lm_space.py 4.74 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
from __future__ import division
import numpy as np
Martin Reinecke's avatar
Martin Reinecke committed
21
from .space import Space
22
23
from .. import Field
from ..basic_arithmetics import exp
Martin Reinecke's avatar
fixes    
Martin Reinecke committed
24
from .. import dobj
theos's avatar
theos committed
25

csongor's avatar
csongor committed
26

Theo Steininger's avatar
Theo Steininger committed
27
class LMSpace(Space):
Martin Reinecke's avatar
Martin Reinecke committed
28
29
30
31
32
33
34
35
    """NIFTY subclass for spherical harmonics components, for representations
    of fields on the two-sphere.

    Parameters
    ----------
    lmax : int
        The maximum :math:`l` value of any spherical harmonics
        :math:`Y_{lm}` that is represented in this Space.
36
37
38
39
40
41
42
        Must be >=0.

    mmax : int *optional*
        The maximum :math:`m` value of any spherical harmonics
        :math:`Y_{lm}` that is represented in this Space.
        If not supplied, it is set to lmax.
        Must be >=0 and <=lmax.
Martin Reinecke's avatar
Martin Reinecke committed
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57

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

    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>`_
csongor's avatar
csongor committed
58
59
    """

60
    def __init__(self, lmax, mmax=None):
Martin Reinecke's avatar
Martin Reinecke committed
61
        super(LMSpace, self).__init__()
62
63
64
65
66
67
68
69
70
        self._needed_for_hash += ["_lmax", "_mmax"]
        self._lmax = np.int(lmax)
        if self._lmax < 0:
            raise ValueError("lmax must be >=0.")
        if mmax is None:
            mmax = self._lmax
        self._mmax = np.int(mmax)
        if self._mmax < 0 or self._mmax > self._lmax:
            raise ValueError("mmax must be >=0 and <=lmax.")
csongor's avatar
csongor committed
71

72
    def __repr__(self):
73
        return ("LMSpace(lmax=%r, mmax=%r)" % (self.lmax, self.mmax))
74

csongor's avatar
csongor committed
75
76
77
    @property
    def harmonic(self):
        return True
csongor's avatar
csongor committed
78
79

    @property
80
81
    def shape(self):
        return (self.dim, )
csongor's avatar
csongor committed
82
83

    @property
84
    def dim(self):
85
86
        l = self._lmax
        m = self._mmax
87
        # the LMSpace consists of the full triangle (including -m's!),
theos's avatar
theos committed
88
        # minus two little triangles if mmax < lmax
89
        return (l+1)**2 - (l-m)*(l-m+1)
csongor's avatar
csongor committed
90

91
    def scalar_dvol(self):
92
        return 1.
csongor's avatar
csongor committed
93

94
    def get_k_length_array(self):
95
96
        lmax = self._lmax
        mmax = self._mmax
Martin Reinecke's avatar
stage1    
Martin Reinecke committed
97
98
99
100
101
102
        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
103
104
105
        for m in range(1, mmax+1):
            ldist[idx:idx+2*(lmax+1-m)] = tmp[2*m:]
            idx += 2*(lmax+1-m)
Martin Reinecke's avatar
fixes    
Martin Reinecke committed
106
        return Field((self,), dobj.from_global_data(ldist))
107

108
    def get_unique_k_lengths(self):
Martin Reinecke's avatar
Martin Reinecke committed
109
110
        return np.arange(self.lmax+1, dtype=np.float64)

Martin Reinecke's avatar
Martin Reinecke committed
111
112
    @staticmethod
    def _kernel(x, sigma):
113
114
115
        # 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
116
117
118
        res = x+1.
        res *= x
        res *= -0.5*sigma*sigma
119
        exp(res, out=res)
Martin Reinecke's avatar
Martin Reinecke committed
120
121
        return res

122
    def get_fft_smoothing_kernel_function(self, sigma):
Martin Reinecke's avatar
Martin Reinecke committed
123
        return lambda x: self._kernel(x, sigma)
124

csongor's avatar
csongor committed
125
126
    @property
    def lmax(self):
Martin Reinecke's avatar
Martin Reinecke committed
127
        """ Returns the maximum :math:`l` value of any spherical harmonic
Theo Steininger's avatar
Theo Steininger committed
128
        :math:`Y_{lm}` that is represented in this Space.
129
        """
csongor's avatar
csongor committed
130
131
132
133
        return self._lmax

    @property
    def mmax(self):
Martin Reinecke's avatar
Martin Reinecke committed
134
135
        """ Returns the maximum :math:`m` value of any spherical harmonic
        :math:`Y_{lm}` that is represented in this Space.
136
        """
137
        return self._mmax
Martin Reinecke's avatar
Martin Reinecke committed
138
139
140
141
142
143
144
145

    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)):
146
            raise TypeError("codomain must be a GLSpace or HPSpace.")