rg_space.py 11.5 KB
Newer Older
1
2
3
4
# 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.
5
#
6
7
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
8
9
10
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
11
# You should have received a copy of the GNU General Public License
12
# along with this program.  If not, see <http://www.gnu.org/licenses/>.
Theo Steininger's avatar
Theo Steininger committed
13
14
15
16
17
#
# Copyright(C) 2013-2017 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik
# and financially supported by the Studienstiftung des deutschen Volkes.
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
    """
        ..      _____   _______
        ..    /   __/ /   _   /
        ..   /  /    /  /_/  /
        ..  /__/     \____  /  space class
        ..          /______/

        NIFTY subclass for spaces of regular Cartesian grids.

Theo Steininger's avatar
Theo Steininger committed
51
52
53
54
        Parameters
        ----------
        shape : {int, numpy.ndarray}
            Number of grid points or numbers of gridpoints along each axis.
55
56
57
58
        zerocenter : {bool, numpy.ndarray} *optional*
            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).
Theo Steininger's avatar
Theo Steininger committed
59
60
61
62
63
64
65
66
67
68
        distances : {float, numpy.ndarray}, *optional*
            Distance between two grid points along each axis
            (default: None).
            If distances==None:
                if harmonic==True, all distances will be set to 1
                if harmonic==False, the distance along each axis will be
                  set to the inverse of the number of points along that
                  axis.
        harmonic : bool, *optional*
        Whether the space represents a grid in position or harmonic space.
Theo Steininger's avatar
Theo Steininger committed
69
            (default: False).
Marco Selig's avatar
Marco Selig committed
70
71
72

        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):
95
96
        self._harmonic = bool(harmonic)

Martin Reinecke's avatar
Martin Reinecke committed
97
        super(RGSpace, self).__init__()
98

99
100
101
        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
102

103
104
    def hermitian_decomposition(self, x, axes=None,
                                preserve_gaussian_variance=False):
Martin Reinecke's avatar
Martin Reinecke committed
105
106
        # check axes
        if axes is None:
Martin Reinecke's avatar
fix    
Martin Reinecke committed
107
            axes = range(len(self.shape))
Martin Reinecke's avatar
Martin Reinecke committed
108
109
110
        assert len(x.shape) >= len(self.shape), "shapes mismatch"
        assert len(axes) == len(self.shape), "axes mismatch"

111
112
113
114
115
116
117
118
        # 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
119
        anti_hermitian_part = (x-hermitian_part)
120

121
122
        return (hermitian_part, anti_hermitian_part)

123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
    def hermitian_fixed_points(self):
        dimensions = len(self.shape)
        mid_index = np.array(self.shape)//2
        ndlist = [1]*dimensions
        for k in range(dimensions):
            if self.shape[k] % 2 == 0:
                ndlist[k] = 2
        ndlist = tuple(ndlist)
        fixed_points = []
        for index in np.ndindex(ndlist):
            for k in range(dimensions):
                if self.shape[k] % 2 != 0 and self.zerocenter[k]:
                    index = list(index)
                    index[k] = 1
                    index = tuple(index)
            fixed_points += [tuple(index * mid_index)]
        return fixed_points
140

141
142
    def _hermitianize_inverter(self, x, axes):
        # calculate the number of dimensions the input array has
Martin Reinecke's avatar
Martin Reinecke committed
143
        dimensions = len(x.shape)
144
145
146
147
148
149
        # prepare the slicing object which will be used for mirroring
        slice_primitive = [slice(None), ] * dimensions
        # copy the input data
        y = x.copy()

        # flip in the desired directions
Martin Reinecke's avatar
Martin Reinecke committed
150
151
        for k in range(len(axes)):
            i = axes[k]
152
153
            slice_picker = slice_primitive[:]
            slice_inverter = slice_primitive[:]
Martin Reinecke's avatar
Martin Reinecke committed
154
            if (not self.zerocenter[k]) or self.shape[k] % 2 == 0:
Martin Reinecke's avatar
Martin Reinecke committed
155
                slice_picker[i] = slice(1, None, None)
156
157
                slice_inverter[i] = slice(None, 0, -1)
            else:
Martin Reinecke's avatar
Martin Reinecke committed
158
                slice_picker[i] = slice(None)
159
                slice_inverter[i] = slice(None, None, -1)
Martin Reinecke's avatar
Martin Reinecke committed
160
            slice_picker = tuple(slice_picker)
161
162
163
            slice_inverter = tuple(slice_inverter)

            try:
Martin Reinecke's avatar
Martin Reinecke committed
164
165
                y.set_data(to_key=slice_picker, data=y,
                           from_key=slice_inverter)
166
167
168
169
            except(AttributeError):
                y[slice_picker] = y[slice_inverter]
        return y

170
171
    # ---Mandatory properties and methods---

172
173
174
175
    def __repr__(self):
        return ("RGSpace(shape=%r, zerocenter=%r, distances=%r, harmonic=%r)"
                % (self.shape, self.zerocenter, self.distances, self.harmonic))

176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
    @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
196
                              harmonic=self.harmonic)
197
198

    def weight(self, x, power=1, axes=None, inplace=False):
199
        weight = reduce(lambda x, y: x*y, self.distances) ** np.float(power)
200
201
202
203
204
205
206
        if inplace:
            x *= weight
            result_x = x
        else:
            result_x = x*weight
        return result_x

207
    def get_distance_array(self, distribution_strategy):
Theo Steininger's avatar
Theo Steininger committed
208
209
        """ 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
210

Theo Steininger's avatar
Theo Steininger committed
211
212
        Parameters
        ----------
Theo Steininger's avatar
Theo Steininger committed
213
214
215
        distribution_strategy : str
            The distribution_strategy which shall be used the returned
            distributed_data_object.
theos's avatar
theos committed
216

Theo Steininger's avatar
Theo Steininger committed
217
218
        Returns
        -------
Theo Steininger's avatar
Theo Steininger committed
219
        distributed_data_object
Theo Steininger's avatar
Theo Steininger committed
220
221
            A d2o containing the distances.

theos's avatar
theos committed
222
        """
Theo Steininger's avatar
Theo Steininger committed
223

theos's avatar
theos committed
224
225
226
        shape = self.shape
        # prepare the distributed_data_object
        nkdict = distributed_data_object(
Martin Reinecke's avatar
Martin Reinecke committed
227
                        global_shape=shape, dtype=np.float64,
theos's avatar
theos committed
228
229
230
231
232
233
234
235
236
                        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:
237
238
            raise ValueError(
                "Unsupported distribution strategy")
theos's avatar
theos committed
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
        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]

254
255
        dists = (cords[0] - shape[0]//2)*dk[0]
        dists *= dists
theos's avatar
theos committed
256
        # apply zerocenterQ shift
257
258
        if not self.zerocenter[0]:
            dists = np.fft.ifftshift(dists)
theos's avatar
theos committed
259
260
261
        # only save the individual slice
        dists = dists[slice_of_first_dimension]
        for ii in range(1, len(shape)):
262
263
            temp = (cords[ii] - shape[ii] // 2) * dk[ii]
            temp *= temp
264
            if not self.zerocenter[ii]:
Martin Reinecke's avatar
Martin Reinecke committed
265
                temp = np.fft.ifftshift(temp)
theos's avatar
theos committed
266
267
268
269
            dists = dists + temp
        dists = np.sqrt(dists)
        return dists

270
    def get_fft_smoothing_kernel_function(self, sigma):
Theo Steininger's avatar
Theo Steininger committed
271
        return lambda x: np.exp(-2. * np.pi*np.pi * x*x * sigma*sigma)
theos's avatar
theos committed
272

273
274
275
276
    # ---Added properties and methods---

    @property
    def distances(self):
Theo Steininger's avatar
Theo Steininger committed
277
278
279
        """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.
280
        """
Theo Steininger's avatar
Theo Steininger committed
281

282
283
284
285
        return self._distances

    @property
    def zerocenter(self):
286
        """Returns True if grid points lie symmetrically around zero.
Theo Steininger's avatar
Theo Steininger committed
287

288
289
        Returns
        -------
Theo Steininger's avatar
Theo Steininger committed
290
291
292
293
294
        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.

295
        """
Theo Steininger's avatar
Theo Steininger committed
296

297
298
299
300
301
302
303
304
305
306
307
308
        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
309
                temp = np.ones_like(self.shape, dtype=np.float64)
310
            else:
Martin Reinecke's avatar
Martin Reinecke committed
311
                temp = 1 / np.array(self.shape, dtype=np.float64)
312
        else:
Martin Reinecke's avatar
Martin Reinecke committed
313
            temp = np.empty(len(self.shape), dtype=np.float64)
314
315
316
317
318
319
320
            temp[:] = distances
        return tuple(temp)

    def _parse_zerocenter(self, zerocenter):
        temp = np.empty(len(self.shape), dtype=bool)
        temp[:] = zerocenter
        return tuple(temp)
321
322
323
324

    # ---Serialization---

    def _to_hdf5(self, hdf5_group):
Jait Dixit's avatar
Jait Dixit committed
325
326
327
        hdf5_group['shape'] = self.shape
        hdf5_group['zerocenter'] = self.zerocenter
        hdf5_group['distances'] = self.distances
328
        hdf5_group['harmonic'] = self.harmonic
Jait Dixit's avatar
Jait Dixit committed
329

330
331
332
        return None

    @classmethod
Theo Steininger's avatar
Theo Steininger committed
333
    def _from_hdf5(cls, hdf5_group, repository):
334
        result = cls(
Jait Dixit's avatar
Jait Dixit committed
335
336
337
            shape=hdf5_group['shape'][:],
            zerocenter=hdf5_group['zerocenter'][:],
            distances=hdf5_group['distances'][:],
338
            harmonic=hdf5_group['harmonic'][()],
Jait Dixit's avatar
Jait Dixit committed
339
            )
340
        return result