sgpykit.tools.type_and_property_check_functions

Functions

`is_sparse_grid`(S)	Check if the input is a sparse grid.
`is_tensor_grid`(S)	Check if a given struct is a tensor grid or a tensor grid in a sparse grid struct.
`isequal_sparse_grids`(S1, S2[, tol])	Compare two sparse grids for equality.
`isequal_tensor_grids`(T1, T2[, tol])	Compare two tensor grids field by field, checking that the two grids are identical and accounting for numerical tolerance when comparing knots and weights.
`islexico`(a, b)	Check lexicographic order of vectors.
`islexico_tol`(a, b, tol)	Check if vector a is lexicographically less-or-equal than vector b up to a numerical tolerance.
`isreduced`(S)	Check if a given object is a reduced sparse grid.

sgpykit.tools.type_and_property_check_functions.is_sparse_grid(S)[source]

Check if the input is a sparse grid.

A sparse grid is a vector of structs with fields ‘knots’, ‘weights’, ‘size’, ‘knots_per_dim’, ‘m’, ‘coeff’, ‘idx’.

Parameters:

Sobject: Input object to check.

Returns:

bool: True if S is a sparse grid, False otherwise.

sgpykit.tools.type_and_property_check_functions.is_tensor_grid(S)[source]

Check if a given struct is a tensor grid or a tensor grid in a sparse grid struct.

Parameters:

Sstruct: Input struct to be checked.

Returns:

int: 1 if S is a tensor grid, -1 if S is a tensor grid in a sparse grid struct, 0 otherwise.

Notes

A tensor grid is a struct with fields: ‘knots’, ‘weights’, ‘size’, ‘knots_per_dim’, ‘m’. A tensor grid in a sparse grid struct is a struct with two more fields: ‘coeff’, ‘idx’.

sgpykit.tools.type_and_property_check_functions.isequal_sparse_grids(S1, S2, tol=1e-14)[source]

Compare two sparse grids for equality.

This function checks if two sparse grids are identical tensor grid by tensor grid, accounting for numerical tolerance when comparing knots and weights.

Parameters:

S1StructArray: First sparse grid to compare.
S2StructArray: Second sparse grid to compare.
tolfloat, optional: Tolerance used when comparing points and weights. Default is 1e-14.

Returns:

iseqbool: True if the sparse grids are equal, False otherwise.
whatfieldstr: Name of the first field found to be different, or ‘length’ if the sparse grids have a different number of tensor grids.

Notes

The function first checks if the inputs are valid sparse grids. Then, it compares the number of tensor grids in each sparse grid. If they differ, it returns False and ‘length’. Otherwise, it iterates through each tensor grid, comparing them using isequal_tensor_grids. If any tensor grid is found to be different, it returns False and the name of the field that differs. If all tensor grids are equal, it returns True and an empty string.

sgpykit.tools.type_and_property_check_functions.isequal_tensor_grids(T1, T2, tol=1e-14)[source]

Compare two tensor grids field by field, checking that the two grids are identical and accounting for numerical tolerance when comparing knots and weights.

Parameters:

T1tensor grid: First tensor grid to compare.
T2tensor grid: Second tensor grid to compare.
tolfloat, optional: Tolerance used when comparing points and weights. Default is 1e-14.

Returns:

iseqbool: True if the tensor grids are equal, False otherwise.
whatfieldstr: The name of the first field of the two tensor grids that are found different, or ‘size’ if the two sparse grids have a different number of tensor grids.

sgpykit.tools.type_and_property_check_functions.islexico(a, b)[source]

Check lexicographic order of vectors.

Checks if vector a is lexicographically less than or equal to vector b. Returns True if a <= b in lexicographic sense, False otherwise.

Parameters:

aarray_like: First vector for comparison.
barray_like: Second vector for comparison.

Returns:

bool: True if a is lexicographically less than or equal to b, False otherwise.

Examples

>>> islexico([1, 2, 3], [1, 2, 5])
True
>>> islexico([1, 2, 3], [1, 2, 3])
True
>>> islexico([1, 2, 3], [1, 2, 1])
False
>>> islexico([2, 2, 3], [1, 7, 1])
False
>>> islexico([1, 7, 3], [1, 5, 3])
False

sgpykit.tools.type_and_property_check_functions.islexico_tol(a, b, tol)[source]

Check if vector a is lexicographically less-or-equal than vector b up to a numerical tolerance.

Parameters:

aarray_like: First input vector.
barray_like: Second input vector.
tolfloat: Numerical tolerance for component-wise comparison.

Returns:

bool: True if a is lexicographically less-or-equal than b up to the given tolerance, False otherwise.

Examples

>>> ii = [1, 3]
>>> jj = [1, 4]
>>> islexico_tol(ii, jj, 1e-12)  # Returns True
>>> ii = [1+1e-13, 3]
>>> islexico_tol(ii, jj, 1e-12)  # Returns True
>>> islexico_tol(ii, jj, 1e-14)  # Returns False

sgpykit.tools.type_and_property_check_functions.isreduced(S)[source]

Check if a given object is a reduced sparse grid.

A reduced sparse grid is a struct with fields ‘knots’, ‘m’, ‘weights’, ‘n’, ‘size’.

Parameters:

Sobject: The object to check.

Returns:

int: 1 if S is a reduced sparse grid, 0 otherwise.