def parallel_spannogram_Dks_eps_psd(k, V, eps, delta):
"""
Args
----
k: int
number of nodes in the output subgraph
V: numpy array
Rank-d approximation matrix
eps, delta: float
Error
Returns
-------
A tuple of (metric, subgraph node index)
Assumption
-----------
- Adjacency matrix (A) is large
"""
n, d = V.shape
supp_opt = 0
metric_opt = 0
Mopt = (1 + 4 / eps) ** d
M = (math.log(delta) - math.log(Mopt)) / math.log(1 - 1 / Mopt)
print(M)
print('V.shape =', V.shape)
t_dot = CumulativeTime("dot")
t_process = CumulativeTime("process")
count = int(round(M))
parspan = ParallelSpannogram(V=V, k=k, threshold=10)
for i in range(count):
progress.render_progress(i / count, width=50)
c = np.random.randn(d, 1)
# Do matrix multiplication
with t_dot.time():
Vc = V.dot(c)
with t_process.time():
parspan.append(Vc)
metric_opt, supp_opt = parspan.process(metric_opt, supp_opt)
with t_process.time():
metric_opt, supp_opt = parspan.flush(metric_opt, supp_opt)
print()
print(t_dot)
print(t_process)
return metric_opt, supp_opt
def spannogram_Dks_eps_psd(k, V, eps, delta):
"""
Args
----
k: int
number of nodes in the output subgraph
V: numpy array
Rank-d approximation matrix
eps, delta: float
Error
Returns
-------
A tuple of (metric, subgraph node index)
Assumption
-----------
- Adjacency matrix (A) is large
"""
n, d = V.shape
supp_opt = 0
metric_opt = 0
Mopt = (1 + 4 / eps) ** d
M = (math.log(delta) - math.log(Mopt)) / math.log(1 - 1 / Mopt)
print(M)
print('V.shape =', V.shape)
t_dot = CumulativeTime("dot")
t_argsort = CumulativeTime("argsort")
t_norm = CumulativeTime("norm-scatter-square")
count = int(round(M))
for i in range(count):
progress.render_progress(i / count, width=50)
c = np.random.randn(d, 1)
# Do matrix multiplication
with t_dot.time():
Vc = V.dot(c)
# Do sort
with t_argsort.time():
indx = np.argsort(Vc, axis=0)
# Get last k
topk = indx[-k:]
# Assume A is huge
with t_norm.time():
metric = np.linalg.norm(V[topk, :]) ** 2
if metric > metric_opt:
metric_opt = metric
supp_opt = topk
print()
print(t_dot)
print(t_argsort)
print(t_norm)
return metric_opt, supp_opt
