__all__ = [
"sliding2d_design",
"Sliding2D",
]
import logging
from typing import Tuple
import numpy as np
from pylops import LinearOperator, aslinearoperator
from pylops.basicoperators import BlockDiag, Diagonal, HStack, Restriction
from pylops.utils.tapers import taper2d
from pylops.utils.typing import InputDimsLike, NDArray
logging.basicConfig(format="%(levelname)s: %(message)s", level=logging.WARNING)
def _slidingsteps(
ntr: int,
nwin: int,
nover: int,
) -> Tuple[NDArray, NDArray]:
"""Identify sliding window initial and end points given overall
trace length, window length and overlap
Parameters
----------
ntr : :obj:`int`
Number of samples in trace
nwin : :obj:`int`
Number of samples of window
nover : :obj:`int`
Number of samples of overlapping part of window
Returns
-------
starts : :obj:`np.ndarray`
Start indices
ends : :obj:`np.ndarray`
End indices
"""
if nwin > ntr:
raise ValueError(f"nwin={nwin} is bigger than ntr={ntr}...")
step = nwin - nover
starts = np.arange(0, ntr - nwin + 1, step, dtype=int)
ends = starts + nwin
return starts, ends
[docs]def sliding2d_design(
dimsd: Tuple[int, int],
nwin: int,
nover: int,
nop: Tuple[int, int],
) -> Tuple[int, Tuple[int, int], Tuple[NDArray, NDArray], Tuple[NDArray, NDArray]]:
"""Design Sliding2D operator
This routine can be used prior to creating the :class:`pylops.signalprocessing.Sliding2D`
operator to identify the correct number of windows to be used based on the dimension of the data (``dimsd``),
dimension of the window (``nwin``), overlap (``nover``),a and dimension of the operator acting in the model
space.
Parameters
----------
dimsd : :obj:`tuple`
Shape of 2-dimensional data.
nwin : :obj:`int`
Number of samples of window.
nover : :obj:`int`
Number of samples of overlapping part of window.
nop : :obj:`tuple`
Size of model in the transformed domain.
Returns
-------
nwins : :obj:`int`
Number of windows.
dims : :obj:`tuple`
Size of 2-dimensional model.
mwins_inends : :obj:`tuple`
Start and end indices for model patches (stored as tuple of tuples).
dwins_inends : :obj:`tuple`
Start and end indices for data patches (stored as tuple of tuples).
"""
# data windows
dwin_ins, dwin_ends = _slidingsteps(dimsd[0], nwin, nover)
dwins_inends = (dwin_ins, dwin_ends)
nwins = len(dwin_ins)
# model windows
dims = (nwins * nop[0], nop[1])
mwin_ins, mwin_ends = _slidingsteps(dims[0], nop[0], 0)
mwins_inends = (mwin_ins, mwin_ends)
# print information about patching
logging.warning("%d windows required...", nwins)
logging.warning(
"data wins - start:%s, end:%s",
dwin_ins,
dwin_ends,
)
logging.warning(
"model wins - start:%s, end:%s",
mwin_ins,
mwin_ends,
)
return nwins, dims, mwins_inends, dwins_inends
[docs]def Sliding2D(
Op: LinearOperator,
dims: InputDimsLike,
dimsd: InputDimsLike,
nwin: int,
nover: int,
tapertype: str = "hanning",
name: str = "S",
) -> LinearOperator:
"""2D Sliding transform operator.
Apply a transform operator ``Op`` repeatedly to slices of the model
vector in forward mode and slices of the data vector in adjoint mode.
More specifically, in forward mode the model vector is divided into
slices, each slice is transformed, and slices are then recombined in a
sliding window fashion. Both model and data are internally reshaped and
interpreted as 2-dimensional arrays: each slice contains a portion
of the array in the first dimension (and the entire second dimension).
This operator can be used to perform local, overlapping transforms (e.g.,
:obj:`pylops.signalprocessing.FFT2D`
or :obj:`pylops.signalprocessing.Radon2D`) on 2-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 first run ``sliding2d_design`` to obtain
the corresponding ``dims`` and number of windows.
.. warning:: Depending on the choice of `nwin` and `nover` as well as the
size of the data, sliding windows may not cover the entire data.
The start and end indices of each window will be displayed and returned
with running ``sliding2d_design``.
Parameters
----------
Op : :obj:`pylops.LinearOperator`
Transform operator
dims : :obj:`tuple`
Shape of 2-dimensional model. Note that ``dims[0]`` should be multiple
of the model size of the transform in the first dimension
dimsd : :obj:`tuple`
Shape of 2-dimensional data
nwin : :obj:`int`
Number of samples of window
nover : :obj:`int`
Number of samples of overlapping part of window
tapertype : :obj:`str`, optional
Type of taper (``hanning``, ``cosine``, ``cosinesquare`` or ``None``)
name : :obj:`str`, optional
.. versionadded:: 2.0.0
Name of operator (to be used by :func:`pylops.utils.describe.describe`)
Returns
-------
Sop : :obj:`pylops.LinearOperator`
Sliding operator
Raises
------
ValueError
Identified number of windows is not consistent with provided model
shape (``dims``).
"""
# data windows
dwin_ins, dwin_ends = _slidingsteps(dimsd[0], nwin, nover)
nwins = len(dwin_ins)
# check patching
if nwins * Op.shape[1] // dims[1] != dims[0]:
raise ValueError(
f"Model shape (dims={dims}) is not consistent with chosen "
f"number of windows. Run sliding2d_design to identify the "
f"correct number of windows for the current "
"model size..."
)
# create tapers
if tapertype is not None:
tap = taper2d(dimsd[1], nwin, nover, tapertype=tapertype)
tapin = tap.copy()
tapin[:nover] = 1
tapend = tap.copy()
tapend[-nover:] = 1
taps = {}
taps[0] = tapin
for i in range(1, nwins - 1):
taps[i] = tap
taps[nwins - 1] = tapend
# transform to apply
if tapertype is None:
OOp = BlockDiag([Op for _ in range(nwins)])
else:
OOp = BlockDiag([Diagonal(taps[itap].ravel()) * Op for itap in range(nwins)])
combining = HStack(
[
Restriction(dimsd, range(win_in, win_end), axis=0, dtype=Op.dtype).H
for win_in, win_end in zip(dwin_ins, dwin_ends)
]
)
Sop = aslinearoperator(combining * OOp)
Sop.dims, Sop.dimsd = (nwins, int(dims[0] // nwins), dims[1]), dimsd
Sop.name = name
return Sop