pylops.FirstDerivative¶
-
class
pylops.
FirstDerivative
(dims, axis=-1, sampling=1.0, kind='centered', edge=False, order=3, dtype='float64', name='F')[source]¶ First derivative.
Apply a first derivative using a multiple-point stencil finite-difference approximation along
axis
.Parameters: - dims :
list
orint
Number of samples for each dimension
- axis :
int
, optional New in version 2.0.0.
Axis along which derivative is applied.
- sampling :
float
, optional Sampling step \(\Delta x\).
- kind :
str
, optional Derivative kind (
forward
,centered
, orbackward
).- edge :
bool
, optional Use reduced order derivative at edges (
True
) or ignore them (False
). This is currently only availablefor centered derivative
- order :
int
, optional New in version 2.0.0.
Derivative order (
3
or5
). This is currently only available for centered derivative- dtype :
str
, optional Type of elements in input array.
- name :
str
, optional New in version 2.0.0.
Name of operator (to be used by
pylops.utils.describe.describe
)
Notes
The FirstDerivative operator applies a first derivative to any chosen direction of a multi-dimensional array using either a second- or third-order centered stencil or first-order forward/backward stencils.
For simplicity, given a one dimensional array, the second-order centered first derivative is:
\[y[i] = (0.5x[i+1] - 0.5x[i-1]) / \Delta x\]while the first-order forward stencil is:
\[y[i] = (x[i+1] - x[i]) / \Delta x\]and the first-order backward stencil is:
\[y[i] = (x[i] - x[i-1]) / \Delta x\]Formulas for the third-order centered stencil can be found at this link.
Attributes: Methods
__init__
(dims[, axis, sampling, kind, edge, …])Initialize this LinearOperator. adjoint
()Hermitian adjoint. apply_columns
(cols)Apply subset of columns of operator cond
([uselobpcg])Condition number of linear operator. conj
()Complex conjugate operator div
(y[, niter, densesolver])Solve the linear problem \(\mathbf{y}=\mathbf{A}\mathbf{x}\). dot
(x)Matrix-matrix or matrix-vector multiplication. eigs
([neigs, symmetric, niter, uselobpcg])Most significant eigenvalues of linear operator. matmat
(X)Matrix-matrix multiplication. matvec
(x)Matrix-vector multiplication. reset_count
()Reset counters rmatmat
(X)Matrix-matrix multiplication. rmatvec
(x)Adjoint matrix-vector multiplication. todense
([backend])Return dense matrix. toimag
([forw, adj])Imag operator toreal
([forw, adj])Real operator tosparse
()Return sparse matrix. trace
([neval, method, backend])Trace of linear operator. transpose
()Transpose this linear operator. - dims :