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)θ+η(x)ϵ.

The criteria is

max

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 and quantile.

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.