lm_space.py 5.95 KB
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# 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/>.
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#
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# Copyright(C) 2013-2019 Max-Planck-Society
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#
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# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik.
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import numpy as np
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from ..field import Field
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from .structured_domain import StructuredDomain
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class LMSpace(StructuredDomain):
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    """Represents a set of spherical harmonic coefficients.
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    Its harmonic partner spaces are :class:`~nifty5.domains.hp_space.HPSpace`
    and :class:`~nifty5.domains.gl_space.GLSpace`.
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    Parameters
    ----------
    lmax : int
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        The maximum :math:`l` value of any spherical harmonic coefficient
        :math:`a_{lm}` that is represented by this object.
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        Must be :math:`\\ge 0`.
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    mmax : int, optional
        The maximum :math:`m` value of any spherical harmonic coefficient
        :math:`a_{lm}` that is represented by this object.
        If not supplied, it is set to `lmax`.
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        Must be :math:`\\ge 0` and :math:`\\le` `lmax`.
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    """

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    _needed_for_hash = ["_lmax", "_mmax"]

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    def __init__(self, lmax, mmax=None):
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        self._lmax = int(lmax)
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        if self._lmax < 0:
            raise ValueError("lmax must be >=0.")
        if mmax is None:
            mmax = self._lmax
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        self._mmax = int(mmax)
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        if self._mmax < 0 or self._mmax > self._lmax:
            raise ValueError("mmax must be >=0 and <=lmax.")
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    def __repr__(self):
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        return "LMSpace(lmax={}, mmax={})".format(self.lmax, self.mmax)
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    @property
    def harmonic(self):
        return True
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    @property
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    def shape(self):
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        return (self.size,)
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    @property
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    def size(self):
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        l, m = self._lmax, self._mmax
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        # the LMSpace consists of the full triangle (including -m's!),
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        # minus two little triangles if mmax < lmax
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        return (l+1)**2 - (l-m)*(l-m+1)
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    @property
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    def scalar_dvol(self):
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        return 1.
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    def get_k_length_array(self):
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        lmax = self._lmax
        mmax = self._mmax
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        ldist = np.empty((self.size,), dtype=np.float64)
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        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
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        for m in range(1, mmax+1):
            ldist[idx:idx+2*(lmax+1-m)] = tmp[2*m:]
            idx += 2*(lmax+1-m)
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        return Field.from_global_data(self, ldist)
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    def get_unique_k_lengths(self):
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        return np.arange(self.lmax+1, dtype=np.float64)

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    @staticmethod
    def _kernel(x, sigma):
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        # cf. "All-sky convolution for polarimetry experiments"
        # by Challinor et al.
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        # https://arxiv.org/abs/astro-ph/0008228
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        from ..sugar import exp
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        return exp((x+1.) * x * (-0.5*sigma*sigma))
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    def get_fft_smoothing_kernel_function(self, sigma):
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        return lambda x: self._kernel(x, sigma)
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    def get_conv_kernel_from_func(self, func):
        """Creates a convolution kernel defined by a function.

        Assumes the function to be radially symmetric,
        e.g. only dependant on theta in radians"""
        from .gl_space import GLSpace
        from ..operators.harmonic_operators import HarmonicTransformOperator
        import pyHealpix
        # define azimuthally symmetric spaces for kernel transform
        gl = GLSpace(self.lmax + 1, 1)
        lm0 = gl.get_default_codomain()
        theta = pyHealpix.GL_thetas(gl.nlat)
        # evaluate the kernel function at the required thetas
        kernel_sphere = Field.from_global_data(gl, func(theta))
        # normalize the kernel such that the integral over the sphere is 4pi
        kernel_sphere = kernel_sphere * (4 * np.pi / kernel_sphere.integrate())
        # compute the spherical harmonic coefficients of the kernel
        op = HarmonicTransformOperator(lm0, gl)
        kernel_lm = op.adjoint_times(kernel_sphere.weight(1)).to_global_data()
        # evaluate the k lengths of the harmonic space
        k_lengths = self.get_k_length_array().to_global_data().astype(np.int)
        return Field.from_global_data(self, kernel_lm[k_lengths])

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    @property
    def lmax(self):
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        """int : maximum allowed :math:`l`

        The maximum :math:`l` value of any spherical harmonic
        coefficient :math:`a_{lm}` that is represented in this domain.
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        """
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        return self._lmax

    @property
    def mmax(self):
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        """int : maximum allowed :math:`m`

        The maximum :math:`m` value of any spherical harmonic
        coefficient :math:`a_{lm}` that is represented in this domain.
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        """
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        return self._mmax
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    def get_default_codomain(self):
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        """Returns a :class:`~nifty5.domains.gl_space.GLSpace` object, which is
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        capable of storing an accurate representation of data residing on
        `self`.

        Returns
        -------
        GLSpace
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            The partner domain
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        """
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        from ..domains.gl_space import GLSpace
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        return GLSpace(self.lmax+1, self.mmax*2+1)

    def check_codomain(self, codomain):
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        """Raises `TypeError` if `codomain` is not a matching partner domain
        for `self`.

        Notes
        -----
        This function only checks whether `codomain` is of type
        :class:`GLSpace` or :class:`HPSpace`.
        """
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        from ..domains.gl_space import GLSpace
        from ..domains.hp_space import HPSpace
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        if not isinstance(codomain, (GLSpace, HPSpace)):
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            raise TypeError("codomain must be a GLSpace or HPSpace.")