def get_stats(name, **kwargs):
'''
Takes a distribution name and paras,
and returns key statistics.
Note: for stat-getting the only choice
is to use *scipy*. We need to be careful
to ensure the parametrization matches
with that used in our get_generator fn,
which runs on numpy Generator methods.
Thus, kwargs here follow *numpy* namings.
'''
_sp = "mv" # moment specification for scipy.stats computations.
if name == "lognormal":
mean, var = lognorm.stats(s=kwargs["sigma"],
scale=np.exp(kwargs["mean"]),
moments=_sp)
elif name == "normal":
mean, var = norm.stats(loc=kwargs["loc"],
scale=kwargs["scale"],
moments=_sp)
elif name == "pareto":
mean, var = pareto.stats(b=kwargs["shape"],
scale=kwargs["scale"],
moments=_sp)
else:
raise ValueError("Please provide a proper distribution name.")
return {"mean": mean, "var": var}
def __init__(self, shape_parameter):
self.shape_parameter = shape_parameter
if self.shape_parameter is not None:
self.bounds = np.array([0.999, np.inf])
if self.shape_parameter > 0:
mean, var, skew, kurt = pareto.stats(self.shape_parameter,
moments='mvsk')
self.parent = pareto(self.shape_parameter)
self.mean = mean
self.variance = var
self.skewness = skew
self.kurtosis = kurt
self.x_range_for_pdf = np.linspace(0.999,
20.0 + shape_parameter,
RECURRENCE_PDF_SAMPLES)
import matplotlib
matplotlib.use('Agg')
import scipy.stats
import matplotlib.pyplot as plt
import seaborn as sns
import numpy as np
from scipy.stats import uniform, pareto, norm
#mean, var, skew, kurt =
b = 1.0
dists = []
dists += [[("pareto"), pareto.stats(2, moments='mvsk'), pareto]]
dists += [[("uniform"), uniform.stats(moments='mvsk'), uniform]]
dists += [[("normal"), norm.stats(moments='mvsk'), norm]]
dists += [[("normal_sc"), norm.stats(moments='mvsk'), norm]]
print(dists)
size = 20000
for dist in dists:
print dist[0]
if (dist[0] == "pareto"):
sample = dist[2].rvs(b, size=size)
sample = sample[(sample < 8)]
if (dist[0] == "normal"):
sample = dist[2].rvs(size=size)
if (dist[0] == "uniform"):
def __init__(self, seed, speed, nr_samples, interval):
np.random.seed(seed)
b = 3
self.samples = (np.random.pareto(b, nr_samples) + 1)
mean, var, skew, kurt = pareto.stats(b, moments='mvsk')
self.gt_mean = mean
self.y_values = []
self.confidence = []
self.x_values = range(2, nr_samples, interval)
for i in self.x_values:
s = self.samples[:i]
self.y_values.append(np.mean(s))
self.confidence.append((np.std(s) / math.sqrt(len(s))) * 1.96)
self.y_values = np.array(self.y_values)
self.confidence = np.array(self.confidence)
fig = plt.figure(figsize=(10, 10))
self.ax1 = fig.add_subplot(2, 2, (1, 2))
self.ax2 = fig.add_subplot(2, 2, 3)
self.ax3 = fig.add_subplot(2, 2, 4)
# history plot
self.ax1.set_title('dancing bar history')
self.ax1.set_xlabel('iteration')
self.ax1.set_ylabel('estimated mean')
self.ax1.set_xlim(0, nr_samples)
self.ax1.set_ylim(np.min(self.y_values - self.confidence),
np.max(self.y_values + self.confidence))
self.ax1_primitives = []
p = Polygon(self._history_polygon_xy(1), True, alpha=0.4, color='blue')
self.ax1_primitives.append(p)
self.ax1.add_patch(p)
l = Line2D([], [], color='blue')
self.ax1_primitives.append(l)
self.ax1.add_line(l)
self.ax1.axhline(y=mean, color='black', linestyle='--', linewidth=0.5)
# bar plot
self.ax2.set_title('dancing bar')
self.ax2.set_ylabel('avg sales')
self.ax2.set_xlim(-0.5, 1)
self.ax2.set_xticks([0.25])
self.ax2.set_xticklabels(['department XYZ'])
self.ax2.set_ylim(0, np.max(self.y_values + self.confidence))
self.ax2_primitives = []
r = Rectangle((0, 0), 0.5, self.y_values[1], alpha=0.4, color='blue')
self.ax2_primitives.append(r)
self.ax2.add_patch(r)
self.ax2.axhline(y=mean, color='black', linestyle='--', linewidth=0.5)
l = Line2D([0.25, 0.25], [
self.y_values[1] - self.confidence[1],
self.y_values[1] + self.confidence[1]
],
color='black')
self.ax2_primitives.append(l)
self.ax2.add_line(l)
# pdf plot
self.ax3.set_title('pareto pdf')
x = np.linspace(pareto.ppf(0.01, b), pareto.ppf(0.99, b), 100)
self.ax3.plot(x, pareto.pdf(x, b) + 1, 'blue', lw=1, alpha=0.6)
animation.TimedAnimation.__init__(self,
fig,
interval=speed,
blit=True,
repeat=False)
def simulate():
"""
"""
print "Pareto distribution with shape:", shape, "mean:", mean_npkts
print "Sanity check on pareto mean packets:", pareto.stats(shape, scale=scale, moments='m')
print "Poisson process with lambda:", lamb
inter_arrival, all_flows, max_packets = generate_flows(num_flows)
print "Starting simulation."
curr_flows = []
all_done_flows = []
curr_time = 0
count = 0
count_step = notify_step
count_big = 0
while not all_flows.empty():
new_flow = all_flows.get()
count += 1
if count/count_step > count_big:
count_big += 1
print "%d flows have arrived..." % count
inter_arrival = new_flow.inter_arrival
init_active_count = len(curr_flows)
# update flows
curr_flows, done_flows = update_flows(curr_flows, inter_arrival, curr_time)
# update loop state
curr_time += inter_arrival
all_done_flows += done_flows
curr_flows.append(new_flow) # newest arriving flow
if debug_flag:
print update_log(curr_time, init_active_count, len(done_flows), len(all_done_flows))
print arrival_log(new_flow)
print
# all flows have arrived, so migrate to updating once every E[arrival] = 1/lamb.
if debug_flag:
print "All flows have arrived. Updating remaining flows..."
update_duration = 1.0/lamb
while len(all_done_flows) != num_flows:
init_active_count = len(curr_flows)
curr_flows, done_flows = update_flows(curr_flows, update_duration, curr_time)
curr_time += update_duration
all_done_flows += done_flows
if debug_flag:
print update_log(curr_time, init_active_count, len(done_flows), len(all_done_flows))
print
print "Finished simulation. FCT results:"
for done_flow in all_done_flows:
if debug_flag:
print "(packets: %d, fct: %.8f, bottleneck: %d flows)" % (done_flow.packet_length, done_flow.fct, done_flow.flow_bottleneck)
fcts_aggregate = packet_info(all_done_flows)
avg_fcts = average_fct(fcts_aggregate)
max_fcts = max_fct(fcts_aggregate)
packet_list = avg_fcts.keys()
packet_list.sort()
ret_list = []
for packet_length in packet_list:
print "Packet length: %d, average FCT: %.8f, max FCT: %.8f" % (packet_length, avg_fcts[packet_length], max_fcts[packet_length])
ret_list.append((packet_length, avg_fcts[packet_length], max_fcts[packet_length]))
return ret_list # tuples (packet_length, average fct)
def simulate():
"""
"""
print "Pareto distribution with shape:", shape, "mean:", mean_npkts
print "Sanity check on pareto mean packets:", pareto.stats(shape,
scale=scale,
moments='m')
print "Poisson process with lambda:", lamb
inter_arrival, all_flows, max_packets = generate_flows(num_flows)
print "Starting simulation."
curr_flows = []
all_done_flows = []
curr_time = 0
count = 0
count_step = notify_step
count_big = 0
while not all_flows.empty():
new_flow = all_flows.get()
count += 1
if count / count_step > count_big:
count_big += 1
print "%d flows have arrived..." % count
inter_arrival = new_flow.inter_arrival
init_active_count = len(curr_flows)
# update flows
curr_flows, done_flows = update_flows(curr_flows, inter_arrival,
curr_time)
# update loop state
curr_time += inter_arrival
all_done_flows += done_flows
curr_flows.append(new_flow) # newest arriving flow
if debug_flag:
print update_log(curr_time, init_active_count, len(done_flows),
len(all_done_flows))
print arrival_log(new_flow)
print
# all flows have arrived, so migrate to updating once every E[arrival] = 1/lamb.
if debug_flag:
print "All flows have arrived. Updating remaining flows..."
update_duration = 1.0 / lamb
while len(all_done_flows) != num_flows:
init_active_count = len(curr_flows)
curr_flows, done_flows = update_flows(curr_flows, update_duration,
curr_time)
curr_time += update_duration
all_done_flows += done_flows
if debug_flag:
print update_log(curr_time, init_active_count, len(done_flows),
len(all_done_flows))
print
print "Finished simulation. FCT results:"
for done_flow in all_done_flows:
if debug_flag:
print "(packets: %d, fct: %.8f, bottleneck: %d flows)" % (
done_flow.packet_length, done_flow.fct,
done_flow.flow_bottleneck)
fcts_aggregate = packet_info(all_done_flows)
avg_fcts = average_fct(fcts_aggregate)
max_fcts = max_fct(fcts_aggregate)
packet_list = avg_fcts.keys()
packet_list.sort()
ret_list = []
for packet_length in packet_list:
print "Packet length: %d, average FCT: %.8f, max FCT: %.8f" % (
packet_length, avg_fcts[packet_length], max_fcts[packet_length])
ret_list.append(
(packet_length, avg_fcts[packet_length], max_fcts[packet_length]))
return ret_list # tuples (packet_length, average fct)
from scipy.stats import pareto import matplotlib.pyplot as plt fig, ax = plt.subplots(1, 1) # Calculate a few first moments: b = 2.62 mean, var, skew, kurt = pareto.stats(b, moments='mvsk') # Display the probability density function (``pdf``): x = np.linspace(pareto.ppf(0.01, b), pareto.ppf(0.99, b), 100) ax.plot(x, pareto.pdf(x, b), 'r-', lw=5, alpha=0.6, label='pareto pdf') # Alternatively, the distribution object can be called (as a function) # to fix the shape, location and scale parameters. This returns a "frozen" # RV object holding the given parameters fixed. # Freeze the distribution and display the frozen ``pdf``: rv = pareto(b) ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf') # Check accuracy of ``cdf`` and ``ppf``: vals = pareto.ppf([0.001, 0.5, 0.999], b) np.allclose([0.001, 0.5, 0.999], pareto.cdf(vals, b)) # True # Generate random numbers:
