fft_operator_support.py 5.96 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/>.
#
# 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.

from __future__ import division
import numpy as np
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from .. import nifty_utilities as utilities
from ..low_level_library import hartley
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from .. import dobj
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from ..field import Field
from ..spaces.gl_space import GLSpace
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class Transformation(object):
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    def __init__(self, pdom, hdom, space):
        self.pdom = pdom
        self.hdom = hdom
        self.space = space
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class RGRGTransformation(Transformation):
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    def __init__(self, pdom, hdom, space):
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        import pyfftw
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        super(RGRGTransformation, self).__init__(pdom, hdom, space)
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        pyfftw.interfaces.cache.enable()
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        # correct for forward/inverse fft.
        # naively one would set power to 0.5 here in order to
        # apply effectively a factor of 1/sqrt(N) to the field.
        # BUT: the pixel volumes of the domain and codomain are different.
        # Hence, in order to produce the same scalar product, power==1.
        self.fct_p2h = pdom[space].scalar_dvol()
        self.fct_h2p = 1./(pdom[space].scalar_dvol()*hdom[space].dim)
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    @property
    def unitary(self):
        return True

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    def transform(self, x):
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        """
        RG -> RG transform method.

        Parameters
        ----------
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        x : Field
            The field to be transformed
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        """
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        from pyfftw.interfaces.numpy_fft import fftn
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        axes = x.domain.axes[self.space]
        p2h = x.domain == self.pdom
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        tdom = self.hdom if p2h else self.pdom
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        oldax = dobj.distaxis(x.val)
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        if dobj.distaxis(x.val) in axes:
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            tmp = dobj.redistribute(x.val, nodist=(oldax,))
            newax = dobj.distaxis(tmp)
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            ldat = dobj.local_data(tmp)
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            if len(axes) == 1:  # only one transform needed
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                ldat = hartley(ldat, axes=(oldax,))
                tmp = dobj.from_local_data(tmp.shape, ldat, distaxis=newax)
                tmp = dobj.redistribute(tmp, dist=oldax)
            else:  # two separate transforms needed, "real" FFT required
                ldat = fftn(ldat, axes=(oldax,))
                tmp = dobj.from_local_data(tmp.shape, ldat, distaxis=newax)
                tmp = dobj.redistribute(tmp, dist=oldax)
                rem_axes = tuple(i for i in axes if i != oldax)
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                ldat = dobj.local_data(tmp)
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                ldat = fftn(ldat, axes=rem_axes)
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                ldat = ldat.real+ldat.imag
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                tmp = dobj.from_local_data(tmp.shape, ldat, distaxis=oldax)
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        else:
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            ldat = dobj.local_data(x.val)
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            ldat = hartley(ldat, axes=axes)
            tmp = dobj.from_local_data(x.val.shape, ldat, distaxis=oldax)
        Tval = Field(tdom, tmp)
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        fct = self.fct_p2h if p2h else self.fct_h2p
        if fct != 1:
            Tval *= fct
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        return Tval
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class SphericalTransformation(Transformation):
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    def __init__(self, pdom, hdom, space):
        super(SphericalTransformation, self).__init__(pdom, hdom, space)
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        from pyHealpix import sharpjob_d

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        self.lmax = self.hdom[self.space].lmax
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        self.mmax = self.hdom[self.space].mmax
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        self.sjob = sharpjob_d()
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        self.sjob.set_triangular_alm_info(self.lmax, self.mmax)
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        if isinstance(self.pdom[self.space], GLSpace):
            self.sjob.set_Gauss_geometry(self.pdom[self.space].nlat,
                                         self.pdom[self.space].nlon)
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        else:
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            self.sjob.set_Healpix_geometry(self.pdom[self.space].nside)
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    @property
    def unitary(self):
        return False

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    def _slice_p2h(self, inp):
        rr = self.sjob.map2alm(inp)
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        assert len(rr) == ((self.mmax+1)*(self.mmax+2))//2 + \
                          (self.mmax+1)*(self.lmax-self.mmax)
        res = np.empty(2*len(rr)-self.lmax-1, dtype=rr[0].real.dtype)
        res[0:self.lmax+1] = rr[0:self.lmax+1].real
        res[self.lmax+1::2] = np.sqrt(2)*rr[self.lmax+1:].real
        res[self.lmax+2::2] = np.sqrt(2)*rr[self.lmax+1:].imag
        return res
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    def _slice_h2p(self, inp):
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        res = np.empty((len(inp)+self.lmax+1)//2, dtype=(inp[0]*1j).dtype)
        assert len(res) == ((self.mmax+1)*(self.mmax+2))//2 + \
                           (self.mmax+1)*(self.lmax-self.mmax)
        res[0:self.lmax+1] = inp[0:self.lmax+1]
        res[self.lmax+1:] = np.sqrt(0.5)*(inp[self.lmax+1::2] +
                                          1j*inp[self.lmax+2::2])
        return self.sjob.alm2map(res)

    def transform(self, x):
        axes = x.domain.axes[self.space]
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        axis = axes[0]
        tval = x.val
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        if dobj.distaxis(tval) == axis:
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            tval = dobj.redistribute(tval, nodist=(axis,))
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        distaxis = dobj.distaxis(tval)
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        p2h = x.domain == self.pdom
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        tdom = self.hdom if p2h else self.pdom
        func = self._slice_p2h if p2h else self._slice_h2p
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        idat = dobj.local_data(tval)
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        odat = np.empty(dobj.local_shape(tdom.shape, distaxis=distaxis),
                        dtype=x.dtype)
        for slice in utilities.get_slice_list(idat.shape, axes):
            odat[slice] = func(idat[slice])
        odat = dobj.from_local_data(tdom.shape, odat, distaxis)
        if distaxis != dobj.distaxis(x.val):
            odat = dobj.redistribute(odat, dist=dobj.distaxis(x.val))
        return Field(tdom, odat)