__all__ = ["Convolve1D"]
from typing import Callable, Tuple, Union
import numpy as np
import numpy.typing as npt
from pylops import LinearOperator
from pylops.utils._internal import _value_or_sized_to_tuple
from pylops.utils.backend import (
get_convolve,
get_fftconvolve,
get_oaconvolve,
to_cupy_conditional,
)
from pylops.utils.decorators import reshaped
from pylops.utils.typing import DTypeLike, InputDimsLike, NDArray
def _choose_convfunc(
x: npt.ArrayLike, method: Union[None, str], dims
) -> Tuple[Callable, str]:
"""Choose convolution function
Choose and return the function handle to be used for convolution
"""
if len(dims) == 1:
if method is None:
method = "direct"
if method not in ("direct", "fft"):
raise NotImplementedError("method must be direct or fft")
convfunc = get_convolve(x)
else:
if method is None:
method = "fft"
if method == "fft":
convfunc = get_fftconvolve(x)
elif method == "overlapadd":
convfunc = get_oaconvolve(x)
else:
raise NotImplementedError("method must be fft or overlapadd")
return convfunc, method
[docs]class Convolve1D(LinearOperator):
r"""1D convolution operator.
Apply one-dimensional convolution with a compact filter to model (and data)
along an ``axis`` of a multi-dimensional array.
Parameters
----------
dims : :obj:`list` or :obj:`int`
Number of samples for each dimension
h : :obj:`numpy.ndarray`
1d compact filter to be convolved to input signal
offset : :obj:`int`
Index of the center of the compact filter
axis : :obj:`int`, optional
.. versionadded:: 2.0.0
Axis along which convolution is applied
method : :obj:`str`, optional
Method used to calculate the convolution (``direct``, ``fft``,
or ``overlapadd``). Note that only ``direct`` and ``fft`` are allowed
when ``dims=None``, whilst ``fft`` and ``overlapadd`` are allowed
when ``dims`` is provided.
dtype : :obj:`str`, optional
Type of elements in input array.
name : :obj:`str`, optional
.. versionadded:: 2.0.0
Name of operator (to be used by :func:`pylops.utils.describe.describe`)
Attributes
----------
shape : :obj:`tuple`
Operator shape
explicit : :obj:`bool`
Operator contains a matrix that can be solved
explicitly (``True``) or not (``False``)
Raises
------
ValueError
If ``offset`` is bigger than ``len(h) - 1``
NotImplementedError
If ``method`` provided is not allowed
Notes
-----
The Convolve1D operator applies convolution between the input signal
:math:`x(t)` and a compact filter kernel :math:`h(t)` in forward model:
.. math::
y(t) = \int\limits_{-\infty}^{\infty} h(t-\tau) x(\tau) \,\mathrm{d}\tau
This operation can be discretized as follows
.. math::
y[n] = \sum_{m=-\infty}^{\infty} h[n-m] x[m]
as well as performed in the frequency domain.
.. math::
Y(f) = \mathscr{F} (h(t)) * \mathscr{F} (x(t))
Convolve1D operator uses :py:func:`scipy.signal.convolve` that
automatically chooses the best domain for the operation to be carried out
for one dimensional inputs. The fft implementation
:py:func:`scipy.signal.fftconvolve` is however enforced for signals in
2 or more dimensions as this routine efficently operates on
multi-dimensional arrays.
As the adjoint of convolution is correlation, Convolve1D operator applies
correlation in the adjoint mode.
In time domain:
.. math::
x(t) = \int\limits_{-\infty}^{\infty} h(t+\tau) x(\tau) \,\mathrm{d}\tau
or in frequency domain:
.. math::
y(t) = \mathscr{F}^{-1} (H(f)^* * X(f))
"""
def __init__(
self,
dims: Union[int, InputDimsLike],
h: NDArray,
offset: int = 0,
axis: int = -1,
method: str = None,
dtype: DTypeLike = "float64",
name: str = "C",
) -> None:
dims = _value_or_sized_to_tuple(dims)
super().__init__(dtype=np.dtype(dtype), dims=dims, dimsd=dims, name=name)
self.axis = axis
if offset > len(h) - 1:
raise ValueError("offset must be smaller than len(h) - 1")
self.h = h
self.hstar = np.flip(self.h, axis=-1)
self.nh = len(h)
self.offset = 2 * (self.nh // 2 - int(offset))
if self.nh % 2 == 0:
self.offset -= 1
if self.offset != 0:
self.h = np.pad(
self.h,
(
self.offset if self.offset > 0 else 0,
-self.offset if self.offset < 0 else 0,
),
mode="constant",
)
self.hstar = np.flip(self.h, axis=-1)
# add dimensions to filter to match dimensions of model and data
hdims = np.ones(len(self.dims), dtype=int)
hdims[self.axis] = len(self.h)
self.h = self.h.reshape(hdims)
self.hstar = self.hstar.reshape(hdims)
# choose method and function handle
self.convfunc, self.method = _choose_convfunc(h, method, self.dims)
@reshaped
def _matvec(self, x: NDArray) -> NDArray:
if type(self.h) != type(x):
self.h = to_cupy_conditional(x, self.h)
self.convfunc, self.method = _choose_convfunc(
self.h, self.method, self.dims
)
return self.convfunc(x, self.h, mode="same")
@reshaped
def _rmatvec(self, x: NDArray) -> NDArray:
if type(self.hstar) != type(x):
self.hstar = to_cupy_conditional(x, self.hstar)
self.convfunc, self.method = _choose_convfunc(
self.hstar, self.method, self.dims
)
return self.convfunc(x, self.hstar, mode="same")