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- Convolution and Filtering (`astropy.convolution`) »
- convolve_fft

# convolve_fft

astropy.convolution.convolve_fft(array, kernel, boundary='fill', fill_value=0.0, nan_treatment='interpolate', normalize_kernel=True, normalization_zero_tol=1e-08, preserve_nan=False, mask=None, crop=True, return_fft=False, fft_pad=None, psf_pad=None, min_wt=0.0, allow_huge=False, fftn=<function fftn>, ifftn=<function ifftn>, complex_dtype=<class '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 or pyFFTW3 , 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 `python: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 `python:callable()` or bool, 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 `python: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 `python: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 of 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 `python: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 `python: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 `python: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])
      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])