__all__ = [
"sliding3d_design",
"Sliding3D",
]
import logging
from typing import Tuple
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 taper3d
from pylops.utils.typing import InputDimsLike, NDArray
logging.basicConfig(format="%(levelname)s: %(message)s", level=logging.WARNING)
[docs]def sliding3d_design(
dimsd: Tuple[int, int, int],
nwin: Tuple[int, int],
nover: Tuple[int, int],
nop: Tuple[int, int, int],
verb: bool = True,
) -> Tuple[
Tuple[int, int],
Tuple[int, int, int],
Tuple[Tuple[NDArray, NDArray], Tuple[NDArray, NDArray]],
Tuple[Tuple[NDArray, NDArray], Tuple[NDArray, NDArray]],
]:
"""Design Sliding3D operator
This routine can be used prior to creating the :class:`pylops.signalprocessing.Sliding3D`
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:`tuple`
Number of windows.
dims : :obj:`tuple`
Shape 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
dwin0_ins, dwin0_ends = _slidingsteps(dimsd[0], nwin[0], nover[0])
dwin1_ins, dwin1_ends = _slidingsteps(dimsd[1], nwin[1], nover[1])
dwins_inends = ((dwin0_ins, dwin0_ends), (dwin1_ins, dwin1_ends))
nwins0 = len(dwin0_ins)
nwins1 = len(dwin1_ins)
nwins = (nwins0, nwins1)
# model windows
dims = (nwins0 * nop[0], nwins1 * nop[1], nop[2])
mwin0_ins, mwin0_ends = _slidingsteps(dims[0], nop[0], 0)
mwin1_ins, mwin1_ends = _slidingsteps(dims[1], nop[1], 0)
mwins_inends = ((mwin0_ins, mwin0_ends), (mwin1_ins, mwin1_ends))
# print information about patching
if verb:
logging.warning("%d-%d windows required...", nwins0, nwins1)
logging.warning(
"data wins - start:%s, end:%s / start:%s, end:%s",
dwin0_ins,
dwin0_ends,
dwin1_ins,
dwin1_ends,
)
logging.warning(
"model wins - start:%s, end:%s / start:%s, end:%s",
mwin0_ins,
mwin0_ends,
mwin1_ins,
mwin1_ends,
)
return nwins, dims, mwins_inends, dwins_inends
[docs]class Sliding3D(LinearOperator):
"""3D Sliding transform operator.w
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 first run ``sliding3d_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] == np.prod(dims)``.
.. 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 ``sliding3d_design``.
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``)
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.
nproc : :obj:`int`, optional
*Deprecated*, will be removed in v3.0.0. Simply kept for
back-compatibility with previous implementation
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``).
"""
def __init__(
self,
Op: LinearOperator,
dims: InputDimsLike,
dimsd: InputDimsLike,
nwin: Tuple[int, int],
nover: Tuple[int, int],
nop: Tuple[int, int, int],
tapertype: str = "hanning",
savetaper: bool = True,
nproc: int = 1,
name: str = "P",
) -> None:
dims: Tuple[int, ...] = _value_or_sized_to_tuple(dims)
dimsd: Tuple[int, ...] = _value_or_sized_to_tuple(dimsd)
# data windows
dwin0_ins, dwin0_ends = _slidingsteps(dimsd[0], nwin[0], nover[0])
dwin1_ins, dwin1_ends = _slidingsteps(dimsd[1], nwin[1], nover[1])
self.dwins_inends = ((dwin0_ins, dwin0_ends), (dwin1_ins, dwin1_ends))
nwins0 = len(dwin0_ins)
nwins1 = len(dwin1_ins)
nwins = nwins0 * nwins1
self.nwin = nwin
self.nover = nover
# model windows
mwin0_ins, mwin0_ends = _slidingsteps(dims[0], nop[0], 0)
mwin1_ins, mwin1_ends = _slidingsteps(dims[1], nop[1], 0)
self.mwins_inends = ((mwin0_ins, mwin0_ends), (mwin1_ins, mwin1_ends))
# check windows
if nwins * Op.shape[1] // dims[2] != dims[0] * dims[1] and Op.shape[
1
] != np.prod(dims):
raise ValueError(
f"Model shape (dims={dims}) is not consistent with chosen "
f"number of windows. Run sliding3d_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 = taper3d(dimsd[2], nwin, nover, tapertype=tapertype).astype(Op.dtype)
# topmost tapers
taptop = tap.copy()
taptop[: nover[0]] = tap[nwin[0] // 2]
# bottommost tapers
tapbottom = tap.copy()
tapbottom[-nover[0] :] = tap[nwin[0] // 2]
# leftmost tapers
tapleft = tap.copy()
tapleft[:, : nover[1]] = tap[:, nwin[1] // 2][:, np.newaxis]
# rightmost tapers
tapright = tap.copy()
tapright[:, -nover[1] :] = tap[:, nwin[1] // 2][:, np.newaxis]
# lefttopcorner taper
taplefttop = tap.copy()
taplefttop[:, : nover[1]] = tap[:, nwin[1] // 2][:, np.newaxis]
taplefttop[: nover[0]] = taplefttop[nwin[0] // 2]
# righttopcorner taper
taprighttop = tap.copy()
taprighttop[:, -nover[1] :] = tap[:, nwin[1] // 2][:, np.newaxis]
taprighttop[: nover[0]] = taprighttop[nwin[0] // 2]
# leftbottomcorner taper
tapleftbottom = tap.copy()
tapleftbottom[:, : nover[1]] = tap[:, nwin[1] // 2][:, np.newaxis]
tapleftbottom[-nover[0] :] = tapleftbottom[nwin[0] // 2]
# rightbottomcorner taper
taprightbottom = tap.copy()
taprightbottom[:, -nover[1] :] = tap[:, nwin[1] // 2][:, np.newaxis]
taprightbottom[-nover[0] :] = taprightbottom[nwin[0] // 2]
if self.savetaper:
taps = [
tap,
] * nwins
for itap in range(0, nwins1):
taps[itap] = taptop
for itap in range(nwins - nwins1, nwins):
taps[itap] = tapbottom
for itap in range(0, nwins, nwins1):
taps[itap] = tapleft
for itap in range(nwins1 - 1, nwins, nwins1):
taps[itap] = tapright
taps[0] = taplefttop
taps[nwins1 - 1] = taprighttop
taps[nwins - nwins1] = tapleftbottom
taps[nwins - 1] = taprightbottom
self.taps = np.vstack(taps).reshape(
nwins0, nwins1, nwin[0], nwin[1], dimsd[2]
)
else:
taps = [
taplefttop,
taptop,
taprighttop,
tapleft,
tap,
tapright,
tapleftbottom,
tapbottom,
taprightbottom,
]
self.taps = np.vstack(taps).reshape(3, 3, nwin[0], nwin[1], dimsd[2])
# check if operator is applied to all windows simultaneously
self.simOp = False
if Op.shape[1] == np.prod(dims):
self.simOp = True
self.Op = Op
super().__init__(
dtype=Op.dtype,
dims=(
nwins0,
nwins1,
int(dims[0] // nwins0),
int(dims[1] // nwins1),
dims[2],
),
dimsd=dimsd,
clinear=False,
name=name,
)
self._register_multiplications(self.savetaper)
def _apply_taper(self, ywins, iwin0, iwin1):
if iwin0 == 0 and iwin1 == 0:
ywins[0, 0] = self.taps[0, 0] * ywins[0, 0]
elif iwin0 == 0 and iwin1 == self.dims[1] - 1:
ywins[0, -1] = self.taps[0, -1] * ywins[0, -1]
elif iwin0 == 0:
ywins[0, iwin1] = self.taps[0, 1] * ywins[0, iwin1]
elif iwin0 == self.dims[0] - 1 and iwin1 == 0:
ywins[-1, 0] = self.taps[-1, 0] * ywins[-1, 0]
elif iwin0 == self.dims[0] - 1 and iwin1 == self.dims[1] - 1:
ywins[-1, -1] = self.taps[-1, -1] * ywins[-1, -1]
elif iwin0 == self.dims[0] - 1:
ywins[-1, iwin1] = self.taps[-1, 1] * ywins[-1, iwin1]
elif iwin1 == 0:
ywins[iwin0, 0] = self.taps[1, 0] * ywins[iwin0, 0]
elif iwin1 == self.dims[1] - 1:
ywins[iwin0, -1] = self.taps[1, -1] * ywins[iwin0, -1]
else:
ywins[iwin0, iwin1] = self.taps[1, 1] * ywins[iwin0, iwin1]
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
for iwin0 in range(self.dims[0]):
for iwin1 in range(self.dims[1]):
if self.simOp:
xx = x[iwin0, iwin1].reshape(
self.nwin[0], self.nwin[1], self.dimsd[-1]
)
else:
xx = self.Op.matvec(x[iwin0, iwin1].ravel()).reshape(
self.nwin[0], self.nwin[1], self.dimsd[-1]
)
if self.tapertype is not None:
xxwin = self.taps[iwin0, iwin1] * xx
else:
xxwin = xx
y[
self.dwins_inends[0][0][iwin0] : self.dwins_inends[0][1][iwin0],
self.dwins_inends[1][0][iwin1] : self.dwins_inends[1][1][iwin1],
] += 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, axis=(0, 1))[
:: self.nwin[0] - self.nover[0], :: self.nwin[1] - self.nover[1]
].transpose(0, 1, 3, 4, 2)
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]):
for iwin1 in range(self.dims[1]):
y[iwin0, iwin1] = self.Op.rmatvec(
ywins[iwin0, iwin1].ravel()
).reshape(self.dims[2], self.dims[3], self.dims[4])
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]):
for iwin1 in range(self.dims[1]):
if self.simOp:
xxwin = x[iwin0, iwin1].reshape(
self.nwin[0], self.nwin[1], self.dimsd[-1]
)
else:
xxwin = self.Op.matvec(x[iwin0, iwin1].ravel()).reshape(
self.nwin[0], self.nwin[1], self.dimsd[-1]
)
if self.tapertype is not None:
if iwin0 == 0 and iwin1 == 0:
xxwin = self.taps[0, 0] * xxwin
elif iwin0 == 0 and iwin1 == self.dims[1] - 1:
xxwin = self.taps[0, -1] * xxwin
elif iwin0 == 0:
xxwin = self.taps[0, 1] * xxwin
elif iwin0 == self.dims[0] - 1 and iwin1 == 0:
xxwin = self.taps[-1, 0] * xxwin
elif iwin0 == self.dims[0] - 1 and iwin1 == self.dims[1] - 1:
xxwin = self.taps[-1, -1] * xxwin
elif iwin0 == self.dims[0] - 1:
xxwin = self.taps[-1, 1] * xxwin
elif iwin1 == 0:
xxwin = self.taps[1, 0] * xxwin
elif iwin1 == self.dims[1] - 1:
xxwin = self.taps[1, -1] * xxwin
else:
xxwin = self.taps[1, 1] * xxwin
y[
self.dwins_inends[0][0][iwin0] : self.dwins_inends[0][1][iwin0],
self.dwins_inends[1][0][iwin1] : self.dwins_inends[1][1][iwin1],
] += 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, axis=(0, 1))[
:: self.nwin[0] - self.nover[0], :: self.nwin[1] - self.nover[1]
]
.transpose(0, 1, 3, 4, 2)
.copy()
)
if self.simOp:
if self.tapertype is not None:
for iwin0 in range(self.dims[0]):
for iwin1 in range(self.dims[1]):
ywins = self._apply_taper(ywins, iwin0, iwin1)
y = self.Op.H @ ywins
else:
y = ncp.zeros(self.dims, dtype=self.dtype)
for iwin0 in range(self.dims[0]):
for iwin1 in range(self.dims[1]):
if self.tapertype is not None:
ywins = self._apply_taper(ywins, iwin0, iwin1)
y[iwin0, iwin1] = self.Op.rmatvec(
ywins[iwin0, iwin1].ravel()
).reshape(self.dims[2], self.dims[3], self.dims[4])
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
