or the center of each axis speparately) or not.
            (default: False).
Martin Reinecke's avatar
Martin Reinecke committed
59
            distances : {float, numpy.ndarray}, *optional*
Marco Selig's avatar
Marco Selig committed
60
61
                Distance between two grid points along each axis
                (default: None).
62
63
64
                If distances==None:
                    if harmonic==True, all distances will be set to 1
                    if harmonic==False, the distance along each axis will be
65
66
                      set to the inverse of the number of points along that
                      axis.
Martin Reinecke's avatar
Martin Reinecke committed
67
            harmonic : bool, *optional*
Theo Steininger's avatar
Theo Steininger committed
68
            Whether the space represents a grid in position or harmonic space.
Marco Selig's avatar
Marco Selig committed
69
70
71
72
                (default: False).

        Attributes
        ----------
Martin Reinecke's avatar
Martin Reinecke committed
73
        harmonic : bool
Theo Steininger's avatar
Theo Steininger committed
74
75
76
77
78
            Whether or not the grid represents a position or harmonic space.
        zerocenter : tuple of bool
            Whether x==0 (or k==0, respectively) is located in the center of
            the grid (or the center of each axis speparately) or not.
        distances : tuple of floats
79
80
81
82
83
84
85
86
87
            Distance between two grid points along the correponding axis.
        dim : np.int
            Total number of dimensionality, i.e. the number of pixels.
        harmonic : bool
            Specifies whether the space is a signal or harmonic space.
        total_volume : np.float
            The total volume of the space.
        shape : tuple of np.ints
            The shape of the space's data array.
Theo Steininger's avatar
Theo Steininger committed
88

Marco Selig's avatar
Marco Selig committed
89
90
    """

91
92
    # ---Overwritten properties and methods---

93
    def __init__(self, shape, zerocenter=False, distances=None,
Martin Reinecke's avatar
Martin Reinecke committed
94
                 harmonic=False):
Marco Selig's avatar
Marco Selig committed
95
        """
96
            Sets the attributes for an RGSpace class instance.
Marco Selig's avatar
Marco Selig committed
97

Theo Steininger's avatar
Theo Steininger committed
98

Marco Selig's avatar
Marco Selig committed
99
100
101
102
103

            Returns
            -------
            None
        """
104
105
        self._harmonic = bool(harmonic)

Martin Reinecke's avatar
Martin Reinecke committed
106
        super(RGSpace, self).__init__()
107

108
109
110
        self._shape = self._parse_shape(shape)
        self._distances = self._parse_distances(distances)
        self._zerocenter = self._parse_zerocenter(zerocenter)
Marco Selig's avatar
Marco Selig committed
111

112
113
    def hermitian_decomposition(self, x, axes=None,
                                preserve_gaussian_variance=False):
114
115
116
117
118
119
120
121
122
        # compute the hermitian part
        flipped_x = self._hermitianize_inverter(x, axes=axes)
        flipped_x = flipped_x.conjugate()
        # average x and flipped_x.
        hermitian_part = x + flipped_x
        hermitian_part /= 2.

        # use subtraction since it is faster than flipping another time
        anti_hermitian_part = (x-hermitian_part)/1j
123
124
125
126
127
128
129

        if preserve_gaussian_variance:
            hermitian_part, anti_hermitian_part = \
                self._hermitianize_correct_variance(hermitian_part,
                                                    anti_hermitian_part,
                                                    axes=axes)

130
131
        return (hermitian_part, anti_hermitian_part)

132
133
134
135
136
137
    def _hermitianize_correct_variance(self, hermitian_part,
                                       anti_hermitian_part, axes):
        # Correct the variance by multiplying sqrt(2)
        hermitian_part = hermitian_part * np.sqrt(2)
        anti_hermitian_part = anti_hermitian_part * np.sqrt(2)

Martin Reinecke's avatar
Martin Reinecke committed
138
        # The fixed points of the point inversion must not be averaged.
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
        # Hence one must divide out the sqrt(2) again
        # -> Get the middle index of the array
        mid_index = np.array(hermitian_part.shape, dtype=np.int) // 2
        dimensions = mid_index.size
        # Use ndindex to iterate over all combinations of zeros and the
        # mid_index in order to correct all fixed points.
        if axes is None:
            axes = xrange(dimensions)

        ndlist = [2 if i in axes else 1 for i in xrange(dimensions)]
        ndlist = tuple(ndlist)
        for i in np.ndindex(ndlist):
            temp_index = tuple(i * mid_index)
            hermitian_part[temp_index] /= np.sqrt(2)
            anti_hermitian_part[temp_index] /= np.sqrt(2)
        return hermitian_part, anti_hermitian_part

156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
    def _hermitianize_inverter(self, x, axes):
        # calculate the number of dimensions the input array has
        dimensions = len(x.shape)
        # prepare the slicing object which will be used for mirroring
        slice_primitive = [slice(None), ] * dimensions
        # copy the input data
        y = x.copy()

        if axes is None:
            axes = xrange(dimensions)

        # flip in the desired directions
        for i in axes:
            slice_picker = slice_primitive[:]
            slice_picker[i] = slice(1, None, None)
            slice_picker = tuple(slice_picker)

            slice_inverter = slice_primitive[:]
            slice_inverter[i] = slice(None, 0, -1)
            slice_inverter = tuple(slice_inverter)

            try:
                y.set_data(to_key=slice_picker, data=y,
                           from_key=slice_inverter)
            except(AttributeError):
                y[slice_picker] = y[slice_inverter]
        return y

184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
    # ---Mandatory properties and methods---

    @property
    def harmonic(self):
        return self._harmonic

    @property
    def shape(self):
        return self._shape

    @property
    def dim(self):
        return reduce(lambda x, y: x*y, self.shape)

    @property
    def total_volume(self):
        return self.dim * reduce(lambda x, y: x*y, self.distances)

    def copy(self):
        return self.__class__(shape=self.shape,
                              zerocenter=self.zerocenter,
                              distances=self.distances,
Martin Reinecke's avatar
Martin Reinecke committed
206
                              harmonic=self.harmonic)
207
208

    def weight(self, x, power=1, axes=None, inplace=False):
209
        weight = reduce(lambda x, y: x*y, self.distances) ** np.float(power)
210
211
212
213
214
215
216
        if inplace:
            x *= weight
            result_x = x
        else:
            result_x = x*weight
        return result_x

217
    def get_distance_array(self, distribution_strategy):
Theo Steininger's avatar
Theo Steininger committed
218
219
        """ Calculates an n-dimensional array with its entries being the
        lengths of the vectors from the zero point of the grid.
theos's avatar
theos committed
220
221
222

            Parameters
            ----------
Theo Steininger's avatar
Theo Steininger committed
223
224
225
        distribution_strategy : str
            The distribution_strategy which shall be used the returned
            distributed_data_object.
theos's avatar
theos committed
226
227
228

            Returns
            -------
Theo Steininger's avatar
Theo Steininger committed
229
230
        distributed_data_object
            A d2o containing the distances
theos's avatar
theos committed
231
        """
Theo Steininger's avatar
Theo Steininger committed
232

theos's avatar
theos committed
233
234
235
        shape = self.shape
        # prepare the distributed_data_object
        nkdict = distributed_data_object(
Martin Reinecke's avatar
Martin Reinecke committed
236
                        global_shape=shape, dtype=np.float64,
theos's avatar
theos committed
237
238
239
240
241
242
243
244
245
                        distribution_strategy=distribution_strategy)

        if distribution_strategy in DISTRIBUTION_STRATEGIES['slicing']:
            # get the node's individual slice of the first dimension
            slice_of_first_dimension = slice(
                                    *nkdict.distributor.local_slice[0:2])
        elif distribution_strategy in DISTRIBUTION_STRATEGIES['not']:
            slice_of_first_dimension = slice(0, shape[0])
        else:
246
247
            raise ValueError(
                "Unsupported distribution strategy")
theos's avatar
theos committed
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
        dists = self._distance_array_helper(slice_of_first_dimension)
        nkdict.set_local_data(dists)

        return nkdict

    def _distance_array_helper(self, slice_of_first_dimension):
        dk = self.distances
        shape = self.shape

        inds = []
        for a in shape:
            inds += [slice(0, a)]

        cords = np.ogrid[inds]

Theo Steininger's avatar
Theo Steininger committed
263
        dists = ((cords[0] - shape[0]//2)*dk[0])**2
theos's avatar
theos committed
264
        # apply zerocenterQ shift
265
266
        if not self.zerocenter[0]:
            dists = np.fft.ifftshift(dists)
theos's avatar
theos committed
267
268
269
270
        # only save the individual slice
        dists = dists[slice_of_first_dimension]
        for ii in range(1, len(shape)):
            temp = ((cords[ii] - shape[ii] // 2) * dk[ii])**2
271
            if not self.zerocenter[ii]:
Martin Reinecke's avatar
Martin Reinecke committed
272
                temp = np.fft.ifftshift(temp)
theos's avatar
theos committed
273
274
275
276
            dists = dists + temp
        dists = np.sqrt(dists)
        return dists

277
    def get_fft_smoothing_kernel_function(self, sigma):
Theo Steininger's avatar
Theo Steininger committed
278

theos's avatar
theos committed
279
280
281
        if sigma is None:
            sigma = np.sqrt(2) * np.max(self.distances)

282
        return lambda x: np.exp(-0.5 * np.pi**2 * x**2 * sigma**2)
theos's avatar
theos committed
283

284
285
286
287
    # ---Added properties and methods---

    @property
    def distances(self):
Theo Steininger's avatar
Theo Steininger committed
288
289
290
        """Distance between two grid points along each axis. It is a tuple
        of positive floating point numbers with the n-th entry giving the
        distances of grid points along the n-th dimension.
291
        """
Theo Steininger's avatar
Theo Steininger committed
292

293
294
295
296
        return self._distances

    @property
    def zerocenter(self):
297
        """Returns True if grid points lie symmetrically around zero.
Theo Steininger's avatar
Theo Steininger committed
298

299
300
        Returns
        -------
Theo Steininger's avatar
Theo Steininger committed
301
302
303
304
305
        bool
            True if the grid points are centered around the 0 grid point. This
            option is most common for harmonic spaces (where both conventions
            are used) but may be used for position spaces, too.

306
        """
Theo Steininger's avatar
Theo Steininger committed
307

308
309
310
311
312
313
314
315
316
317
318
319
        return self._zerocenter

    def _parse_shape(self, shape):
        if np.isscalar(shape):
            shape = (shape,)
        temp = np.empty(len(shape), dtype=np.int)
        temp[:] = shape
        return tuple(temp)

    def _parse_distances(self, distances):
        if distances is None:
            if self.harmonic:
Martin Reinecke's avatar
Martin Reinecke committed
320
                temp = np.ones_like(self.shape, dtype=np.float64)
321
            else:
Martin Reinecke's avatar
Martin Reinecke committed
322
                temp = 1 / np.array(self.shape, dtype=np.float64)
323
        else:
Martin Reinecke's avatar
Martin Reinecke committed
324
            temp = np.empty(len(self.shape), dtype=np.float64)
325
326
327
328
329
330
331
            temp[:] = distances
        return tuple(temp)

    def _parse_zerocenter(self, zerocenter):
        temp = np.empty(len(self.shape), dtype=bool)
        temp[:] = zerocenter
        return tuple(temp)
332
333
334
335

    # ---Serialization---

    def _to_hdf5(self, hdf5_group):
Jait Dixit's avatar
Jait Dixit committed
336
337
338
        hdf5_group['shape'] = self.shape
        hdf5_group['zerocenter'] = self.zerocenter
        hdf5_group['distances'] = self.distances
339
        hdf5_group['harmonic'] = self.harmonic
Jait Dixit's avatar
Jait Dixit committed
340

341
342
343
        return None

    @classmethod
Theo Steininger's avatar
Theo Steininger committed
344
    def _from_hdf5(cls, hdf5_group, repository):
345
        result = cls(
Jait Dixit's avatar
Jait Dixit committed
346
347
348
            shape=hdf5_group['shape'][:],
            zerocenter=hdf5_group['zerocenter'][:],
            distances=hdf5_group['distances'][:],
349
            harmonic=hdf5_group['harmonic'][()],
Jait Dixit's avatar
Jait Dixit committed
350
            )
351
        return result