# Source code for vermouth.geometry

```# -*- coding: utf-8 -*-
# Copyright 2018 University of Groningen
#
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#
# Unless required by applicable law or agreed to in writing, software
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and

"""
Geometric operations.
"""

import numpy as np

[docs]
def distance_matrix(coordinates_a, coordinates_b):
"""
Compute a distance matrix between two set of points.

Notes
-----
This function does **not** account for periodic boundary conditions.

Parameters
----------
coordinates_a: numpy.ndarray
Coordinates of the points in the selections. Each row must correspond
to a point and each column to a dimension.
coordinates_b: numpy.ndarray
Coordinates of the points in the selections. Each row must correspond
to a point and each column to a dimension.

Returns
-------
numpy.ndarray
Rows correspond to the points from `coordinates_a`, columns correspond
from `coordinates_b`.
"""
return np.sqrt(
np.sum(
(coordinates_a[:, np.newaxis, :] - coordinates_b[np.newaxis, :, :]) ** 2,
axis=-1)
)

[docs]
def angle(vector_ba, vector_bc):
"""
Calculate the angle in radians between two vectors.

The function assumes the following situation::

B
/ \\
A   C

It returns the angle between BA and BC.
"""
nominator = np.dot(vector_ba, vector_bc)
denominator = np.linalg.norm(vector_ba) * np.linalg.norm(vector_bc)
cosine = nominator / denominator
# Floating errors at the limits may cause issues.
cosine = np.clip(cosine, -1, 1)
return np.arccos(cosine)

[docs]
def dihedral(coordinates):
"""
Calculate the dihedral angle in radians.

Parameters
----------
coordinates: numpy.ndarray
The coordinates of 4 points defining the dihedral angle. Each row
corresponds to a point, and each column to a dimension.

Returns
-------
float
The calculated angle between -pi and +pi.
"""
vector_ab = coordinates[1, :] - coordinates[0, :]
vector_bc = coordinates[2, :] - coordinates[1, :]
vector_cd = coordinates[3, :] - coordinates[2, :]
normal_abc = np.cross(vector_ab, vector_bc)
normal_bcd = np.cross(vector_bc, vector_cd)
psin = np.dot(normal_abc, vector_cd) * np.linalg.norm(vector_bc)
pcos = np.dot(normal_abc, normal_bcd)
return np.arctan2(psin, pcos)

[docs]
def dihedral_phase(coordinates):
"""
Calculate a dihedral angle in radians with a -pi phase correction.

Parameters
----------
coordinates: numpy.ndarray
The coordinates of 4 points defining the dihedral angle. Each row
corresponds to a point, and each column to a dimension.

Returns
-------
float
The calculated angle between -pi and +pi.