cherab.inversion.regularization.GCV¶

class cherab.inversion.regularization.GCVSource¶

Bases: Criterion

Generalized Cross-Validation (GCV) criterion.

Note

The theory and implementation of GCV criterion can be seen here.

Methods

gcv(solver, beta)	Calculate of GCV criterion function.
optimize(solver, bounds[, stepsize])	Find the optimal parameter by minimizing GCV with basinhopping.
plot_gcv()	Plot GCV as a function of the regularization parameter.

gcv(solver: _SVDBase, beta: float) → floatSource¶

Calculate of GCV criterion function.

GCV function \(\mathcal{G}(\lambda)\) can be expressed with SVD components as:

\[\mathcal{G}(\lambda) = \frac{\rho}{\left[r - \sum_{i=1}^r f_{\lambda, i}\right]^2}.\]

Parameters:

solver: _SVDBase¶

An _SVDBase instance providing rho.

beta: float¶

Regularization parameter.

Returns:

float – Value of GCV function at a given regularization parameter.

optimize(solver: _SVDBase, bounds: tuple[float, float], stepsize: float = 10, **kwargs: Any) → tuple[float, OptimizeResult]Source¶

Find the optimal parameter by minimizing GCV with basinhopping.

Parameters:

solver: _SVDBase¶

An _SVDBase instance.

bounds: tuple[float, float]¶

(log10_lower, log10_upper) search interval.

stepsize: float = 10¶

Step-size for the underlying global optimizer.

**kwargs: Any¶

Extra arguments forwarded to the optimizer.

Returns:

• lambda_opt (float) – Optimal regularization parameter.

• result (OptimizeResult) – Optimizer result object returned by basinhopping.

plot_gcv(solver: _SVDBase | None = None, axes: None = None, bounds: Collection[float | None] | None = None, n_beta: int = 500, show_min_line: bool = True) → tuple[Axes, Figure]Source¶

plot_gcv(solver: _SVDBase | None = None, axes: Axes | None = None, bounds: Collection[float | None] | None = None, n_beta: int = 500, show_min_line: bool = True) → Axes

Plot GCV as a function of the regularization parameter.

Parameters:

solver: _SVDBase | None = None¶

An _SVDBase instance. If None, the last solver used in optimize() is used.

axes: None = None¶

axes: Axes | None = None

Matplotlib axes to plot on. If None, a new figure and axes are created.

bounds: Collection[float | None] | None = None¶

Boundary pair of log10 of regularization parameters, by default None. If None, the bounds are generated by the solver as described in SVD._generate_bounds(). If you set the bounds like (-10, None), the higher bound is set to \(\log_{10}\sigma_1^2\). Raise an error if a >= b in (a, b).

n_beta: int = 500¶

Number of regularization parameters, by default 500.

show_min_line: bool = True¶

Whether to show a vertical line at the optimal regularization parameter.

Returns:

• axes (Axes) – A matplotlib Axes object.

• fig (Figure) – A matplotlib figure object if axes is None, otherwise None.