common_utils

Useful helper functions for several files in the ACE library.

check_triangle(l1, l2, l3)

Check if three quantum angular momenta obey triangle conditions.

Note that the order matters.

Parameters:

• l1 (int) – angular momentum quantum number 1

• l2 (int) – angular momentum quantum number 2

• l3 (int) – angular momentum quantum number 3

Returns:

condition – If True, a triangle can be formed.

Return type:

bool

filled_perm(tuples, rank)

Return sympy Permutation object for permutations tabulated from GAP. This function uses rank to fill in missing permutation indices from GAP.

For example tuples = [(0,1)], rank=4 would yeild Permutation(3)(0,1) corresponding to the cycles (0,1)(2)(3).

Parameters:

• tuples (List) – list of touples indicating the partitions of N (e.g., for the (2,2) partition of 4, tuples should be [(0,1),(2,3)]

• rank (int) – Rank of the descriptor (N)

Returns:

Permutation – Permutation object for the permutations.

Return type:

sympy.combinatorics.Permutation

flatten(list_of_lists)

Flatten a list of lists.

Returns input, if input is not a list of lists.

Parameters:

list_of_lists (List) – List of lists.

Returns:

list – Flattened list.

Return type:

List

get_ms(l_vector, M_R=0)

Retrieve the set of m_i combination with sum_i m_i = M_R.

These combinations are retrieved for an arbitrary l multiset.

Parameters:

• l_vector (List) – collection of angular momentum quantum numbers corresponding to spherical harmonics l1,l2…lN

• M_R (int) – Sum to which combinations sum.

Returns:

m_strs – Set of all combinations of m quantum numbers, obeying appropriate -li <= mi <= li

Return type:

List

group_vector_by_nodes(vector, nodes, remainder=None)

Group a vector according to the mapping given in nodes.

If there is a remainder, it is added to the end of the list.

Parameters:

• vector (List) – Vector to be grouped.

• nodes (List) – List of nodes.

• remainder (int) – Remainder to be added to the end of the list.

Returns:

vector_by_tuples – Grouped vector.

Return type:

List

group_vector_by_nodes_pairwise(vector, nodes, remainder=None)

Group a vector of l quantum numbers pairwise.

Parameters:

• vector (List) – vector of l quantum numbers.

• nodes (List) – List of nodes by which to pair vector.

• remainder – Remainder node for binary trees with odd numbers of leaves.

Returns:

vector_by_tuples

Return type:

List

group_vector_by_orbits(vector, partition)

Group vector by orbits.

The partition is a list of integers that sum to the length of the vector.

Parameters:

• vector (List) – Vector to be grouped.

• partition (List) – Partition to be grouped by.

Returns:

vector_by_orbits – Grouped vector.

Return type:

List