pylops.SecondDerivative¶
-
class
pylops.
SecondDerivative
(N, dims=None, dir=0, sampling=1, edge=False, dtype='float64', kind='centered')[source]¶ Second derivative.
Apply a second derivative using a three-point stencil finite-difference approximation.
Parameters: - N :
int
Number of samples in model.
- dims :
tuple
, optional Number of samples for each dimension (
None
if only one dimension is available)- dir :
int
, optional Direction along which the derivative is applied.
- sampling :
float
, optional Sampling step \(\Delta x\).
- edge :
bool
, optional Use reduced order derivative at edges (
True
) or ignore them (False
) for centered derivative- dtype :
str
, optional Type of elements in input array.
- kind :
str
, optional Derivative kind (
forward
,centered
, orbackward
).
Notes
The SecondDerivative operator applies a second derivative to any chosen direction of a multi-dimensional array.
For simplicity, given a one dimensional array, the second-order centered first derivative is:
\[y[i] = (x[i+1] - 2x[i] + x[i-1]) / \Delta x^2\]while the second-order forward stencil is:
\[y[i] = (x[i+2] - 2x[i+1] + x[i]) / \Delta x^2\]and the second-order backward stencil is:
\[y[i] = (x[i] - 2x[i-1] + x[i-2]) / \Delta x^2\]Attributes: Methods
__init__
(N[, dims, dir, sampling, 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. 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. - N :