fft_operator_support.py 8.4 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 abc
from future.utils import with_metaclass
import numpy as np
from ... import nifty_utilities as utilities


class Transformation(with_metaclass(abc.ABCMeta,
                                    type('NewBase', (object,), {}))):

    def __init__(self, domain, codomain):
        self.domain = domain
        self.codomain = codomain

    @abc.abstractproperty
    def unitary(self):
        raise NotImplementedError

    def transform(self, val, axes=None):
        raise NotImplementedError


class RGRGTransformation(Transformation):

    # ---Overwritten properties and methods---

    def __init__(self, domain, codomain=None):
        import pyfftw
        super(RGRGTransformation, self).__init__(domain, codomain)
        pyfftw.interfaces.cache.enable()
        self._fwd = self.codomain.harmonic

    # ---Mandatory properties and methods---

    @property
    def unitary(self):
        return True

    def _transform_helper(self, val, axes):
        from pyfftw.interfaces.numpy_fft import fftn, ifftn

        # Check if the axes provided are valid given the shape
        if axes is not None and \
                not all(axis in range(len(val.shape)) for axis in axes):
            raise ValueError("Provided axes does not match array shape")

        return fftn(val, axes=axes) if self._fwd else ifftn(val, axes=axes)

    def transform(self, val, axes=None):
        """
        RG -> RG transform method.

        Parameters
        ----------
        val : np.ndarray or distributed_data_object
            The value array which is to be transformed

        axes : None or tuple
            The axes along which the transformation should take place

        """
        fct = 1.
        if self.codomain.harmonic:
            # correct for forward 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.
            fct *= self.domain.weight()

        # Perform the transformation
        if issubclass(val.dtype.type, np.complexfloating):
            Tval_real = self._transform_helper(val.real, axes)
            Tval_imag = self._transform_helper(val.imag, axes)
            if self.codomain.harmonic:
                Tval_real.real += Tval_real.imag
                Tval_imag.real += Tval_imag.imag
                Tval_real.imag = Tval_imag.real
            else:
                Tval_real.real -= Tval_real.imag
                Tval_imag.real -= Tval_imag.imag
                Tval_real.imag = Tval_imag.real

            Tval = Tval_real
        else:
            Tval = self._transform_helper(val, axes)
            if self.codomain.harmonic:
                Tval.real += Tval.imag
            else:
                Tval.real -= Tval.imag
            Tval = Tval.real

        if not self.codomain.harmonic:
            # correct for inverse fft.
            # See discussion above.
            fct /= self.codomain.weight()

        Tval *= fct
        return Tval


class SlicingTransformation(Transformation):

    def transform(self, val, axes=None):
        return_shape = np.array(val.shape)
        return_shape[list(axes)] = self.codomain.shape
        return_shape = tuple(return_shape)
        return_val = np.empty(return_shape, dtype=val.dtype)

        for slice_list in utilities.get_slice_list(val.shape, axes):
            return_val[slice_list] = self._transformation_of_slice(
                                                               val[slice_list])
        return return_val

    @abc.abstractmethod
    def _transformation_of_slice(self, inp):
        raise NotImplementedError


def buildLm(nr, lmax):
    new_dtype = np.result_type(nr.dtype, np.complex64)

    size = (len(nr)-lmax-1)//2+lmax+1
    res = np.empty([size], dtype=new_dtype)
    res[0:lmax+1] = nr[0:lmax+1]
    res[lmax+1:] = np.sqrt(0.5)*(nr[lmax+1::2] + 1j*nr[lmax+2::2])
    return res


def buildIdx(nr, lmax):
    if nr.dtype == np.dtype('complex64'):
        new_dtype = np.float32
    elif nr.dtype == np.dtype('complex128'):
        new_dtype = np.float64
    else:
        raise TypeError("dtype of nr not supported.")

    size = (lmax+1)*(lmax+1)
    final = np.empty(size, dtype=new_dtype)
    final[0:lmax+1] = nr[0:lmax+1].real
    final[lmax+1::2] = np.sqrt(2)*nr[lmax+1:].real
    final[lmax+2::2] = np.sqrt(2)*nr[lmax+1:].imag
    return final


class HPLMTransformation(SlicingTransformation):
    def __init__(self, domain, codomain=None):
        super(HPLMTransformation, self).__init__(domain, codomain)

    @property
    def unitary(self):
        return False

    def _transformation_of_slice(self, inp):
        from pyHealpix import map2alm

        lmax = self.codomain.lmax
        mmax = lmax

        if issubclass(inp.dtype.type, np.complexfloating):
            rr = map2alm(inp.real, lmax, mmax)
            rr = buildIdx(rr, lmax=lmax)
            ri = map2alm(inp.imag, lmax, mmax)
            ri = buildIdx(ri, lmax=lmax)
            return rr + 1j*ri

        else:
            rr = map2alm(inp, lmax, mmax)
            return buildIdx(rr, lmax=lmax)


class LMHPTransformation(SlicingTransformation):
    def __init__(self, domain, codomain=None):
        super(LMHPTransformation, self).__init__(domain, codomain)

    @property
    def unitary(self):
        return False

    def _transformation_of_slice(self, inp):
        from pyHealpix import alm2map

        nside = self.codomain.nside
        lmax = self.domain.lmax
        mmax = lmax

        if issubclass(inp.dtype.type, np.complexfloating):
            rr = buildLm(inp.real, lmax=lmax)
            ri = buildLm(inp.imag, lmax=lmax)
            rr = alm2map(rr, lmax, mmax, nside)
            ri = alm2map(ri, lmax, mmax, nside)
            return rr + 1j*ri

        else:
            rr = buildLm(inp, lmax=lmax)
            return alm2map(rr, lmax, mmax, nside)


class GLLMTransformation(SlicingTransformation):
    def __init__(self, domain, codomain=None):
        super(GLLMTransformation, self).__init__(domain, codomain)

    @property
    def unitary(self):
        return False

    def _transformation_of_slice(self, inp):
        from pyHealpix import sharpjob_d

        lmax = self.codomain.lmax
        mmax = self.codomain.mmax

        sjob = sharpjob_d()
        sjob.set_Gauss_geometry(self.domain.nlat, self.domain.nlon)
        sjob.set_triangular_alm_info(lmax, mmax)
        if issubclass(inp.dtype.type, np.complexfloating):
            rr = sjob.map2alm(inp.real)
            rr = buildIdx(rr, lmax=lmax)
            ri = sjob.map2alm(inp.imag)
            ri = buildIdx(ri, lmax=lmax)
            return rr + 1j*ri
        else:
            rr = sjob.map2alm(inp)
            return buildIdx(rr, lmax=lmax)


class LMGLTransformation(SlicingTransformation):
    def __init__(self, domain, codomain=None):
        super(LMGLTransformation, self).__init__(domain, codomain)

    @property
    def unitary(self):
        return False

    def _transformation_of_slice(self, inp):
        from pyHealpix import sharpjob_d

        lmax = self.domain.lmax
        mmax = self.domain.mmax

        sjob = sharpjob_d()
        sjob.set_Gauss_geometry(self.codomain.nlat, self.codomain.nlon)
        sjob.set_triangular_alm_info(lmax, mmax)
        if issubclass(inp.dtype.type, np.complexfloating):
            rr = buildLm(inp.real, lmax=lmax)
            ri = buildLm(inp.imag, lmax=lmax)
            return sjob.alm2map(rr) + 1j*sjob.alm2map(ri)

        else:
            result = buildLm(inp, lmax=lmax)
            return sjob.alm2map(result)