Source code for pylops.basicoperators.pad

__all__ = ["Pad"]

from typing import Sequence, Tuple, Union

import numpy as np

from pylops import LinearOperator
from pylops.utils._internal import _value_or_sized_to_tuple
from pylops.utils.decorators import reshaped
from pylops.utils.typing import DTypeLike, InputDimsLike, NDArray

[docs]class Pad(LinearOperator): r"""Pad operator. Zero-pad model in forward model and extract non-zero subsequence in adjoint. Padding can be performed in one or multiple directions to any multi-dimensional input arrays. Parameters ---------- dims : :obj:`int` or :obj:`tuple` Number of samples for each dimension pad : :obj:`tuple` Number of samples to pad. If ``dims`` is a scalar, ``pad`` is a single tuple ``(pad_in, pad_end)``. If ``dims`` is a tuple, ``pad`` is a tuple of tuples where each inner tuple contains the number of samples to pad in each dimension 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 any element of ``pad`` is negative. Notes ----- Given an array of size :math:`N`, the *Pad* operator simply adds :math:`\text{pad}_\text{in}` at the start and :math:`\text{pad}_\text{end}` at the end in forward mode: .. math:: y_{i} = x_{i-\text{pad}_\text{in}} \quad \forall i=\text{pad}_\text{in},\ldots,\text{pad}_\text{in}+N-1 and :math:`y_i = 0 \quad \forall i=0,\ldots,\text{pad}_\text{in}-1, \text{pad}_\text{in}+N-1,\ldots,N+\text{pad}_\text{in}+\text{pad}_\text{end}` In adjoint mode, values from :math:`\text{pad}_\text{in}` to :math:`N-\text{pad}_\text{end}` are extracted from the data: .. math:: x_{i} = y_{\text{pad}_\text{in}+i} \quad \forall i=0, N-1 """ def __init__( self, dims: Union[int, InputDimsLike], pad: Union[Tuple[int, int], Sequence[Tuple[int, int]]], dtype: DTypeLike = "float64", name: str = "P", ) -> None: if np.any(np.array(pad) < 0): raise ValueError("Padding must be positive or zero") dims = _value_or_sized_to_tuple(dims) # Accept (padbeg, padend) and [(padbeg, padend)] self.pad: Sequence = [pad] if len(dims) == 1 and len(pad) == 2 else pad dimsd = [dim + before + after for dim, (before, after) in zip(dims, self.pad)] super().__init__(dtype=np.dtype(dtype), dims=dims, dimsd=dimsd, name=name) @reshaped def _matvec(self, x: NDArray) -> NDArray: return np.pad(x, self.pad, mode="constant") @reshaped def _rmatvec(self, x: NDArray) -> NDArray: for ax, (before, _) in enumerate(self.pad): x = np.take(x, np.arange(before, before + self.dims[ax]), axis=ax) return x