# pylops.Smoothing2D#

class pylops.Smoothing2D(nsmooth, dims, axes=(-2, -1), dtype='float64', name='S')[source]#

2D Smoothing.

Apply smoothing to model (and data) along two axes of a multi-dimensional array.

Parameters
nsmooth

Length of smoothing operator in 1st and 2nd dimensions (must be odd)

dimstuple

Number of samples for each dimension

axesint, optional

New in version 2.0.0.

Axes along which model (and data) are smoothed.

dtypestr, optional

Type of elements in input array.

Notes

The 2D Smoothing operator is a special type of convolutional operator that convolves the input model (or data) with a constant 2d filter of size $$n_{\text{smooth}, 1} \times n_{\text{smooth}, 2}$$:

Its application to a two dimensional input signal is:

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

Note that since the filter is symmetrical, the Smoothing2D operator is self-adjoint.

Attributes
shapetuple

Operator shape

explicitbool

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

Methods

 __init__(nsmooth, dims[, axes, dtype, name]) adjoint() apply_columns(cols) Apply subset of columns of operator cond([uselobpcg]) Condition number of linear operator. conj() Complex conjugate operator div(y[, niter, densesolver]) Solve the linear problem $$\mathbf{y}=\mathbf{A}\mathbf{x}$$. dot(x) Matrix-matrix or matrix-vector multiplication. eigs([neigs, symmetric, niter, uselobpcg]) Most significant eigenvalues of linear operator. matmat(X) Matrix-matrix multiplication. matvec(x) Matrix-vector multiplication. reset_count() Reset counters rmatmat(X) Matrix-matrix multiplication. rmatvec(x) Adjoint matrix-vector multiplication. todense([backend]) Return dense matrix. toimag([forw, adj]) Imag operator toreal([forw, adj]) Real operator tosparse() Return sparse matrix. trace([neval, method, backend]) Trace of linear operator. transpose()

## Examples using pylops.Smoothing2D#

2D Smoothing

2D Smoothing

Causal Integration

Causal Integration

19. Automatic Differentiation

19. Automatic Differentiation