smoothing_operator.py 10.5 KB
Newer Older
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
# NIFTy
# Copyright (C) 2017  Theo Steininger
#
# Author: Theo Steininger
#
# 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/>.

Jait Dixit's avatar
Jait Dixit committed
19
20
21
22
23
import numpy as np

import nifty.nifty_utilities as utilities
from nifty.operators.endomorphic_operator import EndomorphicOperator
from nifty.operators.fft_operator import FFTOperator
Mihai Baltac's avatar
Mihai Baltac committed
24
from nifty.operators.smoothing_operator import smooth_util as su
25
from d2o import STRATEGIES
Jait Dixit's avatar
Jait Dixit committed
26

27

28
class SmoothingOperator(EndomorphicOperator):
Jait Dixit's avatar
Jait Dixit committed
29
    # ---Overwritten properties and methods---
30
31
32
    def __init__(self, domain=(), sigma=0, log_distances=False,
                 default_spaces=None):
        super(SmoothingOperator, self).__init__(default_spaces)
33
34

        self._domain = self._parse_domain(domain)
Jait Dixit's avatar
Jait Dixit committed
35
36
37

        if len(self.domain) != 1:
            raise ValueError(
38
39
                'ERROR: SmoothOperator accepts only exactly one '
                'space as input domain.'
Jait Dixit's avatar
Jait Dixit committed
40
            )
Jait Dixit's avatar
Jait Dixit committed
41

42
43
44
        self.sigma = sigma
        self.log_distances = log_distances

45
        self._direct_smoothing_width = 3.
Jait Dixit's avatar
Jait Dixit committed
46

47
    def _inverse_times(self, x, spaces):
48
        return self._smoothing_helper(x, spaces, inverse=True)
Jait Dixit's avatar
Jait Dixit committed
49

50
    def _times(self, x, spaces):
51
        return self._smoothing_helper(x, spaces, inverse=False)
Jait Dixit's avatar
Jait Dixit committed
52

Jait Dixit's avatar
Jait Dixit committed
53
    # ---Mandatory properties and methods---
54
55
56
57
    @property
    def domain(self):
        return self._domain

Jait Dixit's avatar
Jait Dixit committed
58
    @property
Martin Reinecke's avatar
Martin Reinecke committed
59
    def self_adjoint(self):
theos's avatar
theos committed
60
        return True
Jait Dixit's avatar
Jait Dixit committed
61

Jait Dixit's avatar
Jait Dixit committed
62
63
64
    @property
    def unitary(self):
        return False
Jait Dixit's avatar
Jait Dixit committed
65
66

    # ---Added properties and methods---
67

Jait Dixit's avatar
Jait Dixit committed
68
69
70
71
    @property
    def sigma(self):
        return self._sigma

72
73
74
75
76
77
78
79
80
81
82
83
84
    @sigma.setter
    def sigma(self, sigma):
        self._sigma = np.float(sigma)

    @property
    def log_distances(self):
        return self._log_distances

    @log_distances.setter
    def log_distances(self, log_distances):
        self._log_distances = bool(log_distances)

    def _smoothing_helper(self, x, spaces, inverse):
theos's avatar
theos committed
85
86
87
88
89
90
91
92
93
94
        if self.sigma == 0:
            return x.copy()

        # the domain of the smoothing operator contains exactly one space.
        # Hence, if spaces is None, but we passed LinearOperator's
        # _check_input_compatibility, we know that x is also solely defined
        # on that space
        if spaces is None:
            spaces = (0,)
        else:
Jait Dixit's avatar
Jait Dixit committed
95
96
            spaces = utilities.cast_axis_to_tuple(spaces, len(x.domain))

97
98
99
100
101
102
103
        try:
            result = self._fft_smoothing(x, spaces, inverse)
        except ValueError:
            result = self._direct_smoothing(x, spaces, inverse)
        return result

    def _fft_smoothing(self, x, spaces, inverse):
theos's avatar
theos committed
104
        Transformator = FFTOperator(x.domain[spaces[0]])
Jait Dixit's avatar
Jait Dixit committed
105

theos's avatar
theos committed
106
107
108
109
110
        # transform to the (global-)default codomain and perform all remaining
        # steps therein
        transformed_x = Transformator(x, spaces=spaces)
        codomain = transformed_x.domain[spaces[0]]
        coaxes = transformed_x.domain_axes[spaces[0]]
111

theos's avatar
theos committed
112
113
114
        # create the kernel using the knowledge of codomain about itself
        axes_local_distribution_strategy = \
            transformed_x.val.get_axes_local_distribution_strategy(axes=coaxes)
Jait Dixit's avatar
Jait Dixit committed
115

116
        kernel = codomain.get_distance_array(
117
118
119
120
121
            distribution_strategy=axes_local_distribution_strategy)

        if self.log_distances:
            kernel.apply_scalar_function(np.log, inplace=True)

theos's avatar
theos committed
122
        kernel.apply_scalar_function(
123
            codomain.get_fft_smoothing_kernel_function(self.sigma),
theos's avatar
theos committed
124
            inplace=True)
Jait Dixit's avatar
Jait Dixit committed
125

theos's avatar
theos committed
126
127
128
129
130
        # now, apply the kernel to transformed_x
        # this is done node-locally utilizing numpys reshaping in order to
        # apply the kernel to the correct axes
        local_transformed_x = transformed_x.val.get_local_data(copy=False)
        local_kernel = kernel.get_local_data(copy=False)
Jait Dixit's avatar
Jait Dixit committed
131

132
        reshaper = [transformed_x.shape[i] if i in coaxes else 1
theos's avatar
theos committed
133
134
                    for i in xrange(len(transformed_x.shape))]
        local_kernel = np.reshape(local_kernel, reshaper)
Jait Dixit's avatar
Jait Dixit committed
135

theos's avatar
theos committed
136
137
138
139
140
        # apply the kernel
        if inverse:
            local_transformed_x /= local_kernel
        else:
            local_transformed_x *= local_kernel
Jait Dixit's avatar
Jait Dixit committed
141

theos's avatar
theos committed
142
        transformed_x.val.set_local_data(local_transformed_x, copy=False)
Jait Dixit's avatar
Jait Dixit committed
143

theos's avatar
theos committed
144
145
146
147
        smoothed_x = Transformator.inverse_times(transformed_x, spaces=spaces)

        result = x.copy_empty()
        result.set_val(smoothed_x, copy=False)
Jait Dixit's avatar
Jait Dixit committed
148

theos's avatar
theos committed
149
        return result
150
151
152
153
154
155

    def _direct_smoothing(self, x, spaces, inverse):
        # infer affected axes
        # we rely on the knowledge, that `spaces` is a tuple with length 1.
        affected_axes = x.domain_axes[spaces[0]]

156
157
158
159
160
        if len(affected_axes) > 1:
            raise ValueError("By this implementation only one-dimensional "
                             "spaces can be smoothed directly.")

        affected_axis = affected_axes[0]
161
162

        distance_array = x.domain[spaces[0]].get_distance_array(
163
164
            distribution_strategy='not')
        distance_array = distance_array.get_local_data(copy=False)
165
166

        if self.log_distances:
167
            np.log(distance_array, out=distance_array)
168
169
170
171
172
173
174
175
176

        # collect the local data + ghost cells
        local_data_Q = False

        if x.distribution_strategy == 'not':
            local_data_Q = True
        elif x.distribution_strategy in STRATEGIES['slicing']:
            # infer the local start/end based on the slicing information of
            # x's d2o. Only gets non-trivial for axis==0.
177
            if 0 != affected_axis:
178
179
                local_data_Q = True
            else:
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
                start_index = x.val.distributor.local_start
                start_distance = distance_array[start_index]
                augmented_start_distance = \
                    (start_distance - self._direct_smoothing_width*self.sigma)
                augmented_start_index = \
                    np.searchsorted(distance_array, augmented_start_distance)
                true_start = start_index - augmented_start_index
                end_index = x.val.distributor.local_end
                end_distance = distance_array[end_index-1]
                augmented_end_distance = \
                    (end_distance + self._direct_smoothing_width*self.sigma)
                augmented_end_index = \
                    np.searchsorted(distance_array, augmented_end_distance)
                true_end = true_start + x.val.distributor.local_length
                augmented_slice = slice(augmented_start_index,
                                        augmented_end_index)

197
198
199
200
201
                augmented_data = x.val.get_data(augmented_slice,
                                                local_keys=True,
                                                copy=False)
                augmented_data = augmented_data.get_local_data(copy=False)

202
                augmented_distance_array = distance_array[augmented_slice]
203
204

        else:
205
206
            raise ValueError("Direct smoothing not implemented for given"
                             "distribution strategy.")
207
208
209
210
211

        if local_data_Q:
            # if the needed data resides on the nodes already, the necessary
            # are the same; no matter what the distribution strategy was.
            augmented_data = x.val.get_local_data(copy=False)
212
213
214
            augmented_distance_array = distance_array
            true_start = 0
            true_end = x.shape[affected_axis]
215
216

        # perform the convolution along the affected axes
217
218
219
220
221
222
223
224
225
        # currently only one axis is supported
        data_axis = affected_axes[0]
        local_result = self._direct_smoothing_single_axis(
                                                    augmented_data,
                                                    data_axis,
                                                    augmented_distance_array,
                                                    true_start,
                                                    true_end,
                                                    inverse)
226
227
228
229
230
        result = x.copy_empty()
        result.val.set_local_data(local_result, copy=False)
        return result

    def _direct_smoothing_single_axis(self, data, data_axis, distances,
231
                                      true_start, true_end, inverse):
232
        if inverse:
233
            true_sigma = 1. / self.sigma
234
235
236
        else:
            true_sigma = self.sigma

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
        if data.dtype is np.dtype('float32'):
            distances = distances.astype(np.float32, copy=False)
            smoothed_data = su.apply_along_axis_f(
                                  data_axis, data,
                                  startindex=true_start,
                                  endindex=true_end,
                                  distances=distances,
                                  smooth_length=true_sigma,
                                  smoothing_width=self._direct_smoothing_width)
        elif data.dtype is np.dtype('float64'):
            distances = distances.astype(np.float64, copy=False)
            smoothed_data = su.apply_along_axis(
                                  data_axis, data,
                                  startindex=true_start,
                                  endindex=true_end,
                                  distances=distances,
                                  smooth_length=true_sigma,
                                  smoothing_width=self._direct_smoothing_width)

        elif np.issubdtype(data.dtype, np.complexfloating):
            real = self._direct_smoothing_single_axis(data.real,
                                                      data_axis,
                                                      distances,
                                                      true_start,
                                                      true_end, inverse)
            imag = self._direct_smoothing_single_axis(data.imag,
                                                      data_axis,
                                                      distances,
                                                      true_start,
                                                      true_end, inverse)

            return real + 1j*imag

270
        else:
271
272
            raise TypeError("Dtype %s not supported" % str(data.dtype))

273
        return smoothed_data