# Source code for pylops.signalprocessing.Sliding3D

```
import logging
import numpy as np
from pylops.basicoperators import BlockDiag, Diagonal, HStack, Restriction
from pylops.signalprocessing.Sliding2D import _slidingsteps
from pylops.utils.tapers import taper3d
logging.basicConfig(format="%(levelname)s: %(message)s", level=logging.WARNING)
[docs]def Sliding3D(
Op, dims, dimsd, nwin, nover, nop, tapertype="hanning", design=False, nproc=1
):
"""3D Sliding transform operator.
Apply a transform operator ``Op`` repeatedly to patches of the model
vector in forward mode and patches of the data vector in adjoint mode.
More specifically, in forward mode the model vector is divided into patches
each patch is transformed, and patches are then recombined in a sliding
window fashion. Both model and data should be 3-dimensional
arrays in nature as they are internally reshaped and interpreted as
3-dimensional arrays. Each patch contains in fact a portion of the
array in the first and second dimensions (and the entire third dimension).
This operator can be used to perform local, overlapping transforms (e.g.,
:obj:`pylops.signalprocessing.FFTND`
or :obj:`pylops.signalprocessing.Radon3D`) of 3-dimensional arrays.
.. note:: The shape of the model has to be consistent with
the number of windows for this operator not to return an error. As the
number of windows depends directly on the choice of ``nwin`` and
``nover``, it is recommended to use ``design=True`` if unsure about the
choice ``dims`` and use the number of windows printed on screen to
define such input parameter.
.. warning:: Depending on the choice of `nwin` and `nover` as well as the
size of the data, sliding windows may not cover the entire first and/or
second dimensions. The start and end indeces of each window can be
displayed using ``design=True`` while defining the best sliding window
approach.
Parameters
----------
Op : :obj:`pylops.LinearOperator`
Transform operator
dims : :obj:`tuple`
Shape of 3-dimensional model. Note that ``dims[0]`` and ``dims[1]``
should be multiple of the model sizes of the transform in the
first and second dimensions
dimsd : :obj:`tuple`
Shape of 3-dimensional data
nwin : :obj:`tuple`
Number of samples of window
nover : :obj:`tuple`
Number of samples of overlapping part of window
nop : :obj:`tuple`
Number of samples in axes of transformed domain associated
to spatial axes in the data
tapertype : :obj:`str`, optional
Type of taper (``hanning``, ``cosine``, ``cosinesquare`` or ``None``)
design : :obj:`bool`, optional
Print number sliding window (``True``) or not (``False``)
Returns
-------
Sop : :obj:`pylops.LinearOperator`
Sliding operator
Raises
------
ValueError
Identified number of windows is not consistent with provided model
shape (``dims``).
"""
# model windows
mwin0_ins, mwin0_ends = _slidingsteps(dims[0], Op.shape[1] // (nop[1] * dims[2]), 0)
mwin1_ins, mwin1_ends = _slidingsteps(dims[1], Op.shape[1] // (nop[0] * dims[2]), 0)
# data windows
dwin0_ins, dwin0_ends = _slidingsteps(dimsd[0], nwin[0], nover[0])
dwin1_ins, dwin1_ends = _slidingsteps(dimsd[1], nwin[1], nover[1])
nwins0 = len(dwin0_ins)
nwins1 = len(dwin1_ins)
nwins = nwins0 * nwins1
# create tapers
if tapertype is not None:
tap = taper3d(dimsd[2], nwin, nover, tapertype=tapertype)
# check that identified number of windows agrees with mode size
if design:
logging.warning("(%d,%d) windows required...", nwins0, nwins1)
logging.warning(
"model wins - start0:%s, end0:%s, start1:%s, end1:%s",
str(mwin0_ins),
str(mwin0_ends),
str(mwin1_ins),
str(mwin1_ends),
)
logging.warning(
"data wins - start0:%s, end0:%s, start1:%s, end1:%s",
str(dwin0_ins),
str(dwin0_ends),
str(dwin1_ins),
str(dwin1_ends),
)
if nwins * Op.shape[1] // dims[2] != dims[0] * dims[1]:
raise ValueError(
"Model shape (dims=%s) is not consistent with chosen "
"number of windows. Choose dims[0]=%d and "
"dims[1]=%d for the operator to work with "
"estimated number of windows, or create "
"the operator with design=True to find out the"
"optimal number of windows for the current "
"model size..."
% (
str(dims),
nwins0 * Op.shape[1] // (nop[1] * dims[2]),
nwins1 * Op.shape[1] // (nop[0] * dims[2]),
)
)
# transform to apply
if tapertype is None:
OOp = BlockDiag([Op for _ in range(nwins)], nproc=nproc)
else:
OOp = BlockDiag([Diagonal(tap.ravel()) * Op for _ in range(nwins)], nproc=nproc)
hstack = HStack(
[
Restriction(
dimsd[1] * dimsd[2] * nwin[0],
range(win_in, win_end),
dims=(nwin[0], dimsd[1], dimsd[2]),
dir=1,
dtype=Op.dtype,
).H
for win_in, win_end in zip(dwin1_ins, dwin1_ends)
]
)
combining1 = BlockDiag([hstack] * nwins0)
combining0 = HStack(
[
Restriction(
np.prod(dimsd),
range(win_in, win_end),
dims=dimsd,
dir=0,
dtype=Op.dtype,
).H
for win_in, win_end in zip(dwin0_ins, dwin0_ends)
]
)
Sop = combining0 * combining1 * OOp
return Sop
```