Evaluate

During the evaluation of the model, the extrapolation function is defined as

\[f_e(\mathbf{x}^t) = \min_{ \mathbf{x}^c ~\in~\mathbf{X}^c } \lVert \mathbf{x}^t - \mathbf{X}^c \rVert,\]

where \(\mathbf{X}^c\) is the set of centers of the RBF. The extrapolation threshold is defined as

\[d_e = \frac{1}{N_\textrm{R}}\sum_{i=1}^{N_\textrm{R}} \left( \frac{1}{k}\sum_{j=1}^{k} \rVert \mathbf{x}^c_i - \mathbf{x}^c_{i,j} \lVert \right)\]

where \(\mathbf{X}^c_{i,k} = [\mathbf{x}^c_{i,1} \dots \mathbf{x}^c_{i,k}]\) represents the matrix containing the k-nearest neighbors of centroid \(\mathbf{x}^c_i\)

RONAALP.Ronaalp.evaluate(self, x)

Evaluate the reduced-order model at given points.

Parameters

xndarray, shape (n_state,D,)

Array of points where we want to evaluate the surrogate model.

Returns

zndarray, shape(n_state,P,)

Array of interpolated values at x.

extrp_flagndarray, shape(n_state,)

Array of extrapolation flag at x:

0=interpolation, 1=extrapolation.