lm_space.py 5.36 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/>.

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
40
41
42
43
44
45
46
47
48
49
50
51
    """
        ..       __
        ..     /  /
        ..    /  /    __ ____ ___
        ..   /  /   /   _    _   |
        ..  /  /_  /  / /  / /  /
        ..  \___/ /__/ /__/ /__/  space class

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

        Parameters
        ----------
        lmax : int
            Maximum :math:`\ell`-value up to which the spherical harmonics
            coefficients are to be used.

        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
52
53
54
55
56
        Raises
        ------
        ValueError
            If given lmax is negative.

57
58
        Notes
        -----
Theo Steininger's avatar
Theo Steininger committed
59
            This implementation implicitly sets the mmax parameter to lmax.
60

csongor's avatar
csongor committed
61
62
63
64
65
66
67
68
69
70
        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
71
72
    def __init__(self, lmax):
        super(LMSpace, self).__init__()
csongor's avatar
csongor committed
73
        self._lmax = self._parse_lmax(lmax)
csongor's avatar
csongor committed
74

75
76
    def hermitian_decomposition(self, x, axes=None,
                                preserve_gaussian_variance=False):
77
78
79
80
81
82
        hermitian_part = x.copy_empty()
        anti_hermitian_part = x.copy_empty()
        hermitian_part[:] = x.real
        anti_hermitian_part[:] = x.imag
        return (hermitian_part, anti_hermitian_part)

Theo Steininger's avatar
Theo Steininger committed
83
    # ---Mandatory properties and methods---
csongor's avatar
csongor committed
84
85
86
87

    @property
    def harmonic(self):
        return True
csongor's avatar
csongor committed
88
89

    @property
90
91
    def shape(self):
        return (self.dim, )
csongor's avatar
csongor committed
92
93

    @property
94
95
    def dim(self):
        l = self.lmax
96
        # the LMSpace consists of the full triangle (including -m's!),
theos's avatar
theos committed
97
98
        # minus two little triangles if mmax < lmax
        # dim = (((2*(l+1)-1)+1)**2/4 - 2 * (l-m)(l-m+1)/2
99
100
101
        # dim = np.int((l+1)**2 - (l-m)*(l-m+1.))
        # We fix l == m
        return np.int((l+1)**2)
csongor's avatar
csongor committed
102

103
104
105
    @property
    def total_volume(self):
        # the individual pixels have a fixed volume of 1.
Martin Reinecke's avatar
Martin Reinecke committed
106
        return np.float64(self.dim)
csongor's avatar
csongor committed
107

108
    def copy(self):
Martin Reinecke's avatar
Martin Reinecke committed
109
        return self.__class__(lmax=self.lmax)
csongor's avatar
csongor committed
110

111
112
113
    def weight(self, x, power=1, axes=None, inplace=False):
        if inplace:
            return x
csongor's avatar
csongor committed
114
        else:
115
            return x.copy()
csongor's avatar
csongor committed
116

117
118
119
120
121
    def get_distance_array(self, distribution_strategy):
        dists = arange(start=0, stop=self.shape[0],
                       distribution_strategy=distribution_strategy)

        dists = dists.apply_scalar_function(
122
            lambda x: self._distance_array_helper(x, self.lmax),
Martin Reinecke's avatar
Martin Reinecke committed
123
            dtype=np.float64)
124
125
126

        return dists

127
128
129
130
131
132
133
134
    @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

135
    def get_fft_smoothing_kernel_function(self, sigma):
136
        # FIXME why x(x+1) ? add reference to paper!
137
138
        return lambda x: np.exp(-0.5 * x * (x + 1) * sigma**2)

csongor's avatar
csongor committed
139
140
141
142
    # ---Added properties and methods---

    @property
    def lmax(self):
Theo Steininger's avatar
Theo Steininger committed
143
144
        """ Returns the maximal :math:`l` value of any spherical harmonics
        :math:`Y_{lm}` that is represented in this Space.
145
        """
csongor's avatar
csongor committed
146
147
148
149
        return self._lmax

    @property
    def mmax(self):
Theo Steininger's avatar
Theo Steininger committed
150
151
152
153
154
        """ 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.

155
156
        See Also
        --------
Theo Steininger's avatar
Theo Steininger committed
157
158
159
        lmax : Returns the maximal :math:`l`-value of the spherical harmonics
            being used.

160
        """
Theo Steininger's avatar
Theo Steininger committed
161

162
        return self._lmax
csongor's avatar
csongor committed
163
164
165

    def _parse_lmax(self, lmax):
        lmax = np.int(lmax)
166
167
        if lmax < 0:
            raise ValueError("lmax must be >=0.")
csongor's avatar
csongor committed
168
        return lmax
Jait Dixit's avatar
Jait Dixit committed
169
170
171
172
173
174
175
176

    # ---Serialization---

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

    @classmethod
Theo Steininger's avatar
Theo Steininger committed
177
    def _from_hdf5(cls, hdf5_group, repository):
Jait Dixit's avatar
Jait Dixit committed
178
179
180
181
        result = cls(
            lmax=hdf5_group['lmax'][()],
            )
        return result