pylops.FirstDirectionalDerivative¶
-
pylops.
FirstDirectionalDerivative
(dims, v, sampling=1, edge=False, dtype='float64')[source]¶ First Directional derivative.
Apply directional derivative operator to a multi-dimensional array (at least 2 dimensions are required) along either a single common direction or different directions for each point of the array.
Parameters: - dims :
tuple
Number of samples for each dimension.
- v :
np.ndarray
, optional Single direction (array of size \(n_{dims}\)) or group of directions (array of size \([n_{dims} \times n_{d0} \times ... \times n_{n_{dims}}\))
- 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
First directional derivative linear operator
Notes
The FirstDirectionalDerivative applies a first-order derivative to a multi-dimensional array along the direction defined by the unitary vector mathbf{v}:
\[df_\mathbf{v} = \nabla f \mathbf{v}\]or along the directions defined by the unitary vectors \(\mathbf{v}(x, y)\):
\[df_\mathbf{v}(x,y) = \nabla f(x,y) \mathbf{v}(x,y)\]where we have here considered the 2-dimensional case.
This operator can be easily implemented as the concatenation of the
pylops.Gradient
operator and thepylops.Diagonal
operator with :math:mathbf{v} along the main diagonal.- dims :