sgpykit.tools.idxset_functions

Functions

check_index_admissibility(idx, idx_set[, ...])	Check if a multiindex is admissible with respect to an index set.
check_set_admissibility(I[, matlab_idx])	Check if a given index set is admissible and return the admissible set.
define_functions_for_rule(rule, input2)	Define the level-to-knots and index set functions for a given sparse grid rule.
fast_TD_set(N, w[, base])	Generate the total-degree multi-index set TD(w) in N dimensions.
multiidx_box_set(shape[, min_idx])	Generate a set of multi-dimensional box indices up to a given shape.
multiidx_gen(N, rule, w[, base, multiidx, ...])	Generate all multi-indexes of length N with elements such that rule(M_I) <= w.
plot_multiidx_set(ax, I, *args, **kwargs)	Plot the index set I for 2D and 3D cases.

sgpykit.tools.idxset_functions.check_index_admissibility(idx, idx_set, sort_option=None)

Check if a multiindex is admissible with respect to an index set.

Given a multiindex idx as a row vector, checks if it is admissible with respect to the index set idx_set (matrix with indices as rows). If it is admissible, returns is_adm = True. Otherwise, returns is_adm = False and the function will return the completed_set and a list of the indices added stored in missing_set.

Parameters:

idxarray_like

Multiindex to check for admissibility.

idx_setarray_like

Matrix of indices (rows) representing the index set.

sort_optionstr, optional

If ‘sorting’, returns completed_set and missing_set sorted in lexicographic order.

Returns:

is_admbool

True if the multiindex is admissible, False otherwise.

completed_setndarray

The completed index set after adding missing indices.

missing_setndarray

The list of indices added to make the set admissible.

Notes

The starting idx_set is assumed to be admissible, so its multi-indices will not be checked for admissibility. However, being admissible is not necessary for this function to work, since the core is setdiff, which does not assume any ordering. Assumes 0-based indexing.

sgpykit.tools.idxset_functions.check_set_admissibility(I, matlab_idx=True)

Check if a given index set is admissible and return the admissible set.

Parameters:

Iarray_like

The index set to check for admissibility.

matlab_idxbool, optional

If True, the input index set I is assumed to be in 1-based index format. C will use 1-based indexing then. Default is True.

Returns:

admbool

True if the input index set is admissible, False otherwise.

Cndarray

The admissible index set in lexicographic order. If the input set is not admissible, the missing indices are added to make it admissible. If matlab_idx is True, C will use 1-based indexing.

Notes

The function checks each index in the set for admissibility and adds any missing indices to ensure the set is admissible. A warning is logged if the set is not admissible and indices are added.

sgpykit.tools.idxset_functions.define_functions_for_rule(rule, input2)

Define the level-to-knots and index set functions for a given sparse grid rule.

This function sets the functions lev2nodes and idxset to be used in create_sparse_grid to build the desired isotropic or anisotropic sparse grid.

Parameters:

rulestr

The rule for constructing the sparse grid. Can be one of the following: ‘TP’, ‘TD’, ‘HC’, ‘SM’.

input2int or array_like

If scalar, the number of variables (N). If array_like, the rates vector for anisotropic sparse grids.

Returns:

lev2nodesfunction

A function that maps a level to the number of knots.

idxsetfunction

A function that computes the index set for a given multi-index.

Raises:

ValueError

If the rule is unknown.

sgpykit.tools.idxset_functions.fast_TD_set(N, w, base=0)

Generate the total-degree multi-index set TD(w) in N dimensions.

Parameters:

Nint

Number of dimensions.

wint

Total degree.

baseint, optional

Base index to offset the multiindices (default is 0).

Returns:

ndarray or int

The multiindex set as a numpy array (or scalar if TDsize == 1 and N == 1).

sgpykit.tools.idxset_functions.multiidx_box_set(shape, min_idx=0)

Generate a set of multi-dimensional box indices up to a given shape.

Given an index shape, generates C_with, the box indices set up to that shape. min_idx is either 0 or 1. C_without is C_with without shape itself.

Parameters:

shapearray_like

The shape of the box. Can be a scalar or a list/array of non-negative integers.

min_idxint

Minimum index value, either 0 or 1.

Returns:

tuple

A tuple containing two elements: - C_with : ndarray

The full set of multi-indices up to shape.

• C_withoutndarray

  The set of multi-indices without the last index.

Notes

If shape is a column vector with more than one entry, it is converted to a row vector with all entries equal to the minimum value of shape.

sgpykit.tools.idxset_functions.multiidx_gen(N, rule, w, base=0, multiidx=None, MULTI_IDX=None)

Generate all multi-indexes of length N with elements such that rule(M_I) <= w.

This function recursively explores the tree of all possible multi-indexes and stores the valid ones as rows of the matrix MULTI_IDX. The indices start from the specified base (either 0 or 1).

Parameters:

Nint

Length of the multi-index.

rulecallable

Function that evaluates the rule for a given multi-index.

wfloat

Threshold for the rule.

baseint, optional

Starting index for the multi-index elements (default is 0).

multiidxlist, optional

Current multi-index being constructed (default is None).

MULTI_IDXlist or numpy.ndarray, optional

Accumulator for valid multi-indexes (default is None).

Returns:

numpy.ndarray or int

Matrix of valid multi-indexes (or scalar if single element).

Notes

The function works recursively, exploring in depth the tree of all possible multi-indexes. The starting point is the empty multi-index: [], and MULTI_IDX is empty at the first call of the function. That’s why the call from keyboard comes with [], [] as input argument: multiidx_gen(L,rule,w,[],[]).

sgpykit.tools.idxset_functions.plot_multiidx_set(ax, I, *args, **kwargs)

Plot the index set I for 2D and 3D cases.

Parameters:

axmatplotlib.axes.Axes

The axes to plot on.

Inumpy.ndarray

The index set to plot, shape (n, N) where N is the dimension.

*argstuple, optional

Additional positional arguments passed to the plot function.

**kwargsdict, optional

Additional keyword arguments passed to the plot function.

Returns:

hmatplotlib.collections.PathCollection or matplotlib.lines.Line2D

The plot handle.

Raises:

ValueError

If the dimension of I is greater than 3.