aoptimality_criterion

pyapprox.optimal_experimental_design.aoptimality_criterion(homog_outer_prods, design_factors, design_prob_measure, return_grad=True, noise_multiplier=None, regression_type='lstsq')[source]

Evaluate the A-optimality criterion for a given design probability measure for the linear model

y(x)=F(x)θ+η(x)ϵ.

The criteria is

trace[C(μ)]

where

C(μ)=M11M0M1
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

design_prob_measurenp.ndarray (num_design_pts)

The prob measure μ 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 η(x)

regression_typestring

The method used to compute the coefficients of the linear model. Currently supported options are lstsq and quantile.

Returns
valuefloat

The value of the objective function

gradnp.ndarray (num_design_pts)

The gradient of the objective function. Only if return_grad is True.