def get_generalized_distribution(self,
params,
scale=1,
exog=None,
exposure=None,
offset=None):
"""
Returns a random number generator for the predictive distribution.
Parameters
----------
params : array-like
The model parameters.
scale : scalar
The scale parameter.
exog : array-like
The predictor variable matrix.
Returns a frozen random number generator object. Use the
``rvs`` method to generate random values.
Notes
-----
Due to the behavior of ``scipy.stats.distributions objects``,
the returned random number generator must be called with
``gen.rvs(n)`` where ``n`` is the number of observations in
the data set used to fit the model. If any other value is
used for ``n``, misleading results will be produced.
"""
fit = self.predict(params, exog, exposure, offset, linear=False)
import scipy.stats.distributions as dist
if isinstance(self.family, families.Gaussian):
return dist.norm(loc=fit, scale=np.sqrt(scale))
elif isinstance(self.family, families.Binomial):
return dist.binom(n=1, p=fit)
elif isinstance(self.family, families.Poisson):
return dist.poisson(mu=fit)
elif isinstance(self.family, families.Gamma):
alpha = fit / float(scale)
return dist.gamma(alpha, scale=scale)
else:
raise ValueError(
"get_generalized_distribution not implemented for %s" %
self.family.name)
def add(self):
g = self.g
rng = self.rng
n = len(g)
g.add_node(n)
# Random base of new attachment
n1 = random.randint(0, len(g)-2) # exclude endpoint and n
#print 'graph status:', len(g), g.number_of_edges(), n, n1#, g.nodes()
g.add_edge(n, n1)
inner_nodes = set((n, n1))
shell_nodes = inner_nodes
for dist, n_at_dist in enumerate(self.ns):
if self.pois and n_at_dist>0:
n_at_dist = poisson(n_at_dist).rvs()
dist += 1 # dist starts from 1, not zero
nodes_available = set.union(*(set(g.neighbors(_))
for _ in shell_nodes))
#print ' nodes_available:', nodes_available
#print ' inner_nodes:', inner_nodes
shell_nodes = nodes_available - inner_nodes
#print ' shell_nodes:', shell_nodes
#print ' ', dist, n_at_dist, len(inner_nodes), len(nodes_available)
if len(shell_nodes) == 0:
# We can never add any more from now on.
break
n_at_dist = min(n_at_dist, len(shell_nodes))
if n_at_dist == 0:
inner_nodes |= shell_nodes
continue
new_edges = rng.sample(shell_nodes, n_at_dist)
#print ' new edges:', new_edges, len(shell_nodes)
for n2 in new_edges:
#print ' linking to:', n2
if n2 == n or n2 == n1: raise
assert not g.has_edge(n, n2)
g.add_edge(n, n2)
inner_nodes |= nodes_available
def add(self):
g = self.g
rng = self.rng
n = len(g)
nodes_linked = set()
neigh_counts = collections.defaultdict(int)
g.add_node(n)
nodes_linked.add(n)
# First link
n1 = random.choice(xrange(n))
assert not g.has_edge(n, n1)
g.add_edge(n, n1)
nodes_linked.add(n1)
#print "adding", n, n1
# Compute neighbor counts
for neigh in g.neighbors(n1):
neigh_counts[neigh] += 1
def pick_next():
counts = collections.defaultdict(list)
for n, count in neigh_counts.iteritems():
if n in nodes_linked:
continue
counts[count].append(n)
max_count = max(counts)
node = random.choice(counts[max_count])
#print "node %s has %d triads (%s) (%s)"%(
# node, max_count,
# counts[max_count],
# sorted((c, len(ns)) for c,ns in counts.iteritems()))
return node
def pick_T():
itemsweights = [ ]
for n, count in neigh_counts.iteritems():
if n in nodes_linked:
continue
try:
weight = exp(count / float(self.T) )
except OverflowError:
weight = 1e200
itemsweights.append((n, weight))
chooser = pcd.util.WeightedChoice(itemsweights)
#if len(itemsweights) > 1 \
# and any(_>1 for _ in neigh_counts.values()) \
# and len(set(_ for x,_ in itemsweights)) > 1:
# #raise
# pass
return chooser.choice()
def pick_TN():
counts = collections.defaultdict(list)
for n, count in neigh_counts.iteritems():
if n in nodes_linked:
continue
counts[count].append(n)
print [(count, len(x)) for count,x in sorted(counts.iteritems())]
itemsweights = [ ]
for count, ncounts in counts.iteritems():
weight = exp(count / float(self.T) )
itemsweights.append((count, weight))
chooser = pcd.util.WeightedChoice(itemsweights)
count = chooser.choice()
return random.choice(counts[count])
if self.mode == 'T':
pick_next = pick_T
elif self.mode == 'TN':
pick_next = pick_TN
elif self.mode is None:
pass
else:
raise ValueError
# How many extra edges should we add?
if self.mmean > self.m:
from scipy.stats.distributions import poisson
pgen = poisson(self.mmean-self.m)
m = pgen.rvs() + self.mmean
else:
m = self.m
m = min(m, len(g)-1)
# Add additional edges
for i in range(m-1):
if rng.uniform(0,1) <= self.p:
# Add triadic closure edge
n1 = pick_next()
#if n1 is None:
# continue
for neigh in g.neighbors(n1):
neigh_counts[neigh] += 1
else:
while True:
n1 = random.randint(0, len(g)-2) # exclude endpoint and n
if n1 not in nodes_linked:
break
assert not g.has_edge(n, n1)
g.add_edge(n, n1)
#print "adding", n, n1
nodes_linked.add(n1)
return random.choice(counts[count])
if self.mode == 'T':
pick_next = pick_T
elif self.mode == 'TN':
pick_next = pick_TN
elif self.mode is None:
pass
else:
raise ValueError
# How many extra edges should we add?
if self.mmean > self.m:
from scipy.stats.distributions import poisson
pgen = poisson(self.mmean-self.m)
m = pgen.rvs() + self.mmean
else:
m = self.m
m = min(m, len(g)-1)
# Add additional edges
for i in range(m-1):
if rng.uniform(0,1) <= self.p:
# Add triadic closure edge
n1 = pick_next()
#if n1 is None:
# continue
for neigh in g.neighbors(n1):
neigh_counts[neigh] += 1
else:
while True:
if __name__ == "__main__":
print(os.cpu_count())
volfractions = norm(loc=0.3, scale=0.05).ppf(lhs(50, samples=1)).reshape(
50,
) #norm(loc=0.3, scale=0.1).ppf(lhs(50, samples=1)).reshape(50,) # this gives the x values having y-values equal to volume_fraction
# rmins_1 = uniform(1.1, 2).ppf(lhs(50, samples=1)).reshape(50,) # 0.1 < volume fraction < 0.4 => 1.1 < Rmin < 3 ; Rmin suit la loi uniforme (1.1, 3 )
# rmins_2 = uniform(2, 3).ppf(lhs(50, samples=1)).reshape(50,) # 0.4 < volume fraction < 0.6 => 2 < Rmin < 3 ; Rmin suit la loi uniforme (2, 3 )
# rmins_3 = uniform(3, 4).ppf(lhs(50, samples=1)).reshape(50,) # volume fraction > 0.6 => 3 < Rmin < 4; Rmin suit la loi uniforme (3, 4 )
filters = bernoulli(0.5).ppf(lhs(50, samples=1)).reshape(
50, ) # either present (1) or absent (0)
tetas = uniform(0, 180).ppf(lhs(100, samples=1)).reshape(100, ).tolist(
) #uniform(0, 60).ppf(lhs(30, samples=1)).reshape(30,).tolist()+ uniform(60, 130).ppf(lhs(30, samples=1)).reshape(30,).tolist() + uniform(130, 180).ppf(lhs(30, samples=1)).reshape(30,).tolist()
nbr_loads = poisson(2).ppf(lhs(50, samples=1)).reshape(
50, ) # most probable nbr_loads is 2
windows = poisson(100).ppf(lhs(50, samples=1)).reshape(50, )
nx = 100
ny = 100
window = int(nx / 2) #
possible_fixed_nodes = np.arange(0, ny + 1).tolist() + [
m * (ny + 1) - 1 for m in range(2, nx + 1)
] + np.sort(np.arange(
(ny + 1) * nx, (nx + 1) * (ny + 1))).tolist()[::-1] + np.sort(
np.asarray([m * (ny + 1) for m in range(1, nx)])).tolist()[::-1]
total_nbr_samples = 100
params_list = []
for cnt in range(total_nbr_samples):
volfraction = random.choice(volfractions)
rmin = 2.4 # after the first generation phase, we have concluded that rmin should be less than 3 and in the range 2 to 2.8
def simulate_gsm(demand_mean=3, lead_time=12, threshold=0.95, N=200000):
"""
This simulates the "inventory position" at a single node/service station or a single stage,
under a Possion demand profile for each time step.
It is an attempt to simulate, as precisely as possible and consequently, as abstractly as
necessarily, a policy generated in accordance with Willem's published GSM framework.
It models the "inventory position" for a given demand and lead time for when we expect a given
"failure rate".
Lead time: Time to collect any necessary materials from where ever they are process an SKU by
the node/warehouse/service station.
Failure rate is described at one point in the original Willem's paper as "the percentage of time
that the safety stock covers the demand variation". This is an over-arching explanation, but to
be more precise, it is the percentage of time steps for which the "inventory position" is
negative.
N.B. This is not the same as the percentage of SKUs that were not available when required.
Inventory position: Calculated per time step, after any deliveries have been recieved, it is
the number of SKUs in stock - the number of SKUs that are outstanding because they were not
available when required.
We assume that SKUs that were not available when required are ordered on the time step that
were found to be unavailable and these unfullfilled orders are fullfilled in exactly the time
in takes to replenish an SKU.
The time to replenish an SKU (tau [Willems]) is lead time because we assume the service time of
the node is zero and it has no upstream supply nodes, so incoming service time is zero.
As part of the simulation. the base stock levels required at t=0 for the desired failure rate
to be achieved, according to Willem's algorithm, are calculated for this simple, single station
"network".
:param demand_mean: The mean number of SKUs demanded per timestep.
:param lead_time: The time it takes to replenish an SKU.
:param threshold: The percentage of days for which the "inventory position" is negative.
:param N: The number of time steps in the simulation
"""
p = poisson(demand_mean * lead_time)
# Base stock in a integer, so we define bounds:
max_base_stock = p.ppf(threshold)
min_base_stock = max_base_stock - 1
inventory_position = np.array([])
s = np.random.poisson(size=N,
lam=demand_mean) # Sample demand for all time steps
s = np.append(
[0] * lead_time,
s) # Add a buffer of no demand to simulate the time nothing has
# had a chance to be replenished.
# Compute the inventory position at "the end of" each (simulated-instantaneous) time step:
for i in range(N):
inventory_position = np.append(
inventory_position, min_base_stock - np.sum(s[i:i + lead_time]))
# Calculate the percentage of "failed" days:
lowest_expected_failure_rate = np.mean(
inventory_position < -(max_base_stock - min_base_stock))
highest_expected_failure_rate = np.mean(inventory_position < 0)
print("With a base stock of: {}, the simulation has an error rate of {}".
format(min_base_stock, highest_expected_failure_rate))
print("With a base stock of: {}, the simulation has an error rate of {}".
format(max_base_stock, lowest_expected_failure_rate))
failure_rate = (1 - threshold)
print("The desired failure rate of {} IS{}within the simulated bounds".
format(
round(failure_rate, 3), " " if
(lowest_expected_failure_rate < failure_rate <
highest_expected_failure_rate) else " NOT "))
return inventory_position
def poisson(lam=1.0):
return dists.poisson(mu=lam)
def poisson(lam=1.0):
return dists.poisson(mu=lam)
al_df = DataFrame({ 'events' : x ,
'agg_loss' : z})
return al_df
def ragglosses_dnq(n, k, rvlf, rvld):
d_size = int(n / k)
al_df = ragglosses(d_size, rvlf, rvld)
for i in arange(1, k):
al_df = concat([al_df, ragglosses(d_size,
rvlf,
rvld)])
gc.collect()
al_df = al_df.sort('agg_loss')
al_df.index = arange(n)
return al_df
rtlg_0 = ract_tlgamma(29.35061739, 3.29749312, 5063.457993, Inf)
rpois_0 = poisson(44.51)
df_0 = ragglosses_dnq(1e6, 10, rpois_0, rtlg_0)
df_0.to_hdf('test_01.hdf5', key='al_df')
""" ----------------------------------------------------------------------------
End note:
(end note starts here)
============================================================================ """
