goptimality_criterion¶
-
pyapprox.optimal_experimental_design.
goptimality_criterion
(homog_outer_prods, design_factors, pred_factors, design_prob_measure, return_grad=True, noise_multiplier=None, regression_type='lstsq')[source]¶ valuate the G-optimality criterion for a given design probability measure for the linear model
\[y(x) = F(x)\theta+\eta(x)\epsilon.\]The criteria is
\[\max{sup}_{xi\in\Xi_\text{pred}} \sigma^2f(x)^T\left(F(\mathcal{X})^TF(\mathcal{X})\right)^{-1}f(x)\]where
\[C(\mu) = M_1^{-1} M_0 M^{-1}\]- Parameters
- homog_outer_prodsnp.ndarray (num_design_factors,num_design_factors,
num_design_pts)
The hessian M_1 of the error for each design point
- design_factorsnp.ndarray (num_design_pts,num_design_factors)
The design factors evaluated at each of the design points
- pred_factorsnp.ndarray (num_pred_pts,num_pred_factors)
The prediction factors g evaluated at each of the prediction points
- design_prob_measurenp.ndarray (num_design_pts)
The prob measure \(\mu\) on the design points
- return_gradboolean
True - return the value and gradient of the criterion False - return only the value of the criterion
- noise_multipliernp.ndarray (num_design_pts)
The design dependent noise function \(\eta(x)\)
- regression_typestring
The method used to compute the coefficients of the linear model. Currently supported options are
lstsq
andquantile
.
- Returns
- valuenp.ndarray (num_pred_pts)
The value of the objective function
- gradnp.ndarray (num_pred_pts,num_design_pts)
The gradient of the objective function. Only if return_grad is True.