Evaluation Module

ammorph.evaluation.evaluate(rbffunc, points, centers, gamma, beta=None, polynomial_order=None, out=None)

evaluate the RBF-interpolation at points with centers and weights

Evaluates the interpolation according to formula

\[s_i = \sum_j^{N_H} \gamma_j \cdot \phi(\| \boldsymbol{x}_i - \boldsymbol{h}_j \|) + \beta_0 + \beta_1 x_i + \beta_2 y_i + \beta_3 z_i + \beta_4 x_i^2 + \ldots\]

Parameters

• rbffunc (str) – String that defines the rbf function \(\phi(r)\) used for assembly. The function string must contain the character ‘r’ as argument.

• points (array_like) – point coordinates of the active points \(x_i\) to interpolate. points is an array of dimension \(N_A \times d\) where \(N_A\) is the number of active points and \(d\) is the spatial dimension.

• centers (array_like) – point coordinates of the handle points \(h_i\) used as centers for the radial basis functions. centers is an array of dimension \(N_H \times d\) where \(N_H\) is the number of handle points and \(d\) is the spatial dimension.

• gamma (array_like) – weights to weight the radial basis function for interpolation. gamma is an array of dimension :math:’N_H’.

• beta (array_like, optional) – If polynomial order is not None, beta must be specified. It is an array for weighting the augmentation terms (monomials)

• polynomial_order (int, optional) – If None (default), no polynomial terms are used as augmentation for interpolation. If int, polynomial terms up to order polynomial_order are added as augmentation. In this case beta must be specified for defining the weights.

• out (array_like, optional) – Array to write the interpolated redult into (optional)

Returns

s – Interpolated values dimension \(N_A\)

Return type

array_like