Difference between revisions of "Supercell"

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(example picture)
(headers, withmates=1 as default, tab-completion, see also)
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[[File:SupercellExample.png|200px|thumb|right|Example with 2 unit cells in c-direction, created with: supercell 1,1,2,2x19,withmates=1]]
+
[[File:SupercellExample.png|200px|thumb|right|Example with 2 unit cells in c-direction, created with: supercell 1,1,2,2x19]]
  
= Overview =
+
'''supercell''' can display multiple copies of the unit cell.
 
 
Can display multiple copies of the unit cell.
 
 
Can also fill the unit cell (and its copies) with symmetry mates.
 
Can also fill the unit cell (and its copies) with symmetry mates.
  
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Requires [http://numpy.scipy.org numpy].
 
Requires [http://numpy.scipy.org numpy].
  
= Example =
+
== Example ==
  
 
<source lang="python">
 
<source lang="python">
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supercell 2,1,1, 2x19, green
 
supercell 2,1,1, 2x19, green
 
supercell 1,1,2, 2x19, orange, name=super2
 
supercell 1,1,2, 2x19, orange, name=super2
supercell 1,1,2, 2x19, orange, name=super2, withmates=1
 
 
</source>
 
</source>
  
= The Code =
+
== The Code ==
  
 
<source lang="python">
 
<source lang="python">
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return basis * edges # numpy.array multiplication!
 
return basis * edges # numpy.array multiplication!
  
def supercell(a=1, b=1, c=1, object=None, color='blue', name='supercell', withmates=0):
+
def supercell(a=1, b=1, c=1, object=None, color='blue', name='supercell', withmates=1):
 
'''
 
'''
 
DESCRIPTION
 
DESCRIPTION
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     withmates = bool: also create symmetry mates in displayed cells
 
     withmates = bool: also create symmetry mates in displayed cells
     {default: 0}
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     {default: 1}
  
 
SEE ALSO
 
SEE ALSO
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SEE ALSO
 
SEE ALSO
  
     symexp
+
     symexp, http://www.pymolwiki.org/index.php/SuperSym
 
'''
 
'''
 
if object is None:
 
if object is None:
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cmd.extend('symexpcell', symexpcell)
 
cmd.extend('symexpcell', symexpcell)
 
cmd.extend('supercell', supercell)
 
cmd.extend('supercell', supercell)
 +
 +
# tab-completion of arguments
 +
cmd.auto_arg[3]['supercell'] = [ cmd.object_sc, 'object', '']
 
</source>
 
</source>
 +
 +
== See Also ==
 +
 +
* [[SuperSym]]
 +
* [[symexp]]
  
 
[[Category:Script_Library]]
 
[[Category:Script_Library]]
 
[[Category:Math_Scripts]]
 
[[Category:Math_Scripts]]

Revision as of 03:27, 5 August 2011

Example with 2 unit cells in c-direction, created with: supercell 1,1,2,2x19

supercell can display multiple copies of the unit cell. Can also fill the unit cell (and its copies) with symmetry mates.

See thread on pymol-users mailing list.

Requires numpy.

Example

run supercell.py
fetch 2x19, async=0
supercell 2,1,1, 2x19, green
supercell 1,1,2, 2x19, orange, name=super2

The Code

'''
(c) 2010 Thomas Holder

PyMOL python script (load with `run supercell.py`)
Usage: See "help supercell" and "help symexpcell"
'''

from pymol import cmd, cgo, xray
from math import cos, sin, radians, sqrt
import numpy

def cellbasis(angles, edges):
	'''
	For the unit cell with given angles and edge lengths calculate the basis
	transformation (vectors) as a 4x4 numpy.array
	'''
	rad = [radians(i) for i in angles]
	basis = numpy.identity(4)
	basis[0][1] = cos(rad[2])
	basis[1][1] = sin(rad[2])
	basis[0][2] = cos(rad[1])
	basis[1][2] = (cos(rad[0]) - basis[0][1]*basis[0][2])/basis[1][1]
	basis[2][2] = sqrt(1 - basis[0][2]**2 - basis[1][2]**2)
	edges.append(1.0)
	return basis * edges # numpy.array multiplication!

def supercell(a=1, b=1, c=1, object=None, color='blue', name='supercell', withmates=1):
	'''
DESCRIPTION

    Draw a supercell, as requested by Nicolas Bock on the pymol-users
    mailing list (Subject: [PyMOL] feature request: supercell construction
    Date: 04/12/2010 10:12:17 PM (Mon, 12 Apr 2010 14:12:17 -0600))

USAGE

    supercell a, b, c [, object [, color [, name [, withmates]]]]

ARGUMENTS

    a, b, c = integer: repeat cell in x,y,z direction a,b,c times
    {default: 1,1,1}

    object = string: name of object to take cell definition from

    color = string: color of cell {default: blue}

    name = string: name of the cgo object to create {default: supercell}

    withmates = bool: also create symmetry mates in displayed cells
    {default: 1}

SEE ALSO

    show cell

	'''
	if object is None:
		object = cmd.get_object_list()[0]
	withmates = int(withmates)

	sym = cmd.get_symmetry(object)
	cell_edges = sym[0:3]
	cell_angles = sym[3:6]

	basis = cellbasis(cell_angles, cell_edges)
	assert isinstance(basis, numpy.ndarray)

	ts = list()
	for i in range(int(a)):
		for j in range(int(b)):
			for k in range(int(c)):
				ts.append([i,j,k])

	obj = [
		cgo.BEGIN,
		cgo.LINES,
		cgo.COLOR,
	]
	obj.extend(cmd.get_color_tuple(color))
	
	for t in ts:
		shift = basis[0:3,0:3] * t
		shift = shift[:,0] + shift[:,1] + shift[:,2]
	
		for i in range(3):
			vi = basis[0:3,i]
			vj = [
				numpy.array([0.,0.,0.]),
				basis[0:3,(i+1)%3],
				basis[0:3,(i+2)%3],
				basis[0:3,(i+1)%3] + basis[0:3,(i+2)%3]
			]
			for j in range(4):
				obj.append(cgo.VERTEX)
				obj.extend((shift + vj[j]).tolist())
				obj.append(cgo.VERTEX)
				obj.extend((shift + vj[j] + vi).tolist())

		if withmates:
			symexpcell('m%d%d%d_' % tuple(t), object, *t)

	obj.append(cgo.END)

	cmd.delete(name)
	cmd.load_cgo(obj, name)

def symexpcell(prefix='mate', object=None, a=0, b=0, c=0):
	'''
DESCRIPTION

    Creates all symmetry-related objects for the specified object that
    occur with their bounding box center within the unit cell.

USAGE

    symexpcell prefix, object, [a, b, c]

ARGUMENTS

    prefix = string: prefix of new objects

    object = string: object for which to create symmetry mates

    a, b, c = integer: create neighboring cell {default: 0,0,0}

SEE ALSO

    symexp, http://www.pymolwiki.org/index.php/SuperSym
	'''
	if object is None:
		object = cmd.get_object_list()[0]

	sym = cmd.get_symmetry(object)
	cell_edges = sym[0:3]
	cell_angles = sym[3:6]
	spacegroup = sym[6]

	basis = cellbasis(cell_angles, cell_edges)
	basis = numpy.matrix(basis)

	extent = cmd.get_extent(object)
	center = sum(numpy.array(extent)) * 0.5
	center = numpy.matrix(center.tolist() + [1.0]).T
	center_cell = basis.I * center

	extra_shift = [[float(i)] for i in (a,b,c)]

	i = 0
	matrices = xray.sg_sym_to_mat_list(spacegroup)
	for mat in matrices:
		i += 1

		mat = numpy.matrix(mat)
		shift = numpy.floor(mat * center_cell)
		mat[0:3,3] -= shift[0:3,0]
		mat[0:3,3] += extra_shift

		mat = basis * mat * basis.I
		mat_list = list(mat.flat)

		name = '%s%d' % (prefix, i)
		cmd.create(name, object)
		cmd.transform_object(name, mat_list)
		cmd.color(i+1, name)

cmd.extend('symexpcell', symexpcell)
cmd.extend('supercell', supercell)

# tab-completion of arguments
cmd.auto_arg[3]['supercell'] = [ cmd.object_sc, 'object', '']

See Also