rg_space.py 6.8 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 .space import Space
24
25
from .. import Field
from ..basic_arithmetics import exp
Martin Reinecke's avatar
Martin Reinecke committed
26
from .. import dobj
csongor's avatar
csongor committed
27

Marco Selig's avatar
Marco Selig committed
28

Theo Steininger's avatar
Theo Steininger committed
29
class RGSpace(Space):
Martin Reinecke's avatar
Martin Reinecke committed
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
    """NIFTY subclass for spaces of regular Cartesian grids.

    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:
            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.
        (default: False).
Marco Selig's avatar
Marco Selig committed
47
    """
48

Martin Reinecke's avatar
Martin Reinecke committed
49
    def __init__(self, shape, distances=None, harmonic=False):
Martin Reinecke's avatar
Martin Reinecke committed
50
        super(RGSpace, self).__init__()
51
        self._needed_for_hash += ["_distances", "_shape", "_harmonic"]
52

Martin Reinecke's avatar
Martin Reinecke committed
53
        self._harmonic = bool(harmonic)
54
55
        self._shape = self._parse_shape(shape)
        self._distances = self._parse_distances(distances)
56
        self._dvol = float(reduce(lambda x, y: x*y, self._distances))
Martin Reinecke's avatar
Martin Reinecke committed
57
        self._dim = int(reduce(lambda x, y: x*y, self._shape))
Marco Selig's avatar
Marco Selig committed
58

59
    def __repr__(self):
Martin Reinecke's avatar
Martin Reinecke committed
60
61
        return ("RGSpace(shape=%r, distances=%r, harmonic=%r)"
                % (self.shape, self.distances, self.harmonic))
62

63
64
65
66
67
68
69
70
71
72
    @property
    def harmonic(self):
        return self._harmonic

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

    @property
    def dim(self):
Martin Reinecke's avatar
Martin Reinecke committed
73
        return self._dim
74

75
76
    def scalar_dvol(self):
        return self._dvol
77

78
    def get_k_length_array(self):
Martin Reinecke's avatar
PEP8    
Martin Reinecke committed
79
80
        if (not self.harmonic):
            raise NotImplementedError
Martin Reinecke's avatar
Martin Reinecke committed
81
        out = Field((self,), dtype=np.float64)
Martin Reinecke's avatar
Martin Reinecke committed
82
83
84
        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
85
86
        res = np.minimum(res, self.shape[0]-res)*self.distances[0]
        if len(self.shape) == 1:
Martin Reinecke's avatar
Martin Reinecke committed
87
88
            oloc[()] = res
            return out
Martin Reinecke's avatar
Martin Reinecke committed
89
90
        res *= res
        for i in range(1, len(self.shape)):
Martin Reinecke's avatar
Martin Reinecke committed
91
            tmp = np.arange(oloc.shape[i], dtype=np.float64) + ibegin[i]
Martin Reinecke's avatar
Martin Reinecke committed
92
93
94
            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
95
96
        oloc[()] = np.sqrt(res)
        return out
theos's avatar
theos committed
97

98
    def get_unique_k_lengths(self):
Martin Reinecke's avatar
PEP8    
Martin Reinecke committed
99
100
        if (not self.harmonic):
            raise NotImplementedError
Martin Reinecke's avatar
Martin Reinecke committed
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
        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
118
            # FIXME: this needs to improve for MPI. Maybe unique()/gather()?
Martin Reinecke's avatar
Martin Reinecke committed
119
120
            tmp = dobj.to_global_data(self.get_k_length_array().val)
            tmp = np.unique(tmp)
Martin Reinecke's avatar
Martin Reinecke committed
121
122
123
124
125
126
127
            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
128
129
130
131
    @staticmethod
    def _kernel(x, sigma):
        tmp = x*x
        tmp *= -2.*np.pi*np.pi*sigma*sigma
132
        exp(tmp, out=tmp)
Martin Reinecke's avatar
Martin Reinecke committed
133
134
        return tmp

135
    def get_fft_smoothing_kernel_function(self, sigma):
Martin Reinecke's avatar
PEP8    
Martin Reinecke committed
136
137
        if (not self.harmonic):
            raise NotImplementedError
Martin Reinecke's avatar
Martin Reinecke committed
138
        return lambda x: self._kernel(x, sigma)
theos's avatar
theos committed
139

Martin Reinecke's avatar
Martin Reinecke committed
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
    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
160
                        np.array(codomain.distances)-1) < 1e-7):
Martin Reinecke's avatar
Martin Reinecke committed
161
162
163
            raise AttributeError("The grid-distances of domain and codomain "
                                 "do not match.")

164
165
    @property
    def distances(self):
Theo Steininger's avatar
Theo Steininger committed
166
167
168
        """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.
169
        """
170
171
172
173
        return self._distances

    def _parse_shape(self, shape):
        if np.isscalar(shape):
Martin Reinecke's avatar
Martin Reinecke committed
174
175
            return (shape,)
        return tuple(np.array(shape, dtype=np.int))
176
177
178
179

    def _parse_distances(self, distances):
        if distances is None:
            if self.harmonic:
Martin Reinecke's avatar
Martin Reinecke committed
180
                temp = np.ones_like(self.shape, dtype=np.float64)
181
            else:
Martin Reinecke's avatar
Martin Reinecke committed
182
                temp = 1./np.array(self.shape, dtype=np.float64)
183
        else:
Martin Reinecke's avatar
Martin Reinecke committed
184
            temp = np.empty(len(self.shape), dtype=np.float64)
185
186
            temp[:] = distances
        return tuple(temp)