rho()#

Lcurve.rho(beta: float) floatSource#

Calculate squared residual norm \(\rho\).

\(\rho\) can be expressed with SVD components as follows:

\[\begin{split}\rho &= \| \mathbf{T}\mathbf{x}_\lambda - \mathbf{b} \|_\mathbf{Q}^2\\ &= \| (\mathbf{F}_\lambda - \mathbf{I}_r) \mathbf{U}^\mathsf{T}\mathbf{B}\mathbf{b} \|^2.\end{split}\]
Parameters:
betafloat

Regularization parameter.

Returns:
float

Squared residual norm \(\rho\).