pylops.FirstDerivative#

class pylops.FirstDerivative(dims, axis=-1, sampling=1.0, kind='centered', edge=False, order=3, dtype='float64', name='F')[source]#

First derivative.

Apply a first derivative using a multiple-point stencil finite-difference approximation along axis.

Parameters

dimslist or int: Number of samples for each dimension
axisint, optional: New in version 2.0.0.

Axis along which derivative is applied.
samplingfloat, optional: Sampling step \(\Delta x\).
kindstr, optional: Derivative kind (forward, centered, or backward).
edgebool, optional: Use reduced order derivative at edges (True) or ignore them (False). This is currently only available for centered derivative
orderint, optional: New in version 2.0.0.

Derivative order (3 or 5). This is currently only available for centered derivative
dtypestr, optional: Type of elements in input array.
namestr, optional: New in version 2.0.0.

Name of operator (to be used by pylops.utils.describe.describe)

Notes

The FirstDerivative operator applies a first derivative to any chosen direction of a multi-dimensional array using either a second- or third-order centered stencil or first-order forward/backward stencils.

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

\[y[i] = (0.5x[i+1] - 0.5x[i-1]) / \Delta x\]

while the first-order forward stencil is:

\[y[i] = (x[i+1] - x[i]) / \Delta x\]

and the first-order backward stencil is:

\[y[i] = (x[i] - x[i-1]) / \Delta x\]

Formulas for the third-order centered stencil can be found at this link.

Attributes

dimstuple

Shape of the array after the adjoint, but before flattening.

For example, x_reshaped = (Op.H * y.ravel()).reshape(Op.dims).

dimsdtuple

Shape of the array after the forward, but before flattening. In this case, same as dims.

shapetuple

Operator shape.

Methods

`__init__`(dims[, axis, sampling, kind, edge, ...])
`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.
`reset_count`()	Reset counters
`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`()