# Source code for pylops.basicoperators.Smoothing2D

import numpy as np

from pylops.signalprocessing import Convolve2D

[docs]def Smoothing2D(nsmooth, dims, nodir=None, dtype="float64"):
r"""2D Smoothing.

Apply smoothing to model (and data) along two directions of a
multi-dimensional array depending on the choice of nodir.

Parameters
----------
nsmooth : :obj:tuple or :obj:list
Lenght of smoothing operator in 1st and 2nd dimensions (must be odd)
dims : :obj:tuple
Number of samples for each dimension
nodir : :obj:int, optional
Direction along which smoothing is **not** applied (set to None for 2d
arrays)
dtype : :obj:str, optional
Type of elements in input array.

Attributes
----------
shape : :obj:tuple
Operator shape
explicit : :obj:bool
Operator contains a matrix that can be solved explicitly (True) or
not (False)

--------
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
:math:n_{\text{smooth}, 1} \times n_{\text{smooth}, 2}:

Its application to a two dimensional input signal is:

.. math::
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

"""
if isinstance(nsmooth, tuple):
nsmooth = list(nsmooth)
if nsmooth % 2 == 0:
nsmooth += 1
if nsmooth % 2 == 0:
nsmooth += 1

h = np.ones((nsmooth, nsmooth)) / float(nsmooth * nsmooth)
return Convolve2D(
np.prod(np.array(dims)),
h=h,
offset=[(nsmooth - 1) / 2, (nsmooth - 1) / 2],
dims=dims,
nodir=nodir,
dtype=dtype,
)