def __init__(self, alpha, parts, numpy=False, sparse=True):
'''
alpha: tuple of ints, the weak partition of 8 into 3 parts
parts: tuple of ints, the partitions of each part of alpha
cached_loc: string, location of the cached pickle file of S_8 mod S_alpha irreps
'''
self.alpha = alpha
self.parts = parts
self.cos_reps = coset_reps(sn(8), young_subgroup_perm(alpha))
self.cyc_irrep_func = cyclic_irreps(alpha)
self.yor_dict = None
# cache orientation tuple -> cyclic irrep
self.cyclic_irreps_re = {}
self.cyclic_irreps_im = {}
self.fill_cyclic_irreps()
# also cache the cyclic irreps
if numpy:
pkl_loc = IRREP_LOC_FMT.format(alpha, parts)
self.yor_dict = load_pkl(pkl_loc)
elif sparse:
pkl_loc = IRREP_SP_LOC_FMT.format(alpha, parts)
self.yor_dict = load_sparse_pkl(pkl_loc)
else:
# TODO: deprecate
print('neither sparse nor numpy')
pkl_loc = IRREP_LOC_FMT.format(alpha, parts)
self.np_yor_dict = load_pkl(pkl_loc)
def split_transform(fsplit_lst, irrep_dict, alpha, parts, mem_dict=None):
'''
fsplit_pkl: list of pkl file names of the distance values for a chunk of the total distance values
irrep_dict: irrep dict
alpha: weak partition
parts: list/iterable of partitions of the parts of alpha
'''
print(' Computing transform on splits: {}'.format(fsplit_lst))
cos_reps = coset_reps(sn(8), young_subgroup_perm(alpha))
save_dict = {}
cyc_irrep_func = cyclic_irreps(alpha)
pid = os.getpid()
for fsplit_pkl in fsplit_lst:
with open(fsplit_pkl, 'r') as f:
# dict of function values
pkl_dict = load_pkl(fsplit_pkl)
for perm_tup, tup_dict in pkl_dict.items():
for tup, dists in tup_dict.items():
dist_tot = sum(dists)
perm_rep = irrep_dict[
perm_tup] # perm_rep is a dict of (i, j) -> matrix
block_cyclic_rep = block_cyclic_irreps(
tup, cos_reps, cyc_irrep_func)
mult_yor_block(perm_rep, dist_tot, block_cyclic_rep,
save_dict)
if mem_dict is not None:
mem_dict[pid] = max(check_memory(verbose=False),
mem_dict.get(pid, 0))
del pkl_dict
block_size = wreath_dim(parts)
n_cosets = coset_size(alpha)
mat = convert_yor_matrix(save_dict, block_size, n_cosets)
return mat
def text_split_transform(fsplit_lst, irrep_dict, alpha, parts, mem_dict=None):
'''
fsplit_pkl: list of split file names of the distance values for a chunk of the total distance values
irrep_dict: irrep dict
alpha: weak partition
parts: list/iterable of partitions of the parts of alpha
'''
print(' Computing transform on splits: {}'.format(fsplit_lst))
cos_reps = coset_reps(sn(8), young_subgroup_perm(alpha))
save_dict = {}
cyc_irrep_func = cyclic_irreps(alpha)
pid = os.getpid()
for split_f in fsplit_lst:
with open(split_f, 'r') as f:
for line in tqdm(f):
otup, perm_tup, dist = clean_line(line)
perm_rep = irrep_dict[
perm_tup] # perm_rep is a dict of (i, j) -> matrix
block_cyclic_rep = block_cyclic_irreps(otup, cos_reps,
cyc_irrep_func)
mult_yor_block(perm_rep, dist, block_cyclic_rep, save_dict)
if mem_dict is not None:
mem_dict[pid] = max(check_memory(verbose=False),
mem_dict.get(pid, 0))
block_size = wreath_dim(parts)
n_cosets = coset_size(alpha)
mat = convert_yor_matrix(save_dict, block_size, n_cosets)
return mat
def wreath_yor(alpha, _parts, prefix='/local/hopan/'):
'''
alpha: weak partition of 8 into 3 parts?
_parts: list of partitions of each part of alpha
Return a dict mapping group elmeent in S_8 -> rep
The rep actually needs to be a dictionary of tuples (i, j) -> matrix
where the i, j denote the i, j block in the matrix.
Ex:
alpha = (0, 0, 0, 0, 1, 1, 1, 1)
_parts = [(2,2), (3,1)]
'''
n = sum(alpha)
_sn = perm2.sn(n, prefix)
young_sub = young_subgroup_perm(alpha)
young_sub_set = tup_set(young_sub)
young_yor = young_subgroup_yor(alpha, _parts, os.path.join(prefix, 'irreps'))
reps = coset_reps(_sn, young_sub)
rep_dict = {}
# this part can be parallelized
# loop over the group
# things we need are: group element inv, group element multiplication
# then grabbing the yor for the appropriate yor thing
for g in _sn:
g_rep = {}
for i, t_i in enumerate(reps):
for j, t_j in enumerate(reps):
tiinv_g_tj = t_i.inv() * g * t_j
if tiinv_g_tj.tup_rep in young_sub_set:
g_rep[(i, j)] = young_yor[tiinv_g_tj.tup_rep]
break
rep_dict[g.tup_rep] = g_rep
return rep_dict
def wreath_yor_par(alpha, _parts, prefix='/local/hopan/', par=8):
'''
alpha: weak partition of 8 into 3 parts?
_parts: list of partitions of each part of alpha
Return a dict mapping group elmeent in S_8 -> rep
The rep actually needs to be a dictionary of tuples (i, j) -> matrix
where the i, j denote the i, j block in the matrix.
Ex:
alpha = (0, 0, 0, 0, 1, 1, 1, 1)
_parts = [(2,2), (3,1)]
'''
#print('Wreath yor with {} processes'.format(par))
n = sum(alpha)
_sn = perm2.sn(n, prefix)
young_sub = young_subgroup_perm(alpha)
young_sub_set = tup_set(young_sub)
young_yor = young_subgroup_yor(alpha, _parts, os.path.join(prefix, 'irreps'))
reps = coset_reps(_sn, young_sub)
sn_chunks = chunk(_sn, par)
manager = Manager()
rep_dict = manager.dict()
nprocs = []
for i in range(par):
perms = sn_chunks[i]
proc = Process(target=_proc_yor, args=[perms, young_yor, young_sub_set, reps, rep_dict])
nprocs.append(proc)
for p in nprocs:
p.start()
for p in nprocs:
p.join()
return rep_dict
def par_cube_ift(rank, size, alpha, parts):
start = time.time()
try:
df = load_df('/scratch/hopan/cube/')
irrep_dict = load_irrep('/scratch/hopan/cube/', alpha, parts)
fhat = np.load('/scratch/hopan/cube/fourier/{}/{}.npy'.format(
alpha, parts))
except Exception as e:
print('rank {} | memory usg: {} | exception {}'.format(
rank, check_memory(verbose=False), e))
print(
'Rank {:3d} / {} | load irrep: {:.2f}s | mem: {:.2f}mb | {} {}'.format(
rank, size,
time.time() - start, check_memory(verbose=False), alpha, parts))
cos_reps = coset_reps(sn(8), young_subgroup_perm(alpha))
save_dict = {}
cyc_irrep_func = cyclic_irreps(alpha)
chunk_size = len(df) // size
start_idx = chunk_size * rank
mat = np.zeros(chunk_size, dtype=fhat.dtype)
fhat_t_ravel = fhat.T.ravel()
#print('Rank {} | {:7d}-{:7d}'.format(rank, start_idx, start_idx + chunk_size))
if rank == 0:
print(
'Rank {} | elapsed: {:.2f}s | {:.2f}mb | mat shape: {} | done load | {} {}'
.format(rank,
time.time() - start, check_memory(verbose=False),
fhat.shape, alpha, parts))
for idx in range(start_idx, start_idx + chunk_size):
row = df.loc[idx]
otup = tuple(int(i) for i in row[0])
perm_tup = tuple(int(i) for i in row[1])
#dist = int(row[2])
# actually want the inverse
wmat = wreath_rep(otup, perm_tup, irrep_dict, cos_reps, cyc_irrep_func)
wmat_inv = wmat.conj().T
# trace(rho(ginv) fhat) = trace(fhat rho(ginv)) = vec(fhat.T).dot(vec(rho(ginv)))
#feval = np.dot(fhat.T.ravel(), wmat_inv.ravel())
feval = np.dot(fhat_t_ravel, wmat_inv.ravel())
mat[idx - start_idx] = fhat.shape[0] * feval
if rank == 0:
print('Rank {} | elapsed: {:.2f}s | {:.2f}mb | done add'.format(
rank,
time.time() - start, check_memory(verbose=False)))
del irrep_dict
if rank == 0:
print('Rank {} | elapsed: {:.2f}s | {:.2f}mb | done matrix conversion'.
format(rank,
time.time() - start, check_memory(verbose=False)))
return mat
def check_coset(self, G, H):
reps = cu.coset_reps(G, H)
self.assertEqual(len(reps), len(G) / len(H))
for p in reps:
pH = cu.left_coset(p, H)
set_pH = set(pH)
# check that pH is the same as gH for all g in pH
for g in pH:
gH = cu.left_coset(g, H)
set_gH = set(gH)
self.assertTrue(set_pH == set_gH)
def par_cube_ft(rank, size, alpha, parts):
start = time.time()
try:
df = load_df('/scratch/hopan/cube/')
irrep_dict = load_irrep('/scratch/hopan/cube/', alpha, parts)
except Exception as e:
print('rank {} | memory usg: {} | exception {}'.format(rank, check_memory(verbose=False), e))
print('Rank {:3d} / {} | load irrep: {:.2f}s | mem: {}mb'.format(rank, size, time.time() - start, check_memory(verbose=False)))
cos_reps = coset_reps(sn(8), young_subgroup_perm(alpha))
save_dict = {}
cyc_irrep_func = cyclic_irreps(alpha)
chunk_size = len(df) // size
start_idx = chunk_size * rank
#print('Rank {} | {:7d}-{:7d}'.format(rank, start_idx, start_idx + chunk_size))
if rank == 0:
print('Rank {} | elapsed: {:.2f}s | {:.2f}mb | done load'.format(rank, time.time() - start, check_memory(verbose=False)))
for idx in range(start_idx, start_idx + chunk_size):
row = df.loc[idx]
otup = tuple(int(i) for i in row[0])
perm_tup = tuple(int(i) for i in row[1])
dist = int(row[2])
perm_rep = irrep_dict[perm_tup] # perm_rep is a dict of (i, j) -> matrix
block_cyclic_rep = block_cyclic_irreps(otup, cos_reps, cyc_irrep_func)
mult_yor_block(perm_rep, dist, block_cyclic_rep, save_dict)
if rank == 0:
print('Rank {} | elapsed: {:.2f}s | {:.2f}mb | done add'.format(rank, time.time() - start, check_memory(verbose=False)))
del irrep_dict
block_size = wreath_dim(parts)
n_cosets = coset_size(alpha)
mat = convert_yor_matrix(save_dict, block_size, n_cosets)
if rank == 0:
print('Rank {} | elapsed: {:.2f}s | {:.2f}mb | done matrix conversion'.format(rank, time.time() - start, check_memory(verbose=False)))
return mat
def __init__(self, alpha, parts, pickledir=None):
self.alpha = alpha
self.parts = parts
self.cos_reps = coset_reps(
sn(8), young_subgroup_perm(alpha)) # num blocks = num cosets
self.cyc_irrep_func = cyclic_irreps(alpha)
# cache cyclic irreps
self.cyc_irreps = self.compute_cyclic_irreps()
# load induced perm irrep dict
try:
fname = os.path.join(pickledir, str(alpha), str(parts) + '.pkl')
print('Loading pkl from: {}'.format(fname))
self.ind_irrep_dict = load_pkl(fname)
self.block_size = self.ind_irrep_dict[
(1, 2, 3, 4, 5, 6, 7, 8)].shape[0] // len(self.cos_reps)
end = time.time()
except:
raise Exception(f'Cant load cube irrep {alpha}, {parts}')
def test_wreath_full(self):
o1, p1 = get_wreath('YYRMRMWWRWRYWMYMGGGGBBBB') # 14
o2, p2 = get_wreath('YYBWGYRWMRBWMRMGYBRBGGMW') # 3
o3, p3 = get_wreath('GGBWMGBBMRYGMRYRYBYRWWWM') # 4
w1 = WreathCycSn.from_tup(o1, p1, order=3)
w2 = WreathCycSn.from_tup(o2, p2, order=3)
w3 = WreathCycSn.from_tup(o3, p3, order=3)
prod12 = w1 * w2
prod13 = w1 * w3
o12 = prod12.cyc.cyc
o13 = prod13.cyc.cyc
perm12 = prod12.perm.tup_rep
perm13 = prod13.perm.tup_rep
# load some pickle
alpha = (2, 3, 3)
parts = ((1, 1), (1, 1, 1), (2, 1))
cos_reps = coset_reps(perm2.sn(8), young_subgroup_perm(alpha))
cyc_irrep_func = cyclic_irreps(alpha)
start = time.time()
print('Loading {} | {}'.format(alpha, parts))
yor_dict = load_irrep('/local/hopan/cube/', alpha, parts)
if yor_dict is None:
exit()
print('Done loading | {:.2f}s'.format(time.time() - start))
wreath1 = wreath_rep(o1, p1, yor_dict, cos_reps, cyc_irrep_func, alpha)
wreath2 = wreath_rep(o2, p2, yor_dict, cos_reps, cyc_irrep_func, alpha)
wreath3 = wreath_rep(o3, p3, yor_dict, cos_reps, cyc_irrep_func, alpha)
w12 = np.matmul(wreath1, wreath2)
w13 = np.matmul(wreath1, wreath3)
wd12 = wreath_rep(o12, perm12, yor_dict, cos_reps, cyc_irrep_func,
alpha)
wd13 = wreath_rep(o13, perm13, yor_dict, cos_reps, cyc_irrep_func,
alpha)
self.assertTrue(np.allclose(w12, wd12))
self.assertTrue(np.allclose(w13, wd13))
def test_main(alpha, parts):
'''
Computes the ft via the sparse wreath rep and the non-sparse wreath rep
to double check that the sparse wreath rep is actually correct.
'''
_start = time.time()
st = time.time()
sp_irrep_dict = load_pkl(
'/scratch/hopan/cube/pickles_sparse/{}/{}.pkl'.format(alpha, parts))
end = time.time()
print('Loading sparse irrep dict: {:.2f}s'.format(time.time() - st))
check_memory()
st = time.time()
irrep_dict = load_irrep('/scratch/hopan/cube/', alpha, parts)
print('Loading irrep dict: {:.2f}s'.format(time.time() - st))
check_memory()
# generate a random group element?
st = time.time()
df = load_df('/scratch/hopan/cube/')
fhat = np.load('/scratch/hopan/cube/fourier/{}/{}.npy'.format(
alpha, parts))
print('Loading df: {:.2f}s'.format(time.time() - st))
check_memory()
cyc_irrep_func = cyclic_irreps(alpha)
cos_reps = coset_reps(sn(8), young_subgroup_perm(alpha))
st = time.time()
cyc_irrs = all_cyc_irreps(cos_reps, cyc_irrep_func)
print('Time to compute all cyc irreps: {:.5f}s'.format(time.time() - st))
sp_times = []
sp_mult_times = []
sp_results = np.zeros(len(df), dtype=np.complex128)
coo_times = []
th_sp_times = []
times = []
mult_times = []
z3_irreps = []
results = np.zeros(len(df), dtype=np.complex128)
fhat_t_ravel = fhat.T.ravel()
loop_start = time.time()
for idx in range(len(df)):
row = df.loc[idx]
otup = tuple(int(i) for i in row[0])
perm_tup = tuple(int(i) for i in row[1])
# compute wreath rep
st = time.time()
wmat = wreath_rep(otup, perm_tup, irrep_dict, cos_reps, cyc_irrep_func)
reg_time = time.time() - st
# compute wreath rep multiply
st = time.time()
wmat_inv = wmat.conj().T
feval = np.dot(fhat_t_ravel, wmat_inv.ravel())
reg_mult_time = time.time() - st
results[idx] = feval
# compute sparse wreath rep
st = time.time()
wmat_sp = wreath_rep_sp(otup, perm_tup, sp_irrep_dict, cos_reps,
cyc_irrep_func, cyc_irrs)
sp_time = time.time() - st
if not np.allclose(wmat, wmat_sp.todense()):
print('unequal! | idx = {}'.format(idx))
pdb.set_trace()
# compute sparse wreath rep multiply
st = time.time()
wmat_inv_sp = wmat_sp.conj().T
feval_sp = (wmat_inv_sp.multiply(fhat.T)).sum()
sp_mult_time = time.time() - st
sp_results[idx] = feval_sp
times.append(reg_time)
sp_times.append(sp_time)
mult_times.append(reg_mult_time)
sp_mult_times.append(sp_mult_time)
st = time.time()
coo = wmat_sp.tocoo()
end = time.time()
coo_times.append(end - st)
st = time.time()
ix = torch.LongTensor([coo.row, coo.col])
th_sp_re = torch.sparse.FloatTensor(ix,
torch.FloatTensor(coo.data.real),
torch.Size(coo.shape))
th_sp_cplx = torch.sparse.FloatTensor(ix,
torch.FloatTensor(coo.data.imag),
torch.Size(coo.shape))
end = time.time()
th_sp_times.append(end - st)
st = time.time()
block_scalars = block_cyclic_irreps(otup, cos_reps, cyc_irrep_func)
end = time.time()
z3_irreps.append(end - st)
if idx > 200:
break
print('Normal time: {:.6f}s | Sparse time: {:.6f}s'.format(
np.mean(times), np.mean(sp_times)))
print('Mult time: {:.6f}s | Spmult time: {:.6f}s'.format(
np.mean(mult_times), np.mean(sp_mult_times)))
print('To coo time: {:.6f}s | Torchsptime: {:.6f}s'.format(
np.mean(coo_times), np.mean(th_sp_times)))
print('irrep time: {:.6f}s'.format(np.mean(z3_irreps)))
print('Loop time: {:.2f}s'.format(time.time() - loop_start))
print('Total time: {:.2f}s'.format(time.time() - _start))