# mdtraj.utils.box_vectors_to_lengths_and_angles¶

mdtraj.utils.box_vectors_to_lengths_and_angles(a, b, c)

Convert box vectors into the lengths and angles defining the box.

Parameters
anp.ndarray

the vector defining the first edge of the periodic box (length 3), or an array of this vector in multiple frames, where a[i,:] gives the length 3 array of vector a in each frame of a simulation

bnp.ndarray

the vector defining the second edge of the periodic box (length 3), or an array of this vector in multiple frames, where b[i,:] gives the length 3 array of vector a in each frame of a simulation

cnp.ndarray

the vector defining the third edge of the periodic box (length 3), or an array of this vector in multiple frames, where c[i,:] gives the length 3 array of vector a in each frame of a simulation

Returns
a_lengthscalar or np.ndarray

length of Bravais unit vector a

b_lengthscalar or np.ndarray

length of Bravais unit vector b

c_lengthscalar or np.ndarray

length of Bravais unit vector c

alphascalar or np.ndarray

angle between vectors b and c, in degrees.

betascalar or np.ndarray

angle between vectors c and a, in degrees.

gammascalar or np.ndarray

angle between vectors a and b, in degrees.

Examples

>>> a = np.array([2,0,0], dtype=float)
>>> b = np.array([0,1,0], dtype=float)
>>> c = np.array([0,1,1], dtype=float)
>>> l1, l2, l3, alpha, beta, gamma = box_vectors_to_lengths_and_angles(a, b, c)
>>> (l1 == 2.0) and (l2 == 1.0) and (l3 == np.sqrt(2))
True
>>> np.abs(alpha - 45) < 1e-6
True
>>> np.abs(beta - 90.0) < 1e-6
True
>>> np.abs(gamma - 90.0) < 1e-6
True