Source code for pylops.basicoperators.Laplacian

import numpy as np

from pylops.basicoperators import SecondDerivative
from pylops.LinearOperator import aslinearoperator

[docs]def Laplacian( dims, dirs=(0, 1), weights=(1, 1), sampling=(1, 1), edge=False, dtype="float64", kind="centered", ): 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. dirs : :obj:`tuple`, optional Directions along which 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 dtype : :obj:`str`, optional Type of elements in input array. kind : :obj:`str`, optional Derivative kind (``forward``, ``centered``, or ``backward``) Returns ------- l2op : :obj:`pylops.LinearOperator` Laplacian linear operator Raises ------ ValueError If ``dirs``. ``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) """ if not (len(dirs) == len(weights) == len(sampling)): raise ValueError("dirs, weights, and sampling have different size") l2op = weights[0] * SecondDerivative(, dims=dims, dir=dirs[0], sampling=sampling[0], edge=edge, kind=kind, dtype=dtype, ) for dir, samp, weight in zip(dirs[1:], sampling[1:], weights[1:]): l2op += weight * SecondDerivative(, dims=dims, dir=dir, sampling=samp, edge=edge, dtype=dtype, ) return aslinearoperator(l2op)