polymerist.maths.lattices.coordinates

Representation of vectors of coordinates and elementary distance geometry operations

Attributes

Num

Classes

`Coordinates`	Represention class for encapsulating N-vectors of D-dimensional coordinates, with basic coordinate operations
`BoundingBox`	For representing a minimum bounding box around an N-coordinate vector of D-dimensional points

Module Contents

polymerist.maths.lattices.coordinates.Num

class polymerist.maths.lattices.coordinates.Coordinates(points: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.N, polymerist.genutils.typetools.numpytypes.D], Num] | None = None)[source]

Bases: Generic[Num]

Represention class for encapsulating N-vectors of D-dimensional coordinates, with basic coordinate operations

points = None

n_dims

property n_points: int: The number of points currently stored in the coordinates vector

property dimensions: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.D], Num]: The side lengths of the bounding box along each dimension

property minimum: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.D], Num]: The bounding box vertex with the smallest coordinates in each dimension

property maximum: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.D], Num]: The bounding box vertex with the largest coordinates in each dimension

property extrema: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[2, polymerist.genutils.typetools.numpytypes.D], Num]: A 2xN array of the minimal and maximal bounding box vertices

validate_point(point: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.D], Num]) → None[source]: Check if a point is compatible with the coordinates, or else raise Exception with reason why not

dists_to_point(point: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.D], Num], norm_order: int | None = None) → numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.N], Num][source]: The distance between each point in a coordinate array and a single arbitrary point

weighted_centroid(weights: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.N], Num] | None = None) → numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.D], Num][source]: The average (center-of-mass) coordinate of a vector of coordinates, with optional array of weights for each coordinates

property centroid: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.D], Num]: The unweighted average coordinate of the vector

dists_to_centroid(norm_order: int | None = None, weights: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.N], Num] | None = None) → numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.N], Num][source]: The distance of each coordinate in an array of coordinates to the coordinates’ centroid

property lex_ordered_idxs: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.N, polymerist.genutils.typetools.numpytypes.D], int]: Returns a vector of the position that each point in self.points occupies when ordered lexicographically

property lex_ordered_points: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.N, polymerist.genutils.typetools.numpytypes.D], Num]: Return copy of the points in the lattice in lexicographic order

lex_order_points() → None[source]: Sort points in the lattice in lexicographic order

randomize_points() → None[source]: Place the points in the lattice in a random order

translate(displacement: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.D], Num]) → None[source]: Apply affine shift (translation only) to all points

linear_transformation(matrix: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.D, polymerist.genutils.typetools.numpytypes.D], float], as_coords: bool = False) → numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.N, polymerist.genutils.typetools.numpytypes.D], float] | Coordinates[source]: Accepts an NxN matrix (where D is the dimension of the lattice), returns a linearly-transformed copy of the coordinate points

affine_transformation(matrix: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.D, polymerist.genutils.typetools.numpytypes.D], float], as_coords: bool = False) → numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.N, polymerist.genutils.typetools.numpytypes.D], float] | Coordinates[source]: Accepts an NxN matrix (where D is the dimension of the lattice), returns an affinely-transformed copy of the coordinate points

class polymerist.maths.lattices.coordinates.BoundingBox(coords: Coordinates | numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.N, polymerist.genutils.typetools.numpytypes.D], Num])[source]

Bases: Coordinates

For representing a minimum bounding box around an N-coordinate vector of D-dimensional points

property vertices: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.N, polymerist.genutils.typetools.numpytypes.D], Num]: Alias of the “points” attribute to distinguish use via syntax

property face_indices: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.N, polymerist.genutils.typetools.numpytypes.D], int]: Returns a [2**(n_dim-1) x 2*n_dim] whose points are the indices of (2*n_dims)-tuplets which form a “face” of the bounding box (i.e. shared values of exactly one coordinate)

property face_coords: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.N, polymerist.genutils.typetools.numpytypes.D, 3], int]: Return a [2**(n_dim-1) x 2*n_dim x 3] array in which each row is the set

surrounds(coords: Coordinates | numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.N, polymerist.genutils.typetools.numpytypes.D], Num], strict: bool = False) → numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.N, polymerist.genutils.typetools.numpytypes.D], bool][source]: Boolean mask of whether the coordinates in a point vector lies within the bounding box