eulerpi.core.sparsegrid module
- This module provides functions to handle create Sparse Grids (SGs) and work with them.
All pure SG functions are defined on the unit hypercube $[0,1]^d$.
Warning
The inference with this class is not tested and not recommended for use!
- class SparseGrid(dim: int, max_level_sum: int)[source]
Bases:
object
Each object of this class respresents a sparse grid. In this implementation, a sparse grid is a list of Smolnyak-subspaces. Each subspace is in principle a regular grid of a certain grid width but every second grid point is negelcted.
- dim
The dimension of the sparse grid. This is the same as the dimension of the parameter space.
- Type:
int
- max_level_sum
The maximum sum of all levels of the subspaces. This is the same as the maximum level of the sparse grid.
- Type:
int
- subspace_list
A list of all subspaces that are part of the sparse grid.
- Type:
list
- levels2index
A dictionary that maps the level combination of a subspace to its index in the subspace_list.
- Type:
dict
- nSubspaces
The number of subspaces in the sparse grid.
- Type:
int
- n_points
The number of grid points in the sparse grid.
- Type:
int
- index_list4top_down_sparse_grid_traverse[
A list of indices that defines an ordering of subspaces where low-level subspaces come before high-level ones.
- Type:
list
- allPoints
A matrix of shape #Points x #Dims defining all grid points in the sparse grid.
- Type:
np.ndarray
- compute_coefficients()[source]
When using sparse grids for function interpolation (and quadrature), this function computes the coefficients of all basis function of the whole sparse grid.
Args:
Returns:
- compute_index_list4top_down_sparse_grid_traverse()[source]
Create an ordering of subspaces where low-level subspaces come before high-level ones.
- compute_integral()[source]
Perform sparse grid integration over whole Sparse Grid using the computed coefficients (coeffs) and the volume of each basis function (basis_func_vol)
- compute_n_points()[source]
Iterates over all subspaces of the sparse grid and accumulates the total number of gridpoints.
- eval_function_sg(function: Callable)[source]
Evaluate the provided function for all subspaces of a sparse grid by using Subspace.eval_function
- Parameters:
function (Callable) – The function that is to be evaluated. It must be possible to evaluate the function in a single sparse grid point.
- refine_subspace(current_levels: ndarray, indexRefinedLevel: int) None [source]
Recursive function used to accumulate all subspaces up to a specified level sum in the form of a list It returns the list itself together with a dictionary that maps the level-combination of each subspace onto its index inside the list. This function only lists each subspace once.
- Parameters:
current_levels (np.ndarray) – The level combination of the subspace that is currently being refined. Shape (dim,)
indexRefinedLevel (int) – The index of the level that was refined to form the current subspace.
- class Subspace(levels: ndarray, SG: SparseGrid)[source]
Bases:
object
Objects represent one Smolnyak-Subspace of a sparse grid and are only defined by a level for each dimension.
- eval_function(function: Callable)[source]
Evaluate a function in all points of the respective subspace. This function is typically called by SparseGrid.eval_function_sg.
- Parameters:
function (Callable) – The function that is to be evaluated. It must be possible to evaluate the function in a single sparse grid point.
- basis_1d(points1D: ndarray, centre1D: float64, level: int) ndarray [source]
Evaluate a 1D hat function in an array of doubles. The hat is centered around centre1D and the hat’s level defines its support. The support shrinks exponentially with growing level and a level of 0 is equivalent with full support on [0,1].
- Parameters:
points1D (np.ndarray) – The points at which the hat function should be evaluated.
centre1D (np.double) – The centre of the hat function.
level (int) – The level of the hat function. The level defines the support of the hat function.
- Returns:
The hat function evaluated at the given points.
- Return type:
np.ndarray
- basis_nd(points: ndarray, centre: ndarray, levels: ndarray) ndarray [source]
Use a tensor product to generalise the 1D basis function to arbitrarily high dimensions.
- Parameters:
points (np.ndarray) – The points at which the basis function should be evaluated. Shape: (numPoints, numDims)
centre (np.ndarray) – The centre of the basis function. Shape: (numDims,)
levels (np.ndarray) – The levels of the basis function. Shape: (numDims,)
- Returns:
The basis function evaluated at the given points. Shape: (numPoints,)
- Return type:
np.ndarray
- evaluate_on_sparse_grid(args: Tuple[ndarray, Model, ndarray, DataTransformation, ndarray, ndarray]) ndarray [source]
This function is used to evaluate a function on a sparse grid in parallel. The input args is a tuple containing the function, the sparse grid and the number of processes to be used.
- Parameters:
params (np.ndarray) – The parameters to be evaluated.
model (Model) – The model used for the inference.
data (np.ndarray) – The data points used for the inference.
data_transformation (DataTransformation) – The data transformation used to normalize the data.
data_stdevs (np.ndarray) – The standard deviations of the data points. (Currently the kernel width, #TODO!)
slice (np.ndarray) – The slice defines for which dimensions of the grid points / paramater vectors the marginal density should be evaluated.
- Returns:
The density values for the given params.
- Return type:
np.ndarray
- inference_sparse_grid(model: Model, data: ndarray, data_transformation: DataTransformation, result_manager: ResultManager, slices: List[ndarray], num_processes: int, num_levels: int = 5) Tuple[Dict[str, ndarray], Dict[str, ndarray], Dict[str, ndarray], ResultManager] [source]
Evaluates the transformed parameter density over a set of points resembling a sparse grid, thereby attempting parameter inference. If a data path is given, it is used to load the data for the model. Else, the default data path of the model is used.
- Parameters:
model (Model) – The model describing the mapping from parameters to data.
data (np.ndarray) – The data to be used for inference.
data_transformation (DataTransformation) – The data transformation used to normalize the data.
num_processes (int) – number of processes to use for parallel evaluation of the model.
num_levels (int, optional) – Maximum sparse grid level depth that mainly defines the number of points. Defaults to 5.
- Returns:
The parameter samples, the corresponding simulation results, the corresponding density evaluations for each slice and the result manager used for the inference.
- Return type:
Tuple[Dict[str, np.ndarray], Dict[str, np.ndarray], Dict[str, np.ndarray], ResultManager]
- meshgrid2matrix(meshgrid: list) ndarray [source]
Convert a np.meshgrid into a np.2darray of grid points. The function is mainly used when assigning grid points to Smolnyak-Subspaces.
- Parameters:
meshgrid (list) – A list of np.arrays returned by np.meshgrid
- Returns:
A matrix of shape #Points x #Dims defining all grid points
- Return type:
np.ndarray