# pylops.Laplacian¶

pylops.Laplacian(dims, axes=(-2, -1), weights=(1, 1), sampling=(1, 1), edge=False, kind='centered', dtype='float64')[source]

Laplacian.

Apply second-order centered Laplacian operator to a multi-dimensional array.

Note

At least 2 dimensions are required, use pylops.SecondDerivative for 1d arrays.

Parameters: dims : tuple Number of samples for each dimension. axes : int, optional New in version 2.0.0. Axes along which the Laplacian is applied. weights : tuple, optional Weight to apply to each direction (real laplacian operator if weights=(1, 1)) sampling : tuple, optional Sampling steps for each direction edge : bool, optional Use reduced order derivative at edges (True) or ignore them (False) for centered derivative kind : str, optional Derivative kind (forward, centered, or backward) dtype : str, optional Type of elements in input array. l2op : pylops.LinearOperator Laplacian linear operator 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:

$y[i, j] = (x[i+1, j] + x[i-1, j] + x[i, j-1] +x[i, j+1] - 4x[i, j]) / (\Delta x \Delta y)$

## Examples using pylops.Laplacian¶ Bilinear Interpolation Causal Integration Derivatives 06. 2D Interpolation 16. CT Scan Imaging