pylops.FirstDerivative

class pylops.FirstDerivative(N, dims=None, dir=0, sampling=1.0, edge=False, dtype='float64')[source]

First derivative.

Apply second-order centered first 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 FirstDerivative operator applies a first derivative to any chosen direction of a multi-dimensional array.

For simplicity, given a one dimensional array, the second-order centered first derivative is:

\[y[i] = (0.5x[i+1] - 0.5x[i-1]) / dx\]
Attributes:
shape : tuple

Operator shape

explicit : bool

Operator contains a matrix that can be solved explicitly (True) or not (False)

Methods

__init__(self, N[, dims, dir, sampling, …]) Initialize this LinearOperator.
adjoint(self) Hermitian adjoint.
apply_columns(self, cols) Apply subset of columns of operator
cond(self, \*\*kwargs_eig) Condition number of linear operator.
conj(self) Complex conjugate operator
div(self, y[, niter]) Solve the linear problem \(\mathbf{y}=\mathbf{A}\mathbf{x}\).
dot(self, x) Matrix-matrix or matrix-vector multiplication.
eigs(self[, neigs, symmetric, niter]) Most significant eigenvalues of linear operator.
matmat(self, X) Matrix-matrix multiplication.
matvec(self, x) Matrix-vector multiplication.
rmatmat(self, X) Adjoint matrix-matrix multiplication.
rmatvec(self, x) Adjoint matrix-vector multiplication.
todense(self) Return dense matrix.
transpose(self) Transpose this linear operator.