pylops.SecondDirectionalDerivative¶

pylops.
SecondDirectionalDerivative
(dims, v, sampling=1, edge=False, dtype='float64')[source]¶ Second Directional derivative.
Apply a second directional derivative operator to a multidimensional array along either a single common direction or different directions for each point of the array.
Note
At least 2 dimensions are required, consider using
pylops.SecondDerivative
for 1d arrays.Parameters:  dims :
tuple
Number of samples for each dimension.
 v :
np.ndarray
, optional Single direction (array of size \(n_\text{dims}\)) or group of directions (array of size \([n_\text{dims} \times n_{d_0} \times ... \times n_{d_{n_\text{dims}}}]\))
 sampling :
tuple
, optional Sampling steps for each direction.
 edge :
bool
, optional Use reduced order derivative at edges (
True
) or ignore them (False
). dtype :
str
, optional Type of elements in input array.
Returns:  ddop :
pylops.LinearOperator
Second directional derivative linear operator
Notes
The SecondDirectionalDerivative applies a secondorder derivative to a multidimensional array along the direction defined by the unitary vector \(\mathbf{v}\):
\[d^2f_\mathbf{v} =  D_\mathbf{v}^T [D_\mathbf{v} f]\]where \(D_\mathbf{v}\) is the firstorder directional derivative implemented by
pylops.SecondDirectionalDerivative
.This operator is sometimes also referred to as directional Laplacian in the literature.
 dims :