lm_space.py 6.06 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 [#]_.

52
53
54
55
56
57
58
        Notes
        -----
        Hermitian symmetry, i.e. :math:`a_{\ell -m} = \overline{a}_{\ell m}` is
        always assumed for the spherical harmonics components, i.e. only fields
        on the two-sphere with real-valued representations in position space
        can be handled.

csongor's avatar
csongor committed
59
60
61
62
63
64
65
66
67
68
        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
69
    def __init__(self, lmax):
csongor's avatar
csongor committed
70
71
72
73
74
75
76
77
78
79
80
81
        """
            Sets the attributes for an lm_space class instance.

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

            Returns
            -------
            None.
82
83
84
85
86
            
            Raises
            ------
            ValueError
                If lmax is negative.
csongor's avatar
csongor committed
87
88
89

        """

Martin Reinecke's avatar
Martin Reinecke committed
90
        super(LMSpace, self).__init__()
csongor's avatar
csongor committed
91
        self._lmax = self._parse_lmax(lmax)
csongor's avatar
csongor committed
92

93
94
    def hermitian_decomposition(self, x, axes=None,
                                preserve_gaussian_variance=False):
95
96
97
98
99
100
        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
101
    # ---Mandatory properties and methods---
csongor's avatar
csongor committed
102
103
104
105

    @property
    def harmonic(self):
        return True
csongor's avatar
csongor committed
106
107

    @property
108
109
    def shape(self):
        return (self.dim, )
csongor's avatar
csongor committed
110
111

    @property
112
113
    def dim(self):
        l = self.lmax
114
        # the LMSpace consists of the full triangle (including -m's!),
theos's avatar
theos committed
115
116
        # minus two little triangles if mmax < lmax
        # dim = (((2*(l+1)-1)+1)**2/4 - 2 * (l-m)(l-m+1)/2
117
118
119
        # 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
120

121
122
123
    @property
    def total_volume(self):
        # the individual pixels have a fixed volume of 1.
Martin Reinecke's avatar
Martin Reinecke committed
124
        return np.float64(self.dim)
csongor's avatar
csongor committed
125

126
    def copy(self):
Martin Reinecke's avatar
Martin Reinecke committed
127
        return self.__class__(lmax=self.lmax)
csongor's avatar
csongor committed
128

129
130
131
    def weight(self, x, power=1, axes=None, inplace=False):
        if inplace:
            return x
csongor's avatar
csongor committed
132
        else:
133
            return x.copy()
csongor's avatar
csongor committed
134

135
136
137
138
139
    def get_distance_array(self, distribution_strategy):
        dists = arange(start=0, stop=self.shape[0],
                       distribution_strategy=distribution_strategy)

        dists = dists.apply_scalar_function(
140
            lambda x: self._distance_array_helper(x, self.lmax),
Martin Reinecke's avatar
Martin Reinecke committed
141
            dtype=np.float64)
142
143
144

        return dists

145
146
147
148
149
150
151
152
    @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

153
    def get_fft_smoothing_kernel_function(self, sigma):
154
        # FIXME why x(x+1) ? add reference to paper!
155
156
        return lambda x: np.exp(-0.5 * x * (x + 1) * sigma**2)

csongor's avatar
csongor committed
157
158
159
160
    # ---Added properties and methods---

    @property
    def lmax(self):
161
162
163
164
165
        """Returns the maximal :math:`l`-value of the spherical harmonics being used.
        Returns
        -------
        int : maximal :math:`l` value of any spherical harmonic :math:`Y_{lm}` that is represented in this Space.
        """
csongor's avatar
csongor committed
166
167
168
169
        return self._lmax

    @property
    def mmax(self):
170
171
172
173
174
175
176
177
178
        """Returns the maximal :math:`m`-value of the spherical harmonics being used.
        See Also
        --------
        lmax : Returns the maximal :math:`l`-value of the spherical harmonics being used.
        Returns
        -------
        int : 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.
        """
179
        return self._lmax
csongor's avatar
csongor committed
180
181
182

    def _parse_lmax(self, lmax):
        lmax = np.int(lmax)
183
184
        if lmax < 0:
            raise ValueError("lmax must be >=0.")
csongor's avatar
csongor committed
185
        return lmax
Jait Dixit's avatar
Jait Dixit committed
186
187
188
189
190
191
192
193

    # ---Serialization---

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

    @classmethod
Theo Steininger's avatar
Theo Steininger committed
194
    def _from_hdf5(cls, hdf5_group, repository):
Jait Dixit's avatar
Jait Dixit committed
195
196
197
198
        result = cls(
            lmax=hdf5_group['lmax'][()],
            )
        return result