autopdex.spaces.moving_least_squares

autopdex.spaces.moving_least_squares(x, xI, fI, beta, support_radius, static_settings, set)[source]

Compute the moving least squares (MLS) approximation for a given set of points and data.

Parameters:

  • x (jnp.ndarray) – The position of the evaluation point.

  • xI (jnp.ndarray) – The positions of neighboring nodes.

  • fI (jnp.ndarray) – The data at neighboring nodes.

  • beta (float) – The hyperparameter for smoothness, typically in the range [3, 5].

  • support_radius (float) – The radius within which neighboring nodes are considered.

  • static_settings (dict) – Dictionary containing static settings that define the solution space and other parameters. Keywords used: - ‘order of basis functions’: Order of polynomial basis functions. - ‘shape function mode’: Mode of shape function computation (‘direct’ or ‘compiled’). - ‘weight function type’: Type of weight function (‘gaussian’, ‘bump’, ‘gaussian perturbed kronecker’, ‘bump perturbed kronecker’).

  • set (int) – The index of the current set of settings being used.

  • settings (dict) – Dictionary containing dynamic settings. Keywords used: - ‘beta’: Hyperparameter for smoothness. - ‘node coordinates’: Coordinates of nodes. - ‘connectivity’: Connectivity information of integration points with respect to nodes. - ‘support radius’: Support radius for weight function.

Returns:

The computed MLS approximation at the evaluation point, either as shape functions or the evaluated function, depending on wether the compiled mode or direct mode is chosen.

Return type:

jnp.ndarray