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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]]
| + | {{Infobox psico |
| | + | |module = psico.xtal |
| | + | }} |
| | | | |
| − | = Overview =
| + | [[File:SupercellExample.png|200px|thumb|right|Example with 2 unit cells in c-direction, created with: supercell 1,1,2,2x19]] |
| | | | |
| − | Can display multiple copies of the unit cell.
| + | '''supercell''' 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"> |
| − | run supercell.py | + | # import psico.xtal, or run the standalone script: |
| | + | run https://raw.githubusercontent.com/speleo3/pymol-psico/master/psico/xtal.py |
| | + | |
| | fetch 2x19, async=0 | | fetch 2x19, async=0 |
| | 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 = | + | == See Also == |
| − | | |
| − | <source lang="python">
| |
| − | '''
| |
| − | (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=0):
| |
| − | '''
| |
| − | 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
| + | * [[SuperSym]] |
| − | | + | * [[symexp]] |
| − | 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: 0}
| |
| − | | |
| − | 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)):
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| − | for k in range(int(c)):
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| − | ts.append([i,j,k])
| |
| − | | |
| − | obj = [
| |
| − | cgo.BEGIN,
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| − | cgo.LINES,
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| − | cgo.COLOR,
| |
| − | ]
| |
| − | obj.extend(cmd.get_color_tuple(color))
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| − |
| |
| − | 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 = [
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| − | numpy.array([0.,0.,0.]),
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| − | basis[0:3,(i+1)%3],
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| − | basis[0:3,(i+2)%3],
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| − | basis[0:3,(i+1)%3] + basis[0:3,(i+2)%3]
| |
| − | ]
| |
| − | for j in range(4):
| |
| − | obj.append(cgo.VERTEX)
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| − | obj.extend((shift + vj[j]).tolist())
| |
| − | obj.append(cgo.VERTEX)
| |
| − | obj.extend((shift + vj[j] + vi).tolist())
| |
| − | | |
| − | if withmates:
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| − | 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
| |
| − | '''
| |
| − | 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)
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| − | 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)
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| − | cmd.create(name, object)
| |
| − | cmd.transform_object(name, mat_list)
| |
| − | cmd.color(i+1, name)
| |
| − | | |
| − | cmd.extend('symexpcell', symexpcell)
| |
| − | cmd.extend('supercell', supercell)
| |
| − | </source>
| |
| | | | |
| | [[Category:Script_Library]] | | [[Category:Script_Library]] |
| | [[Category:Math_Scripts]] | | [[Category:Math_Scripts]] |
