cherab.phix.inversion.Lcurve.curvature#
- Lcurve.curvature(beta)Source#
Calculate L-curve curvature.
This method calculates the L-curve curvature \(\kappa\) specified by a regularization parameter \(\beta\) as follows:
\[\begin{split}\begin{align} \kappa(\beta) &= \frac{f^{\prime\prime}(x)}{\left[1 + f^{\prime}(x)^2\right]^{3/2}} = -2 \eta\rho \frac{\beta^2 \eta + \beta \rho + \rho\eta/\eta^\prime} {(\beta^2 \eta^2 + \rho^2)^{3/2}},\\ \rho &\equiv ||Ax_\beta - b||_2^2,\\ \eta &\equiv ||L(x_\beta - x_0)||_2^2,\\ \eta^\prime &\equiv \frac{d\eta}{d\beta}. \end{align}\end{split}\]