wcenter_pos

mdtools.structure.wcenter_pos(pos, weights=None, wrap_pos=False, wrap_result=False, box=None, dtype=None)[source]

Calculate the weighted center of an position array.

Parameters:

pos (array_like) – The position array for which to calculate the weighted center. Must be either of shape (3,), (n, 3) or (k, n, 3), where n is the number of particles and k is the number of frames. If pos has shape (k, n, 3), the center for each frame is computed. If pos has shape (3,), i.e. pos contains the position of a single particle, the weighted center is identical to pos.
weights (None or array_like, optional) – Array of shape (n,) containing the weight of each particle contained in pos. If weights is None, all particles are assumed to have a weight equal to one.
wrap_pos (bool, optional) – If True, wrap all positions in pos back to the primary unit cell using mdtools.box.wrap_pos() before calculating the weighted center. Note that this likely splits molecules across periodic boundaries, which is undesired when calculating their centers. If True, box must be provided.
wrap_result (bool, optional) – If True, wrap the calculated center(s) into the primary unit cell using mdtools.box.wrap_pos(). If True, box must be provided.
box (None or array_like, optional) – See mdtools.box.wrap_pos(). Is ignored if neither wrap_pos nor wrap_result is True.
dtype (type, optional) – The data type of the output array. If None, the data type is inferred from the input array(s).

Returns:

center (numpy.ndarray) – The weighted center of all particle positions in pos per frame.

Shapes when box is `None`.
pos	center
`(3,)`	`(3,)`
`(n, 3)`	`(3,)`
`(k, n, 3)`	`(k, 1, 3)`

Shapes when box is not `None`.
pos	box	center
`(3,)`	`(6,)`	`(3,)`
`(3,)`	`(k, 6)`	`(k, 1, 3)`
`(n, 3)`	`(6,)`	`(3,)`
`(n, 3)`	`(k, 6)`	`(k, 1, 3)`
`(k, n, 3)`	`(6,)`	`(k, 1, 3)`
`(k, n, 3)`	`(k, 6)`	`(k, 1, 3)`

n particles are lumped into one center for each individual frame k.

See also

numpy.average(): Compute the weighted average
MDAnalysis.core.groups.AtomGroup.center(): Weighted center of (compounds of) the group
MDAnalysis.core.groups.AtomGroup.center_of_geometry(): Center of geometry of (compounds of) the group
MDAnalysis.core.groups.AtomGroup.center_of_mass(): Center of mass of (compounds of) the group
mdtools.structure.center(): Different types of centers of (compounds of) an MDAnalysis AtomGroup
mdtools.structure.wcenter(): Weighted center of (compounds of) an MDAnalysis AtomGroup
mdtools.structure.coc(): Center of charge of (compounds of) an MDAnalysis AtomGroup
mdtools.structure.cog(): Center of geometry of (compounds of) an MDAnalysis AtomGroup
mdtools.structure.com(): Center of mass of (compounds of) an MDAnalysis AtomGroup

Notes

The weighted center is calculated according to

\[\mathbf{r}_{center} = \frac{1}{\sum_{i=1}^N w_i} \ \sum_{i=1}^N w_i \mathbf{r}_i\]

where \(r_i\) is the position vector of the \(i\)-th particle, \(w_i\) is its weight and \(N\) is the number of particles.

Examples

Shape of pos is (3,):

>>> pos = np.array([0, 2, 5])
>>> mdt.strc.wcenter_pos(pos)
array([0, 2, 5])
>>> mdt.strc.wcenter_pos(pos, weights=[3])
array([0, 2, 5])
>>> box = np.array([1, 2, 3, 90, 90, 90])
>>> mdt.box.wrap_pos(pos, box=box)
array([0., 0., 2.])
>>> mdt.strc.wcenter_pos(pos, wrap_pos=True, box=box)
array([0., 0., 2.])
>>> mdt.strc.wcenter_pos(pos, wrap_result=True, box=box)
array([0., 0., 2.])
>>> box = np.array([[1, 2, 3, 90, 90, 90],
...                 [2, 3, 4, 90, 90, 90]])
>>> mdt.box.wrap_pos(pos, box=box)
array([[[0., 0., 2.]],

       [[0., 2., 1.]]])
>>> mdt.strc.wcenter_pos(pos, wrap_pos=True, box=box)
array([[[0., 0., 2.]],

       [[0., 2., 1.]]])
>>> mdt.strc.wcenter_pos(pos, wrap_result=True, box=box)
array([[[0., 0., 2.]],

       [[0., 2., 1.]]])
>>> mdt.strc.wcenter_pos(pos, wrap_result=True)
Traceback (most recent call last):
...
ValueError: ...

Shape of pos is (n, 3):

>>> pos = np.array([[0, 2, 5],
...                 [1, 0, 1]])
>>> mdt.strc.wcenter_pos(pos)
array([0.5, 1. , 3. ])
>>> mdt.strc.wcenter_pos(pos, weights=[3, 1])
array([0.25, 1.5 , 4.  ])
>>> box = np.array([1, 2, 3, 90, 90, 90])
>>> mdt.box.wrap_pos(pos, box=box)
array([[0., 0., 2.],
       [0., 0., 1.]])
>>> mdt.strc.wcenter_pos(pos, wrap_pos=True, box=box)
array([0. , 0. , 1.5])
>>> mdt.strc.wcenter_pos(pos, wrap_result=True, box=box)
array([0.5, 1. , 0. ])
>>> box = np.array([[1, 2, 3, 90, 90, 90],
...                 [2, 3, 4, 90, 90, 90]])
>>> mdt.box.wrap_pos(pos, box=box)
array([[[0., 0., 2.],
        [0., 0., 1.]],

       [[0., 2., 1.],
        [1., 0., 1.]]])
>>> mdt.strc.wcenter_pos(pos, wrap_pos=True, box=box)
array([[[0. , 0. , 1.5]],

       [[0.5, 1. , 1. ]]])
>>> mdt.strc.wcenter_pos(pos, wrap_result=True, box=box)
array([[[0.5, 1. , 0. ]],

       [[0.5, 1. , 3. ]]])

Shape of pos is (k, n, 3):

>>> pos = np.array([[[0, 2, 5],
...                  [1, 0, 1]],
...
...                 [[1, 0, 1],
...                  [0, 2, 5]]])
>>> mdt.strc.wcenter_pos(pos)
array([[[0.5, 1. , 3. ]],

       [[0.5, 1. , 3. ]]])
>>> mdt.strc.wcenter_pos(pos, weights=[3, 1])
array([[[0.25, 1.5 , 4.  ]],

       [[0.75, 0.5 , 2.  ]]])
>>> box = np.array([1, 2, 3, 90, 90, 90])
>>> mdt.box.wrap_pos(pos, box=box)
array([[[0., 0., 2.],
        [0., 0., 1.]],

       [[0., 0., 1.],
        [0., 0., 2.]]])
>>> mdt.strc.wcenter_pos(pos, wrap_pos=True, box=box)
array([[[0. , 0. , 1.5]],

       [[0. , 0. , 1.5]]])
>>> mdt.strc.wcenter_pos(pos, wrap_result=True, box=box)
array([[[0.5, 1. , 0. ]],

       [[0.5, 1. , 0. ]]])
>>> box = np.array([[1, 2, 3, 90, 90, 90],
...                 [2, 3, 4, 90, 90, 90]])
>>> mdt.box.wrap_pos(pos, box=box)
array([[[0., 0., 2.],
        [0., 0., 1.]],

       [[1., 0., 1.],
        [0., 2., 1.]]])
>>> mdt.strc.wcenter_pos(pos, wrap_pos=True, box=box)
array([[[0. , 0. , 1.5]],

       [[0.5, 1. , 1. ]]])
>>> mdt.strc.wcenter_pos(pos, wrap_result=True, box=box)
array([[[0.5, 1. , 0. ]],

       [[0.5, 1. , 3. ]]])

Triclinic boxes:

>>> pos = np.array([[0, 2, 5],
...                 [1, 0, 1]])
>>> mdt.strc.wcenter_pos(pos)
array([0.5, 1. , 3. ])
>>> box = np.array([2, 3, 4, 80, 90, 100])
>>> mdt.box.wrap_pos(pos, box=box)
array([[0.        , 1.29469208, 1.0626734 ],
       [0.47905547, 2.95442326, 1.        ]])
>>> mdt.strc.wcenter_pos(pos, wrap_pos=True, box=box)
array([0.23952773, 2.12455767, 1.0313367 ])
>>> mdt.strc.wcenter_pos(pos, wrap_result=True, box=box)
array([0.5, 1. , 3. ])