convolve_fft¶

astropy.convolution.
convolve_fft
(array, kernel, boundary='fill', fill_value=0.0, nan_treatment='interpolate', normalize_kernel=True, normalization_zero_tol=1e08, 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=<function fftn>, ifftn=<function ifftn>, complex_dtype=<class 'complex'>)[source] [edit on github]¶ Convolve an ndarray with an ndkernel. Returns a convolved image with
shape = array.shape
. Assumes kernel is centered.convolve_fft
is very similar toconvolve
in that it replacesNaN
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 fromscipy.signal.fftconvolve
in a few ways: It can treat
NaN
values as zeros or interpolate over them. inf
values are treated asNaN
 (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 or
pyFFTW3 , which can lead to
performance improvements, depending on your system configuration. pyFFTW3
is threaded, and therefore may yield significant performance benefits on
multicore machines at the cost of greater memory requirements. Specify
the
fftn
andifftn
keywords to override the default, which isnumpy.fft.fft
andnumpy.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
orastropy.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 nonfft
convolve
function. The kernel will be normalized ifnormalize_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 FFTbased 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, seefill_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 tonormalize_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 “1e8”.
 preserve_nan : bool
After performing convolution, should pixels that were originally NaN again become NaN?
 mask :
None
ornumpy.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. IfNone
, no masking will be performed unlessarray
is a masked array. Ifmask
is notNone
andarray
is a masked array, a pixel is masked of it is masked in eithermask
orarray.mask
.
Returns:  default : ndarray
array
convolved withkernel
. Ifreturn_fft
is set, returnsfft(array) * fft(kernel)
. If crop is not set, returns the image, but with the fftpadded size instead of the input size
Other Parameters:  min_wt : float, optional
If ignoring
NaN
/ zeros, force all grid points with a weight less than this value toNaN
(the weight of a grid point with no ignored neighbors is 1.0). Ifmin_wt
is zero, then all zeroweight points will be set to zero instead ofNaN
(which they would be otherwise, because 1/0 = nan). See the examples below fft_pad : bool, optional
Default on. Zeropad image to the nearest 2^n. With
boundary='wrap'
, this will be disabled. psf_pad : bool, optional
Zeropad image to be at least the sum of the image sizes to avoid edgewrapping when smoothing. This is enabled by default with
boundary='fill'
, but it can be overridden with a boolean option.boundary='wrap'
andpsf_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 isifft(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 nonfft 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 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=1e8) 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.])
 It can treat