# 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

# Check if kernel is kernel instance

if isinstance(kernel, Kernel):

# Check if array is also kernel instance, if so convolve and

# return new kernel instance

if 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

kernel = kernel.array

# Check that the arguments are lists or Numpy arrays

try:

# Note this won't copy if it doesn't have to -- which is okay

# because none of what follows modifies array_internal.

array_internal = np.asanyarray(array, dtype=float)

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)

if isinstance(kernel, (list, tuple)):

kernel_internal = np.array(kernel, dtype=float)

elif isinstance(kernel, np.ndarray):

# Note this always makes a copy, since we will be modifying it

kernel_internal = kernel.astype(float)

else:

raise TypeError("kernel should be a list or a Numpy array")

# 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.')

# anything that's masked must be turned into NaNs for the interpolation.

# This requires copying the array_internal

array_internal_copied = False

if np.ma.is_masked(array):

array_internal = array_internal.filled(np.nan)

array_internal_copied = True

if mask is not None:

if not array_internal_copied:

array_internal = array_internal.copy()

array_internal_copied = True

# mask != 0 yields a bool mask for all ints/floats/bool

array_internal[mask != 0] = np.nan

if np.ma.is_masked(kernel):

# *kernel* doesn't support NaN interpolation, so instead we just fill it

kernel_internal = kernel_internal.filled(fill_value)

# 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)]

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)