/
tucker.py
175 lines (149 loc) · 4.96 KB
/
tucker.py
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from multiprocessing import Pool, cpu_count
from consecutive_ones import circular_ones
from matrify import matrify
import numpy as np
from memoized import memoized
from itertools import combinations, imap, izip, repeat, starmap, product
from sage.all import matrix, SymmetricGroup, permutation_action, uniq, \
Set, partitions, multinomial, vector
from progressbar import ProgressBar
M1_COL = [(1,0,1),(0,1,1),(1,1,0)]
ALL_COL = list(product([0,1], repeat=3))
NONM1_COL = [c for c in ALL_COL if c not in M1_COL]
def __base_matrix(n,k):
base = [1,1] + [0]*n
return np.vstack([np.roll(base,i) for i in range(k)])
@matrify
def m1(n):
return __base_matrix(n,n+2)
@matrify
def m2(n):
base2 = [0] + [1]*(n+2)
mat = np.hstack([__base_matrix(n,n+1), np.zeros([n+1,1],dtype=int)])
return np.vstack([mat, [np.roll(base2,i) for i in [n+1,0]]])
@matrify
def m3(n):
mat = np.hstack([__base_matrix(n,n+1), np.zeros([n+1,1],dtype=int)])
return np.vstack([mat, ([0] + [1]*n + [0,1])])
@matrify
def m4():
base = [1,1] + [0]*4
return np.vstack([np.roll(base,i*2) for i in range(3)] + [[0,1]*3])
@matrify
def m5():
return [[1,1,0,0,0], [1,1,1,1,0], [0,0,1,1,0], [1,0,0,1,1]]
@memoized
def split_to_vector(n, split):
v = np.zeros(n, dtype=int)
split = split if 0 not in split else \
[i for i in range(n) if i not in split]
v[list(split)]=1
return v
def all_submatrices(M, m, n):
return (M.matrix_from_rows_and_columns(list(r),list(c))
for r in combinations(range(M.nrows()), m)
for c in combinations(range(M.ncols()), n))
def matrix_contains(M, S):
"Does M contain a configuration of S as a submatrix?"
m,n = (S.nrows(), S.ncols())
configs = submatrix_configurations(S)
return any(sm in configs for sm in all_submatrices(M, m, n))
def orbit(S):
m,n = (S.nrows(), S.ncols())
Sr = SymmetricGroup(m)
Sc = SymmetricGroup(n)
ret = []
mats = [
permutation_action(h, permutation_action(g, S).transpose()).transpose()
for g in Sr for h in Sc
]
for M in mats:
if M not in ret:
ret.append(M)
return ret
def col_permutation_action(g, M):
M = permutation_action(g, M.transpose()).transpose()
M.set_immutable()
return M
def row_orbit(M):
mats = [permutation_action(g, M) for g in SymmetricGroup(M.nrows())]
[m.set_immutable() for m in mats]
return mats
@memoized
def submatrix_configurations(S):
configs = orbit(S)
[m.set_immutable() for m in configs]
return uniq(configs)
@memoized
def ss_to_matrix(n, ss):
M = matrix(np.vstack([split_to_vector(n,sp) for sp in ss]))
M.set_immutable()
return M
def __incomp_helper(tup):
n,M,S = tup
return (M,matrix_contains(M,S))
def incomp_tucker(n,k,S,parallel=True):
# ss = ProgressBar()(circular_ones(n,k,True))
ss = [ ss_to_matrix(n,ss) for ss in circular_ones(n,k,True) ]
if parallel:
p = Pool(cpu_count())
args = izip(repeat(n),ss,repeat(S))
iter = p.imap_unordered(__incomp_helper, args, 1000)
else:
args = izip(repeat(n),ProgressBar()(ss),repeat(S))
iter = imap(__incomp_helper, args)
return [ss for ss,cont in iter if cont]
def matrices_with_cols(mats, cols):
cols = map(tuple, cols)
return filter(lambda M: sorted(cols) in
imap(sorted, combinations(map(tuple, M.columns()), len(cols))),
mats)
def interesting_permutations(S):
m,n = (S.nrows(), S.ncols())
Sr = SymmetricGroup(m)
Sc = SymmetricGroup(n)
try:
( (g,h) for g in Sr for h in Sc
if g != Sr.identity() and h != Sc.identity() and
S == permutation_action(h, permutation_action(g, S).transpose()).transpose() ).next()
except StopIteration:
return 0
return 1
@memoized
def classify_mats(mats):
d = {}
numones = {}
sys_col = [(1,0,1),(0,1,1),(1,1,0)]
pb = ProgressBar()(mats)
for m in pb:
cols = map(tuple, list(m.columns())[:-1])
map(cols.remove, sys_col)
M = matrix(cols).transpose()
M.set_immutable()
Mcs = submatrix_configurations(M)
try:
k = (k for k in d.keys() if k in Mcs).next()
d[k] += 1
except StopIteration:
d[M] = 1
return d
def mat_class_pp(d):
n = d.keys()[0].ncols() + 3
mtable = dict(zip(starmap(multinomial, partitions(n)), partitions(n)))
for k,v in sorted(d.iteritems(), key=lambda tup:tup[1]):
cols = k.columns()
rows = k.rows()
[c.set_immutable() for c in cols]
[r.set_immutable() for r in rows]
print "%s %s: %i \n" % (k, mtable.get(v, "??"), v)
def class_mats_m1(lst):
d = {0:[],1:[],2:[]}
for M in lst:
x = sum(min(1, M.columns().count(vector(c))) for c in SYS_COL)
d[x].append(M)
return d
def construct_lift(M, v):
M2 = M.matrix_from_columns(range(M.ncols() - 1))
M2 = M2.augment(matrix([v, [0]*3]).transpose())
M2.set_immutable()
return M2