utilities.py 11.4 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/>.
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#
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# Copyright(C) 2013-2018 Max-Planck-Society
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#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik
# and financially supported by the Studienstiftung des deutschen Volkes.
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from __future__ import absolute_import, division, print_function
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import abc
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import collections
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from itertools import product

import numpy as np
from future.utils import with_metaclass

from .compat import *
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__all__ = ["get_slice_list", "safe_cast", "parse_spaces", "infer_space",
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           "memo", "NiftyMetaBase", "fft_prep", "hartley", "my_fftn_r2c",
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           "my_fftn", "my_sum", "my_lincomb_simple", "my_lincomb",
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           "my_product", "frozendict", "special_add_at"]
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def my_sum(iterable):
    return reduce(lambda x, y: x+y, iterable)
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def my_lincomb_simple(terms, factors):
    terms2 = map(lambda v: v[0]*v[1], zip(terms, factors))
    return my_sum(terms2)


def my_lincomb(terms, factors):
    terms2 = map(lambda v: v[0] if v[1] == 1. else v[0]*v[1],
                 zip(terms, factors))
    return my_sum(terms2)


def my_product(iterable):
    return reduce(lambda x, y: x*y, iterable)
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def get_slice_list(shape, axes):
    """
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    Helper function which generates slice list(s) to traverse over all
    combinations of axes, other than the selected axes.
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    Parameters
    ----------
    shape: tuple
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        Shape of the data array to traverse over.
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    axes: tuple
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        Axes which should not be iterated over.
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    Yields
    ------
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    list
        The next list of indices and/or slice objects for each dimension.

    Raises
    ------
    ValueError
        If shape is empty.
        If axes(axis) does not match shape.
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    """
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    if shape is None:
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        raise ValueError("shape cannot be None.")
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    if axes:
        if not all(axis < len(shape) for axis in axes):
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            raise ValueError("axes(axis) does not match shape.")
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        axes_select = [0 if x in axes else 1 for x in range(len(shape))]
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        axes_iterables = \
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            [list(range(y)) for x, y in enumerate(shape) if x not in axes]
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        for index in product(*axes_iterables):
            it_iter = iter(index)
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            slice_list = tuple(
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                next(it_iter)
                if axis else slice(None, None) for axis in axes_select
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            )
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            yield slice_list
    else:
        yield [slice(None, None)]
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def safe_cast(tfunc, val):
    tmp = tfunc(val)
    if val != tmp:
        raise ValueError("value changed during cast")
    return tmp


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def parse_spaces(spaces, nspc):
    nspc = safe_cast(int, nspc)
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    if spaces is None:
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        return tuple(range(nspc))
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    elif np.isscalar(spaces):
        spaces = (safe_cast(int, spaces),)
    else:
        spaces = tuple(safe_cast(int, item) for item in spaces)
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    if len(spaces) == 0:
        return spaces
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    tmp = tuple(set(spaces))
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    if tmp[0] < 0 or tmp[-1] >= nspc:
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        raise ValueError("space index out of range")
    if len(tmp) != len(spaces):
        raise ValueError("multiply defined space indices")
    return spaces
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def infer_space(domain, space):
    if space is None:
        if len(domain) != 1:
            raise ValueError("need a Field with exactly one domain")
        space = 0
    space = int(space)
    if space < 0 or space >= len(domain):
        raise ValueError("space index out of range")
    return space


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def memo(f):
    name = f.__name__

    def wrapped_f(self):
        if not hasattr(self, "_cache"):
            self._cache = {}
        try:
            return self._cache[name]
        except KeyError:
            self._cache[name] = f(self)
            return self._cache[name]
    return wrapped_f


class _DocStringInheritor(type):
    """
    A variation on
    http://groups.google.com/group/comp.lang.python/msg/26f7b4fcb4d66c95
    by Paul McGuire
    """
    def __new__(meta, name, bases, clsdict):
        if not('__doc__' in clsdict and clsdict['__doc__']):
            for mro_cls in (mro_cls for base in bases
                            for mro_cls in base.mro()):
                doc = mro_cls.__doc__
                if doc:
                    clsdict['__doc__'] = doc
                    break
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        for attr, attribute in clsdict.items():
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            if not attribute.__doc__:
                for mro_cls in (mro_cls for base in bases
                                for mro_cls in base.mro()
                                if hasattr(mro_cls, attr)):
                    doc = getattr(getattr(mro_cls, attr), '__doc__')
                    if doc:
                        if isinstance(attribute, property):
                            clsdict[attr] = property(attribute.fget,
                                                     attribute.fset,
                                                     attribute.fdel,
                                                     doc)
                        else:
                            attribute.__doc__ = doc
                        break
        return super(_DocStringInheritor, meta).__new__(meta, name,
                                                        bases, clsdict)


class NiftyMeta(_DocStringInheritor, abc.ABCMeta):
    pass
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def NiftyMetaBase():
    return with_metaclass(NiftyMeta, type('NewBase', (object,), {}))


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def nthreads():
    if nthreads._val is None:
        import os
        nthreads._val = int(os.getenv("OMP_NUM_THREADS", "1"))
    return nthreads._val
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nthreads._val = None
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# Optional extra arguments for the FFT calls
# _fft_extra_args = {}
# if exact reproducibility is needed, use this:
_fft_extra_args = dict(planner_effort='FFTW_ESTIMATE')


def fft_prep():
    import pyfftw
    pyfftw.interfaces.cache.enable()
    pyfftw.interfaces.cache.set_keepalive_time(1000.)

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def hartley(a, axes=None):
    # Check if the axes provided are valid given the shape
    if axes is not None and \
            not all(axis < len(a.shape) for axis in axes):
        raise ValueError("Provided axes do not match array shape")
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    if np.issubdtype(a.dtype, np.complexfloating):
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        raise TypeError("Hartley transform requires real-valued arrays.")
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    from pyfftw.interfaces.numpy_fft import rfftn
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    tmp = rfftn(a, axes=axes, threads=nthreads(), **_fft_extra_args)
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    def _fill_array(tmp, res, axes):
        if axes is None:
            axes = tuple(range(tmp.ndim))
        lastaxis = axes[-1]
        ntmplast = tmp.shape[lastaxis]
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        slice1 = (slice(None),)*lastaxis + (slice(0, ntmplast),)
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        np.add(tmp.real, tmp.imag, out=res[slice1])

        def _fill_upper_half(tmp, res, axes):
            lastaxis = axes[-1]
            nlast = res.shape[lastaxis]
            ntmplast = tmp.shape[lastaxis]
            nrem = nlast - ntmplast
            slice1 = [slice(None)]*lastaxis + [slice(ntmplast, None)]
            slice2 = [slice(None)]*lastaxis + [slice(nrem, 0, -1)]
            for i in axes[:-1]:
                slice1[i] = slice(1, None)
                slice2[i] = slice(None, 0, -1)
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            slice1 = tuple(slice1)
            slice2 = tuple(slice2)
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            np.subtract(tmp[slice2].real, tmp[slice2].imag, out=res[slice1])
            for i, ax in enumerate(axes[:-1]):
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                dim1 = (slice(None),)*ax + (slice(0, 1),)
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                axes2 = axes[:i] + axes[i+1:]
                _fill_upper_half(tmp[dim1], res[dim1], axes2)

        _fill_upper_half(tmp, res, axes)
        return res
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    return _fill_array(tmp, np.empty_like(a), axes)
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# Do a real-to-complex forward FFT and return the _full_ output array
def my_fftn_r2c(a, axes=None):
    # Check if the axes provided are valid given the shape
    if axes is not None and \
            not all(axis < len(a.shape) for axis in axes):
        raise ValueError("Provided axes do not match array shape")
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    if np.issubdtype(a.dtype, np.complexfloating):
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        raise TypeError("Transform requires real-valued input arrays.")

    from pyfftw.interfaces.numpy_fft import rfftn
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    tmp = rfftn(a, axes=axes, threads=nthreads(), **_fft_extra_args)
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    def _fill_complex_array(tmp, res, axes):
        if axes is None:
            axes = tuple(range(tmp.ndim))
        lastaxis = axes[-1]
        ntmplast = tmp.shape[lastaxis]
        slice1 = [slice(None)]*lastaxis + [slice(0, ntmplast)]
        res[slice1] = tmp

        def _fill_upper_half_complex(tmp, res, axes):
            lastaxis = axes[-1]
            nlast = res.shape[lastaxis]
            ntmplast = tmp.shape[lastaxis]
            nrem = nlast - ntmplast
            slice1 = [slice(None)]*lastaxis + [slice(ntmplast, None)]
            slice2 = [slice(None)]*lastaxis + [slice(nrem, 0, -1)]
            for i in axes[:-1]:
                slice1[i] = slice(1, None)
                slice2[i] = slice(None, 0, -1)
            # np.conjugate(tmp[slice2], out=res[slice1])
            res[slice1] = np.conjugate(tmp[slice2])
            for i, ax in enumerate(axes[:-1]):
                dim1 = [slice(None)]*ax + [slice(0, 1)]
                axes2 = axes[:i] + axes[i+1:]
                _fill_upper_half_complex(tmp[dim1], res[dim1], axes2)

        _fill_upper_half_complex(tmp, res, axes)
        return res

    return _fill_complex_array(tmp, np.empty_like(a, dtype=tmp.dtype), axes)
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def my_fftn(a, axes=None):
    from pyfftw.interfaces.numpy_fft import fftn
    return fftn(a, axes=axes, **_fft_extra_args)
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class frozendict(collections.Mapping):
    """
    An immutable wrapper around dictionaries that implements the complete
    :py:class:`collections.Mapping` interface. It can be used as a drop-in
    replacement for dictionaries where immutability is desired.
    """

    dict_cls = dict

    def __init__(self, *args, **kwargs):
        self._dict = self.dict_cls(*args, **kwargs)
        self._hash = None

    def __getitem__(self, key):
        return self._dict[key]

    def __contains__(self, key):
        return key in self._dict

    def copy(self, **add_or_replace):
        return self.__class__(self, **add_or_replace)

    def __iter__(self):
        return iter(self._dict)

    def __len__(self):
        return len(self._dict)

    def __repr__(self):
        return '<%s %r>' % (self.__class__.__name__, self._dict)

    def __hash__(self):
        if self._hash is None:
            h = 0
            for key, value in self._dict.items():
                h ^= hash((key, value))
            self._hash = h
        return self._hash
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def special_add_at(a, axis, index, b):
    if a.dtype != b.dtype:
        raise TypeError("data type mismatch")
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    sz1 = int(np.prod(a.shape[:axis]))
    sz3 = int(np.prod(a.shape[axis+1:]))
    a2 = a.reshape([sz1, -1, sz3])
    b2 = b.reshape([sz1, -1, sz3])
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    if np.issubdtype(a.dtype, np.complexfloating):
        dt2 = a.real.dtype
        a2 = a2.view(dt2)
        b2 = b2.view(dt2)
        sz3 *= 2
    for i1 in range(sz1):
        for i3 in range(sz3):
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            a2[i1, :, i3] += np.bincount(index, b2[i1, :, i3],
                                         minlength=a2.shape[1])
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    if np.issubdtype(a.dtype, np.complexfloating):
        a2 = a2.view(a.dtype)
    return a2.reshape(a.shape)