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# Licensed under a 3-clause BSD style license - see LICENSE.rst
import warnings
import numpy as np
from functools import partial
from .core import Kernel, Kernel1D, Kernel2D, MAX_NORMALIZATION
from ..utils.exceptions import AstropyUserWarning
from ..utils.console import human_file_size
from ..utils.decorators import deprecated_renamed_argument
from .. import units as u
from ..nddata import support_nddata
from ..modeling.core import _make_arithmetic_operator, BINARY_OPERATORS
from ..modeling.core import _CompoundModelMeta
# Disabling all doctests in this module until a better way of handling warnings
# in doctests can be determined
__doctest_skip__ = ['*']
BOUNDARY_OPTIONS = [None, 'fill', 'wrap', 'extend']
@support_nddata(data='array')
def convolve(array, kernel, boundary='fill', fill_value=0.,
nan_treatment='interpolate', normalize_kernel=True, mask=None,
preserve_nan=False, normalization_zero_tol=1e-8):
'''
Convolve an array with a kernel.
This routine differs from `scipy.ndimage.convolve` because
it includes a special treatment for ``NaN`` values. Rather than
including ``NaN`` values in the array in the convolution calculation, which
causes large ``NaN`` holes in the convolved array, ``NaN`` values are
replaced with interpolated values using the kernel as an interpolation
function.
Parameters
----------
array : `~astropy.nddata.NDData` or `numpy.ndarray` or array-like
The array to convolve. This should be a 1, 2, or 3-dimensional array
or a list or a set of nested lists representing a 1, 2, or
3-dimensional array. If an `~astropy.nddata.NDData`, the ``mask`` of
the `~astropy.nddata.NDData` will be used as the ``mask`` argument.
kernel : `numpy.ndarray` or `~astropy.convolution.Kernel`
The convolution kernel. The number of dimensions should match those for
the array, and the dimensions should be odd in all directions. If a
masked array, the masked values will be replaced by ``fill_value``.
boundary : str, optional
A flag indicating how to handle boundaries:
* `None`
Set the ``result`` values to zero where the kernel
extends beyond the edge of the array.
* 'fill'
Set values outside the array boundary to ``fill_value`` (default).
* 'wrap'
Periodic boundary that wrap to the other side of ``array``.
* 'extend'
Set values outside the array to the nearest ``array``
value.
fill_value : float, optional
The value to use outside the array when using ``boundary='fill'``
normalize_kernel : bool, optional
Whether to normalize the kernel to have a sum of one prior to
convolving
nan_treatment : 'interpolate', 'fill'
interpolate will result in renormalization of the kernel at each
position ignoring (pixels that are NaN in the image) in both the image
and the kernel.
'fill' will replace the NaN pixels with a fixed numerical value (default
zero, see ``fill_value``) prior to convolution
Note that if the kernel has a sum equal to zero, NaN interpolation
is not possible and will raise an exception
preserve_nan : bool
After performing convolution, should pixels that were originally NaN
again become NaN?
mask : `None` or `numpy.ndarray`
A "mask" array. Shape must match ``array``, and anything that is masked
(i.e., not 0/`False`) will be set to NaN for the convolution. If
`None`, no masking will be performed unless ``array`` is a masked array.
If ``mask`` is not `None` *and* ``array`` is a masked array, a pixel is
masked of it is masked in either ``mask`` *or* ``array.mask``.
normalization_zero_tol: float, optional
The absolute tolerance on whether the kernel is different than zero.
If the kernel sums to zero to within this precision, it cannot be
normalized. Default is "1e-8".
Returns
-------
result : `numpy.ndarray`
An array with the same dimensions and as the input array,
convolved with kernel. The data type depends on the input
array type. If array is a floating point type, then the
return array keeps the same data type, otherwise the type
is ``numpy.float``.
Notes
-----
For masked arrays, masked values are treated as NaNs. The convolution
is always done at ``numpy.float`` precision.
'''
from .boundary_none import (convolve1d_boundary_none,
convolve2d_boundary_none,
convolve3d_boundary_none)
from .boundary_extend import (convolve1d_boundary_extend,
convolve2d_boundary_extend,
convolve3d_boundary_extend)
from .boundary_fill import (convolve1d_boundary_fill,
convolve2d_boundary_fill,
convolve3d_boundary_fill)
from .boundary_wrap import (convolve1d_boundary_wrap,
convolve2d_boundary_wrap,
convolve3d_boundary_wrap)
if boundary not in BOUNDARY_OPTIONS:
raise ValueError("Invalid boundary option: must be one of {0}"
.format(BOUNDARY_OPTIONS))
if nan_treatment not in ('interpolate', 'fill'):
raise ValueError("nan_treatment must be one of 'interpolate','fill'")
# The cython routines all need float type inputs (so, a particular
# bit size, endianness, etc.). So we have to convert, which also
# has the effect of making copies so we don't modify the inputs.
# After this, the variables we work with will be array_internal, and
# kernel_internal. However -- we do want to keep track of what type
# the input array was so we can cast the result to that at the end
# if it's a floating point type. Don't bother with this for lists --
# just always push those as float.
# It is always necessary to make a copy of kernel (since it is modified),
# but, if we just so happen to be lucky enough to have the input array
# have exactly the desired type, we just alias to array_internal
# If array and kernel are both Kernal instances, convolve here and return.
if isinstance(kernel, Kernel) and isinstance(array, Kernel):
if isinstance(array, Kernel1D) and isinstance(kernel, Kernel1D):
new_array = convolve1d_boundary_fill(array.array, kernel.array,
0, True)
new_kernel = Kernel1D(array=new_array)
elif isinstance(array, Kernel2D) and isinstance(kernel, Kernel2D):
new_array = convolve2d_boundary_fill(array.array, kernel.array,
0, True)
new_kernel = Kernel2D(array=new_array)
else:
raise Exception("Can't convolve 1D and 2D kernel.")
new_kernel._separable = kernel._separable and array._separable
new_kernel._is_bool = False
return new_kernel
# Copy or alias array to array_internal
try:
# Anything that's masked must be turned into NaNs for the interpolation.
# This requires copying. A copy is also needed for nan_treatment == 'fill'
# A copy prevents possible function side-effects of the input array.
if nan_treatment == 'fill' or np.ma.is_masked(array) or mask is not None:
if np.ma.is_masked(array):
# ``np.ma.maskedarray.filled()`` returns a copy, however there is no way to specify the return type
# or order etc.
# In addition ``np.nan`` is a ``float`` and there is no conversion to an ``int`` type.
# Therefore, a pre-fill copy is needed for non ``float`` masked arrays.
# ``subok=True`` is needed to retain ``np.ma.maskedarray.filled()``.
# ``copy=False`` allows the fill to act as the copy if type and order are already correct.
array_internal = np.array(array, dtype=float, copy=False, order='C', subok=True)
array_internal = array_internal.filled(np.nan)
else:
# Since we're making a copy, we might as well use `subok=False` to save,
# what is probably, a negligible amount of memory.
array_internal = np.array(array, dtype=float, copy=True, order='C', subok=False)
if mask is not None:
# mask != 0 yields a bool mask for all ints/floats/bool
array_internal[mask != 0] = np.nan
else:
# The call below is synonymous with np.asanyarray(array, ftype=float, order='C')
# The advantage of `subok=True` is that it won't copy when array is an ndarray subclass. If it
# is and `subok=False` (default), then it will copy even if `copy=False`. This uses less memory
# when ndarray subclasses are passed in.
array_internal = np.array(array, dtype=float, copy=False, order='C', subok=True)
except (TypeError, ValueError) as e:
raise TypeError('array should be a Numpy array or something '
'convertable into a float array', e)
array_dtype = getattr(array, 'dtype', array_internal.dtype)
# Copy or alias kernel to kernel_internal
# Due to NaN interpolation and kernel normalization, a copy must always be made.
# 1st alias and then copy after depending on whether kernel is masked (so as not to copy twice).
if isinstance(kernel, Kernel):
kernel_internal = kernel.array
else:
kernel_internal = kernel
if np.ma.is_masked(kernel_internal):
# *kernel* doesn't support NaN interpolation, so instead we just fill it.
# np.ma.maskedarray.filled() returns a copy.
kernel_internal = kernel_internal.filled(fill_value)
# MaskedArray.astype() has neither copy nor order params like ndarray.astype has.
# np.ma.maskedarray.filled() returns an ndarray not a maksedarray (implicit default subok=False).
# astype must be called after filling the masked data to avoid possible additional copying.
kernel_internal = kernel_internal.astype(float, copy=False, order='C', subok=True) # subok=True is redundant here but leave for future.
else:
try:
kernel_internal = np.array(kernel_internal, dtype=float, copy=True, order='C', subok=False)
except (TypeError, ValueError) as e:
raise TypeError('kernel should be a Numpy array or something '
'convertable into a float array', e)
# Check that the number of dimensions is compatible
if array_internal.ndim != kernel_internal.ndim:
raise Exception('array and kernel have differing number of '
'dimensions.')
# Mark the NaN values so we can replace them later if interpolate_nan is
# not set
if preserve_nan:
badvals = np.isnan(array_internal)
if nan_treatment == 'fill':
initially_nan = np.isnan(array_internal)
array_internal[initially_nan] = fill_value
# Because the Cython routines have to normalize the kernel on the fly, we
# explicitly normalize the kernel here, and then scale the image at the
# end if normalization was not requested.
kernel_sum = kernel_internal.sum()
kernel_sums_to_zero = np.isclose(kernel_sum, 0, atol=normalization_zero_tol)
if (kernel_sum < 1. / MAX_NORMALIZATION or kernel_sums_to_zero) and normalize_kernel:
raise Exception("The kernel can't be normalized, because its sum is "
"close to zero. The sum of the given kernel is < {0}"
.format(1. / MAX_NORMALIZATION))
if not kernel_sums_to_zero:
kernel_internal /= kernel_sum
renormalize_by_kernel = not kernel_sums_to_zero
if array_internal.ndim == 0:
raise Exception("cannot convolve 0-dimensional arrays")
elif array_internal.ndim == 1:
if boundary == 'extend':
result = convolve1d_boundary_extend(array_internal,
kernel_internal,
renormalize_by_kernel)
elif boundary == 'fill':
result = convolve1d_boundary_fill(array_internal,
kernel_internal,
float(fill_value),
renormalize_by_kernel)
elif boundary == 'wrap':
result = convolve1d_boundary_wrap(array_internal,
kernel_internal,
renormalize_by_kernel)
elif boundary is None:
result = convolve1d_boundary_none(array_internal,
kernel_internal,
renormalize_by_kernel)
elif array_internal.ndim == 2:
if boundary == 'extend':
result = convolve2d_boundary_extend(array_internal,
kernel_internal,
renormalize_by_kernel,
)
elif boundary == 'fill':
result = convolve2d_boundary_fill(array_internal,
kernel_internal,
float(fill_value),
renormalize_by_kernel,
)
elif boundary == 'wrap':
result = convolve2d_boundary_wrap(array_internal,
kernel_internal,
renormalize_by_kernel,
)
elif boundary is None:
result = convolve2d_boundary_none(array_internal,
kernel_internal,
renormalize_by_kernel,
)
elif array_internal.ndim == 3:
if boundary == 'extend':
result = convolve3d_boundary_extend(array_internal,
kernel_internal,
renormalize_by_kernel)
elif boundary == 'fill':
result = convolve3d_boundary_fill(array_internal,
kernel_internal,
float(fill_value),
renormalize_by_kernel)
elif boundary == 'wrap':
result = convolve3d_boundary_wrap(array_internal,
kernel_internal,
renormalize_by_kernel)
elif boundary is None:
result = convolve3d_boundary_none(array_internal,
kernel_internal,
renormalize_by_kernel)
else:
raise NotImplementedError('convolve only supports 1, 2, and 3-dimensional '
'arrays at this time')
# If normalization was not requested, we need to scale the array (since
# the kernel is effectively normalized within the cython functions)
if not normalize_kernel and not kernel_sums_to_zero:
result *= kernel_sum
if preserve_nan:
result[badvals] = np.nan
if nan_treatment == 'fill':
array_internal[initially_nan] = np.nan
# Try to preserve the input type if it's a floating point type
if array_dtype.kind == 'f':
# Avoid making another copy if possible
try:
return result.astype(array_dtype, copy=False)
except TypeError:
return result.astype(array_dtype)
else:
return result
@deprecated_renamed_argument('interpolate_nan', 'nan_treatment', 'v2.0.0')
@support_nddata(data='array')
def convolve_fft(array, kernel, boundary='fill', fill_value=0.,
nan_treatment='interpolate', normalize_kernel=True,
normalization_zero_tol=1e-8,
preserve_nan=False, mask=None, crop=True, return_fft=False,
fft_pad=None, psf_pad=None, quiet=False,
min_wt=0.0, allow_huge=False,
fftn=np.fft.fftn, ifftn=np.fft.ifftn,
complex_dtype=complex):
"""
Convolve an ndarray with an nd-kernel. Returns a convolved image with
``shape = array.shape``. Assumes kernel is centered.
`convolve_fft` is very similar to `convolve` in that it replaces ``NaN``
values in the original image with interpolated values using the kernel as
an interpolation function. However, it also includes many additional
options specific to the implementation.
`convolve_fft` differs from `scipy.signal.fftconvolve` in a few ways:
* It can treat ``NaN`` values as zeros or interpolate over them.
* ``inf`` values are treated as ``NaN``
* (optionally) It pads to the nearest 2^n size to improve FFT speed.
* Its only valid ``mode`` is 'same' (i.e., the same shape array is returned)
* It lets you use your own fft, e.g.,
`pyFFTW <https://pypi.python.org/pypi/pyFFTW>`_ or
`pyFFTW3 <https://pypi.python.org/pypi/PyFFTW3/0.2.1>`_ , which can lead to
performance improvements, depending on your system configuration. pyFFTW3
is threaded, and therefore may yield significant performance benefits on
multi-core machines at the cost of greater memory requirements. Specify
the ``fftn`` and ``ifftn`` keywords to override the default, which is
`numpy.fft.fft` and `numpy.fft.ifft`.
Parameters
----------
array : `numpy.ndarray`
Array to be convolved with ``kernel``. It can be of any
dimensionality, though only 1, 2, and 3d arrays have been tested.
kernel : `numpy.ndarray` or `astropy.convolution.Kernel`
The convolution kernel. The number of dimensions should match those
for the array. The dimensions *do not* have to be odd in all directions,
unlike in the non-fft `convolve` function. The kernel will be
normalized if ``normalize_kernel`` is set. It is assumed to be centered
(i.e., shifts may result if your kernel is asymmetric)
boundary : {'fill', 'wrap'}, optional
A flag indicating how to handle boundaries:
* 'fill': set values outside the array boundary to fill_value
(default)
* 'wrap': periodic boundary
The `None` and 'extend' parameters are not supported for FFT-based
convolution
fill_value : float, optional
The value to use outside the array when using boundary='fill'
nan_treatment : 'interpolate', 'fill'
``interpolate`` will result in renormalization of the kernel at each
position ignoring (pixels that are NaN in the image) in both the image
and the kernel. ``fill`` will replace the NaN pixels with a fixed
numerical value (default zero, see ``fill_value``) prior to
convolution. Note that if the kernel has a sum equal to zero, NaN
interpolation is not possible and will raise an exception.
normalize_kernel : function or boolean, optional
If specified, this is the function to divide kernel by to normalize it.
e.g., ``normalize_kernel=np.sum`` means that kernel will be modified to be:
``kernel = kernel / np.sum(kernel)``. If True, defaults to
``normalize_kernel = np.sum``.
normalization_zero_tol: float, optional
The absolute tolerance on whether the kernel is different than zero.
If the kernel sums to zero to within this precision, it cannot be
normalized. Default is "1e-8".
preserve_nan : bool
After performing convolution, should pixels that were originally NaN
again become NaN?
mask : `None` or `numpy.ndarray`
A "mask" array. Shape must match ``array``, and anything that is masked
(i.e., not 0/`False`) will be set to NaN for the convolution. If
`None`, no masking will be performed unless ``array`` is a masked array.
If ``mask`` is not `None` *and* ``array`` is a masked array, a pixel is
masked of it is masked in either ``mask`` *or* ``array.mask``.
Other Parameters
----------------
min_wt : float, optional
If ignoring ``NaN`` / zeros, force all grid points with a weight less than
this value to ``NaN`` (the weight of a grid point with *no* ignored
neighbors is 1.0).
If ``min_wt`` is zero, then all zero-weight points will be set to zero
instead of ``NaN`` (which they would be otherwise, because 1/0 = nan).
See the examples below
fft_pad : bool, optional
Default on. Zero-pad image to the nearest 2^n. With
``boundary='wrap'``, this will be disabled.
psf_pad : bool, optional
Zero-pad image to be at least the sum of the image sizes to avoid
edge-wrapping when smoothing. This is enabled by default with
``boundary='fill'``, but it can be overridden with a boolean option.
``boundary='wrap'`` and ``psf_pad=True`` are not compatible.
crop : bool, optional
Default on. Return an image of the size of the larger of the input
image and the kernel.
If the image and kernel are asymmetric in opposite directions, will
return the largest image in both directions.
For example, if an input image has shape [100,3] but a kernel with shape
[6,6] is used, the output will be [100,6].
return_fft : bool, optional
Return the ``fft(image)*fft(kernel)`` instead of the convolution (which is
``ifft(fft(image)*fft(kernel))``). Useful for making PSDs.
fftn, ifftn : functions, optional
The fft and inverse fft functions. Can be overridden to use your own
ffts, e.g. an fftw3 wrapper or scipy's fftn,
``fft=scipy.fftpack.fftn``
complex_dtype : numpy.complex, optional
Which complex dtype to use. `numpy` has a range of options, from 64 to
256.
quiet : bool, optional
Silence warning message about NaN interpolation
allow_huge : bool, optional
Allow huge arrays in the FFT? If False, will raise an exception if the
array or kernel size is >1 GB
Raises
------
ValueError:
If the array is bigger than 1 GB after padding, will raise this exception
unless ``allow_huge`` is True
See Also
--------
convolve:
Convolve is a non-fft version of this code. It is more memory
efficient and for small kernels can be faster.
Returns
-------
default : ndarray
``array`` convolved with ``kernel``. If ``return_fft`` is set, returns
``fft(array) * fft(kernel)``. If crop is not set, returns the
image, but with the fft-padded size instead of the input size
Notes
-----
With ``psf_pad=True`` and a large PSF, the resulting data can become
very large and consume a lot of memory. See Issue
https://github.com/astropy/astropy/pull/4366 for further detail.
Examples
--------
>>> convolve_fft([1, 0, 3], [1, 1, 1])
array([ 1., 4., 3.])
>>> convolve_fft([1, np.nan, 3], [1, 1, 1])
array([ 1., 4., 3.])
>>> convolve_fft([1, 0, 3], [0, 1, 0])
array([ 1., 0., 3.])
>>> convolve_fft([1, 2, 3], [1])
array([ 1., 2., 3.])
>>> convolve_fft([1, np.nan, 3], [0, 1, 0], nan_treatment='interpolate')
...
array([ 1., 0., 3.])
>>> convolve_fft([1, np.nan, 3], [0, 1, 0], nan_treatment='interpolate',
... min_wt=1e-8)
array([ 1., nan, 3.])
>>> convolve_fft([1, np.nan, 3], [1, 1, 1], nan_treatment='interpolate')
array([ 1., 4., 3.])
>>> convolve_fft([1, np.nan, 3], [1, 1, 1], nan_treatment='interpolate',
... normalize_kernel=True)
array([ 1., 2., 3.])
>>> import scipy.fftpack # optional - requires scipy
>>> convolve_fft([1, np.nan, 3], [1, 1, 1], nan_treatment='interpolate',
... normalize_kernel=True,
... fftn=scipy.fftpack.fft, ifftn=scipy.fftpack.ifft)
array([ 1., 2., 3.])
"""
# Checking copied from convolve.py - however, since FFTs have real &
# complex components, we change the types. Only the real part will be
# returned! Note that this always makes a copy.
# Check kernel is kernel instance
if isinstance(kernel, Kernel):
kernel = kernel.array
if isinstance(array, Kernel):
raise TypeError("Can't convolve two kernels with convolve_fft. "
"Use convolve instead.")
if nan_treatment not in ('interpolate', 'fill'):
raise ValueError("nan_treatment must be one of 'interpolate','fill'")
# Convert array dtype to complex
# and ensure that list inputs become arrays
array = np.asarray(array, dtype=complex)
kernel = np.asarray(kernel, dtype=complex)
# Check that the number of dimensions is compatible
if array.ndim != kernel.ndim:
raise ValueError("Image and kernel must have same number of "
"dimensions")
arrayshape = array.shape
kernshape = kernel.shape
array_size_B = (np.product(arrayshape, dtype=np.int64) *
np.dtype(complex_dtype).itemsize)*u.byte
if array_size_B > 1*u.GB and not allow_huge:
raise ValueError("Size Error: Arrays will be {}. Use "
"allow_huge=True to override this exception."
.format(human_file_size(array_size_B.to_value(u.byte))))
# mask catching - masks must be turned into NaNs for use later in the image
if np.ma.is_masked(array):
mamask = array.mask
array = np.array(array)
array[mamask] = np.nan
elif mask is not None:
# copying here because we have to mask it below. But no need to copy
# if mask is None because we won't modify it.
array = np.array(array)
if mask is not None:
# mask != 0 yields a bool mask for all ints/floats/bool
array[mask != 0] = np.nan
# the *kernel* doesn't support NaN interpolation, so instead we just fill it
if np.ma.is_masked(kernel):
kernel = kernel.filled(0)
# NaN and inf catching
nanmaskarray = np.isnan(array) | np.isinf(array)
array[nanmaskarray] = 0
nanmaskkernel = np.isnan(kernel) | np.isinf(kernel)
kernel[nanmaskkernel] = 0
if normalize_kernel is True:
if kernel.sum() < 1. / MAX_NORMALIZATION:
raise Exception("The kernel can't be normalized, because its sum is "
"close to zero. The sum of the given kernel is < {0}"
.format(1. / MAX_NORMALIZATION))
kernel_scale = kernel.sum()
normalized_kernel = kernel / kernel_scale
kernel_scale = 1 # if we want to normalize it, leave it normed!
elif normalize_kernel:
# try this. If a function is not passed, the code will just crash... I
# think type checking would be better but PEPs say otherwise...
kernel_scale = normalize_kernel(kernel)
normalized_kernel = kernel / kernel_scale
else:
kernel_scale = kernel.sum()
if np.abs(kernel_scale) < normalization_zero_tol:
if nan_treatment == 'interpolate':
raise ValueError('Cannot interpolate NaNs with an unnormalizable kernel')
else:
# the kernel's sum is near-zero, so it can't be scaled
kernel_scale = 1
normalized_kernel = kernel
else:
# the kernel is normalizable; we'll temporarily normalize it
# now and undo the normalization later.
normalized_kernel = kernel / kernel_scale
if boundary is None:
warnings.warn("The convolve_fft version of boundary=None is "
"equivalent to the convolve boundary='fill'. There is "
"no FFT equivalent to convolve's "
"zero-if-kernel-leaves-boundary", AstropyUserWarning)
if psf_pad is None:
psf_pad = True
if fft_pad is None:
fft_pad = True
elif boundary == 'fill':
# create a boundary region at least as large as the kernel
if psf_pad is False:
warnings.warn("psf_pad was set to {0}, which overrides the "
"boundary='fill' setting.".format(psf_pad),
AstropyUserWarning)
else:
psf_pad = True
if fft_pad is None:
# default is 'True' according to the docstring
fft_pad = True
elif boundary == 'wrap':
if psf_pad:
raise ValueError("With boundary='wrap', psf_pad cannot be enabled.")
psf_pad = False
if fft_pad:
raise ValueError("With boundary='wrap', fft_pad cannot be enabled.")
fft_pad = False
fill_value = 0 # force zero; it should not be used
elif boundary == 'extend':
raise NotImplementedError("The 'extend' option is not implemented "
"for fft-based convolution")
# find ideal size (power of 2) for fft.
# Can add shapes because they are tuples
if fft_pad: # default=True
if psf_pad: # default=False
# add the dimensions and then take the max (bigger)
fsize = 2 ** np.ceil(np.log2(
np.max(np.array(arrayshape) + np.array(kernshape))))
else:
# add the shape lists (max of a list of length 4) (smaller)
# also makes the shapes square
fsize = 2 ** np.ceil(np.log2(np.max(arrayshape + kernshape)))
newshape = np.array([fsize for ii in range(array.ndim)], dtype=int)
else:
if psf_pad:
# just add the biggest dimensions
newshape = np.array(arrayshape) + np.array(kernshape)
else:
newshape = np.array([np.max([imsh, kernsh])
for imsh, kernsh in zip(arrayshape, kernshape)])
# perform a second check after padding
array_size_C = (np.product(newshape, dtype=np.int64) *
np.dtype(complex_dtype).itemsize)*u.byte
if array_size_C > 1*u.GB and not allow_huge:
raise ValueError("Size Error: Arrays will be {}. Use "
"allow_huge=True to override this exception."
.format(human_file_size(array_size_C)))
# For future reference, this can be used to predict "almost exactly"
# how much *additional* memory will be used.
# size * (array + kernel + kernelfft + arrayfft +
# (kernel*array)fft +
# optional(weight image + weight_fft + weight_ifft) +
# optional(returned_fft))
# total_memory_used_GB = (np.product(newshape)*np.dtype(complex_dtype).itemsize
# * (5 + 3*((interpolate_nan or ) and kernel_is_normalized))
# + (1 + (not return_fft)) *
# np.product(arrayshape)*np.dtype(complex_dtype).itemsize
# + np.product(arrayshape)*np.dtype(bool).itemsize
# + np.product(kernshape)*np.dtype(bool).itemsize)
# ) / 1024.**3
# separate each dimension by the padding size... this is to determine the
# appropriate slice size to get back to the input dimensions
arrayslices = []
kernslices = []
for ii, (newdimsize, arraydimsize, kerndimsize) in enumerate(zip(newshape, arrayshape, kernshape)):
center = newdimsize - (newdimsize + 1) // 2
arrayslices += [slice(center - arraydimsize // 2,
center + (arraydimsize + 1) // 2)]
kernslices += [slice(center - kerndimsize // 2,
center + (kerndimsize + 1) // 2)]
arrayslices = tuple(arrayslices)
kernslices = tuple(kernslices)
if not np.all(newshape == arrayshape):
if np.isfinite(fill_value):
bigarray = np.ones(newshape, dtype=complex_dtype) * fill_value
else:
bigarray = np.zeros(newshape, dtype=complex_dtype)
bigarray[arrayslices] = array
else:
bigarray = array
if not np.all(newshape == kernshape):
bigkernel = np.zeros(newshape, dtype=complex_dtype)
bigkernel[kernslices] = normalized_kernel
else:
bigkernel = normalized_kernel
arrayfft = fftn(bigarray)
# need to shift the kernel so that, e.g., [0,0,1,0] -> [1,0,0,0] = unity
kernfft = fftn(np.fft.ifftshift(bigkernel))
fftmult = arrayfft * kernfft
interpolate_nan = (nan_treatment == 'interpolate')
if interpolate_nan:
if not np.isfinite(fill_value):
bigimwt = np.zeros(newshape, dtype=complex_dtype)
else:
bigimwt = np.ones(newshape, dtype=complex_dtype)
bigimwt[arrayslices] = 1.0 - nanmaskarray * interpolate_nan
wtfft = fftn(bigimwt)
# You can only get to this point if kernel_is_normalized
wtfftmult = wtfft * kernfft
wtsm = ifftn(wtfftmult)
# need to re-zero weights outside of the image (if it is padded, we
# still don't weight those regions)
bigimwt[arrayslices] = wtsm.real[arrayslices]
else:
bigimwt = 1
if np.isnan(fftmult).any():
# this check should be unnecessary; call it an insanity check
raise ValueError("Encountered NaNs in convolve. This is disallowed.")
# restore NaNs in original image (they were modified inplace earlier)
# We don't have to worry about masked arrays - if input was masked, it was
# copied
array[nanmaskarray] = np.nan
kernel[nanmaskkernel] = np.nan
fftmult *= kernel_scale
if return_fft:
return fftmult
if interpolate_nan:
rifft = (ifftn(fftmult)) / bigimwt
if not np.isscalar(bigimwt):
if min_wt > 0.:
rifft[bigimwt < min_wt] = np.nan
else:
# Set anything with no weight to zero (taking into account
# slight offsets due to floating-point errors).
rifft[bigimwt < 10 * np.finfo(bigimwt.dtype).eps] = 0.0
else:
rifft = ifftn(fftmult)
if preserve_nan:
rifft[arrayslices][nanmaskarray] = np.nan
if crop:
result = rifft[arrayslices].real
return result
else:
return rifft.real
def interpolate_replace_nans(array, kernel, convolve=convolve, **kwargs):
"""
Given a data set containing NaNs, replace the NaNs by interpolating from
neighboring data points with a given kernel.
Parameters
----------
array : `numpy.ndarray`
Array to be convolved with ``kernel``. It can be of any
dimensionality, though only 1, 2, and 3d arrays have been tested.
kernel : `numpy.ndarray` or `astropy.convolution.Kernel`
The convolution kernel. The number of dimensions should match those
for the array. The dimensions *do not* have to be odd in all directions,
unlike in the non-fft `convolve` function. The kernel will be
normalized if ``normalize_kernel`` is set. It is assumed to be centered
(i.e., shifts may result if your kernel is asymmetric). The kernel
*must be normalizable* (i.e., its sum cannot be zero).
convolve : `convolve` or `convolve_fft`
One of the two convolution functions defined in this package.
Returns
-------
newarray : `numpy.ndarray`
A copy of the original array with NaN pixels replaced with their
interpolated counterparts
"""
if not np.any(np.isnan(array)):
return array.copy()
newarray = array.copy()
convolved = convolve(array, kernel, nan_treatment='interpolate',
normalize_kernel=True, **kwargs)
isnan = np.isnan(array)
newarray[isnan] = convolved[isnan]
return newarray
def convolve_models(model, kernel, mode='convolve_fft', **kwargs):
"""
Convolve two models using `~astropy.convolution.convolve_fft`.
Parameters
----------
model : `~astropy.modeling.core.Model`
Functional model
kernel : `~astropy.modeling.core.Model`
Convolution kernel
mode : str
Keyword representing which function to use for convolution.
* 'convolve_fft' : use `~astropy.convolution.convolve_fft` function.
* 'convolve' : use `~astropy.convolution.convolve`.
kwargs : dict
Keyword arguments to me passed either to `~astropy.convolution.convolve`
or `~astropy.convolution.convolve_fft` depending on ``mode``.
Returns
-------
default : CompoundModel
Convolved model
"""
if mode == 'convolve_fft':
BINARY_OPERATORS['convolve_fft'] = _make_arithmetic_operator(partial(convolve_fft, **kwargs))
elif mode == 'convolve':
BINARY_OPERATORS['convolve'] = _make_arithmetic_operator(partial(convolve, **kwargs))
else:
raise ValueError('Mode {} is not supported.'.format(mode))
return _CompoundModelMeta._from_operator(mode, model, kernel)