pylops.SecondDerivative¶
-
class
pylops.
SecondDerivative
(N, dims=None, dir=0, sampling=1, edge=False, dtype='float64')[source]¶ Second derivative.
Apply second-order second derivative.
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 smoothing is applied.
- sampling :
float
, optional Sampling step
dx
.- edge :
bool
, optional Use reduced order derivative at edges (
True
) or ignore them (False
)- dtype :
str
, optional Type of elements in input array.
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:
\[y[i] = (x[i+1] - 2x[i] + x[i-1]) / dx^2\]Attributes: Methods
__init__
(N[, dims, dir, sampling, edge, dtype])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])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)Adjoint matrix-matrix multiplication. rmatvec
(x)Adjoint matrix-vector multiplication. todense
()Return dense matrix. tosparse
()Return sparse matrix. transpose
()Transpose this linear operator. - N :