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.
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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].
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bary_coords
(point)[source]¶ - Parameters
() (point) – Point coordinates.
- Returns
Barycentric coordinations.
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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.
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line_intersection
(point1, point2, tolerance=1e-08)[source]¶ Computes the intersection points of a line with a simplex :param point1: Points that determine the line :type point1: [float] :param point2: Points that determine the line :type point2: [float]
- Returns
points where the line intersects the simplex (0, 1, or 2)
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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]
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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)
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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
subset – List of coords
superset – List of coords
- Returns
list of indices such that superset[indices] = subset
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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
subset – List of frac_coords
superset – List of frac_coords
- Returns
list of indices such that superset[indices] = subset
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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.
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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.
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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.
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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.
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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.
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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.
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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
subset – List of coords
superset – List of coords
- Returns
True if all of subset is in superset.
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is_coord_subset_pbc
(subset, superset, atol=1e-08, mask=None)[source]¶ Tests if all fractional coords in subset are contained in superset.
- Parameters
subset – List of fractional coords
superset – 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[1] cannot be matched to superset[2]
- Returns
True if all of subset is in superset.
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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
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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]
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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[1] cannot be matched to superset[2]
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