Source code for pylops.basicoperators.Laplacian

import numpy as np
from pylops.LinearOperator import aslinearoperator
from pylops.basicoperators import SecondDerivative

[docs]def Laplacian(dims, dirs=(0, 1), weights=(1, 1), sampling=(1, 1), edge=False, dtype='float64'): r"""Laplacian. Apply second-order centered Laplacian operator to a multi-dimensional array (at least 2 dimensions are required) 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``) dtype : :obj:`str`, optional Type of elements in input array. Returns ------- l2op : :obj:`pylops.LinearOperator` Laplacian linear operator 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]) / (dx*dy) """ l2op = weights[0]*SecondDerivative(, dims=dims, dir=dirs[0], sampling=sampling[0], edge=edge, dtype=dtype) l2op += weights[1]*SecondDerivative(, dims=dims, dir=dirs[1], sampling=sampling[1], edge=edge, dtype=dtype) return aslinearoperator(l2op)