rg_space.py 6.73 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

from __future__ import division
Martin Reinecke's avatar
Martin Reinecke committed
20
from builtins import range
Martin Reinecke's avatar
Martin Reinecke committed
21
from functools import reduce
Marco Selig's avatar
Marco Selig committed
22
import numpy as np
Martin Reinecke's avatar
Martin Reinecke committed
23
from .structured_domain import StructuredDomain
Martin Reinecke's avatar
cleanup    
Martin Reinecke committed
24
from ..field import Field, exp
Martin Reinecke's avatar
Martin Reinecke committed
25
from .. import dobj
csongor's avatar
csongor committed
26

Marco Selig's avatar
Marco Selig committed
27

Martin Reinecke's avatar
Martin Reinecke committed
28
29
class RGSpace(StructuredDomain):
    """NIFTy subclass for regular Cartesian grids.
Martin Reinecke's avatar
Martin Reinecke committed
30
31
32
33
34
35
36
37
38

    Parameters
    ----------
    shape : {int, numpy.ndarray}
        Number of grid points or numbers of gridpoints along each axis.
    distances : {float, numpy.ndarray}, *optional*
        Distance between two grid points along each axis
        (default: None).
        If distances==None:
39
40
41
        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.
Martin Reinecke's avatar
Martin Reinecke committed
42
    harmonic : bool, *optional*
43
        Whether the space represents a grid in position or harmonic space.
Martin Reinecke's avatar
Martin Reinecke committed
44
        (default: False).
Marco Selig's avatar
Marco Selig committed
45
    """
46

Martin Reinecke's avatar
Martin Reinecke committed
47
    def __init__(self, shape, distances=None, harmonic=False):
Martin Reinecke's avatar
Martin Reinecke committed
48
        super(RGSpace, self).__init__()
49
        self._needed_for_hash += ["_distances", "_shape", "_harmonic"]
50

Martin Reinecke's avatar
Martin Reinecke committed
51
        self._harmonic = bool(harmonic)
Martin Reinecke's avatar
Martin Reinecke committed
52
53
54
        if np.isscalar(shape):
            shape = (shape,)
        self._shape = tuple(int(i) for i in shape)
Martin Reinecke's avatar
tweaks    
Martin Reinecke committed
55
56
57
58
59
60
61
62
63
64
65
66
67

        if distances is None:
            if self.harmonic:
                self._distances = (1.,) * len(self._shape)
            else:
                self._distances = tuple(1./s for s in self._shape)
        elif np.isscalar(distances):
            self._distances = (float(distances),) * len(self._shape)
        else:
            temp = np.empty(len(self.shape), dtype=np.float64)
            temp[:] = distances
            self._distances = tuple(temp)

68
        self._dvol = float(reduce(lambda x, y: x*y, self._distances))
Martin Reinecke's avatar
Martin Reinecke committed
69
        self._size = int(reduce(lambda x, y: x*y, self._shape))
Marco Selig's avatar
Marco Selig committed
70

71
    def __repr__(self):
Martin Reinecke's avatar
Martin Reinecke committed
72
73
        return ("RGSpace(shape=%r, distances=%r, harmonic=%r)"
                % (self.shape, self.distances, self.harmonic))
74

75
76
77
78
79
80
81
82
83
    @property
    def harmonic(self):
        return self._harmonic

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

    @property
Martin Reinecke's avatar
Martin Reinecke committed
84
85
    def size(self):
        return self._size
86

87
88
    def scalar_dvol(self):
        return self._dvol
89

90
    def get_k_length_array(self):
Martin Reinecke's avatar
PEP8    
Martin Reinecke committed
91
92
        if (not self.harmonic):
            raise NotImplementedError
Martin Reinecke's avatar
Martin Reinecke committed
93
        out = Field((self,), dtype=np.float64)
Martin Reinecke's avatar
Martin Reinecke committed
94
95
96
        oloc = dobj.local_data(out.val)
        ibegin = dobj.ibegin(out.val)
        res = np.arange(oloc.shape[0], dtype=np.float64) + ibegin[0]
Martin Reinecke's avatar
Martin Reinecke committed
97
98
        res = np.minimum(res, self.shape[0]-res)*self.distances[0]
        if len(self.shape) == 1:
Martin Reinecke's avatar
Martin Reinecke committed
99
100
            oloc[()] = res
            return out
Martin Reinecke's avatar
Martin Reinecke committed
101
102
        res *= res
        for i in range(1, len(self.shape)):
Martin Reinecke's avatar
Martin Reinecke committed
103
            tmp = np.arange(oloc.shape[i], dtype=np.float64) + ibegin[i]
Martin Reinecke's avatar
Martin Reinecke committed
104
105
106
            tmp = np.minimum(tmp, self.shape[i]-tmp)*self.distances[i]
            tmp *= tmp
            res = np.add.outer(res, tmp)
Martin Reinecke's avatar
Martin Reinecke committed
107
108
        oloc[()] = np.sqrt(res)
        return out
109

110
    def get_unique_k_lengths(self):
Martin Reinecke's avatar
PEP8    
Martin Reinecke committed
111
112
        if (not self.harmonic):
            raise NotImplementedError
Martin Reinecke's avatar
Martin Reinecke committed
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
        dimensions = len(self.shape)
        if dimensions == 1:  # extra easy
            maxdist = self.shape[0]//2
            return np.arange(maxdist+1, dtype=np.float64) * self.distances[0]
        if np.all(self.distances == self.distances[0]):  # shortcut
            maxdist = np.asarray(self.shape)//2
            tmp = np.sum(maxdist*maxdist)
            tmp = np.zeros(tmp+1, dtype=np.bool)
            t2 = np.arange(maxdist[0]+1, dtype=np.int64)
            t2 *= t2
            for i in range(1, dimensions):
                t3 = np.arange(maxdist[i]+1, dtype=np.int64)
                t3 *= t3
                t2 = np.add.outer(t2, t3)
            tmp[t2] = True
            return np.sqrt(np.nonzero(tmp)[0])*self.distances[0]
        else:  # do it the hard way
Martin Reinecke's avatar
tweaks    
Martin Reinecke committed
130
            # FIXME: this needs to improve for MPI. Maybe unique()/gather()?
Martin Reinecke's avatar
Martin Reinecke committed
131
132
            tmp = dobj.to_global_data(self.get_k_length_array().val)
            tmp = np.unique(tmp)
Martin Reinecke's avatar
Martin Reinecke committed
133
134
135
136
137
138
139
            tol = 1e-12*tmp[-1]
            # remove all points that are closer than tol to their right
            # neighbors.
            # I'm appending the last value*2 to the array to treat the
            # rightmost point correctly.
            return tmp[np.diff(np.r_[tmp, 2*tmp[-1]]) > tol]

Martin Reinecke's avatar
Martin Reinecke committed
140
141
142
143
    @staticmethod
    def _kernel(x, sigma):
        tmp = x*x
        tmp *= -2.*np.pi*np.pi*sigma*sigma
144
        exp(tmp, out=tmp)
Martin Reinecke's avatar
Martin Reinecke committed
145
146
        return tmp

147
    def get_fft_smoothing_kernel_function(self, sigma):
Martin Reinecke's avatar
PEP8    
Martin Reinecke committed
148
149
        if (not self.harmonic):
            raise NotImplementedError
Martin Reinecke's avatar
Martin Reinecke committed
150
        return lambda x: self._kernel(x, sigma)
151

Martin Reinecke's avatar
Martin Reinecke committed
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
    def get_default_codomain(self):
        distances = 1. / (np.array(self.shape)*np.array(self.distances))
        return RGSpace(self.shape, distances, not self.harmonic)

    def check_codomain(self, codomain):
        if not isinstance(codomain, RGSpace):
            raise TypeError("domain is not a RGSpace")

        if self.shape != codomain.shape:
            raise AttributeError("The shapes of domain and codomain must be "
                                 "identical.")

        if self.harmonic == codomain.harmonic:
            raise AttributeError("domain.harmonic and codomain.harmonic must "
                                 "not be the same.")

        # Check if the distances match, i.e. dist' = 1 / (num * dist)
        if not np.all(
            np.absolute(np.array(self.shape) *
                        np.array(self.distances) *
Martin Reinecke's avatar
Martin Reinecke committed
172
                        np.array(codomain.distances)-1) < 1e-7):
Martin Reinecke's avatar
Martin Reinecke committed
173
174
175
            raise AttributeError("The grid-distances of domain and codomain "
                                 "do not match.")

176
177
    @property
    def distances(self):
Martin Reinecke's avatar
Martin Reinecke committed
178
        """Distance between grid points along each axis. It is a tuple
Theo Steininger's avatar
Theo Steininger committed
179
        of positive floating point numbers with the n-th entry giving the
Martin Reinecke's avatar
Martin Reinecke committed
180
        distance between neighboring grid points along the n-th dimension.
181
        """
182
        return self._distances