# Licensed under a 3-clause BSD style license - see LICENSE.rst

import warnings

from functools import partial

import numpy as np

from astropy import units as u

from astropy.modeling.convolution import Convolution

from astropy.modeling.core import SPECIAL_OPERATORS, CompoundModel

from astropy.nddata import support_nddata

from astropy.utils.console import human_file_size

from astropy.utils.exceptions import AstropyUserWarning

from ._convolve import _convolveNd_c

from .core import MAX_NORMALIZATION, Kernel, Kernel1D, Kernel2D

from .utils import KernelSizeError, has_even_axis

# np.unique([scipy.fft.next_fast_len(i, real=True) for i in range(10000)])

# fmt: off

_good_sizes = np.array(

[

0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 12,

15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40,

45, 48, 50, 54, 60, 64, 72, 75, 80, 81, 90,

96, 100, 108, 120, 125, 128, 135, 144, 150, 160, 162,

180, 192, 200, 216, 225, 240, 243, 250, 256, 270, 288,

300, 320, 324, 360, 375, 384, 400, 405, 432, 450, 480,

486, 500, 512, 540, 576, 600, 625, 640, 648, 675, 720,

729, 750, 768, 800, 810, 864, 900, 960, 972, 1000, 1024,

1080, 1125, 1152, 1200, 1215, 1250, 1280, 1296, 1350, 1440, 1458,

1500, 1536, 1600, 1620, 1728, 1800, 1875, 1920, 1944, 2000, 2025,

2048, 2160, 2187, 2250, 2304, 2400, 2430, 2500, 2560, 2592, 2700,

2880, 2916, 3000, 3072, 3125, 3200, 3240, 3375, 3456, 3600, 3645,

3750, 3840, 3888, 4000, 4050, 4096, 4320, 4374, 4500, 4608, 4800,

4860, 5000, 5120, 5184, 5400, 5625, 5760, 5832, 6000, 6075, 6144,

6250, 6400, 6480, 6561, 6750, 6912, 7200, 7290, 7500, 7680, 7776,

8000, 8100, 8192, 8640, 8748, 9000, 9216, 9375, 9600, 9720, 10000,

]

)

# fmt: on

_good_range = int(np.log10(_good_sizes[-1]))

# Disabling doctests when scipy isn't present.

__doctest_requires__ = {("convolve_fft",): ["scipy.fft"]}

BOUNDARY_OPTIONS = [None, "fill", "wrap", "extend"]

def _next_fast_lengths(shape):

"""

Find optimal or good sizes to pad an array of ``shape`` to for better

performance with `numpy.fft.*fft` and `scipy.fft.*fft`.

Calculated directly with `scipy.fft.next_fast_len`, if available; otherwise

looked up from list and scaled by powers of 10, if necessary.

"""

try:

import scipy.fft

return np.array([scipy.fft.next_fast_len(j) for j in shape])

except ImportError:

pass

newshape = np.empty(len(np.atleast_1d(shape)), dtype=int)

for i, j in enumerate(shape):

scale = 10 ** max(int(np.ceil(np.log10(j))) - _good_range, 0)

for n in _good_sizes:

if n * scale >= j:

newshape[i] = n * scale

break

else:

raise ValueError(

f"No next fast length for {j} found in list of _good_sizes "

f"<= {_good_sizes[-1] * scale}."

)

return newshape

def _copy_input_if_needed(

input, dtype=float, order="C", nan_treatment=None, mask=None, fill_value=None

):

# Alias input

input = input.array if isinstance(input, Kernel) else input

# strip quantity attributes

if hasattr(input, "unit"):

input = input.value

output = input

# Copy input

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(input) or mask is not None:

if np.ma.is_masked(input):

# ``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.

output = np.array(

input, dtype=dtype, copy=False, order=order, subok=True

)

output = output.filled(fill_value)

else:

# Since we're making a copy, we might as well use `subok=False` to save,

# what is probably, a negligible amount of memory.

output = np.array(

input, dtype=dtype, copy=True, order=order, subok=False

)

if mask is not None:

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

output[mask != 0] = fill_value

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.

output = np.array(input, dtype=dtype, copy=False, order=order, subok=True)

except (TypeError, ValueError) as e:

raise TypeError(

"input should be a Numpy array or something convertible into a float array",

e,

)

return output

@support_nddata(data="array")

def convolve(

array,

kernel,

boundary="fill",

fill_value=0.0,

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 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.

nan_treatment : {'interpolate', 'fill'}, optional

The method used to handle NaNs in the input ``array``:

* ``'interpolate'``: ``NaN`` values are replaced with

interpolated values using the kernel as an interpolation

function. Note that if the kernel has a sum equal to

zero, NaN interpolation is not possible and will raise an

exception.

* ``'fill'``: ``NaN`` values are replaced by ``fill_value``

prior to convolution.

preserve_nan : bool, optional

After performing convolution, should pixels that were originally NaN

again become NaN?

mask : None or ndarray, optional

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 if 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.

"""

if boundary not in BOUNDARY_OPTIONS:

raise ValueError(f"Invalid boundary option: must be one of {BOUNDARY_OPTIONS}")

if nan_treatment not in ("interpolate", "fill"):

raise ValueError("nan_treatment must be one of 'interpolate','fill'")

# OpenMP support is disabled at the C src code level, changing this will have

# no effect.

n_threads = 1

# Keep refs to originals

passed_kernel = kernel

passed_array = array

# The C 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

# Convert kernel to ndarray if not already

# Copy or alias array to array_internal

array_internal = _copy_input_if_needed(

passed_array,

dtype=float,

order="C",

nan_treatment=nan_treatment,

mask=mask,

fill_value=np.nan,

)

array_dtype = getattr(passed_array, "dtype", array_internal.dtype)

# Copy or alias kernel to kernel_internal

kernel_internal = _copy_input_if_needed(

passed_kernel,

dtype=float,

order="C",

nan_treatment=None,

mask=None,

fill_value=fill_value,

)

# Make sure kernel has all odd axes

if has_even_axis(kernel_internal):

raise KernelSizeError("Kernel size must be odd in all axes.")

# If both image array and kernel are Kernel instances

# constrain convolution method

# This must occur before the main alias/copy of ``passed_kernel`` to

# ``kernel_internal`` as it is used for filling masked kernels.

if isinstance(passed_array, Kernel) and isinstance(passed_kernel, Kernel):

warnings.warn(

"Both array and kernel are Kernel instances, hardwiring "

"the following parameters: boundary='fill', fill_value=0,"

" normalize_Kernel=True, nan_treatment='interpolate'",

AstropyUserWarning,

)

boundary = "fill"

fill_value = 0

normalize_kernel = True

nan_treatment = "interpolate"

# -----------------------------------------------------------------------

# From this point onwards refer only to ``array_internal`` and

# ``kernel_internal``.

# Assume both are base np.ndarrays and NOT subclasses e.g. NOT

# ``Kernel`` nor ``np.ma.maskedarray`` classes.

# -----------------------------------------------------------------------

# Check dimensionality

if array_internal.ndim == 0:

raise Exception("cannot convolve 0-dimensional arrays")

elif array_internal.ndim > 3:

raise NotImplementedError(

"convolve only supports 1, 2, and 3-dimensional arrays at this time"

)

elif array_internal.ndim != kernel_internal.ndim:

raise Exception("array and kernel have differing number of dimensions.")

array_shape = np.array(array_internal.shape)

kernel_shape = np.array(kernel_internal.shape)

pad_width = kernel_shape // 2

# For boundary=None only the center space is convolved. All array indices within a

# distance kernel.shape//2 from the edge are completely ignored (zeroed).

# E.g. (1D list) only the indices len(kernel)//2 : len(array)-len(kernel)//2

# are convolved. It is therefore not possible to use this method to convolve an

# array by a kernel that is larger (see note below) than the array - as ALL pixels

# would be ignored leaving an array of only zeros.

# Note: For even kernels the correctness condition is array_shape > kernel_shape.

# For odd kernels it is:

# array_shape >= kernel_shape OR

# array_shape > kernel_shape-1 OR

# array_shape > 2*(kernel_shape//2).

# Since the latter is equal to the former two for even lengths, the latter condition is

# complete.

if boundary is None and not np.all(array_shape > 2 * pad_width):

raise KernelSizeError(

"for boundary=None all kernel axes must be smaller than array's - "

"use boundary in ['fill', 'extend', 'wrap'] instead."

)

# NaN interpolation significantly slows down the C convolution

# computation. Since nan_treatment = 'interpolate', is the default

# check whether it is even needed, if not, don't interpolate.

# NB: np.isnan(array_internal.sum()) is faster than np.isnan(array_internal).any()

nan_interpolate = (nan_treatment == "interpolate") and np.isnan(

array_internal.sum()

)

# Check if kernel is normalizable

if normalize_kernel or nan_interpolate:

kernel_sum = kernel_internal.sum()

kernel_sums_to_zero = np.isclose(kernel_sum, 0, atol=normalization_zero_tol)

if kernel_sum < 1.0 / MAX_NORMALIZATION or kernel_sums_to_zero:

if nan_interpolate:

raise ValueError(

"Setting nan_treatment='interpolate' "

"requires the kernel to be normalized, "

"but the input kernel has a sum close "

"to zero. For a zero-sum kernel and "

"data with NaNs, set nan_treatment='fill'."

)

else:

raise ValueError(

"The kernel can't be normalized, because "

"its sum is close to zero. The sum of the "

f"given kernel is < {1.0 / MAX_NORMALIZATION}"

)

# Mark the NaN values so we can replace them later if interpolate_nan is

# not set

if preserve_nan or nan_treatment == "fill":

initially_nan = np.isnan(array_internal)

if nan_treatment == "fill":

array_internal[initially_nan] = fill_value

# Avoid any memory allocation within the C code. Allocate output array

# here and pass through instead.

result = np.zeros(array_internal.shape, dtype=float, order="C")

embed_result_within_padded_region = True

array_to_convolve = array_internal

if boundary in ("fill", "extend", "wrap"):

embed_result_within_padded_region = False

if boundary == "fill":

# This method is faster than using numpy.pad(..., mode='constant')

array_to_convolve = np.full(

array_shape + 2 * pad_width,

fill_value=fill_value,

dtype=float,

order="C",

)

# Use bounds [pad_width[0]:array_shape[0]+pad_width[0]] instead of

# [pad_width[0]:-pad_width[0]]

# to account for when the kernel has size of 1 making pad_width = 0.

if array_internal.ndim == 1:

array_to_convolve[

pad_width[0] : array_shape[0] + pad_width[0]

] = array_internal

elif array_internal.ndim == 2:

array_to_convolve[

pad_width[0] : array_shape[0] + pad_width[0],

pad_width[1] : array_shape[1] + pad_width[1],

] = array_internal

else:

array_to_convolve[

pad_width[0] : array_shape[0] + pad_width[0],

pad_width[1] : array_shape[1] + pad_width[1],

pad_width[2] : array_shape[2] + pad_width[2],

] = array_internal

else:

np_pad_mode_dict = {"fill": "constant", "extend": "edge", "wrap": "wrap"}

np_pad_mode = np_pad_mode_dict[boundary]

pad_width = kernel_shape // 2

if array_internal.ndim == 1:

np_pad_width = (pad_width[0],)

elif array_internal.ndim == 2:

np_pad_width = ((pad_width[0],), (pad_width[1],))

else:

np_pad_width = ((pad_width[0],), (pad_width[1],), (pad_width[2],))

array_to_convolve = np.pad(

array_internal, pad_width=np_pad_width, mode=np_pad_mode

)

_convolveNd_c(

result,

array_to_convolve,

kernel_internal,

nan_interpolate,

embed_result_within_padded_region,

n_threads,

)

# So far, normalization has only occurred for nan_treatment == 'interpolate'

# because this had to happen within the C extension so as to ignore

# any NaNs

if normalize_kernel:

if not nan_interpolate:

result /= kernel_sum

elif nan_interpolate:

result *= kernel_sum

if nan_interpolate and not preserve_nan and np.isnan(result.sum()):

warnings.warn(

"nan_treatment='interpolate', however, NaN values detected "

"post convolution. A contiguous region of NaN values, larger "

"than the kernel size, are present in the input array. "

"Increase the kernel size to avoid this.",

AstropyUserWarning,

)

if preserve_nan:

result[initially_nan] = np.nan

# Convert result to original data type

array_unit = getattr(passed_array, "unit", None)

if array_unit is not None:

result <<= array_unit

if isinstance(passed_array, Kernel):

if isinstance(passed_array, Kernel1D):

new_result = Kernel1D(array=result)

elif isinstance(passed_array, Kernel2D):

new_result = Kernel2D(array=result)

else:

raise TypeError("Only 1D and 2D Kernels are supported.")

new_result._is_bool = False

new_result._separable = passed_array._separable

if isinstance(passed_kernel, Kernel):

new_result._separable = new_result._separable and passed_kernel._separable

return new_result

elif array_dtype.kind == "f":

# Try to preserve the input type if it's a floating point type

# Avoid making another copy if possible

try:

return result.astype(array_dtype, copy=False)

except TypeError:

return result.astype(array_dtype)

else:

return result

@support_nddata(data="array")

def convolve_fft(

array,

kernel,

boundary="fill",

fill_value=0.0,

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,

min_wt=0.0,

allow_huge=False,

fftn=np.fft.fftn,

ifftn=np.fft.ifftn,

complex_dtype=complex,

dealias=False,

):

"""

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``

* It optionally pads to the nearest faster sizes to improve FFT speed.

These sizes are optimized for the numpy and scipy implementations, and

``fftconvolve`` uses them by default as well; when using other external

functions (see below), results may vary.

* 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.org/project/pyFFTW/>`_ or

`pyFFTW3 <https://pypi.org/project/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.fftn` and `numpy.fft.ifftn`. The `scipy.fft` functions also

offer somewhat better performance and a multi-threaded option.

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'}, optional

The method used to handle NaNs in the input ``array``:

* ``'interpolate'``: ``NaN`` values are replaced with

interpolated values using the kernel as an interpolation

function. Note that if the kernel has a sum equal to

zero, NaN interpolation is not possible and will raise an

exception.

* ``'fill'``: ``NaN`` values are replaced by ``fill_value``

prior to convolution.

normalize_kernel : callable 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, optional

After performing convolution, should pixels that were originally NaN

again become NaN?

mask : None or ndarray, optional

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 if it is masked in either ``mask`` *or* ``array.mask``.

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.

fft_pad : bool, optional

Default on. Zero-pad image to the nearest size supporting more efficient

execution of the FFT, generally values factorizable into the first 3-5

prime numbers. 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.

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.

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.

fftn : callable, optional

The fft function. Can be overridden to use your own ffts,

e.g. an fftw3 wrapper or scipy's fftn, ``fft=scipy.fftpack.fftn``.

ifftn : callable, optional

The inverse fft function. Can be overridden the same way ``fttn``.

complex_dtype : complex type, optional

Which complex dtype to use. `numpy` has a range of options, from 64 to

256.

dealias: bool, optional

Default off. Zero-pad image to enable explicit dealiasing

of convolution. With ``boundary='wrap'``, this will be disabled.

Note that for an input of nd dimensions this will increase

the size of the temporary arrays by at least ``1.5**nd``.

This may result in significantly more memory usage.

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.

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.

Notes

-----

With ``psf_pad=True`` and a large PSF, the resulting data

can become large and consume a lot of memory. See Issue

https://github.com/astropy/astropy/pull/4366 and the update in

https://github.com/astropy/astropy/pull/11533 for further details.

Dealiasing of pseudospectral convolutions is necessary for

numerical stability of the underlying algorithms. A common

method for handling this is to zero pad the image by at least

1/2 to eliminate the wavenumbers which have been aliased

by convolution. This is so that the aliased 1/3 of the

results of the convolution computation can be thrown out. See

https://doi.org/10.1175/1520-0469(1971)028%3C1074:OTEOAI%3E2.0.CO;2

https://iopscience.iop.org/article/10.1088/1742-6596/318/7/072037

Note that if dealiasing is necessary to your application, but your

process is memory constrained, you may want to consider using

FFTW++: https://github.com/dealias/fftwpp. It includes python

wrappers for a pseudospectral convolution which will implicitly

dealias your convolution without the need for additional padding.

Note that one cannot use FFTW++'s convlution directly in this

method as in handles the entire convolution process internally.

Additionally, FFTW++ includes other useful pseudospectral methods to

consider.

Examples

--------

>>> convolve_fft([1, 0, 3], [1, 1, 1])

array([0.33333333, 1.33333333, 1. ])

>>> convolve_fft([1, np.nan, 3], [1, 1, 1])

array([0.5, 2. , 1.5])

>>> convolve_fft([1, 0, 3], [0, 1, 0]) # doctest: +FLOAT_CMP

array([ 1.00000000e+00, -3.70074342e-17, 3.00000000e+00])

>>> 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([0.5, 2. , 1.5])

>>> convolve_fft([1, np.nan, 3], [1, 1, 1], nan_treatment='interpolate',

... normalize_kernel=True)

array([0.5, 2. , 1.5])

>>> import scipy.fft # optional - requires scipy

>>> convolve_fft([1, np.nan, 3], [1, 1, 1], nan_treatment='interpolate',

... normalize_kernel=True,

... fftn=scipy.fft.fftn, ifftn=scipy.fft.ifftn)

array([0.5, 2. , 1.5])

>>> fft_mp = lambda a: scipy.fft.fftn(a, workers=-1) # use all available cores

>>> ifft_mp = lambda a: scipy.fft.ifftn(a, workers=-1)

>>> convolve_fft([1, np.nan, 3], [1, 1, 1], nan_treatment='interpolate',

... normalize_kernel=True, fftn=fft_mp, ifftn=ifft_mp)

array([0.5, 2. , 1.5])

"""

# 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'")

# Get array quantity if it exists

array_unit = getattr(array, "unit", None)

# Convert array dtype to complex

# and ensure that list inputs become arrays

array = _copy_input_if_needed(

array,

dtype=complex,

order="C",

nan_treatment=nan_treatment,

mask=mask,

fill_value=np.nan,

)

kernel = _copy_input_if_needed(

kernel, dtype=complex, order="C", nan_treatment=None, mask=None, fill_value=0

)

# 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.prod(arrayshape, dtype=np.int64) * np.dtype(complex_dtype).itemsize

) * u.byte

if array_size_B > 1 * u.GB and not allow_huge:

raise ValueError(

f"Size Error: Arrays will be {human_file_size(array_size_B)}. "

"Use allow_huge=True to override this exception."

)

# NaN and inf catching

nanmaskarray = np.isnan(array) | np.isinf(array)

if nan_treatment == "fill":

array[nanmaskarray] = fill_value

else:

array[nanmaskarray] = 0

nanmaskkernel = np.isnan(kernel) | np.isinf(kernel)

kernel[nanmaskkernel] = 0

if normalize_kernel is True:

if kernel.sum() < 1.0 / MAX_NORMALIZATION:

raise Exception(

"The kernel can't be normalized, because its sum is close to zero. The"

f" sum of the given kernel is < {1.0 / 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(

f"psf_pad was set to {psf_pad}, which overrides the "

"boundary='fill' setting.",

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

if dealias:

raise ValueError("With boundary='wrap', dealias cannot be enabled.")

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"

)

# Add shapes elementwise for psf_pad.

if psf_pad: # default=False

# add the sizes along each dimension (bigger)

newshape = np.array(arrayshape) + np.array(kernshape)

else:

# take the larger shape in each dimension (smaller)

newshape = np.maximum(arrayshape, kernshape)

if dealias:

# Extend shape by 1/2 for dealiasing

newshape += np.ceil(newshape / 2).astype(int)

# Find ideal size for fft (was power of 2, now any powers of prime factors 2, 3, 5).

if fft_pad: # default=True

# Get optimized sizes from scipy.

newshape = _next_fast_lengths(newshape)

# perform a second check after padding

array_size_C = (

np.prod(newshape, dtype=np.int64) * np.dtype(complex_dtype).itemsize

) * u.byte

if array_size_C > 1 * u.GB and not allow_huge:

raise ValueError(

f"Size Error: Arrays will be {human_file_size(array_size_C)}. "

"Use allow_huge=True to override this exception."

)

# 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.prod(newshape)*np.dtype(complex_dtype).itemsize

# * (5 + 3*((interpolate_nan or ) and kernel_is_normalized))

# + (1 + (not return_fft)) *

# np.prod(arrayshape)*np.dtype(complex_dtype).itemsize

# + np.prod(arrayshape)*np.dtype(bool).itemsize

# + np.prod(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 newdimsize, arraydimsize, kerndimsize in 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.")

fftmult *= kernel_scale

if array_unit is not None:

fftmult <<= array_unit

if return_fft:

return fftmult

if interpolate_nan:

with np.errstate(divide="ignore", invalid="ignore"):

# divide by zeros are expected here; if the weight is zero, we want

# the output to be nan or inf

rifft = (ifftn(fftmult)) / bigimwt

if not np.isscalar(bigimwt):

if min_wt > 0.0:

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,

preserve_nan=False,

**kwargs,

)

isnan = np.isnan(array)

newarray[isnan] = convolved[isnan]

return newarray

def convolve_models(model, kernel, mode="convolve_fft", **kwargs):