def reciprocal_space(space, axes=None, halfcomplex=False, shift=True,
**kwargs):
"""Return the range of the Fourier transform on ``space``.
Parameters
----------
space : `DiscreteLp`
Real space whose reciprocal is calculated. It must be
uniformly discretized.
axes : sequence of ints, optional
Dimensions along which the Fourier transform is taken.
Default: all axes
halfcomplex : bool, optional
If ``True``, take only the negative frequency part along the last
axis for. For ``False``, use the full frequency space.
This option can only be used if ``space`` is a space of
real-valued functions.
shift : bool or sequence of bools, optional
If ``True``, the reciprocal grid is shifted by half a stride in
the negative direction. With a boolean sequence, this option
is applied separately to each axis.
If a sequence is provided, it must have the same length as
``axes`` if supplied. Note that this must be set to ``True``
in the halved axis in half-complex transforms.
Default: ``True``
impl : string, optional
Implementation back-end for the created space.
Default: ``'numpy'``
exponent : float, optional
Create a space with this exponent. By default, the conjugate
exponent ``q = p / (p - 1)`` of the exponent of ``space`` is
used, where ``q = inf`` for ``p = 1`` and vice versa.
dtype : optional
Complex data type of the created space. By default, the
complex counterpart of ``space.dtype`` is used.
Returns
-------
rspace : `DiscreteLp`
Reciprocal of the input ``space``. If ``halfcomplex=True``, the
upper end of the domain (where the half space ends) is chosen to
coincide with the grid node.
"""
if not isinstance(space, DiscreteLp):
raise TypeError('`space` {!r} is not a `DiscreteLp` instance'
''.format(space))
if axes is None:
axes = tuple(range(space.ndim))
axes = normalized_axes_tuple(axes, space.ndim)
if not all(space.is_uniform_byaxis[axis] for axis in axes):
raise ValueError('`space` is not uniformly discretized in the '
'`axes` of the transform')
if halfcomplex and space.field != RealNumbers():
raise ValueError('`halfcomplex` option can only be used with real '
'spaces')
exponent = kwargs.pop('exponent', None)
if exponent is None:
exponent = conj_exponent(space.exponent)
dtype = kwargs.pop('dtype', None)
if dtype is None:
dtype = complex_dtype(space.dtype)
else:
if not is_complex_floating_dtype(dtype):
raise ValueError('{} is not a complex data type'
''.format(dtype_repr(dtype)))
impl = kwargs.pop('impl', 'numpy')
# Calculate range
recip_grid = reciprocal_grid(space.grid, shift=shift,
halfcomplex=halfcomplex, axes=axes)
# Make a partition with nodes on the boundary in the last transform axis
# if `halfcomplex == True`, otherwise a standard partition.
if halfcomplex:
max_pt = {axes[-1]: recip_grid.max_pt[axes[-1]]}
part = uniform_partition_fromgrid(recip_grid, max_pt=max_pt)
else:
part = uniform_partition_fromgrid(recip_grid)
# Use convention of adding a hat to represent fourier transform of variable
axis_labels = list(space.axis_labels)
for i in axes:
# Avoid double math
label = axis_labels[i].replace('$', '')
axis_labels[i] = '$\^{{{}}}$'.format(label)
recip_spc = uniform_discr_frompartition(part, exponent=exponent,
dtype=dtype, impl=impl,
axis_labels=axis_labels)
return recip_spc
def reciprocal_space(space, axes=None, halfcomplex=False, shift=True,
**kwargs):
"""Return the range of the Fourier transform on ``space``.
Parameters
----------
space : `DiscreteLp`
Real space whose reciprocal is calculated. It must be
uniformly discretized.
axes : sequence of ints, optional
Dimensions along which the Fourier transform is taken.
Default: all axes
halfcomplex : bool, optional
If ``True``, take only the negative frequency part along the last
axis for. For ``False``, use the full frequency space.
This option can only be used if ``space`` is a space of
real-valued functions.
shift : bool or sequence of bools, optional
If ``True``, the reciprocal grid is shifted by half a stride in
the negative direction. With a boolean sequence, this option
is applied separately to each axis.
If a sequence is provided, it must have the same length as
``axes`` if supplied. Note that this must be set to ``True``
in the halved axis in half-complex transforms.
Default: ``True``
impl : string, optional
Implementation back-end for the created space.
Default: ``'numpy'``
exponent : float, optional
Create a space with this exponent. By default, the conjugate
exponent ``q = p / (p - 1)`` of the exponent of ``space`` is
used, where ``q = inf`` for ``p = 1`` and vice versa.
dtype : optional
Complex data type of the created space. By default, the
complex counterpart of ``space.dtype`` is used.
Returns
-------
rspace : `DiscreteLp`
Reciprocal of the input ``space``. If ``halfcomplex=True``, the
upper end of the domain (where the half space ends) is chosen to
coincide with the grid node.
"""
if not isinstance(space, DiscreteLp):
raise TypeError('`space` {!r} is not a `DiscreteLp` instance'
''.format(space))
if not space.is_uniform:
raise ValueError('`space` is not uniformly discretized')
if axes is None:
axes = tuple(range(space.ndim))
axes = normalized_axes_tuple(axes, space.ndim)
if halfcomplex and space.field != RealNumbers():
raise ValueError('`halfcomplex` option can only be used with real '
'spaces')
exponent = kwargs.pop('exponent', None)
if exponent is None:
exponent = conj_exponent(space.exponent)
dtype = kwargs.pop('dtype', None)
if dtype is None:
dtype = complex_dtype(space.dtype)
else:
if not is_complex_floating_dtype(dtype):
raise ValueError('{} is not a complex data type'
''.format(dtype_repr(dtype)))
impl = kwargs.pop('impl', 'numpy')
# Calculate range
recip_grid = reciprocal_grid(space.grid, shift=shift,
halfcomplex=halfcomplex, axes=axes)
# Make a partition with nodes on the boundary in the last transform axis
# if `halfcomplex == True`, otherwise a standard partition.
if halfcomplex:
max_pt = {axes[-1]: recip_grid.max_pt[axes[-1]]}
part = uniform_partition_fromgrid(recip_grid, max_pt=max_pt)
else:
part = uniform_partition_fromgrid(recip_grid)
# Use convention of adding a hat to represent fourier transform of variable
axis_labels = list(space.axis_labels)
for i in axes:
# Avoid double math
label = axis_labels[i].replace('$', '')
axis_labels[i] = '$\^{{{}}}$'.format(label)
recip_spc = uniform_discr_frompartition(part, exponent=exponent,
dtype=dtype, impl=impl,
axis_labels=axis_labels)
return recip_spc