rg_space.py 8.22 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.
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#
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# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
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# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
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# You should have received a copy of the GNU General Public License
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# along with this program.  If not, see <http://www.gnu.org/licenses/>.
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#
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# Copyright(C) 2013-2021 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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from functools import reduce
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import numpy as np
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from ..field import Field
from .structured_domain import StructuredDomain
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class RGSpace(StructuredDomain):
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    """Represents a regular Cartesian grid.
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    Parameters
    ----------
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    shape : int or tuple of int
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        Number of grid points or numbers of gridpoints along each axis.
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    distances : None or float or tuple of float, optional
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        Distance between two grid points along each axis.
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        By default (distances=None):
          - If harmonic==True, all distances will be set to 1
          - If harmonic==False, the distance along each axis will be
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            set to the inverse of the number of points along that axis.

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    harmonic : bool, optional
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        Whether the space represents a grid in position or harmonic space.
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        Default: False.
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    Notes
    -----
    Topologically, a n-dimensional RGSpace is a n-Torus, i.e. it has periodic
    boundary conditions.
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    """
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    _needed_for_hash = ["_rdistances", "_shape", "_harmonic"]
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    def __init__(self, shape, distances=None, harmonic=False, _realdistances=None):
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        self._harmonic = bool(harmonic)
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        if np.isscalar(shape):
            shape = (shape,)
        self._shape = tuple(int(i) for i in shape)
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        if min(self._shape) < 0:
            raise ValueError('Negative number of pixels encountered')
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        if _realdistances is not None:
            self._rdistances = _realdistances
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        else:
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            if distances is None:
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                self._rdistances = tuple(1. / (np.array(self._shape)))
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            elif np.isscalar(distances):
                if self.harmonic:
                    self._rdistances = tuple(
                        1. / (np.array(self._shape) * float(distances)))
                else:
                    self._rdistances = (float(distances),) * len(self._shape)
            else:
                temp = np.empty(len(self.shape), dtype=np.float64)
                temp[:] = distances
                if self._harmonic:
                    temp = 1. / (np.array(self._shape) * temp)
                self._rdistances = tuple(temp)
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        self._hdistances = tuple(
            1. / (np.array(self.shape)*np.array(self._rdistances)))
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        if min(self._rdistances) <= 0:
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            raise ValueError('Non-positive distances encountered')
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        self._dvol = float(reduce(lambda x, y: x*y, self.distances))
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        self._size = int(reduce(lambda x, y: x*y, self._shape))
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    def __repr__(self):
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        return ("RGSpace(shape={}, distances={}, harmonic={})"
                .format(self.shape, self.distances, self.harmonic))
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    @property
    def harmonic(self):
        return self._harmonic

    @property
    def shape(self):
        return self._shape

    @property
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    def size(self):
        return self._size
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    @property
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    def scalar_dvol(self):
        return self._dvol
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    def _get_dist_array(self):
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        res = np.arange(self.shape[0], dtype=np.float64)
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        res = np.minimum(res, self.shape[0]-res)*self.distances[0]
        if len(self.shape) == 1:
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            return Field.from_raw(self, res)
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        res *= res
        for i in range(1, len(self.shape)):
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            tmp = np.arange(self.shape[i], dtype=np.float64)
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            tmp = np.minimum(tmp, self.shape[i]-tmp)*self.distances[i]
            tmp *= tmp
            res = np.add.outer(res, tmp)
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        return Field.from_raw(self, np.sqrt(res))
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    def get_k_length_array(self):
        if (not self.harmonic):
            raise NotImplementedError
        return self._get_dist_array()

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    def get_unique_k_lengths(self):
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        if (not self.harmonic):
            raise NotImplementedError
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        dimensions = len(self.shape)
        if dimensions == 1:  # extra easy
            maxdist = self.shape[0]//2
            return np.arange(maxdist+1, dtype=np.float64) * self.distances[0]
        if np.all(self.distances == self.distances[0]):  # shortcut
            maxdist = np.asarray(self.shape)//2
            tmp = np.sum(maxdist*maxdist)
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            tmp = np.zeros(tmp+1, dtype=bool)
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            t2 = np.arange(maxdist[0]+1, dtype=np.int64)
            t2 *= t2
            for i in range(1, dimensions):
                t3 = np.arange(maxdist[i]+1, dtype=np.int64)
                t3 *= t3
                t2 = np.add.outer(t2, t3)
            tmp[t2] = True
            return np.sqrt(np.nonzero(tmp)[0])*self.distances[0]
        else:  # do it the hard way
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            tmp = self.get_k_length_array().val
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            tmp = np.unique(tmp)
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            tol = 1e-12*tmp[-1]
            # remove all points that are closer than tol to their right
            # neighbors.
            # I'm appending the last value*2 to the array to treat the
            # rightmost point correctly.
            return tmp[np.diff(np.r_[tmp, 2*tmp[-1]]) > tol]

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    @staticmethod
    def _kernel(x, sigma):
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        return (x*x * (-2.*np.pi*np.pi*sigma*sigma)).ptw("exp")
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    def get_fft_smoothing_kernel_function(self, sigma):
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        if (not self.harmonic):
            raise NotImplementedError
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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.

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        Assumes the function to be radially symmetric, e.g. only dependant on
        distance.

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        Parameters
        ----------
        func: function
            This function needs to take exactly one argument, which is
            distance from center (in the same units as the RGSpace distances),
            and return the kernel amplitude at that distance.
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        """
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        from ..operators.harmonic_operators import HarmonicTransformOperator
        if (not self.harmonic):
            raise NotImplementedError
        op = HarmonicTransformOperator(self, self.get_default_codomain())
        dist = op.target[0]._get_dist_array()
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        kernel = Field(op.target, func(dist.val))
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        kernel = kernel / kernel.s_integrate()
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        return op.adjoint_times(kernel.weight(1))

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    def get_default_codomain(self):
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        """Returns a :class:`RGSpace` object representing the (position or
        harmonic) partner domain of `self`, depending on `self.harmonic`.

        Returns
        -------
        RGSpace
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            The partner domain
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        """
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        return RGSpace(self.shape, None, not self.harmonic, self._rdistances)
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    def check_codomain(self, codomain):
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        """Raises `TypeError` if `codomain` is not a matching partner domain
        for `self`.
        """
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        if not isinstance(codomain, RGSpace):
            raise TypeError("domain is not a RGSpace")

        if self.shape != codomain.shape:
            raise AttributeError("The shapes of domain and codomain must be "
                                 "identical.")

        if self.harmonic == codomain.harmonic:
            raise AttributeError("domain.harmonic and codomain.harmonic must "
                                 "not be the same.")

        # Check if the distances match, i.e. dist' = 1 / (num * dist)
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        if not np.all(abs(np.array(self.shape) *
                          np.array(self.distances) *
                          np.array(codomain.distances)-1) < 1e-7):
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            raise AttributeError("The grid-distances of domain and codomain "
                                 "do not match.")

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    @property
    def distances(self):
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        """tuple of float : Distance between grid points along each axis.
        The n-th entry of the tuple is the distance between neighboring
        grid points along the n-th dimension.
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        """
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        return self._hdistances if self._harmonic else self._rdistances