lm_space.py 6.72 KB
Newer Older
1
2
3
4
5
6
7
8
9
10
11
12
# 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/>.
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.
18

csongor's avatar
csongor committed
19
20
21
22
from __future__ import division

import numpy as np

23
from nifty.spaces.space import Space
theos's avatar
theos committed
24

Jait Dixit's avatar
Jait Dixit committed
25
26
from d2o import arange

csongor's avatar
csongor committed
27

Theo Steininger's avatar
Theo Steininger committed
28
class LMSpace(Space):
csongor's avatar
csongor committed
29
30
31
32
33
34
35
36
37
38
39
    """
        ..       __
        ..     /  /
        ..    /  /    __ ____ ___
        ..   /  /   /   _    _   |
        ..  /  /_  /  / /  / /  /
        ..  \___/ /__/ /__/ /__/  space class

        NIFTY subclass for spherical harmonics components, for representations
        of fields on the two-sphere.

40
41
42
43
44
45
        Parameters
        ----------
        lmax : int
            The maximal :math:`l` value of any spherical harmonics
            :math:`Y_{lm}` that is represented in this Space.

46
        Attributes
csongor's avatar
csongor committed
47
48
        ----------
        lmax : int
49
50
51
52
53
            The maximal :math:`l` value of any spherical harmonics
            :math:`Y_{lm}` that is represented in this Space.
        mmax : int
            The maximal :math:`m` value of any spherical harmonic
            :math:`Y_{lm}` that is represented in this Space.
54
55
56
57
58
59
60
61
        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.
csongor's avatar
csongor committed
62
63
64
65
66
67
68

        See Also
        --------
        hp_space : A class for the HEALPix discretization of the sphere [#]_.
        gl_space : A class for the Gauss-Legendre discretization of the
            sphere [#]_.

Theo Steininger's avatar
Theo Steininger committed
69
70
71
72
73
        Raises
        ------
        ValueError
            If given lmax is negative.

74
75
        Notes
        -----
Theo Steininger's avatar
Theo Steininger committed
76
            This implementation implicitly sets the mmax parameter to lmax.
77

csongor's avatar
csongor committed
78
79
80
81
82
83
84
85
86
87
        References
        ----------
        .. [#] K.M. Gorski et al., 2005, "HEALPix: A Framework for
               High-Resolution Discretization and Fast Analysis of Data
               Distributed on the Sphere", *ApJ* 622..759G.
        .. [#] M. Reinecke and D. Sverre Seljebotn, 2013, "Libsharp - spherical
               harmonic transforms revisited";
               `arXiv:1303.4945 <http://www.arxiv.org/abs/1303.4945>`_
    """

Martin Reinecke's avatar
Martin Reinecke committed
88
89
    def __init__(self, lmax):
        super(LMSpace, self).__init__()
csongor's avatar
csongor committed
90
        self._lmax = self._parse_lmax(lmax)
csongor's avatar
csongor committed
91

92
93
    def hermitian_decomposition(self, x, axes=None,
                                preserve_gaussian_variance=False):
94
95
96
97
98
99
100
101
102
103
104
105
106
        if issubclass(x.dtype.type, np.complexfloating):
            hermitian_part = x.copy_empty()
            anti_hermitian_part = x.copy_empty()
            hermitian_part[:] = x.real
            anti_hermitian_part[:] = x.imag * 1j
            if preserve_gaussian_variance:
                hermitian_part *= np.sqrt(2)
                anti_hermitian_part *= np.sqrt(2)
        else:
            hermitian_part = x.copy()
            anti_hermitian_part = x.copy_empty()
            anti_hermitian_part.val[:] = 0

107
108
        return (hermitian_part, anti_hermitian_part)

109
110
#    def hermitian_fixed_points(self):
#        return None
111

Theo Steininger's avatar
Theo Steininger committed
112
    # ---Mandatory properties and methods---
csongor's avatar
csongor committed
113

114
115
116
    def __repr__(self):
        return ("LMSpace(lmax=%r)" % self.lmax)

csongor's avatar
csongor committed
117
118
119
    @property
    def harmonic(self):
        return True
csongor's avatar
csongor committed
120
121

    @property
122
123
    def shape(self):
        return (self.dim, )
csongor's avatar
csongor committed
124
125

    @property
126
127
    def dim(self):
        l = self.lmax
128
        # the LMSpace consists of the full triangle (including -m's!),
theos's avatar
theos committed
129
130
        # minus two little triangles if mmax < lmax
        # dim = (((2*(l+1)-1)+1)**2/4 - 2 * (l-m)(l-m+1)/2
131
132
        # dim = np.int((l+1)**2 - (l-m)*(l-m+1.))
        # We fix l == m
133
        return np.int((l+1)*(l+1))
csongor's avatar
csongor committed
134

135
136
137
    @property
    def total_volume(self):
        # the individual pixels have a fixed volume of 1.
Martin Reinecke's avatar
Martin Reinecke committed
138
        return np.float64(self.dim)
csongor's avatar
csongor committed
139

140
    def copy(self):
Martin Reinecke's avatar
Martin Reinecke committed
141
        return self.__class__(lmax=self.lmax)
csongor's avatar
csongor committed
142

143
144
145
    def weight(self, x, power=1, axes=None, inplace=False):
        if inplace:
            return x
csongor's avatar
csongor committed
146
        else:
147
            return x.copy()
csongor's avatar
csongor committed
148

149
150
151
152
153
    def get_distance_array(self, distribution_strategy):
        dists = arange(start=0, stop=self.shape[0],
                       distribution_strategy=distribution_strategy)

        dists = dists.apply_scalar_function(
154
            lambda x: self._distance_array_helper(x, self.lmax),
Martin Reinecke's avatar
Martin Reinecke committed
155
            dtype=np.float64)
156
157
158

        return dists

159
160
161
162
163
164
165
166
    @staticmethod
    def _distance_array_helper(index_array, lmax):
        u = 2*lmax + 1
        index_half = (index_array+np.minimum(lmax, index_array)+1)//2
        m = (np.ceil((u - np.sqrt(u*u - 8*(index_half - lmax)))/2)).astype(int)
        res = (index_half - m*(u - m)//2).astype(np.float64)
        return res

167
    def get_fft_smoothing_kernel_function(self, sigma):
Theo Steininger's avatar
Theo Steininger committed
168
169
170
        # cf. "All-sky convolution for polarimetry experiments"
        # by Challinor et al.
        # http://arxiv.org/abs/astro-ph/0008228
171
        return lambda x: np.exp(-0.5 * x * (x + 1) * sigma*sigma)
172

csongor's avatar
csongor committed
173
174
175
176
    # ---Added properties and methods---

    @property
    def lmax(self):
Theo Steininger's avatar
Theo Steininger committed
177
178
        """ Returns the maximal :math:`l` value of any spherical harmonics
        :math:`Y_{lm}` that is represented in this Space.
179
        """
csongor's avatar
csongor committed
180
181
182
183
        return self._lmax

    @property
    def mmax(self):
Theo Steininger's avatar
Theo Steininger committed
184
185
186
187
188
        """ Returns the maximal :math:`m` value of any spherical harmonic
        :math:`Y_{lm}` that is represented in this Space. As :math:`m` goes
        from :math:`-l` to :math:`l` for every :math:`l` this just returns the
        same as lmax.

189
190
        See Also
        --------
Theo Steininger's avatar
Theo Steininger committed
191
192
193
        lmax : Returns the maximal :math:`l`-value of the spherical harmonics
            being used.

194
        """
Theo Steininger's avatar
Theo Steininger committed
195

196
        return self._lmax
csongor's avatar
csongor committed
197
198
199

    def _parse_lmax(self, lmax):
        lmax = np.int(lmax)
200
201
        if lmax < 0:
            raise ValueError("lmax must be >=0.")
csongor's avatar
csongor committed
202
        return lmax
Jait Dixit's avatar
Jait Dixit committed
203
204
205
206
207
208
209
210

    # ---Serialization---

    def _to_hdf5(self, hdf5_group):
        hdf5_group['lmax'] = self.lmax
        return None

    @classmethod
Theo Steininger's avatar
Theo Steininger committed
211
    def _from_hdf5(cls, hdf5_group, repository):
Jait Dixit's avatar
Jait Dixit committed
212
213
214
215
        result = cls(
            lmax=hdf5_group['lmax'][()],
            )
        return result