pylops.Smoothing1D

pylops.Smoothing1D(nsmooth, dims, axis=-1, dtype='float64')[source]

1D Smoothing.

Apply smoothing to model (and data) to a multi-dimensional array along axis.

Parameters:
nsmooth : int

Length of smoothing operator (must be odd)

dims : tuple or int

Number of samples for each dimension

axis : int, optional

New in version 2.0.0.

Axis along which model (and data) are smoothed.

dtype : str, optional

Type of elements in input array.

Notes

The Smoothing1D operator is a special type of convolutional operator that convolves the input model (or data) with a constant filter of size \(n_\text{smooth}\):

\[\mathbf{f} = [ 1/n_\text{smooth}, 1/n_\text{smooth}, ..., 1/n_\text{smooth} ]\]

When applied to the first direction:

\[y[i,j,k] = 1/n_\text{smooth} \sum_{l=-(n_\text{smooth}-1)/2}^{(n_\text{smooth}-1)/2} x[l,j,k]\]

Similarly when applied to the second direction:

\[y[i,j,k] = 1/n_\text{smooth} \sum_{l=-(n_\text{smooth}-1)/2}^{(n_\text{smooth}-1)/2} x[i,l,k]\]

and the third direction:

\[y[i,j,k] = 1/n_\text{smooth} \sum_{l=-(n_\text{smooth}-1)/2}^{(n_\text{smooth}-1)/2} x[i,j,l]\]

Note that since the filter is symmetrical, the Smoothing1D operator is self-adjoint.

Attributes:
shape : tuple

Operator shape

explicit : bool

Operator contains a matrix that can be solved explicitly (True) or not (False)