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#!/usr/bin/sage
import sys
import numpy as np
from sage.all import *
def get_VSpU( M ):
N = copy(M)
for i in range(N.nrows()):
N[i,i%3] -= 1
S,U,V = N.smith_form()
Sp = Matrix( QQ, S.transpose() )
for i in range(3):
if not Sp[i,i]==0:
Sp[i,i] = 1.0 / Sp[i,i]
return V*Sp*U
def get_VSpU_sets(g1s, g2s):
VSpU_sets = []
generator_sets = []
for g3 in ( False, True ): # for inversion
for g1 in g1s:
for g2 in g2s:
if g2 is not False:
if np.equal(g1, g2).all():
continue
if np.equal(g1, np.dot(inv, g2)).all():
continue
genes = [g1, g2]
else:
genes = [g1,]
if g3:
genes_new = []
for g in genes:
if np.linalg.det(g) < 0:
genes_new.append(np.dot(inv, g))
else:
genes_new.append(g)
genes_new.append(inv)
if np.linalg.det(g1) < 0:
is_found = False
for g1_comp in g1s:
if np.equal(genes_new[0], g1_comp).all():
is_found = True
break
if is_found:
continue
if g2 is not False:
if np.linalg.det(g2) < 0:
is_found = False
for g2_comp in g2s:
if np.equal(genes_new[1], g2_comp).all():
is_found = True
break
if is_found:
continue
else:
genes_new = genes
M = Matrix(3, 3, genes_new[0])
if len(genes_new) > 1:
for g in genes_new[1:]:
M = M.stack(Matrix(3, 3, g))
VSpU_sets.append(get_VSpU(M))
generator_sets.append( M )
return VSpU_sets, generator_sets
def get_rotation_primitive( g1s, g2s, T ):
if T is not None:
g1s_new = []
g2s_new = []
g1s_old = []
g2s_old = []
for g in g1s:
# print g, "-->"
try:
M = Matrix(ZZ,T*Matrix(QQ, g)*T.inverse())
# print M
g1s_new.append(np.array(M))
g1s_old.append(g)
except TypeError:
print "Not integer matrix, pass this matrix"
for g in g2s:
if g:
# print g, "-->"
try:
M = Matrix(ZZ, T*Matrix(QQ, g)*T.inverse())
# print M
g2s_new.append(np.array(M))
g2s_old.append(g)
except TypeError:
print "Not integer matrix, pass this matrix"
else:
g2s_new.append(False)
g2s_old.append(False)
return g1s_new, g2s_new, g1s_old, g2s_old
def write_generators(generator_sets):
print "{"
for count, M in enumerate( generator_sets ):
print " { /* %d */" % (count+1)
for i in range( 3 ):
print " { ",
for j in range( 3 ):
for k in range( 3 ):
if M.nrows() // 3 > i:
print "%d," % M[i*3+j,k],
else:
print " 0,",
print "},"
print " },"
print "};"
def write_VSpU(VSpU_sets):
print "{"
for count, VSpU in enumerate( VSpU_sets ):
print " { /* %d */" % (count+1)
for colvals in VSpU:
print " {",
for i in range( 9 ):
if i < len( colvals ):
num = colvals[i].numerator()
den = colvals[i].denominator()
if den == 1:
print "%d," % ( num ),
else:
print "%d.0/%d," % ( num, den ),
else:
print " 0,",
print "},"
print " },"
print "};"
identity = [[ 1, 0, 0],
[ 0, 1, 0],
[ 0, 0, 1]]
inv = [[-1, 0, 0],
[ 0,-1, 0],
[ 0, 0,-1]]
# Tetragonal
rot4z = [[ 0,-1, 0],
[ 1, 0, 0],
[ 0, 0, 1]]
rot4zi = [[ 0, 1, 0],
[-1, 0, 0],
[ 0, 0,-1]]
rot2z = [[-1, 0, 0],
[ 0,-1, 0],
[ 0, 0, 1]]
rot2zi = [[ 1, 0, 0],
[ 0, 1, 0],
[ 0, 0,-1]]
rot2x = [[ 1, 0, 0],
[ 0,-1, 0],
[ 0, 0,-1]]
rot2xi = [[-1, 0, 0],
[ 0, 1, 0],
[ 0, 0, 1]]
rot3xyz = [[ 0, 0, 1],
[ 1, 0, 0],
[ 0, 1, 0]]
rot3xyzi = [[ 0, 0,-1],
[-1, 0, 0],
[ 0,-1, 0]]
hexa2_ab = [[ 0,-1, 0],
[-1, 0, 0],
[ 0, 0,-1]]
hexa2_abi = [[ 0, 1, 0],
[ 1, 0, 0],
[ 0, 0, 1]]
rot6z = [[ 1,-1, 0],
[ 1, 0, 0],
[ 0, 0, 1]]
rot6zi = [[-1, 1, 0],
[-1, 0, 0],
[ 0, 0,-1]]
trigo2ab = [[ 0, 1, 0],
[ 1, 0, 0],
[ 0, 0,-1]]
trigo2abi = [[ 0,-1, 0],
[-1, 0, 0],
[ 0, 0, 1]]
rot3z = [[ 0,-1, 0],
[ 1,-1, 0],
[ 0, 0, 1]]
rot3zi = [[ 0, 1, 0],
[-1, 1, 0],
[ 0, 0,-1]]
rot2y = [[-1, 0, 0],
[ 0, 1, 0],
[ 0, 0,-1]]
rot2yi = [[ 1, 0, 0],
[ 0,-1, 0],
[ 0, 0, 1]]
BCC = Matrix(QQ, [[ 0, 1, 1],
[ 1, 0, 1],
[ 1, 1, 0]])
FCC = Matrix(QQ, [[-1, 1, 1],
[ 1,-1, 1],
[ 1, 1,-1]])
CC = Matrix(QQ, [[ 1,-1, 0],
[ 1, 1, 0],
[ 0, 0, 1]])
BC = Matrix(QQ, [[ 1, 0, 1],
[ 0, 1, 0],
[-1, 0, 1]])
AC = Matrix(QQ, [[ 1, 0, 0],
[ 0, 1, 1],
[ 0,-1, 1]])
RC = Matrix(QQ, [[ 1, 0, 1],
[-1, 1, 1],
[ 0,-1, 1]])
# Parse options
from optparse import OptionParser
parser = OptionParser()
parser.set_defaults(is_tricli=False,
is_monocli=False,
is_ortho=False,
is_tetra=False,
is_rhombo=False,
is_trigo=False,
is_hexa=False,
is_cubic=False,
is_bcc=False,
is_fcc=False,
is_ac=False,
is_bc=False,
is_cc=False,
is_rc=False)
parser.add_option("--tricli", dest="is_tricli",
action="store_true")
parser.add_option("--monocli", dest="is_monocli",
action="store_true")
parser.add_option("--ortho", dest="is_ortho",
action="store_true")
parser.add_option("--tetra", dest="is_tetra",
action="store_true")
parser.add_option("--rhombo", dest="is_rhombo",
action="store_true")
parser.add_option("--trigo", dest="is_trigo",
action="store_true")
parser.add_option("--hexa", dest="is_hexa",
action="store_true")
parser.add_option("--cubic", dest="is_cubic",
action="store_true")
parser.add_option("--bcc", dest="is_bcc",
action="store_true")
parser.add_option("--fcc", dest="is_fcc",
action="store_true")
parser.add_option("--ac", dest="is_ac",
action="store_true")
parser.add_option("--bc", dest="is_bc",
action="store_true")
parser.add_option("--cc", dest="is_cc",
action="store_true")
parser.add_option("--rc", dest="is_rc",
action="store_true")
parser.add_option("-g", dest="is_generator",
action="store_true")
(options, args) = parser.parse_args()
g1s = None
g2s = None
g1s_old = None
g2s_old = None
if options.is_tricli:
g1s = ( identity, )
g2s = ( False, )
if options.is_monocli:
g1s = ( rot2x, rot2y, rot2z, rot2xi, rot2yi, rot2zi )
g2s = ( False, )
if options.is_bcc:
g1s, g2s, g1s_old, g2s_old = get_rotation_primitive( g1s, g2s, BCC )
if options.is_ac:
g1s, g2s, g1s_old, g2s_old = get_rotation_primitive( g1s, g2s, AC )
if options.is_bc:
g1s, g2s, g1s_old, g2s_old = get_rotation_primitive( g1s, g2s, BC )
if options.is_cc:
g1s, g2s, g1s_old, g2s_old = get_rotation_primitive( g1s, g2s, CC )
if options.is_ortho:
g1s = ( rot2z, rot2zi )
g2s = ( rot2x, rot2xi )
if options.is_bcc:
g1s, g2s, g1s_old, g2s_old = get_rotation_primitive( g1s, g2s, BCC )
if options.is_fcc:
g1s, g2s, g1s_old, g2s_old = get_rotation_primitive( g1s, g2s, FCC )
if options.is_ac:
g1s, g2s, g1s_old, g2s_old = get_rotation_primitive( g1s, g2s, AC )
if options.is_bc:
g1s, g2s, g1s_old, g2s_old = get_rotation_primitive( g1s, g2s, BC )
if options.is_cc:
g1s, g2s, g1s_old, g2s_old = get_rotation_primitive( g1s, g2s, CC )
if options.is_tetra:
g1s = ( rot4z, rot4zi )
g2s = ( False, rot2x, rot2xi )
if options.is_bcc:
g1s, g2s, g1s_old, g2s_old = get_rotation_primitive( g1s, g2s, BCC )
# if options.is_rhombo:
# g1s = ( rot3xyz, rot3xyzi )
# g2s = ( False, hexa2_ab, trigo2ab )
if options.is_trigo:
g1s = ( rot3z, rot3zi )
g2s = ( False, hexa2_ab, trigo2ab, hexa2_abi, trigo2abi )
if options.is_rc: # hP
g1s, g2s, g1s_old, g2s_old = get_rotation_primitive( g1s, g2s, RC )
if options.is_rhombo: # hR
g1s = ( rot3z, rot3zi )
g2s = ( False, hexa2_ab, trigo2ab, hexa2_abi, trigo2abi )
g1s, g2s, g1s_old, g2s_old = get_rotation_primitive( g1s, g2s, RC )
g1s_old = None
g2s_old = None
if options.is_hexa:
g1s = ( rot6z, rot6zi )
g2s = ( False, hexa2_ab, hexa2_abi )
if options.is_cubic:
g1s = ( rot4z, rot2z, rot4zi, rot2zi )
g2s = ( rot3xyz, rot3xyzi )
if options.is_bcc:
g1s, g2s, g1s_old, g2s_old = get_rotation_primitive( g1s, g2s, BCC )
if options.is_fcc:
g1s, g2s, g1s_old, g2s_old = get_rotation_primitive( g1s, g2s, FCC )
if g1s is None:
print "Option is needed. See \'make_VSpU.py -h\'"
else:
if g1s_old is None:
VSpU_sets, generator_sets = get_VSpU_sets( g1s, g2s )
else:
VSpU_sets = get_VSpU_sets( g1s, g2s )[0]
generator_sets = get_VSpU_sets( g1s_old, g2s_old )[1]
centering = ""
if options.is_fcc:
centering = "_F"
if options.is_bcc:
centering = "_I"
if options.is_ac:
centering = "_A"
if options.is_bc:
centering = "_B"
if options.is_cc:
centering = "_C"
if options.is_generator:
if options.is_tricli:
print "static int tricli_generators[][3][9] ="
if options.is_monocli:
print "static int monocli_generators[][3][9] ="
if options.is_ortho:
print "static int ortho_generators[][3][9] ="
if options.is_tetra:
print "static int tetra_generators[][3][9] ="
if options.is_trigo:
if options.is_rc:
print "static int rhombo_h_generators[][3][9] ="
else:
print "static int trigo_generators[][3][9] ="
if options.is_rhombo:
print "static int rhombo_p_generators[][3][9] ="
if options.is_hexa:
print "static int hexa_generators[][3][9] ="
if options.is_cubic:
print "static int cubic_generators[][3][9] ="
write_generators(generator_sets)
print
else:
if options.is_tricli:
print "static double tricli_VSpU[][3][9] ="
if options.is_monocli:
print "static double monocli%s_VSpU[][3][9] =" % centering
if options.is_ortho:
print "static double ortho%s_VSpU[][3][9] =" % centering
if options.is_tetra:
print "static double tetra%s_VSpU[][3][9] =" % centering
if options.is_trigo:
if options.is_rc:
print "static double rhombo_h_VSpU[][3][9] ="
else:
print "static double trigo_VSpU[][3][9] ="
if options.is_rhombo:
print "static double rhombo_p_VSpU[][3][9] ="
if options.is_hexa:
print "static double hexa_VSpU[][3][9] ="
if options.is_cubic:
print "static double cubic%s_VSpU[][3][9] ="
write_VSpU(VSpU_sets)
print
|
