triclinic_vectors

mdtools.box.triclinic_vectors(box, dtype=None)[source]

Convert the length-angle representation of a simulation box to the matrix representation.

Convert the length-angle representation [lx, ly, lz, alpha, beta, gamma] (as returned by MDAnalysis.coordinates.base.Timestep.dimensions) to the the matrix representation [[lx1, lx2, lx3], [[lz1, lz2, lz3]], [[lz1, lz2, lz3]]] (as returned by MDAnalysis.coordinates.base.Timestep.triclinic_dimensions).

Parameters:

box (array_like) – The unit cell dimensions of the system, which can be orthogonal or triclinic and must be provided in the same format as returned by MDAnalysis.coordinates.base.Timestep.dimensions: [lx, ly, lz, alpha, beta, gamma]. box can also be an array of boxes of shape (k, 6) (one box for each frame).
dtype (type, optional) – The data type of the output array. If None, the data type is inferred from the input array.

Returns:

box_mat (numpy.ndarray) – The unit cell dimensions of the system in the same format as returned by MDAnalysis.coordinates.base.Timestep.triclinic_dimensions: [[lx1, lx2, lx3], [[lz1, lz2, lz3]], [[lz1, lz2, lz3]]] box_mat will be an array of shape (k, 3, 3) if box had shape (k, 6). Each 3x3 box matrix contains the box vectors as rows!

Shapes
box	box_mat
`(6,)`	`(3, 3)`
`(k, 6)`	`(k, 3, 3)`

See also

mdtools.box.triclinic_box(): Inverse function: Convert the matrix representation of a simulation box to the length-angle representation.
MDAnalysis.lib.mdamath.triclinic_vectors(): Same function: Convert the length-angle representation of a simulation box to the matrix representation.

Notes

The first vector is guaranteed to point along the x-axis, i.e., it has the form (lx, 0, 0).
The second vector is guaranteed to lie in the x/y-plane, i.e., its z-component is guaranteed to be zero.
If any box length is negative or zero, or if any box angle is zero, the box is treated as invalid and an all-zero-matrix is returned.

This function is just a wrapper around MDAnalysis.lib.mdamath.triclinic_vectors() that also allows to parse arrays of boxes.

Examples

>>> box = [1, 2, 3, 90, 90, 90]
>>> mdt.box.triclinic_vectors(box)
array([[1., 0., 0.],
       [0., 2., 0.],
       [0., 0., 3.]])
>>> box = [box, [4, 5, 6, 90, 90, 90]]
>>> mdt.box.triclinic_vectors(box)
array([[[1., 0., 0.],
        [0., 2., 0.],
        [0., 0., 3.]],

       [[4., 0., 0.],
        [0., 5., 0.],
        [0., 0., 6.]]])

>>> import MDAnalysis.lib.mdamath as mdamath
>>> box = [1, 2, 3, 40, 60, 80]
>>> box1 = mdt.box.triclinic_vectors(box)
>>> box1
array([[1.        , 0.        , 0.        ],
       [0.34729636, 1.96961551, 0.        ],
       [1.5       , 2.06909527, 1.57125579]])
>>> box2 = mdamath.triclinic_vectors(box)
>>> box2
array([[1.        , 0.        , 0.        ],
       [0.34729636, 1.9696155 , 0.        ],
       [1.5       , 2.0690954 , 1.5712558 ]], dtype=float32)
>>> np.allclose(box1, box2)
True
>>> box = [4, 5, 6, 100, 110, 120]
>>> box1 = mdt.box.triclinic_vectors(box)
>>> box1
array([[ 4.        ,  0.        ,  0.        ],
       [-2.5       ,  4.33012702,  0.        ],
       [-2.05212086, -2.3878624 ,  5.10753494]])
>>> box2 = mdamath.triclinic_vectors(box)
>>> box2
array([[ 4.       ,  0.       ,  0.       ],
       [-2.5      ,  4.3301272,  0.       ],
       [-2.052121 , -2.3878624,  5.107535 ]], dtype=float32)
>>> np.allclose(box1, box2)
True