lm_space.py 5.85 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

Martin Reinecke's avatar
Martin Reinecke committed
23
from ..space import Space
theos's avatar
theos committed
24

csongor's avatar
csongor committed
25

Theo Steininger's avatar
Theo Steininger committed
26
class LMSpace(Space):
csongor's avatar
csongor committed
27
28
29
30
31
32
33
34
35
36
37
    """
        ..       __
        ..     /  /
        ..    /  /    __ ____ ___
        ..   /  /   /   _    _   |
        ..  /  /_  /  / /  / /  /
        ..  \___/ /__/ /__/ /__/  space class

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

38
39
40
41
42
43
        Parameters
        ----------
        lmax : int
            The maximal :math:`l` value of any spherical harmonics
            :math:`Y_{lm}` that is represented in this Space.

44
        Attributes
csongor's avatar
csongor committed
45
46
        ----------
        lmax : int
47
48
49
50
51
            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.
52
53
54
55
56
57
58
59
        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
60
61
62
63
64
65
66

        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
67
68
69
70
71
        Raises
        ------
        ValueError
            If given lmax is negative.

72
73
        Notes
        -----
Theo Steininger's avatar
Theo Steininger committed
74
            This implementation implicitly sets the mmax parameter to lmax.
75

csongor's avatar
csongor committed
76
77
78
79
80
81
82
83
84
85
        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
86
87
    def __init__(self, lmax):
        super(LMSpace, self).__init__()
88
        self._needed_for_hash += ["_lmax"]
csongor's avatar
csongor committed
89
        self._lmax = self._parse_lmax(lmax)
csongor's avatar
csongor committed
90

91
92
93
    def __repr__(self):
        return ("LMSpace(lmax=%r)" % self.lmax)

csongor's avatar
csongor committed
94
95
96
    @property
    def harmonic(self):
        return True
csongor's avatar
csongor committed
97
98

    @property
99
100
    def shape(self):
        return (self.dim, )
csongor's avatar
csongor committed
101
102

    @property
103
104
    def dim(self):
        l = self.lmax
105
        # the LMSpace consists of the full triangle (including -m's!),
theos's avatar
theos committed
106
107
        # minus two little triangles if mmax < lmax
        # dim = (((2*(l+1)-1)+1)**2/4 - 2 * (l-m)(l-m+1)/2
108
109
        # dim = np.int((l+1)**2 - (l-m)*(l-m+1.))
        # We fix l == m
110
        return np.int((l+1)*(l+1))
csongor's avatar
csongor committed
111

112
113
114
    @property
    def total_volume(self):
        # the individual pixels have a fixed volume of 1.
Martin Reinecke's avatar
Martin Reinecke committed
115
        return np.float64(self.dim)
csongor's avatar
csongor committed
116

117
118
119
    def scalar_weight(self):
        return 1.

120
121
    def weight(self):
        return 1.
csongor's avatar
csongor committed
122

123
    def get_k_length_array(self):
Martin Reinecke's avatar
stage1    
Martin Reinecke committed
124
125
126
127
128
129
130
131
132
133
134
        lmax = self.lmax
        ldist = np.empty((self.dim,), dtype=np.float64)
        ldist[0:lmax+1] = np.arange(lmax+1, dtype=np.float64)
        tmp = np.empty((2*lmax+2), dtype=np.float64)
        tmp[0::2] = np.arange(lmax+1)
        tmp[1::2] = np.arange(lmax+1)
        idx = lmax+1
        for l in range(1, lmax+1):
            ldist[idx:idx+2*(lmax+1-l)] = tmp[2*l:]
            idx += 2*(lmax+1-l)
        return ldist
135

136
    def get_unique_k_lengths(self):
Martin Reinecke's avatar
Martin Reinecke committed
137
138
        return np.arange(self.lmax+1, dtype=np.float64)

Martin Reinecke's avatar
Martin Reinecke committed
139
140
141
142
143
144
145
146
    @staticmethod
    def _kernel(x, sigma):
        res = x+1.
        res *= x
        res *= -0.5*sigma*sigma
        np.exp(res, out=res)
        return res

147
    def get_fft_smoothing_kernel_function(self, sigma):
Theo Steininger's avatar
Theo Steininger committed
148
149
150
        # cf. "All-sky convolution for polarimetry experiments"
        # by Challinor et al.
        # http://arxiv.org/abs/astro-ph/0008228
Martin Reinecke's avatar
Martin Reinecke committed
151
        return lambda x: self._kernel(x, sigma)
152

csongor's avatar
csongor committed
153
154
    @property
    def lmax(self):
Theo Steininger's avatar
Theo Steininger committed
155
156
        """ Returns the maximal :math:`l` value of any spherical harmonics
        :math:`Y_{lm}` that is represented in this Space.
157
        """
csongor's avatar
csongor committed
158
159
160
161
        return self._lmax

    @property
    def mmax(self):
Theo Steininger's avatar
Theo Steininger committed
162
163
164
165
166
        """ 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.

167
168
        See Also
        --------
Theo Steininger's avatar
Theo Steininger committed
169
170
171
        lmax : Returns the maximal :math:`l`-value of the spherical harmonics
            being used.

172
        """
Theo Steininger's avatar
Theo Steininger committed
173

174
        return self._lmax
csongor's avatar
csongor committed
175
176
177

    def _parse_lmax(self, lmax):
        lmax = np.int(lmax)
178
179
        if lmax < 0:
            raise ValueError("lmax must be >=0.")
csongor's avatar
csongor committed
180
        return lmax
Martin Reinecke's avatar
Martin Reinecke committed
181
182
183
184
185
186
187
188
189

    def get_default_codomain(self):
        from .. import GLSpace
        return GLSpace(self.lmax+1, self.mmax*2+1)

    def check_codomain(self, codomain):
        from .. import GLSpace, HPSpace
        if not isinstance(codomain, (GLSpace, HPSpace)):
            raise TypeError("codomain must be a GLSpace.")