__all__ = [
"sliding1d_design",
"Sliding1D",
]
import logging
from typing import Tuple, Union
import numpy as np
from pylops import LinearOperator
from pylops.signalprocessing.sliding2d import _slidingsteps
from pylops.utils._internal import _value_or_sized_to_tuple
from pylops.utils.backend import (
get_array_module,
get_sliding_window_view,
to_cupy_conditional,
)
from pylops.utils.decorators import reshaped
from pylops.utils.tapers import taper
from pylops.utils.typing import InputDimsLike, NDArray
logging.basicConfig(format="%(levelname)s: %(message)s", level=logging.WARNING)
[docs]def sliding1d_design(
dimd: int,
nwin: int,
nover: int,
nop: int,
verb: bool = True,
) -> Tuple[int, int, Tuple[NDArray, NDArray], Tuple[NDArray, NDArray]]:
"""Design Sliding1D operator
This routine can be used prior to creating the :class:`pylops.signalprocessing.Sliding1D`
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:`tuple`
Number of samples of window.
nover : :obj:`tuple`
Number of samples of overlapping part of window.
nop : :obj:`tuple`
Size of model in the transformed domain.
verb : :obj:`bool`, optional
Verbosity flag. If ``verb==True``, print the data
and model windows start-end indices
Returns
-------
nwins : :obj:`int`
Number of windows.
dim : :obj:`int`
Shape of 2-dimensional model.
mwins_inends : :obj:`tuple`
Start and end indices for model patches.
dwins_inends : :obj:`tuple`
Start and end indices for data patches.
"""
# data windows
dwin_ins, dwin_ends = _slidingsteps(dimd, nwin, nover)
dwins_inends = (dwin_ins, dwin_ends)
nwins = len(dwin_ins)
# model windows
dim = nwins * nop
mwin_ins, mwin_ends = _slidingsteps(dim, nop, 0)
mwins_inends = (mwin_ins, mwin_ends)
# print information about patching
if verb:
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, dim, mwins_inends, dwins_inends
[docs]class Sliding1D(LinearOperator):
r"""1D 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.
This operator can be used to perform local, overlapping transforms (e.g.,
:obj:`pylops.signalprocessing.FFT`) on 1-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 ``sliding1d_design`` to obtain
the corresponding ``dims`` and number of windows.
.. note:: Two kind of operators ``Op`` can be provided: the first
applies a single transformation to each window separately; the second
applies the transformation to all of the windows at the same time. This
is directly inferred during initialization when the following condition
holds ``Op.shape[1] == dim[0]``.
.. 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 ``sliding1d_design``.
Parameters
----------
Op : :obj:`pylops.LinearOperator`
Transform operator
dim : :obj:`tuple`
Shape of 1-dimensional model.
dimd : :obj:`tuple`
Shape of 1-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``)
savetaper : :obj:`bool`, optional
.. versionadded:: 2.3.0
Save all tapers and apply them in one go (``True``) or save unique tapers and apply them one by one (``False``).
The first option is more computationally efficient, whilst the second is more memory efficient.
name : :obj:`str`, optional
.. versionadded:: 2.0.0
Name of operator (to be used by :func:`pylops.utils.describe.describe`)
Raises
------
ValueError
Identified number of windows is not consistent with provided model
shape (``dims``).
"""
def __init__(
self,
Op: LinearOperator,
dim: Union[int, InputDimsLike],
dimd: Union[int, InputDimsLike],
nwin: int,
nover: int,
tapertype: str = "hanning",
savetaper: bool = True,
name: str = "S",
) -> None:
dim: Tuple[int, ...] = _value_or_sized_to_tuple(dim)
dimd: Tuple[int, ...] = _value_or_sized_to_tuple(dimd)
# data windows
dwin_ins, dwin_ends = _slidingsteps(dimd[0], nwin, nover)
self.dwin_inends = (dwin_ins, dwin_ends)
nwins = len(dwin_ins)
self.nwin = nwin
self.nover = nover
# check windows
if nwins * Op.shape[1] != dim[0] and Op.shape[1] != dim[0]:
raise ValueError(
f"Model shape (dim={dim}) is not consistent with chosen "
f"number of windows. Run sliding1d_design to identify the "
f"correct number of windows for the current "
"model size..."
)
# create tapers
self.tapertype = tapertype
self.savetaper = savetaper
if self.tapertype is not None:
tap = taper(nwin, nover, tapertype=self.tapertype)
tapin = tap.copy()
tapin[:nover] = 1
tapend = tap.copy()
tapend[-nover:] = 1
if self.savetaper:
self.taps = [
tapin,
]
for _ in range(1, nwins - 1):
self.taps.append(tap)
self.taps.append(tapend)
self.taps = np.vstack(self.taps)
else:
self.taps = np.vstack([tapin, tap, tapend])
# check if operator is applied to all windows simultaneously
self.simOp = False
if Op.shape[1] == dim[0]:
self.simOp = True
self.Op = Op
super().__init__(
dtype=Op.dtype,
dims=(nwins, int(dim[0] // nwins)),
dimsd=dimd,
clinear=False,
name=name,
)
self._register_multiplications(self.savetaper)
def _apply_taper(self, ywins, iwin0):
if iwin0 == 0:
ywins[0] = ywins[0] * self.taps[0]
elif iwin0 == self.dims[0] - 1:
ywins[-1] = ywins[-1] * self.taps[-1]
else:
ywins[iwin0] = ywins[iwin0] * self.taps[1]
return ywins
@reshaped
def _matvec_savetaper(self, x: NDArray) -> NDArray:
ncp = get_array_module(x)
if self.tapertype is not None:
self.taps = to_cupy_conditional(x, self.taps)
y = ncp.zeros(self.dimsd, dtype=self.dtype)
if self.simOp:
x = self.Op @ x
if self.tapertype is not None:
x = self.taps * x
for iwin0 in range(self.dims[0]):
if self.simOp:
xxwin = x[iwin0]
else:
xxwin = self.Op.matvec(x[iwin0])
if self.tapertype is not None:
xxwin = self.taps[iwin0] * xxwin
y[self.dwin_inends[0][iwin0] : self.dwin_inends[1][iwin0]] += xxwin
return y
@reshaped
def _rmatvec_savetaper(self, x: NDArray) -> NDArray:
ncp = get_array_module(x)
ncp_sliding_window_view = get_sliding_window_view(x)
if self.tapertype is not None:
self.taps = to_cupy_conditional(x, self.taps)
ywins = ncp_sliding_window_view(x, self.nwin)[:: self.nwin - self.nover]
if self.tapertype is not None:
ywins = ywins * self.taps
if self.simOp:
y = self.Op.H @ ywins
else:
y = ncp.zeros(self.dims, dtype=self.dtype)
for iwin0 in range(self.dims[0]):
y[iwin0] = self.Op.rmatvec(ywins[iwin0])
return y
@reshaped
def _matvec_nosavetaper(self, x: NDArray) -> NDArray:
ncp = get_array_module(x)
if self.tapertype is not None:
self.taps = to_cupy_conditional(x, self.taps)
y = ncp.zeros(self.dimsd, dtype=self.dtype)
if self.simOp:
x = self.Op @ x
for iwin0 in range(self.dims[0]):
if self.simOp:
xxwin = x[iwin0]
else:
xxwin = self.Op.matvec(x[iwin0])
if self.tapertype is not None:
if iwin0 == 0:
xxwin = self.taps[0] * xxwin
elif iwin0 == self.dims[0] - 1:
xxwin = self.taps[-1] * xxwin
else:
xxwin = self.taps[1] * xxwin
y[self.dwin_inends[0][iwin0] : self.dwin_inends[1][iwin0]] += xxwin
return y
@reshaped
def _rmatvec_nosavetaper(self, x: NDArray) -> NDArray:
ncp = get_array_module(x)
ncp_sliding_window_view = get_sliding_window_view(x)
if self.tapertype is not None:
self.taps = to_cupy_conditional(x, self.taps)
ywins = ncp_sliding_window_view(x, self.nwin)[:: self.nwin - self.nover].copy()
if self.simOp:
if self.tapertype is not None:
for iwin0 in range(self.dims[0]):
ywins = self._apply_taper(ywins, iwin0)
y = self.Op.H @ ywins
else:
y = ncp.zeros(self.dims, dtype=self.dtype)
for iwin0 in range(self.dims[0]):
if self.tapertype is not None:
ywins = self._apply_taper(ywins, iwin0)
y[iwin0] = self.Op.rmatvec(ywins[iwin0])
return y
def _register_multiplications(self, savetaper: bool) -> None:
if savetaper:
self._matvec = self._matvec_savetaper
self._rmatvec = self._rmatvec_savetaper
else:
self._matvec = self._matvec_nosavetaper
self._rmatvec = self._rmatvec_nosavetaper
