# pymatgen.optimization package

Optimization utilities.

## pymatgen.optimization.linear_assignment module

This module contains an algorithm to solve the Linear Assignment Problem

class LinearAssignment(costs, epsilon=1e-13)[source]

Bases: `object`

This class finds the solution to the Linear Assignment Problem. It finds a minimum cost matching between two sets, given a cost matrix.

This class is an implementation of the LAPJV algorithm described in: R. Jonker, A. Volgenant. A Shortest Augmenting Path Algorithm for Dense and Sparse Linear Assignment Problems. Computing 38, 325-340 (1987)

Parameters:
• costs – The cost matrix of the problem. cost[i,j] should be the cost of matching x[i] to y[j]. The cost matrix may be rectangular

• epsilon – Tolerance for determining if solution vector is < 0

## pymatgen.optimization.neighbors module

find_points_in_spheres(all_coords, center_coords, r, pbc, lattice, tol=1e-08, min_r=1.0)[source]

For each point in center_coords, get all the neighboring points in all_coords that are within the cutoff radius r. All the coordinates should be Cartesian.

Parameters:
• all_coords – (np.ndarray[double, dim=2]) all available points. When periodic boundary is considered, this is all the points in the lattice.

• center_coords – (np.ndarray[double, dim=2]) all centering points

• r – (float) cutoff radius

• pbc – (np.ndarray[long, dim=1]) whether to set periodic boundaries

• lattice – (np.ndarray[double, dim=2]) 3x3 lattice matrix

• tol – (float) numerical tolerance

• min_r – (float) minimal cutoff to calculate the neighbor list directly. If the cutoff is less than this value, the algorithm will calculate neighbor list using min_r as cutoff and discard those that have larger distances.

Returns:

index1 (n, ), index2 (n, ), offset_vectors (n, 3), distances (n, ). index1 of center_coords, and index2 of all_coords that form the neighbor pair offset_vectors are the periodic image offsets for the all_coords.