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
tuple
orlist
Length of smoothing operator in 1st and 2nd dimensions (must be odd)
- dims
tuple
Number of samples for each dimension
- axes
int
, optional New in version 2.0.0.
Axes along which model (and data) are smoothed.
- dtype
str
, optional Type of elements in input array.
- nsmooth
See also
pylops.signalprocessing.Convolve2D
2D convolution
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
- shape
tuple
Operator shape
- explicit
bool
Operator contains a matrix that can be solved explicitly (
True
) or not (False
)
- shape
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
()