_SVDBase

class cherab.inversion.core._SVDBase(s, U, basis, B=None, *, data=None)Source

Bases: object

Base class for inversion calculation based on Singular Value Decomposition (SVD) method.

Note

The implementation of this class is based on the inversion theory.

Note

This class is designed to be inherited by subclasses which define the objective function to optimize the regularization parameter \(\lambda\) using the basinhopping function.

Parameters:

s(r, ) array_like

Singular values like \(\mathbf{s} = (\sigma_1, \sigma_2, ...) \in \mathbb{R}^r\).

U(M, r) array_like

Left singular vectors like \(\mathbf{U}\in\mathbb{R}^{M\times r}\).

basis(N, r) array_like

Inverted solution basis like \(\tilde{\mathbf{V}} \in \mathbb{R}^{N\times r}\).

B(M, M) array_like

Matrix \(\mathbf{B}\) coming from \(\mathbf{Q} = \mathbf{B}^\mathsf{T}\mathbf{B}\), by default None, i.e. \(\mathbf{B} = \mathbf{I}\).

data(M, ) array_like

Given data as a vector \(\mathbf{b}\in\mathbb{R}^M\), by default None.

Methods

eta(beta)	Calculate squared regularization norm \(\eta\).
eta_diff(beta)	Calculate differential of \(\eta\).
filter(beta)	Calculate the filter factors \(f_{\lambda, i}\).
regularization_norm(beta)	Return the regularization norm: \(\sqrt{\eta} = \|\mathbf{x}_\lambda\|_\mathbf{H}\).
residual_norm(beta)	Return the residual norm: \(\sqrt{\rho} = \|\mathbf{T}\mathbf{x}_\lambda - \mathbf{b}\|_{\mathbf{Q}}\).
rho(beta)	Calculate squared residual norm \(\rho\).
solution(beta)	Calculate the solution vector \(\mathbf{x}_\lambda\).
solve([bounds, stepsize])	Solve the ill-posed inversion equation.

Attributes

B	Matrix \(\mathbf{B}\) from \(\mathbf{Q} = \mathbf{B}^\mathsf{T}\mathbf{B}\).
U	Left singular vectors \(\mathbf{U}\).
basis	Inverted solution basis \(\tilde{\mathbf{V}}\).
bounds	Bound of log10 of regularization parameter \(\lambda\).
data	Given data for inversion calculation \(\mathbf{b}\).
lambda_opt	Optimal regularization parameter defined after solve is executed.
s	Singular values \(\mathbf{s}\).