# pylops.Smoothing1D#

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

1D Smoothing.

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

Parameters
nsmoothint

Length of smoothing operator (must be odd)

dims

Number of samples for each dimension

axisint, optional

New in version 2.0.0.

Axis along which model (and data) are smoothed.

dtypestr, 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
shapetuple

Operator shape

explicitbool

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

Methods

 __init__(nsmooth, dims[, axis, 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.Smoothing1D#

1D Smoothing

1D Smoothing

Causal Integration

Causal Integration

Wavelet estimation

Wavelet estimation

03. Solvers

03. Solvers