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scipy.ndimage.

# gaussian_filter1d

scipy.ndimage.gaussian_filter1d(input, sigma, axis=-1, order=0, output=None, mode='reflect', cval=0.0, truncate=4.0, *, radius=None)

  1-D Gaussian filter.

  Parameters:
    input array_like

      The input array.

    sigma scalar

      standard deviation for Gaussian kernel

    axis int, optional

      The axis of input along which to calculate. Default is -1.

    order int, optional

      An order of 0 corresponds to convolution with a Gaussian kernel. A positive order corresponds to convolution with that derivative of a Gaussian.

    output array or dtype, optional

      The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created.

    mode{‘reflect’, ‘constant’, ‘nearest’, ‘mirror’, ‘wrap’}, optional

      The mode parameter determines how the input array is extended beyond its boundaries. Default is ‘reflect’. Behavior for each valid value is as follows:

      ‘reflect’ (d c b a | a b c d | d c b a)

        The input is extended by reflecting about the edge of the last pixel. This mode is also sometimes referred to as half-sample symmetric.

      ‘constant’ (k k k k | a b c d | k k k k)

        The input is extended by filling all values beyond the edge with the same constant value, defined by the cval parameter.

      ‘nearest’ (a a a a | a b c d | d d d d)

        The input is extended by replicating the last pixel.

      ‘mirror’ (d c b | a b c d | c b a)

        The input is extended by reflecting about the center of the last pixel. This mode is also sometimes referred to as whole-sample symmetric.

      ‘wrap’ (a b c d | a b c d | a b c d)

        The input is extended by wrapping around to the opposite edge.

      For consistency with the interpolation functions, the following mode names can also be used:

      ‘grid-mirror’

        This is a synonym for ‘reflect’.

      ‘grid-constant’

        This is a synonym for ‘constant’.

      ‘grid-wrap’

        This is a synonym for ‘wrap’.

    cval scalar, optional

      Value to fill past edges of input if mode is ‘constant’. Default is 0.0.

    truncate float, optional

      Truncate the filter at this many standard deviations. Default is 4.0.

    radius None or int, optional

      Radius of the Gaussian kernel. If specified, the size of the kernel will be `2*radius + 1`, and truncate is ignored. Default is None.

  Returns:
    gaussian_filter1d ndarray

      Returned array of same shape as input.

  Notes

  The Gaussian kernel will have size `2*radius + 1` along each axis. If radius is None, a default `radius = round(truncate * sigma)` will be used.

  Array API Standard Support

  `gaussian_filter1d` has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable `SCIPY_ARRAY_API=1` and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

  Library | CPU | GPU
  --- | --- | ---
  NumPy | ✅ | n/a
  CuPy | n/a | ✅
  PyTorch | ✅ | ⛔
  JAX | ⚠️ no JIT | ⛔
  Dask | ⚠️ computes graph | n/a

  See Support for the array API standard for more information.

  Examples

      >>> from scipy.ndimage import gaussian_filter1d
      >>> import numpy as np
      >>> gaussian_filter1d([1.0, 2.0, 3.0, 4.0, 5.0], 1)
      array([ 1.42704095,  2.06782203,  3.        ,  3.93217797,  4.57295905])
      >>> gaussian_filter1d([1.0, 2.0, 3.0, 4.0, 5.0], 4)
      array([ 2.91948343,  2.95023502,  3.        ,  3.04976498,  3.08051657])
      >>> import matplotlib.pyplot as plt
      >>> rng = np.random.default_rng()
      >>> x = rng.standard_normal(101).cumsum()
      >>> y3 = gaussian_filter1d(x, 3)
      >>> y6 = gaussian_filter1d(x, 6)
      >>> plt.plot(x, 'k', label='original data')
      >>> plt.plot(y3, '--', label='filtered, sigma=3')
      >>> plt.plot(y6, ':', label='filtered, sigma=6')
      >>> plt.legend()
      >>> plt.grid()
      >>> plt.show()