# pymatgen.util.coord module¶

Utilities for manipulating coordinates or list of coordinates, under periodic boundary conditions or otherwise. Many of these are heavily vectorized in numpy for performance.

class Simplex(coords)[source]

Bases: object

A generalized simplex object. See http://en.wikipedia.org/wiki/Simplex.

Initializes a Simplex from vertex coordinates.

Parameters

coords ([[float]]) – Coords of the vertices of the simplex. E.g., [[1, 2, 3], [2, 4, 5], [6, 7, 8], [8, 9, 10].

bary_coords(point)[source]
Parameters

() (point) – Point coordinates.

Returns

Barycentric coordinations.

property coords[source]

Returns a copy of the vertex coordinates in the simplex.

in_simplex(point, tolerance=1e-08)[source]

Checks if a point is in the simplex using the standard barycentric coordinate system algorithm.

Taking an arbitrary vertex as an origin, we compute the basis for the simplex from this origin by subtracting all other vertices from the origin. We then project the point into this coordinate system and determine the linear decomposition coefficients in this coordinate system. If the coeffs satisfy that all coeffs >= 0, the composition is in the facet.

Parameters
• point ([float]) – Point to test

• tolerance (float) – Tolerance to test if point is in simplex.

line_intersection(point1, point2, tolerance=1e-08)[source]

Computes the intersection points of a line with a simplex :param point1, point2: Points that determine the line :type point1, point2: [float]

Returns

points where the line intersects the simplex (0, 1, or 2)

point_from_bary_coords(bary_coords)[source]
Parameters

() (bary_coords) – Barycentric coordinates

Returns

Point coordinates

property volume[source]

Volume of the simplex.

all_distances(coords1, coords2)[source]

Returns the distances between two lists of coordinates

Parameters
• coords1 – First set of cartesian coordinates.

• coords2 – Second set of cartesian coordinates.

Returns

2d array of cartesian distances. E.g the distance between coords1[i] and coords2[j] is distances[i,j]

barycentric_coords(coords, simplex)[source]

Converts a list of coordinates to barycentric coordinates, given a simplex with d+1 points. Only works for d >= 2.

Parameters
• coords – list of n coords to transform, shape should be (n,d)

• simplex – list of coordinates that form the simplex, shape should be (d+1, d)

Returns

a LIST of barycentric coordinates (even if the original input was 1d)

coord_list_mapping(subset, superset, atol=1e-08)[source]

Gives the index mapping from a subset to a superset. Subset and superset cannot contain duplicate rows

Parameters

superset (subset,) – List of coords

Returns

list of indices such that superset[indices] = subset

coord_list_mapping_pbc(subset, superset, atol=1e-08)[source]

Gives the index mapping from a subset to a superset. Superset cannot contain duplicate matching rows

Parameters

superset (subset,) – List of frac_coords

Returns

list of indices such that superset[indices] = subset

find_in_coord_list(coord_list, coord, atol=1e-08)[source]

Find the indices of matches of a particular coord in a coord_list.

Parameters
• coord_list – List of coords to test

• coord – Specific coordinates

• atol – Absolute tolerance. Defaults to 1e-8. Accepts both scalar and array.

Returns

Indices of matches, e.g., [0, 1, 2, 3]. Empty list if not found.

find_in_coord_list_pbc(fcoord_list, fcoord, atol=1e-08)[source]

Get the indices of all points in a fractional coord list that are equal to a fractional coord (with a tolerance), taking into account periodic boundary conditions.

Parameters
• fcoord_list – List of fractional coords

• fcoord – A specific fractional coord to test.

• atol – Absolute tolerance. Defaults to 1e-8.

Returns

Indices of matches, e.g., [0, 1, 2, 3]. Empty list if not found.

get_angle(v1, v2, units='degrees')[source]

Calculates the angle between two vectors.

Parameters
• v1 – Vector 1

• v2 – Vector 2

• units – “degrees” or “radians”. Defaults to “degrees”.

Returns

Angle between them in degrees.

get_linear_interpolated_value(x_values, y_values, x)[source]

Returns an interpolated value by linear interpolation between two values. This method is written to avoid dependency on scipy, which causes issues on threading servers.

Parameters
• x_values – Sequence of x values.

• y_values – Corresponding sequence of y values

• x – Get value at particular x

Returns

Value at x.

in_coord_list(coord_list, coord, atol=1e-08)[source]

Tests if a particular coord is within a coord_list.

Parameters
• coord_list – List of coords to test

• coord – Specific coordinates

• atol – Absolute tolerance. Defaults to 1e-8. Accepts both scalar and array.

Returns

True if coord is in the coord list.

in_coord_list_pbc(fcoord_list, fcoord, atol=1e-08)[source]

Tests if a particular fractional coord is within a fractional coord_list.

Parameters
• fcoord_list – List of fractional coords to test

• fcoord – A specific fractional coord to test.

• atol – Absolute tolerance. Defaults to 1e-8.

Returns

True if coord is in the coord list.

is_coord_subset(subset, superset, atol=1e-08)[source]

Tests if all coords in subset are contained in superset. Doesn’t use periodic boundary conditions

Parameters

superset (subset,) – List of coords

Returns

True if all of subset is in superset.

is_coord_subset_pbc(subset, superset, atol=1e-08, mask=None)[source]

Tests if all fractional coords in subset are contained in superset.

Parameters
• superset (subset,) – List of fractional coords

• atol (float or size 3 array) – Tolerance for matching

• mask (boolean array) – Mask of matches that are not allowed. i.e. if mask[1,2] == True, then subset cannot be matched to superset

Returns

True if all of subset is in superset.

lattice_points_in_supercell(supercell_matrix)[source]

Returns the list of points on the original lattice contained in the supercell in fractional coordinates (with the supercell basis). e.g. [[2,0,0],[0,1,0],[0,0,1]] returns [[0,0,0],[0.5,0,0]]

Parameters

supercell_matrix – 3x3 matrix describing the supercell

Returns

numpy array of the fractional coordinates

pbc_diff(fcoords1, fcoords2)[source]

Returns the ‘fractional distance’ between two coordinates taking into account periodic boundary conditions.

Parameters
• fcoords1 – First set of fractional coordinates. e.g., [0.5, 0.6, 0.7] or [[1.1, 1.2, 4.3], [0.5, 0.6, 0.7]]. It can be a single coord or any array of coords.

• fcoords2 – Second set of fractional coordinates.

Returns

Fractional distance. Each coordinate must have the property that abs(a) <= 0.5. Examples: pbc_diff([0.1, 0.1, 0.1], [0.3, 0.5, 0.9]) = [-0.2, -0.4, 0.2] pbc_diff([0.9, 0.1, 1.01], [0.3, 0.5, 0.9]) = [-0.4, -0.4, 0.11]

pbc_shortest_vectors(lattice, fcoords1, fcoords2, mask=None, return_d2=False)[source]

Returns the shortest vectors between two lists of coordinates taking into account periodic boundary conditions and the lattice.

Parameters
• lattice – lattice to use

• fcoords1 – First set of fractional coordinates. e.g., [0.5, 0.6, 0.7] or [[1.1, 1.2, 4.3], [0.5, 0.6, 0.7]]. It can be a single coord or any array of coords.

• fcoords2 – Second set of fractional coordinates.

• mask (boolean array) – Mask of matches that are not allowed. i.e. if mask[1,2] == True, then subset cannot be matched to superset

• return_d2 (boolean) – whether to also return the squared distances

Returns

array of displacement vectors from fcoords1 to fcoords2 first index is fcoords1 index, second is fcoords2 index