relentless.model.Square#

class relentless.model.Square(L)#

Square box.

A Square is a special type of Rectangle where all vectors have the same length \(L\).

Parameters:: L (float) – The edge length of the square.

Methods

`as_array`([convention])	Convert to array of lengths and tilt factor.
`coordinate_to_fraction`(r)	Make fractional coordinates from Cartesian coordinates.
`fraction_to_coordinate`(x)	Make Cartesian coordinates from fractional coordinates.
`from_json`(data)	Deserialize from a dictionary.
`to_json`()	Serialize as a dictionary.
`wrap`(positions)	Wrap positions subject to periodic boundary conditions.

Attributes

`extent`	Extent of the region.
`high`
`low`

as_array(convention=None)#

Convert to array of lengths and tilt factor.

Parameters:: convention ({'LAMMPS','HOOMD'}, optional) – Convention to use for the tilt factors. Default of None will use the convention for the box.
Returns:: An array containing (Lx,Ly,xy) according to the convention.
Return type:: numpy.ndarray

coordinate_to_fraction(r)#

Make fractional coordinates from Cartesian coordinates.

The Cartesian coordinates r are projected onto the two (potentially nonorthogonal) basis vectors defining the box to yield fractional coordinates x such that:

\[\mathbf{r} = \mathbf{r}_{\rm low} + (\mathbf{a}\quad\mathbf{b}) \cdot \mathbf{x}\]

where \(\mathbf{r}_{\rm low}\) is the lower bound of the box, i.e., low.

Parameters:: r (array_like) – Cartesian coordinates (or array of).
Returns:: Fractional coordinates x corresponding to r.
Return type:: numpy.ndarray

property extent#

Extent of the region.

Type:: float

fraction_to_coordinate(x)#

Make Cartesian coordinates from fractional coordinates.

The fractional coordinates x are converted to Cartesian coordinates r using the basis vectors of the box. See coordinate_to_fraction() for the definition of these coordinates.

Parameters:: r (array_like) – Fractional coordinates (or array of).
Returns:: Cartesian coordinates r corresponding to x.
Return type:: numpy.ndarray

classmethod from_json(data)#

Deserialize from a dictionary.

Parameters:: data (dict) – The serialized equivalent of the Square object. The keys of data should be ('L',), and its value should be a float.
Returns:: A new Square object constructed from the data.
Return type:: Square

to_json()#

Serialize as a dictionary.

The dictionary contains the box length L.

Returns:: The serialized Square.
Return type:: dict

wrap(positions)#

Wrap positions subject to periodic boundary conditions.

Two-dimensional periodic boundary conditions are applied to ensure the positions lie within the box. This is achieved by converting to fractional coordinates, bounding the fractional coordinates within \([0,1)\), then converting back to Cartesian coordinates.

Parameters:: positions (array_like) – Position vector(s).
Returns:: Wrapped position(s).
Return type:: numpy.ndarray