cherab.phix.inversion._SVDBase.inverted_solution

_SVDBase.inverted_solution(beta)Source

Calculate the inverted solution using SVD components at given regularization parameter.

The solution is calculated as follows:

\[\begin{split}x_\lambda = \tilde{V}W\Sigma^{-1}U^\mathsf{T}b = \tilde{V} \begin{pmatrix} w_1(\lambda)\frac{1}{\sigma_1} & & \\ & \ddots & \\ & & w_r(\lambda)\frac{1}{\sigma_r} \end{pmatrix} U^\mathsf{T} b,\end{split}\]

where \(\tilde{V} \in \mathbb{R}^{n\times r}\) is the inverted solution basis, which is defined by basis as a property.

Parameters:

beta (float) – regularization parameter

Returns:

solution vector

Return type:

vector_like (N, )