coptimality_criterion

pyapprox.optimal_experimental_design.coptimality_criterion(homog_outer_prods, design_factors, design_prob_measure, return_grad=True, noise_multiplier=None, regression_type='lstsq')

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

$$y(x) = F(x)\theta+\eta(x)\epsilon.$$

The criteria is

$$c^T C(\mu) c$$

where

$$C(\mu) = M_1^{-1} M_0 M^{-1}$$

for some vector $c$. Here we assume without loss of genearlity $c=(1,1,...,1)^T$

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 $\mu$ 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

valuefloat

The value of the objective function

gradnp.ndarray (num_design_pts)

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