pylops.FirstDerivative¶
-
class
pylops.FirstDerivative(N, dims=None, dir=0, sampling=1.0, edge=False, dtype='float64', kind='centered')[source]¶ First derivative.
Apply first derivative.
Parameters: - N :
int Number of samples in model.
- dims :
tuple, optional Number of samples for each dimension (
Noneif only one dimension is available)- dir :
int, optional Direction along which the derivative 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.
- kind :
str, optional Derivative kind (
forward,centered, orbackward).
Notes
The FirstDerivative operator applies a first derivative to any chosen direction of a multi-dimensional array using either a second-order centered stencil or first-order forward/backward stencils.
For simplicity, given a one dimensional array, the second-order centered first derivative is:
\[y[i] = (0.5x[i+1] - 0.5x[i-1]) / dx\]while the first-order forward stencil is:
\[y[i] = (x[i+1] - x[i]) / dx\]and the first-order backward stencil is:
\[y[i] = (x[i] - x[i-1]) / dx\]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])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. transpose()Transpose this linear operator. - N :
