Mfr#

class cherab.inversion.Mfr(T, dmats: Collection[Collection[spmatrix | sparray]], *, Q=None, data=None)Source #

Inverses provided data using Minimum Fisher Regularization (MFR) scheme.

Note

The theory and implementation of the MFR are described here.

Parameters:

T(M, N) array_like: Matrix \(\mathbf{T}\in\mathbb{R}^{M\times N}\) of the forward problem (geometry matrix, ray transfer matrix, etc.).
dmatsCollection[Collection[scipy.sparse.spmatrix, scipy.sparse.spmatrix]]: Iterable of pairs of derivative matrices \(\mathbf{D}_i\) and \(\mathbf{D}_j\) along to \(i\) and \(j\) coordinate directions, respectively.
Q(M, M) array_like, optional: Weighted matrix for the residual norm \(\mathbf{Q}\in\mathbb{R}^{M\times M}\), by default None (meaning \(\mathbf{Q} = \mathbf{I}\)). This matrix must be a symmetric positive semi-definite matrix.
data(M, ) array_like, optional: Given data as a vector \(\mathbf{b}\in\mathbb{R}^M\), by default None.

Examples

>>> mfr = Mfr(T, dmats, data=data)

Methods

`regularization_matrix`(x[, eps, ...])	Compute nonlinear regularization matrix from provided derivative matrices and a solution vector.
`solve`([x0, derivative_weights, eps, tol, ...])	Solve the inverse problem using MFR scheme.

Attributes

`Q`	Weighted matrix \(\mathbf{Q}\) for the residual norm.
`T`	Matrix \(\mathbf{T}\) of the forward problem.
`data`	Given data as a vector \(\mathbf{b}\).
`dmats`	List of pairs of derivative matrices \(\mathbf{D}_i\) and \(\mathbf{D}_j\).