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#! /usr/bin/env python |
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|
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"""Dipolar Lattice Builder |
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|
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Creates cubic lattices of dipoles to test the dipole-dipole |
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interaction code. |
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|
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Usage: buildDipolarArray |
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|
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Options: |
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-h, --help show this help |
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-x, --array-type-X use one of the basic "X" arrays |
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-y, --array-type-Y use one of the basic "Y" arrays |
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-z, --array-type-Z use one of the basic "Z" arrays |
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-a, --array-type-A use array type "A" (default) |
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-b, --array-type-B use array type "B" |
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-l, --lattice=... use the specified lattice ( SC, FCC, or BCC ) |
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-d, --direction=... use dipole orientation (001, 111, or 011) |
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-c, --constant=... use the specified lattice constant |
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-n use the specified number of unit cells |
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-o, --output-file=... use specified output (.xyz) file |
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|
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Type "A" arrays have nearest neighbor strings of antiparallel dipoles. |
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|
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Type "B" arrays have nearest neighbor strings of antiparallel dipoles |
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if the dipoles are contained in a plane perpendicular to the dipole |
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direction that passes through the dipole. |
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|
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Example: |
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buildDipolarArray -a -l fcc -d 001 -c 5 -n 3 -o A_fcc_001.xyz |
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|
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""" |
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|
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__author__ = "Dan Gezelter (gezelter@nd.edu)" |
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__version__ = "$Revision: 1639 $" |
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__date__ = "$Date: 2011-09-24 16:18:07 -0400 (Sat, 24 Sep 2011) $" |
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|
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__copyright__ = "Copyright (c) 2013 by the University of Notre Dame" |
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__license__ = "OpenMD" |
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|
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import sys |
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import getopt |
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import string |
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import math |
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import numpy |
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|
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def usage(): |
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print __doc__ |
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|
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|
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|
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def createLattice(latticeType, latticeNumber, latticeConstant, dipoleDirection, arrayType, outputFileName): |
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# The following section creates 24 basic arrays from Luttinger and |
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# Tisza: |
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|
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# The six unit vectors are: 3 spatial and 3 to describe the |
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# orientation of the dipole. |
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|
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e1 = numpy.array([1.0,0.0,0.0,0.0,0.0,0.0]) |
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e2 = numpy.array([0.0,1.0,0.0,0.0,0.0,0.0]) |
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e3 = numpy.array([0.0,0.0,1.0,0.0,0.0,0.0]) |
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e4 = numpy.array([0.0,0.0,0.0,1.0,0.0,0.0]) |
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e5 = numpy.array([0.0,0.0,0.0,0.0,1.0,0.0]) |
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e6 = numpy.array([0.0,0.0,0.0,0.0,0.0,1.0]) |
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|
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# Parameters describing the 8 basic arrays: |
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cell = numpy.array([[0,0,0],[0,0,1],[1,0,0],[0,1,0], |
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[1,1,0],[0,1,1],[1,0,1],[1,1,1]]) |
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|
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X = numpy.zeros(384).reshape((8,8,6)) |
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Y = numpy.zeros(384).reshape((8,8,6)) |
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Z = numpy.zeros(384).reshape((8,8,6)) |
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# mX, mY, and mZ arrays have dipole direction flipped |
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mX = numpy.zeros(384).reshape((8,8,6)) |
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mY = numpy.zeros(384).reshape((8,8,6)) |
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mZ = numpy.zeros(384).reshape((8,8,6)) |
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|
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# create the 24 basic arrays using Eq. 12 in Luttinger & Tisza: |
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for i in range(8): |
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which = 0 |
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for l1 in range(2): |
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for l2 in range(2): |
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for l3 in range(2): |
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lvals = numpy.array([l1,l2,l3]) |
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value = math.pow(-1, numpy.dot(cell[i], lvals)) |
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Xvec = (l1*e1 + l2*e2 + l3*e3) + value * e4 |
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Yvec = (l1*e1 + l2*e2 + l3*e3) + value * e5 |
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Zvec = (l1*e1 + l2*e2 + l3*e3) + value * e6 |
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mXvec = (l1*e1 + l2*e2 + l3*e3) - value * e4 |
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mYvec = (l1*e1 + l2*e2 + l3*e3) - value * e5 |
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mZvec = (l1*e1 + l2*e2 + l3*e3) - value * e6 |
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X[i][which] = Xvec |
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Y[i][which] = Yvec |
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Z[i][which] = Zvec |
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mX[i][which] = mXvec |
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mY[i][which] = mYvec |
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mZ[i][which] = mZvec |
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which = which + 1 |
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|
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# The simple cubic array has only one site at the lattice point: |
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lp = numpy.array([0.0,0.0,0.0,0.0,0.0,0.0]) |
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|
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# The body-centered cubic array also has a body-centerered site: |
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bc = numpy.array([0.5,0.5,0.5,0.0,0.0,0.0]) |
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|
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# The face-centered cubic array also has 3 face-centered sites: |
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xy = numpy.array([0.5,0.5,0.0,0.0,0.0,0.0]) |
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yz = numpy.array([0.0,0.5,0.5,0.0,0.0,0.0]) |
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xz = numpy.array([0.5,0.0,0.5,0.0,0.0,0.0]) |
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|
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sc = numpy.array([[0.0,0.0,0.0]]) |
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|
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bcc = numpy.array([[0.0,0.0,0.0], |
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[0.5,0.5,0.5]]) |
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|
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fcc = numpy.array([[0.0,0.0,0.0], |
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[0.5,0.5,0.0], |
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[0.0,0.5,0.5], |
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[0.5,0.0,0.5]]) |
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|
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known_case = False |
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|
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if (arrayType == 'X'): |
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if (int(latticeType)): |
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which = int(latticeType) - 1 |
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basic_array = X[which] |
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known_case = True |
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if (arrayType == 'Y'): |
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if (int(latticeType)): |
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which = int(latticeType) - 1 |
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basic_array = Y[which] |
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known_case = True |
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if (arrayType == 'Z'): |
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if (int(latticeType)): |
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which = int(latticeType) - 1 |
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basic_array = Z[which] |
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known_case = True |
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if (arrayType == 'A'): |
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if (latticeType.lower() == 'sc'): |
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basic_array = Z[5]+lp |
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known_case = True |
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if (latticeType.lower() == 'bcc'): |
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if (dipoleDirection.lower() == '001'): |
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basic_array = numpy.append(Z[1]+lp, mZ[1]+bc, axis=0) |
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known_case = True |
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if (dipoleDirection.lower() == '111'): |
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basic_array = numpy.append(Z[5]+X[7]+Y[6]+lp, |
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Z[5]+X[7]+Y[6]+bc, axis=0) |
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known_case = True |
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if (latticeType.lower() == 'fcc'): |
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if (dipoleDirection.lower() == '001'): |
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basic_array = numpy.append(Z[1]+lp, Z[1]+xy, axis=0) |
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basic_array = numpy.append(basic_array, mZ[1]+yz, axis=0) |
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basic_array = numpy.append(basic_array, mZ[1]+xz, axis=0) |
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known_case = True |
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if (dipoleDirection.lower() == '011'): |
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basic_array = numpy.append(Z[1]+Y[1]+lp, Z[1]+Y[1]+yz, axis=0) |
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basic_array = numpy.append(basic_array, mZ[1]+mY[1]+xy, axis=0) |
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basic_array = numpy.append(basic_array, mZ[1]+mY[1]+xz, axis=0) |
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known_case = True |
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else: |
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if (latticeType.lower() == 'sc'): |
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basic_array = Z[5]+lp |
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known_case = True |
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if (latticeType.lower() == 'bcc'): |
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if (dipoleDirection.lower() == '001'): |
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basic_array = numpy.append(Z[5]+lp, mZ[5]+bc, axis=0) |
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known_case = True |
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if (dipoleDirection.lower() == '111'): |
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basic_array = numpy.append(Z[5]+X[7]+Y[6]+lp, |
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Z[5]+X[7]+Y[6]+bc, axis=0) |
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known_case = True |
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if (latticeType.lower() == 'fcc'): |
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if (dipoleDirection.lower() == '001'): |
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basic_array = numpy.append(Z[1]+lp, Z[1]+yz, axis=0) |
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basic_array = numpy.append(basic_array, mZ[1]+xy, axis=0) |
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basic_array = numpy.append(basic_array, mZ[1]+xz, axis=0) |
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known_case = True |
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if (dipoleDirection.lower() == '011'): |
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basic_array = numpy.append(Z[8]+Y[8]+lp, Z[8]+Y[8]+xy, axis=0) |
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basic_array = numpy.append(basic_array, Z[8]+Y[8]+yz, axis=0) |
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basic_array = numpy.append(basic_array, mZ[8]+mY[8]+xz, axis=0) |
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known_case = True |
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|
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if (not known_case): |
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print "unhandled combination of lattice and dipole direction" |
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print __doc__ |
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|
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print basic_array |
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|
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bravais_lattice = [] |
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for i in range(latticeNumber): |
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for j in range(latticeNumber): |
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for k in range(latticeNumber): |
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for l in range(len(basic_array)): |
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bravais_lattice.append(2*i*e1 + 2*j*e2 + 2*k*e3 + basic_array[l]) |
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|
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outputFile = open(outputFileName, 'w') |
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|
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outputFile.write('<OpenMD version=2>\n') |
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outputFile.write(' <MetaData>\n') |
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outputFile.write(' molecule{\n') |
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outputFile.write(' name = \"D\";\n') |
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outputFile.write(' \n') |
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outputFile.write(' atom[0]{\n') |
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outputFile.write(' type = \"D\";\n') |
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outputFile.write(' position(0.0, 0.0, 0.0);\n') |
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outputFile.write(' orientation(0.0, 0.0, 0.0);\n') |
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outputFile.write(' }\n') |
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outputFile.write(' }\n') |
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outputFile.write(' component{\n') |
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outputFile.write(' type = \"D\";\n') |
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outputFile.write(' nMol = '+ repr(len(bravais_lattice)) + ';\n') |
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outputFile.write(' }\n') |
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|
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outputFile.write(' ensemble = NVE;\n') |
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outputFile.write(' forceField = \"Multipole\";\n') |
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|
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outputFile.write(' cutoffMethod = \"shifted_force\";\n') |
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outputFile.write(' electrostaticScreeningMethod = \"damped\";\n') |
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|
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outputFile.write(' cutoffRadius = 9.0;\n') |
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outputFile.write(' dampingAlpha = 0.18;\n') |
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outputFile.write(' statFileFormat = \"TIME|TOTAL_ENERGY|POTENTIAL_ENERGY|KINETIC_ENERGY|TEMPERATURE|PRESSURE|VOLUME|CONSERVED_QUANTITY|ELECTROSTATIC_POTENTIAL\";\n') |
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outputFile.write(' dt = 1.0;\n') |
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outputFile.write(' runTime = 1.0;\n') |
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outputFile.write(' sampleTime = 1.0;\n') |
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outputFile.write(' statusTime = 1.0;\n') |
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outputFile.write(' </MetaData>\n') |
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outputFile.write(' <Snapshot>\n') |
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outputFile.write(' <FrameData>\n'); |
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outputFile.write(" Time: %.10g\n" % (0.0)) |
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|
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Hxx = 2.0 * latticeConstant * latticeNumber |
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Hyy = 2.0 * latticeConstant * latticeNumber |
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Hzz = 2.0 * latticeConstant * latticeNumber |
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|
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outputFile.write(' Hmat: {{%d, 0, 0}, {0, %d, 0}, {0, 0, %d}}\n' % (Hxx, Hyy, Hzz)) |
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outputFile.write(' </FrameData>\n') |
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outputFile.write(' <StuntDoubles>\n') |
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sdFormat = 'pvqj' |
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index = 0 |
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|
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for i in range(len(bravais_lattice)): |
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xcart = latticeConstant*(bravais_lattice[i][0]) |
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ycart = latticeConstant*(bravais_lattice[i][1]) |
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zcart = latticeConstant*(bravais_lattice[i][2]) |
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dx = bravais_lattice[i][3] |
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dy = bravais_lattice[i][4] |
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dz = bravais_lattice[i][5] |
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|
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uz = numpy.array([dx, dy, dz]) |
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uz = uz/numpy.linalg.norm(uz) |
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|
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uy = numpy.array([0.0, 1.0, 0.0]) |
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uy = uy - uz * numpy.vdot(uy, uz) / numpy.vdot(uz, uz) |
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uy = uy/numpy.linalg.norm(uy) |
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|
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ux = numpy.cross(uy, uz) |
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|
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RotMat = [ux, uy, uz] |
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|
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q = [0.0, 0.0, 0.0, 0.0] |
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|
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# RotMat to Quat code is out of OpenMD's SquareMatrix3.hpp code: |
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|
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t = RotMat[0][0] + RotMat[1][1] + RotMat[2][2] + 1.0 |
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|
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if( t > 1e-6 ): |
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s = 0.5 / math.sqrt( t ) |
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q[0] = 0.25 / s |
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q[1] = (RotMat[1][2] - RotMat[2][1]) * s |
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q[2] = (RotMat[2][0] - RotMat[0][2]) * s |
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q[3] = (RotMat[0][1] - RotMat[1][0]) * s |
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else: |
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ad1 = RotMat[0][0] |
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ad2 = RotMat[1][1] |
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ad3 = RotMat[2][2] |
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|
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if( ad1 >= ad2 and ad1 >= ad3 ): |
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s = 0.5 / math.sqrt( 1.0 + RotMat[0][0] - RotMat[1][1] - RotMat[2][2] ) |
| 282 |
q[0] = (RotMat[1][2] - RotMat[2][1]) * s |
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q[1] = 0.25 / s |
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q[2] = (RotMat[0][1] + RotMat[1][0]) * s |
| 285 |
q[3] = (RotMat[0][2] + RotMat[2][0]) * s |
| 286 |
elif ( ad2 >= ad1 and ad2 >= ad3 ): |
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s = 0.5 / math.sqrt( 1.0 + RotMat[1][1] - RotMat[0][0] - RotMat[2][2] ) |
| 288 |
q[0] = (RotMat[2][0] - RotMat[0][2] ) * s |
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q[1] = (RotMat[0][1] + RotMat[1][0]) * s |
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q[2] = 0.25 / s |
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q[3] = (RotMat[1][2] + RotMat[2][1]) * s |
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else: |
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s = 0.5 / math.sqrt( 1.0 + RotMat[2][2] - RotMat[0][0] - RotMat[1][1] ) |
| 294 |
q[0] = (RotMat[0][1] - RotMat[1][0]) * s |
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q[1] = (RotMat[0][2] + RotMat[2][0]) * s |
| 296 |
q[2] = (RotMat[1][2] + RotMat[2][1]) * s |
| 297 |
q[3] = 0.25 / s |
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|
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qlen = math.sqrt(q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3]) |
| 300 |
q[0] = q[0]/qlen |
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q[1] = q[1]/qlen |
| 302 |
q[2] = q[2]/qlen |
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q[3] = q[3]/qlen |
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|
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outputFile.write("%10d %7s %18.10g %18.10g %18.10g %13e %13e %13e %13e %13e %13e %13e %13e %13e %13e\n" % (index, sdFormat, xcart, ycart, zcart, 0.0, 0.0, 0.0, q[0], q[1], q[2], q[3], 0.0, 0.0, 0.0)) |
| 306 |
index = index+1 |
| 307 |
|
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outputFile.write(" </StuntDoubles>\n") |
| 309 |
outputFile.write(" </Snapshot>\n") |
| 310 |
outputFile.write("</OpenMD>\n") |
| 311 |
outputFile.close() |
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|
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outputFile.close() |
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|
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def main(argv): |
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|
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arrayType = "A" |
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haveOutputFileName = False |
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latticeType = "fcc" |
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dipoleDirection = "001" |
| 321 |
latticeNumber = 3 |
| 322 |
latticeConstant = 4 |
| 323 |
try: |
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opts, args = getopt.getopt(argv, "hxyzabl:d:c:n:o:", ["help","array-type-X", "array-type-Y", "array-type-Z", "array-type-A", "array-type-B", "lattice=" "direction=", "constant=", "output-file="]) |
| 325 |
except getopt.GetoptError: |
| 326 |
usage() |
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sys.exit(2) |
| 328 |
for opt, arg in opts: |
| 329 |
if opt in ("-h", "--help"): |
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usage() |
| 331 |
sys.exit() |
| 332 |
elif opt in ("-x", "--array-type-X"): |
| 333 |
arrayType = "X" |
| 334 |
elif opt in ("-y", "--array-type-Y"): |
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arrayType = "Y" |
| 336 |
elif opt in ("-z", "--array-type-Z"): |
| 337 |
arrayType = "Z" |
| 338 |
elif opt in ("-b", "--array-type-B"): |
| 339 |
arrayType = "B" |
| 340 |
elif opt in ("-l", "--lattice"): |
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latticeType = arg |
| 342 |
elif opt in ("-d", "--direction"): |
| 343 |
dipoleDirection = arg |
| 344 |
elif opt in ("-c", "--constant"): |
| 345 |
latticeConstant = float(arg) |
| 346 |
elif opt in ("-n"): |
| 347 |
latticeNumber = int(arg) |
| 348 |
elif opt in ("-o", "--output-file"): |
| 349 |
outputFileName = arg |
| 350 |
haveOutputFileName = True |
| 351 |
if (not haveOutputFileName): |
| 352 |
usage() |
| 353 |
print "No output file was specified" |
| 354 |
sys.exit() |
| 355 |
|
| 356 |
createLattice(latticeType, latticeNumber, latticeConstant, dipoleDirection, arrayType, outputFileName); |
| 357 |
|
| 358 |
if __name__ == "__main__": |
| 359 |
if len(sys.argv) == 1: |
| 360 |
usage() |
| 361 |
sys.exit() |
| 362 |
main(sys.argv[1:]) |
