pylops.SecondDerivative¶
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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 (
Noneif 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 :
