eta_diff()#

_SVDBase.eta_diff(beta: float) floatSource#

Calculate differential of \(\eta\).

\(\eta'\equiv\frac{\partial\eta}{\partial\lambda}\) can be calculated with SVD components as follows:

\[\eta' = \frac{2}{\lambda} (\mathbf{U}^\mathsf{T}\mathbf{B}\mathbf{b})^\mathsf{T} (\mathbf{F}_\lambda - \mathbf{I}_r) \mathbf{F}_\lambda^2\mathbf{S}^{-2}\ \mathbf{U}^\mathsf{T}\mathbf{B}\mathbf{b}.\]
Parameters:
betafloat

Regularization parameter \(\lambda\).

Returns:
float

Differential of \(\eta\) with respect to \(\lambda\).