lm_space.py 5.73 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
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
    """
        ..       __
        ..     /  /
        ..    /  /    __ ____ ___
        ..   /  /   /   _    _   |
        ..  /  /_  /  / /  / /  /
        ..  \___/ /__/ /__/ /__/  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.
        dtype : numpy.dtype, *optional*
            Data type of the field values (default: numpy.complex128).

        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 [#]_.

        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.

        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>`_

        Attributes
        ----------
        dtype : numpy.dtype
            Data type of the field values.
    """

76
    def __init__(self, lmax, dtype=None):
csongor's avatar
csongor committed
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
        """
            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.
            dtype : numpy.dtype, *optional*
                Data type of the field values (default: numpy.complex128).

            Returns
            -------
            None.

        """

csongor's avatar
csongor committed
94
95
        super(LMSpace, self).__init__(dtype)
        self._lmax = self._parse_lmax(lmax)
csongor's avatar
csongor committed
96

97
98
    def hermitian_decomposition(self, x, axes=None,
                                preserve_gaussian_variance=False):
99
100
101
102
103
104
        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
105
    # ---Mandatory properties and methods---
csongor's avatar
csongor committed
106
107
108
109

    @property
    def harmonic(self):
        return True
csongor's avatar
csongor committed
110
111

    @property
112
113
    def shape(self):
        return (self.dim, )
csongor's avatar
csongor committed
114
115

    @property
116
117
    def dim(self):
        l = self.lmax
118
        # the LMSpace consists of the full triangle (including -m's!),
theos's avatar
theos committed
119
120
        # minus two little triangles if mmax < lmax
        # dim = (((2*(l+1)-1)+1)**2/4 - 2 * (l-m)(l-m+1)/2
121
122
123
        # 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
124

125
126
127
128
    @property
    def total_volume(self):
        # the individual pixels have a fixed volume of 1.
        return np.float(self.dim)
csongor's avatar
csongor committed
129

130
131
132
    def copy(self):
        return self.__class__(lmax=self.lmax,
                              dtype=self.dtype)
csongor's avatar
csongor committed
133

134
135
136
    def weight(self, x, power=1, axes=None, inplace=False):
        if inplace:
            return x
csongor's avatar
csongor committed
137
        else:
138
            return x.copy()
csongor's avatar
csongor committed
139

140
141
142
143
144
    def get_distance_array(self, distribution_strategy):
        dists = arange(start=0, stop=self.shape[0],
                       distribution_strategy=distribution_strategy)

        dists = dists.apply_scalar_function(
145
            lambda x: self._distance_array_helper(x, self.lmax),
146
147
148
149
            dtype=np.float)

        return dists

150
151
152
153
154
155
156
157
    @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

158
    def get_fft_smoothing_kernel_function(self, sigma):
159
160
        return lambda x: np.exp(-0.5 * x * (x + 1) * sigma**2)

csongor's avatar
csongor committed
161
162
163
164
165
166
167
168
    # ---Added properties and methods---

    @property
    def lmax(self):
        return self._lmax

    @property
    def mmax(self):
169
        return self._lmax
csongor's avatar
csongor committed
170
171
172

    def _parse_lmax(self, lmax):
        lmax = np.int(lmax)
173
174
        if lmax < 0:
            raise ValueError("lmax must be >=0.")
csongor's avatar
csongor committed
175
        return lmax
Jait Dixit's avatar
Jait Dixit committed
176
177
178
179
180

    # ---Serialization---

    def _to_hdf5(self, hdf5_group):
        hdf5_group['lmax'] = self.lmax
181
        hdf5_group.attrs['dtype'] = self.dtype.name
Jait Dixit's avatar
Jait Dixit committed
182
183
184
        return None

    @classmethod
Theo Steininger's avatar
Theo Steininger committed
185
    def _from_hdf5(cls, hdf5_group, repository):
Jait Dixit's avatar
Jait Dixit committed
186
187
        result = cls(
            lmax=hdf5_group['lmax'][()],
188
            dtype=np.dtype(hdf5_group.attrs['dtype'])
Jait Dixit's avatar
Jait Dixit committed
189
190
            )
        return result
191
192
193
194


    def plot(self):
        pass