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symmetries.py
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symmetries.py
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# #################### Symmetry related functions. Symmetry considerations increase the performance of the solver.######
import os
from os import path
import array as ar
import cubie as cb
from defs import N_TWIST, N_SYM, N_SYM_D4h, N_FLIP, N_SLICE, N_CORNERS, N_UD_EDGES, N_MOVE, N_FLIPSLICE_CLASS, \
N_CORNERS_CLASS, FOLDER
from enums import Corner as Co, Edge as Ed, Move as Mv, BS
INVALID = 65535
uint32 = 'I' if ar.array('I').itemsize >= 4 else 'L' # type codes differ between architectures
# #################### Permutations and orientation changes of the basic symmetries ###################################
# 120° clockwise rotation around the long diagonal URF-DBL
cpROT_URF3 = [Co.URF, Co.DFR, Co.DLF, Co.UFL, Co.UBR, Co.DRB, Co.DBL, Co.ULB]
coROT_URF3 = [1, 2, 1, 2, 2, 1, 2, 1]
epROT_URF3 = [Ed.UF, Ed.FR, Ed.DF, Ed.FL, Ed.UB, Ed.BR, Ed.DB, Ed.BL, Ed.UR, Ed.DR, Ed.DL, Ed.UL]
eoROT_URF3 = [1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1]
# 180° rotation around the axis through the F and B centers
cpROT_F2 = [Co.DLF, Co.DFR, Co.DRB, Co.DBL, Co.UFL, Co.URF, Co.UBR, Co.ULB]
coROT_F2 = [0, 0, 0, 0, 0, 0, 0, 0]
epROT_F2 = [Ed.DL, Ed.DF, Ed.DR, Ed.DB, Ed.UL, Ed.UF, Ed.UR, Ed.UB, Ed.FL, Ed.FR, Ed.BR, Ed.BL]
eoROT_F2 = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
# 90° clockwise rotation around the axis through the U and D centers
cpROT_U4 = [Co.UBR, Co.URF, Co.UFL, Co.ULB, Co.DRB, Co.DFR, Co.DLF, Co.DBL]
coROT_U4 = [0, 0, 0, 0, 0, 0, 0, 0]
epROT_U4 = [Ed.UB, Ed.UR, Ed.UF, Ed.UL, Ed.DB, Ed.DR, Ed.DF, Ed.DL, Ed.BR, Ed.FR, Ed.FL, Ed.BL]
eoROT_U4 = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1]
# reflection at the plane through the U, D, F, B centers
cpMIRR_LR2 = [Co.UFL, Co.URF, Co.UBR, Co.ULB, Co.DLF, Co.DFR, Co.DRB, Co.DBL]
coMIRR_LR2 = [3, 3, 3, 3, 3, 3, 3, 3]
epMIRR_LR2 = [Ed.UL, Ed.UF, Ed.UR, Ed.UB, Ed.DL, Ed.DF, Ed.DR, Ed.DB, Ed.FL, Ed.FR, Ed.BR, Ed.BL]
eoMIRR_LR2 = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
basicSymCube = [cb.CubieCube()] * 4
basicSymCube[BS.ROT_URF3] = cb.CubieCube(cpROT_URF3, coROT_URF3, epROT_URF3, eoROT_URF3)
basicSymCube[BS.ROT_F2] = cb.CubieCube(cpROT_F2, coROT_F2, epROT_F2, eoROT_F2)
basicSymCube[BS.ROT_U4] = cb.CubieCube(cpROT_U4, coROT_U4, epROT_U4, eoROT_U4)
basicSymCube[BS.MIRR_LR2] = cb.CubieCube(cpMIRR_LR2, coMIRR_LR2, epMIRR_LR2, eoMIRR_LR2)
# ######################################################################################################################
# ######################################## Fill SymCube list ###########################################################
# 48 CubieCubes will represent the 48 cube symmetries
symCube = []
cc = cb.CubieCube() # Identity cube
idx = 0
for urf3 in range(3):
for f2 in range(2):
for u4 in range(4):
for lr2 in range(2):
symCube.append(cb.CubieCube(cc.cp, cc.co, cc.ep, cc.eo))
idx += 1
cc.multiply(basicSymCube[BS.MIRR_LR2])
cc.multiply(basicSymCube[BS.ROT_U4])
cc.multiply(basicSymCube[BS.ROT_F2])
cc.multiply(basicSymCube[BS.ROT_URF3])
########################################################################################################################
# ########################################## Fill the inv_idx array ####################################################
# Indices for the inverse symmetries: SymCube[inv_idx[idx]] == SymCube[idx]^(-1)
inv_idx = ar.array('B', [0] * N_SYM)
for j in range(N_SYM):
for i in range(N_SYM):
cc = cb.CubieCube(symCube[j].cp, symCube[j].co, symCube[j].ep, symCube[j].eo)
cc.corner_multiply(symCube[i])
if cc.cp[Co.URF] == Co.URF and cc.cp[Co.UFL] == Co.UFL and cc.cp[Co.ULB] == Co.ULB:
inv_idx[j] = i
break
########################################################################################################################
# ################################# Generate the group table for the 48 cube symmetries ################################
mult_sym = ar.array('B', [0] * (N_SYM * N_SYM))
for i in range(N_SYM):
for j in range(N_SYM):
cc = cb.CubieCube(symCube[i].cp, symCube[i].co, symCube[i].ep, symCube[i].eo)
cc.multiply(symCube[j])
for k in range(N_SYM):
if cc == symCube[k]: # SymCube[i]*SymCube[j] == SymCube[k]
mult_sym[N_SYM * i + j] = k
break
########################################################################################################################
# #### Generate the table for the conjugation of a move m by a symmetry s. conj_move[N_MOVE*s + m] = s*m*s^-1 ##########
conj_move = ar.array('H', [0] * (N_MOVE * N_SYM))
for s in range(N_SYM):
for m in Mv:
ss = cb.CubieCube(symCube[s].cp, symCube[s].co, symCube[s].ep, symCube[s].eo) # copy cube
ss.multiply(cb.moveCube[m]) # s*m
ss.multiply(symCube[inv_idx[s]]) # s*m*s^-1
for m2 in Mv:
if ss == cb.moveCube[m2]:
conj_move[N_MOVE * s + m] = m2
########################################################################################################################
if not os.path.exists(FOLDER):
os.mkdir(FOLDER)
# ###### Generate the phase 1 table for the conjugation of the twist t by a symmetry s. twist_conj[t, s] = s*t*s^-1 ####
fname = "conj_twist"
if not path.isfile(os.path.join(FOLDER, fname)):
print('On the first run, several tables will be created. This takes about 1/2 hour or longer '
'(depending on the hardware).')
print('All tables are stored in ' + path.dirname(path.abspath(path.join(FOLDER, fname))))
print()
print("creating " + fname + " table...")
twist_conj = ar.array('H', [0] * (N_TWIST * N_SYM_D4h))
for t in range(N_TWIST):
cc = cb.CubieCube()
cc.set_twist(t)
for s in range(N_SYM_D4h):
ss = cb.CubieCube(symCube[s].cp, symCube[s].co, symCube[s].ep, symCube[s].eo) # copy cube
ss.corner_multiply(cc) # s*t
ss.corner_multiply(symCube[inv_idx[s]]) # s*t*s^-1
twist_conj[N_SYM_D4h * t + s] = ss.get_twist()
fh = open(os.path.join(FOLDER, fname), "wb")
twist_conj.tofile(fh)
else:
print("loading " + fname + " table...")
fh = open(path.join(FOLDER, fname), 'rb')
twist_conj = ar.array('H')
twist_conj.fromfile(fh, N_TWIST * N_SYM_D4h)
fh.close()
# ######################################################################################################################
# #################### Generate the phase 2 table for the conjugation of the URtoDB coordinate by a symmetrie ##########
fname = "conj_ud_edges"
if not path.isfile(path.join(FOLDER, fname)):
print("creating " + fname + " table...")
ud_edges_conj = ar.array('H', [0] * (N_UD_EDGES * N_SYM_D4h))
for t in range(N_UD_EDGES):
if (t + 1) % 400 == 0:
print('.', end='', flush=True)
if (t + 1) % 32000 == 0:
print('')
cc = cb.CubieCube()
cc.set_ud_edges(t)
for s in range(N_SYM_D4h):
ss = cb.CubieCube(symCube[s].cp, symCube[s].co, symCube[s].ep, symCube[s].eo) # copy cube
ss.edge_multiply(cc) # s*t
ss.edge_multiply(symCube[inv_idx[s]]) # s*t*s^-1
ud_edges_conj[N_SYM_D4h * t + s] = ss.get_ud_edges()
print('')
fh = open(path.join(FOLDER, fname), "wb")
ud_edges_conj.tofile(fh)
else:
print("loading " + fname + " table...")
fh = open(path.join(FOLDER, fname), "rb")
ud_edges_conj = ar.array('H')
ud_edges_conj.fromfile(fh, N_UD_EDGES * N_SYM_D4h)
fh.close()
# ######################################################################################################################
# ############## Generate the tables to handle the symmetry reduced flip-slice coordinate in phase 1 ##################
fname1 = "fs_classidx"
fname2 = "fs_sym"
fname3 = "fs_rep"
if not (path.isfile(path.join(FOLDER, fname1)) and path.isfile(path.join(FOLDER, fname2)) and path.isfile(
path.join(FOLDER, fname3))):
print("creating " + "flipslice sym-tables...")
flipslice_classidx = ar.array('H', [INVALID] * (N_FLIP * N_SLICE)) # idx -> classidx
flipslice_sym = ar.array('B', [0] * (N_FLIP * N_SLICE)) # idx -> symmetry
flipslice_rep = ar.array(uint32, [0] * N_FLIPSLICE_CLASS) # classidx -> idx of representant
classidx = 0
cc = cb.CubieCube()
for slc in range(N_SLICE):
cc.set_slice(slc)
for flip in range(N_FLIP):
cc.set_flip(flip)
idx = N_FLIP * slc + flip
if (idx + 1) % 4000 == 0:
print('.', end='', flush=True)
if (idx + 1) % 320000 == 0:
print('')
if flipslice_classidx[idx] == INVALID:
flipslice_classidx[idx] = classidx
flipslice_sym[idx] = 0
flipslice_rep[classidx] = idx
else:
continue
for s in range(N_SYM_D4h): # conjugate representant by all 16 symmetries
ss = cb.CubieCube(symCube[inv_idx[s]].cp, symCube[inv_idx[s]].co, symCube[inv_idx[s]].ep,
symCube[inv_idx[s]].eo) # copy cube
ss.edge_multiply(cc)
ss.edge_multiply(symCube[s]) # s^-1*cc*s
idx_new = N_FLIP * ss.get_slice() + ss.get_flip()
if flipslice_classidx[idx_new] == INVALID:
flipslice_classidx[idx_new] = classidx
flipslice_sym[idx_new] = s
classidx += 1
print('')
fh = open(path.join(FOLDER, fname1), 'wb')
flipslice_classidx.tofile(fh)
fh.close()
fh = open(path.join(FOLDER, fname2), 'wb')
flipslice_sym.tofile(fh)
fh.close()
fh = open(path.join(FOLDER, fname3), 'wb')
flipslice_rep.tofile(fh)
fh.close()
else:
print("loading " + "flipslice sym-tables...")
fh = open(path.join(FOLDER, fname1), 'rb')
flipslice_classidx = ar.array('H')
flipslice_classidx.fromfile(fh, N_FLIP * N_SLICE)
fh.close()
fh = open(path.join(FOLDER, fname2), 'rb')
flipslice_sym = ar.array('B')
flipslice_sym.fromfile(fh, N_FLIP * N_SLICE)
fh.close()
fh = open(path.join(FOLDER, fname3), 'rb')
flipslice_rep = ar.array(uint32)
flipslice_rep.fromfile(fh, N_FLIPSLICE_CLASS)
fh.close()
########################################################################################################################
# ############ Generate the tables to handle the symmetry reduced corner permutation coordinate in phase 2 #############
fname1 = "co_classidx"
fname2 = "co_sym"
fname3 = "co_rep"
if not (path.isfile(path.join(FOLDER, fname1)) and path.isfile(path.join(FOLDER, fname2)) and path.isfile(
path.join(FOLDER, fname3))):
print("creating " + "corner sym-tables...")
corner_classidx = ar.array('H', [INVALID] * N_CORNERS) # idx -> classidx
corner_sym = ar.array('B', [0] * N_CORNERS) # idx -> symmetry
corner_rep = ar.array('H', [0] * N_CORNERS_CLASS) # classidx -> idx of representant
classidx = 0
cc = cb.CubieCube()
for cp in range(N_CORNERS):
cc.set_corners(cp)
if (cp + 1) % 8000 == 0:
print('.', end='', flush=True)
if corner_classidx[cp] == INVALID:
corner_classidx[cp] = classidx
corner_sym[cp] = 0
corner_rep[classidx] = cp
else:
continue
for s in range(N_SYM_D4h): # conjugate representant by all 16 symmetries
ss = cb.CubieCube(symCube[inv_idx[s]].cp, symCube[inv_idx[s]].co, symCube[inv_idx[s]].ep,
symCube[inv_idx[s]].eo) # copy cube
ss.corner_multiply(cc)
ss.corner_multiply(symCube[s]) # s^-1*cc*s
cp_new = ss.get_corners()
if corner_classidx[cp_new] == INVALID:
corner_classidx[cp_new] = classidx
corner_sym[cp_new] = s
classidx += 1
print('')
fh = open(path.join(FOLDER, fname1), 'wb')
corner_classidx.tofile(fh)
fh.close()
fh = open(path.join(FOLDER, fname2), 'wb')
corner_sym.tofile(fh)
fh.close()
fh = open(path.join(FOLDER, fname3), 'wb')
corner_rep.tofile(fh)
fh.close()
else:
print("loading " + "corner sym-tables...")
fh = open(path.join(FOLDER, fname1), 'rb')
corner_classidx = ar.array('H')
corner_classidx.fromfile(fh, N_CORNERS)
fh.close()
fh = open(path.join(FOLDER, fname2), 'rb')
corner_sym = ar.array('B')
corner_sym.fromfile(fh, N_CORNERS)
fh.close()
fh = open(path.join(FOLDER, fname3), 'rb')
corner_rep = ar.array('H')
corner_rep.fromfile(fh, N_CORNERS_CLASS)
fh.close()
########################################################################################################################