Source code for pylops.basicoperators.laplacian

__all__ = ["Laplacian"]

from typing import Tuple

from numpy.core.multiarray import normalize_axis_index

from pylops import LinearOperator, aslinearoperator
from pylops.basicoperators import SecondDerivative
from pylops.utils.typing import DTypeLike, InputDimsLike

[docs]def Laplacian( dims: InputDimsLike, axes: InputDimsLike = (-2, -1), weights: Tuple[float, ...] = (1, 1), sampling: Tuple[float, ...] = (1, 1), edge: bool = False, kind: str = "centered", dtype: DTypeLike = "float64", ) -> LinearOperator: r"""Laplacian. Apply second-order centered Laplacian operator to a multi-dimensional array. .. note:: At least 2 dimensions are required, use :py:func:`pylops.SecondDerivative` for 1d arrays. Parameters ---------- dims : :obj:`tuple` Number of samples for each dimension. axes : :obj:`int`, optional .. versionadded:: 2.0.0 Axes along which the Laplacian is applied. weights : :obj:`tuple`, optional Weight to apply to each direction (real laplacian operator if ``weights=(1, 1)``) sampling : :obj:`tuple`, optional Sampling steps for each direction edge : :obj:`bool`, optional Use reduced order derivative at edges (``True``) or ignore them (``False``) for centered derivative kind : :obj:`str`, optional Derivative kind (``forward``, ``centered``, or ``backward``) dtype : :obj:`str`, optional Type of elements in input array. Returns ------- l2op : :obj:`pylops.LinearOperator` Laplacian linear operator Raises ------ ValueError If ``axes``. ``weights``, and ``sampling`` do not have the same size Notes ----- The Laplacian operator applies a second derivative along two directions of a multi-dimensional array. For simplicity, given a two dimensional array, the Laplacian is: .. math:: y[i, j] = (x[i+1, j] + x[i-1, j] + x[i, j-1] +x[i, j+1] - 4x[i, j]) / (\Delta x \Delta y) """ axes = tuple(normalize_axis_index(ax, len(dims)) for ax in axes) if not (len(axes) == len(weights) == len(sampling)): raise ValueError("axes, weights, and sampling have different size") l2op = SecondDerivative( dims, axis=axes[0], sampling=sampling[0], edge=edge, kind=kind, dtype=dtype ) dims, dimsd = l2op.dims, l2op.dimsd l2op *= weights[0] for ax, samp, weight in zip(axes[1:], sampling[1:], weights[1:]): l2op += weight * SecondDerivative( dims, axis=ax, sampling=samp, edge=edge, dtype=dtype ) l2op = aslinearoperator(l2op) l2op.dims = dims l2op.dimsd = dimsd l2op.axes = axes l2op.weights = weights l2op.sampling = sampling l2op.edge = edge l2op.kind = kind return l2op