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
)
- dims
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, ...])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
()