def generate_random_exponential_timeseries(dlamb, ndays=100, num=100):
"""
This function will generate some random exponential 2d data
in a time series.
parameters:
dlamb: float - the exponential lambda parameter
ndays: int - number of days in the time series
num: int - total number of locations
returns:
numpy array of coordinates with day index
"""
a = np.zeros([ndays * num, 3])
b = np.array(range(0, ndays))
b = np.repeat(b, num)
a[:, 0] = b
for row in a:
row[1] = expon.rvs(loc=0, scale=dlamb)
row[2] = expon.rvs(loc=0, scale=dlamb)
return a
def bcc_sim(S, lambd, mu, simtime):
remaining = simtime
i = 0 # Estado actual
ts = 0
time = np.zeros(S+1)
while remaining > 0:
if i == 0:
T1 = expon.rvs(scale=1./lambd, size=1)
T2 = np.inf
elif i == S:
T1 = np.inf
T2 = expon.rvs(scale=1./(i*mu), size=1)
else:
T1 = expon.rvs(scale=1./lambd, size=1)
T2 = expon.rvs(scale=1./(i*mu), size=1)
if np.all(T1 < T2):
ts = T1
time[i] = time[i] + ts
i = i+1
else:
ts = T2
time[i] = time[i] + ts
i = i-1
remaining = remaining - ts[0]
progress = (simtime - remaining) / simtime
# print "{0}% --> {1} remaining".format(progress*100.0, remaining)
return time/simtime
def poisson_rate(exposuretime: u.s, geomarea: u.cm**2) -> u.s:
'''Generate Poisson distributed times.
Parameters
----------
exposuretime : `~astropy.units.quantity.Quantity`
Exposure time
geomarea : `~astropy.units.quantity.Quantity`
Geometric opening area of telescope
Returns
-------
times : `~astropy.units.quantity.Quantity`
Poisson distributed times.
'''
fullrate = rate * geomarea
# Make 10 % more numbers then we expect to need, because it's random
times = expon.rvs(scale=1./fullrate.to(1 / u.s),
size=int((exposuretime * fullrate * 1.1).to(u.dimensionless_unscaled)))
# If we don't have enough numbers right now, add some more.
while (times.sum() * u.s) < exposuretime:
times = np.hstack([times, expon.rvs(scale=1/fullrate.to(1 / u.s),
size=int(((exposuretime - times.sum() * u.s) * fullrate * 1.1).to(u.dimensionless_unscaled)))])
times = np.cumsum(times) * u.s
return times[times < exposuretime]
def generate_random_exponential_timeseries(dlamb, ndays=100, num=100):
"""
This function will generate some random exponential 2d data
in a time series.
parameters:
dlamb: float - the exponential lambda parameter
ndays: int - number of days in the time series
num: int - total number of locations
returns:
numpy array of coordinates with day index
"""
a = np.zeros([ndays*num, 3])
b = np.array(range(0, ndays))
b = np.repeat(b, num)
a[:,0] = b
for row in a:
row[1] = expon.rvs(loc=0, scale = dlamb)
row[2] = expon.rvs(loc=0, scale = dlamb)
return a
def lindley(m=55000, d=5000):
''' Estimates waiting time with m customers, discarding the first d customers
Lindley approximation for waiting time in a M/G/1 queue
'''
replications = 10
lindley = []
for rep in range(replications):
y = 0
SumY = 0
for i in range(1, d):
# Random number variable generation from scipy.stats
# shape = 0, rate =1, 1 value
a = expon.rvs(0, 1)
# rate = .8/3, shape = 3
x = erlang.rvs(3, scale=0.8 / 3, size=1)
y = max(0, y + x - a)
for i in range(d, m):
a = expon.rvs(0, 1)
# rate = .8/3, shape = 3
x = erlang.rvs(3, scale=0.8 / 3, size=1)
y = max(0, y + x - a)
SumY += y
result = SumY / (m - d)
lindley.append(result)
return lindley
def fast_sim(x, tH=1 / 70, nodec=5, isi=35., gen_var=1):
"""
Simulates a dataset with x trials and true hazardrate tH. Does so faster.
nodec = minimum points between decisions. Nodec points are shown, after that 'isi' determines decision probability.
"""
inter_choice_dists = np.cumsum(expon.rvs(scale=1 / (1 / isi), size=10000))
inter_choice_dists = np.array([int(j + nodec + nodec * (np.where(inter_choice_dists == j)[0]))
for j in inter_choice_dists]) # adds 5 (nodec) points between every decision
inter_choice_dists = inter_choice_dists[inter_choice_dists < x]
mus = []
values = []
start = random.choice([0.5, -0.5])
cnt = 0
while cnt < x:
i = 1 + int(np.round(expon.rvs(scale=1 / tH)))
mus.append([start] * i)
values.append(norm.rvs(start, gen_var, size=i))
start *= -1
cnt += i
df = pd.DataFrame({'rule': np.concatenate(mus)[:x],
'value': np.concatenate(values)[:x]})
# df.columns = ['rule', 'values']
df.loc[:, 'message'] = 'GL_TRIAL_LOCATION'
df.loc[inter_choice_dists, 'message'] = 'decision'
df.loc[:, 'index'] = np.arange(len(df))
return df
def sim():
state = 0
p0h_cnt = 0
p1h_cnt = 0
l_p0hat = []
l_p1hat = []
t = 0
while t < 10001:
if state == 0:
state = 1
ran = int(round(e.rvs(1 / lam)))
t += ran
p0h_cnt += ran
l_p0hat.extend([p0h_cnt / 10000 for _ in range(0, ran)])
l_p1hat.extend([p1h_cnt / 10000 for _ in range(0, ran)])
else:
state = 0
ran = int(round(e.rvs(1 / mu)))
t += ran
p1h_cnt += ran
l_p0hat.extend([p0h_cnt / 10000 for _ in range(0, ran)])
l_p1hat.extend([p1h_cnt / 10000 for _ in range(0, ran)])
x = np.arange(10000) / 100
print(len(l_p0hat))
plt.plot(l_p0hat, '-', label='p0hat', markersize=0.1, linewidth=1)
plt.plot(l_p1hat, '-', label='p1hat', markersize=0.1, linewidth=1)
plt.legend()
def schedule_processes(self):
id = 0
while True:
waiting_time = expon.rvs(loc=0, scale=self.params['expected_wait'])
std_norm = norm.rvs()
gas_required = std_norm * self.params[
'gas_required_std'] + self.params['gas_required_std']
gas_required = max([0, gas_required])
lay_time = expon.rvs(loc=0, scale=self.params['expected_lay_time'])
yield self.env.timeout(waiting_time)
self.processes.append(
Car(id=id,
gas_required=gas_required,
lay_time=lay_time,
gas_station=self.gas_station,
env=self.env,
params=self.params))
id += 1
def __expon_churn(self):
while True:
delay = expon.rvs(scale=self.__expon_online_beta)
if delay >= self.__expon_online_threshold:
delay = min(self.__expon_max_online, max(self.__expon_min_online, delay))
if self._community is None:
if __debug__:
dprint("expon wants us online for the next ", delay, " seconds")
self.log("scenario-expon", state="online", duration=delay)
self._community = self.community_class.load_community(
self._master_member, *self.community_args, **self.community_kargs
)
else:
if __debug__:
dprint("expon wants us online for the next ", delay, " seconds (we are already online)")
self.log("scenario-expon", state="stay-online", duration=delay)
yield float(delay)
delay = expon.rvs(scale=self.__expon_offline_beta)
if delay >= self.__expon_offline_threshold:
delay = min(self.__expon_max_offline, max(self.__expon_min_offline, delay))
if self._community is None:
if __debug__:
dprint("expon wants us offline for the next ", delay, " seconds (we are already offline)")
self.log("scenario-expon", state="stay-offline", duration=delay)
else:
if __debug__:
dprint("expon wants us offline for the next ", delay, " seconds")
self.log("scenario-expon", state="offline", duration=delay)
self._community.unload_community()
self._community = None
yield float(delay)
def __init__(self, numCustomers=100):
"""Initializes the simulation."""
self.numCustomers = numCustomers
self.customers = []
# initialize State Variables
self.clock = 0
self.Idle = 0
self.Busy = 1
self.s1 = self.Idle
self.s2 = self.Idle
self.q1 = 0
self.q2 = 0
### additional values to be tracked during simulation
# average waiting time for all customers
self.averageWaitingTime = 0
self.averageQ1Time = 0
self.averageQ2Time = 0
# avg waiting time for customers who wait
self.averageWaitTimeWhoWait = 0
self.averageQ1TimeWait = 0
self.averageQ2TimeWait = 0
# average service time for all customers
self.averageServiceTime = 0
self.averageService1Time = 0
self.averageService2Time = 0
# avg interarrival time for all customers
self.averageInterarrrivalTime = 0
# avg total system time for all customers
self.averageSystemTime = 0
# probability a customer has to wait
self.waitProbability = 0
# percentage of time server is idle
self.idleProbability = 0
# queue sizes at the moment each customer arrived
self.q1sizes = {}
self.q2sizes = {}
### generate values for random variables
self.interarrivalTimeValues = poisson.rvs(4, 0, size=numCustomers).tolist()
self.serviceTime1Values = expon.rvs(6, size=numCustomers).tolist()
self.serviceTime2Values = expon.rvs(8, size=numCustomers).tolist()
self.balkValues = [random.random() for x in xrange(numCustomers)]
# print self.interarrivalTimeValues
# print expon.rvs(6, 0, size=numCustomers)
# print self.serviceTime2Values
# print self.balkValues
self.populate() # Ready. Set. Go!
def rvs(self):
if not self.size:
self.size = randint.rvs(low = self.min_size, high = self.max_size, size = 1)
if self.scale:
return expon.rvs(loc = self.loc * 0.09, scale = self.scale, size = self.size)
else:
return expon.rvs(loc = self.loc * 0.09, scale = self.loc * 8.0, size = self.size)
def create_data(n=N_SAMPLES, c=N_CLUSTERS, f=N_FEATURES, param=PARAM, time_str=""):
feat_means = np.array([expon.rvs(size=f) for _ in range(c)])
feat_clusters = assign_clusters(f, c, param)
cov = np.zeros([f,f])
for ii in range(f):
for jj in range(ii,f):
if feat_clusters[ii] == feat_clusters[jj]:
cv = expon.rvs(size=1)
cov[ii,jj] = cv
cov[jj,ii] = cv
# feat_sds = np.array([expon.rvs(size=f) for _ in range(c)])
cluster_assignments = assign_clusters(n, c, param)
cluster_assignments_test = assign_clusters(TEST_SIZE, c, param)
features = create_features(feat_means, cov, cluster_assignments)
features_test = create_features(feat_means, cov, cluster_assignments_test)
labels = cluster_assignments%2
labels_test = cluster_assignments_test%2
fstr = "data/{}_" + time_str
np.save(fstr.format("importances"), feat_means)
np.save(fstr.format("X"), features)
np.save(fstr.format("y"), labels)
np.save(fstr.format("X_test"), features_test)
np.save(fstr.format("y_test"), labels_test)
np.save(fstr.format("cl"), cluster_assignments)
np.save(fstr.format("cl_test"), cluster_assignments_test)
return features, labels
def random_bow(df_scale=0.1, **kwargs):
return ('bow', {
'max_df': 1 - expon.rvs(loc=0, scale=df_scale, size=1).item(), # max % of times a term can be found
'min_df': expon.rvs(loc=0, scale=df_scale, size=1).item(), # min % of times a term can be found
# 'max_features': # not sure how to randomly pick this
'binary': bernoulli.rvs(0.2, size=1).item(), # whether to make bow binary
})
def __expon_churn(self):
while True:
delay = expon.rvs(scale=self.__expon_online_beta)
if delay >= self.__expon_online_threshold:
delay = min(self.__expon_max_online, max(self.__expon_min_online, delay))
if self._community is None:
if __debug__: dprint("expon wants us online for the next ", delay, " seconds")
self.log("scenario-expon", state="online", duration=delay)
self._community = self.community_class.load_community(self._master_member, *self.community_args, **self.community_kargs)
else:
if __debug__: dprint("expon wants us online for the next ", delay, " seconds (we are already online)")
self.log("scenario-expon", state="stay-online", duration=delay)
yield float(delay)
delay = expon.rvs(scale=self.__expon_offline_beta)
if delay >= self.__expon_offline_threshold:
delay = min(self.__expon_max_offline, max(self.__expon_min_offline, delay))
if self._community is None:
if __debug__: dprint("expon wants us offline for the next ", delay, " seconds (we are already offline)")
self.log("scenario-expon", state="stay-offline", duration=delay)
else:
if __debug__: dprint("expon wants us offline for the next ", delay, " seconds")
self.log("scenario-expon", state="offline", duration=delay)
self._community.unload_community()
self._community = None
yield float(delay)
def random_tfidf(df_scale=0.1, **kwargs):
return ('tfidf', {
'max_df': 1 - expon.rvs(loc=0, scale=df_scale, size=1).item(), # max # of times a term can be found
'min_df': expon.rvs(loc=0, scale=df_scale, size=1).item(), # min # of times a term can be found
# 'max_features': # not sure how to randomly pick this
'binary': bernoulli.rvs(0.2, size=1).item(), # whether to make bow binary
'norm': np.random.choice(['l2', 'l1', None], p=[0.8, 0.15, 0.05]), # how to normalize the vectors
})
def __init__(self):
self.state=estats.GeneradorInactiu
self.index=-1
self.tempsArribada = expon.rvs(size=configuracio.aliments_a_processar, loc=configuracio.loc_temps_entre_arribades, scale=configuracio.scale_temps_entre_arribades)
for i in range(len(self.tempsArribada)):
while self.tempsArribada[i] < 0:
self.tempsArribada[i] = expon.rvs(size=1, loc=configuracio.loc_temps_entre_arribades, scale=configuracio.scale_temps_entre_arribades)
self.tempsArribada[i] = round(self.tempsArribada[i], 2)
def BLDGenerator(p,samplesize,lmbd,C):
#Going to do a fixed species tree with given probabilities of introgression.
outputList=[]
for x in range (0,samplesize):
if numpy.random.random_sample()<p:
outputList.append(expon.rvs()*lmbd)
else:
outputList.append(expon.rvs()*lmbd+(C-truncexpon.rvs(C))*lmbd)
# print (expon.rvs()*lmbd+(C-truncexpon.rvs(C))*lmbd)
return [[('testA','testB','testC'),outputList,[],[]]]
def _resimulate(node, factor=1.0, skewed_admixture_prior=False):
if node[2] is not None:
if skewed_admixture_prior:
node[2] = linear_distribution.rvs()
else:
node[2] = uniform.rvs()
if node[3] is not None:
node[3] = expon.rvs() / factor
if node[4] is not None:
node[4] = expon.rvs() / factor
return node
def driving_process(params, step, sL, s):
'''
Driving process for adding new participants (their funds) and new proposals.
'''
arrival_rate = 10 / (1 + sentiment)
rv1 = np.random.rand()
new_participant = bool(rv1 < 1 / arrival_rate)
supporters = get_edges_by_type(s['network'], 'support')
len_parts = len(get_nodes_by_type(s['network'], 'participant'))
#supply = s['supply']
expected_holdings = .1 * supply / len_parts
if new_participant:
h_rv = expon.rvs(loc=0.0, scale=expected_holdings)
new_participant_holdings = h_rv
else:
new_participant_holdings = 0
network = s['network']
affinities = [network.edges[e]['affinity'] for e in supporters]
median_affinity = np.median(affinities)
proposals = get_nodes_by_type(network, 'proposal')
fund_requests = [
network.nodes[j]['funds_requested'] for j in proposals
if network.nodes[j]['status'] == 'candidate'
]
funds = s['funds']
total_funds_requested = np.sum(fund_requests)
proposal_rate = 1 / median_affinity * (1 + total_funds_requested / funds)
rv2 = np.random.rand()
new_proposal = bool(rv2 < 1 / proposal_rate)
#sentiment = s['sentiment']
funds = s['funds']
scale_factor = funds * sentiment**2 / 10000
if scale_factor < 1:
scale_factor = 1
#this shouldn't happen but expon is throwing domain errors
if sentiment > .4:
funds_arrival = expon.rvs(loc=0, scale=scale_factor)
else:
funds_arrival = 0
return ({
'new_participant': new_participant,
'new_participant_holdings': new_participant_holdings,
'new_proposal': new_proposal,
'funds_arrival': funds_arrival
})
def generate_parametric_services(new_ai, sol_m1, sol_m2):
# ti are the same
new_si = []
for a_new in new_ai:
if a_new == 1:
new_si.append(expon.rvs(scale=1 / sol_m2))
else:
new_si.append(expon.rvs(scale=1 / sol_m1))
#print("New average S_i: ", np.mean(new_si))
return new_si
def InitialRepu(dist):
if dist == "no":
temp = 0
elif dist == "norm":
temp = norm.rvs(loc=0.5, scale=0.15)
while temp < 0 or 1 < temp:
temp = norm.rvs(loc=0.5, scale=0.5)
elif dist == "exp":
temp = expon.rvs(scale=0.3)
while temp < 0 or 1 < temp:
temp = expon.rvs(scale=0.3)
return temp
def supermarket_log(starting_time, finish_time, warehouse,
file): # one day operation
"""
Simulating one day of restock and sells in a supermarket, the events in the supermarket follow an exponential
distribution with an average time between events of 5 minutes. Each time that an event occur, the next event
(restock or sell) is chosen with a binomial distribution where a sell has probability 0.65 and a restock 0.35.
When a client buy a product, that product is selected randomly uniformly, whereas the quantity is chosen
from a binomial with n=(max quantity of the product chosen) and p=0.15
We are making one restock at once, each time that a restock is made the product selected is randomly uniformly
chosen, meanwhile the quantity of the product to restock is chosen from a binomial where
n=(max quantity allowed in shelves), p=0.65
Parameters
----------
starting_time:
supermarket opening time
finish_time:
supermarket closing time
warehouse:
class Warehouse where our products catalog is saved, we need this information to know products and their codes
in our supermarket
file:
file path in which save our daily log
"""
log = []
last_hour = starting_time
while last_hour < finish_time: # our loop finish when the last transaction has passed finish_time
if binom.rvs(1, 0.65):
product_chosen = list(
warehouse.products.keys())[randint.rvs(1, 19) - 1]
last_hour += timedelta(minutes=float(expon.rvs(scale=5, size=1)))
aux = [
'venta', last_hour, product_chosen,
binom.rvs(n=warehouse[product_chosen][0], p=0.15, loc=1)
]
log.append(aux)
else:
last_hour += timedelta(minutes=float(expon.rvs(scale=5, size=1)))
product_chosen = list(warehouse.products.keys())[randint.rvs(
0,
len(amazon.products) - 1)]
log.append([
'repo', last_hour, product_chosen,
binom.rvs(n=warehouse[product_chosen][0], p=0.65, loc=1)
])
with open(file, 'w') as f:
text = ""
for el in log:
text += el[0] + ' ' + format_date(el[1]) + " " + el[2] + " " + str(
el[3]) + "\n"
f.write(text)
def handle_xml_request(self, msg):
if not 'http://' in msg.get_payload():
raise ValueError('url_mpd parameter should starts with http://')
url_tokens = msg.get_payload().split('/')[2:]
port = '80'
host_name = url_tokens[0]
path_name = '/' + '/'.join(url_tokens[1:])
mdp_file = ''
try:
connection = http.client.HTTPConnection(host_name, port)
connection.request('GET', path_name)
mdp_file = connection.getresponse().read().decode()
connection.close()
except Exception as err:
print('> Houston, we have a problem!')
print(f'> trying to connecto to: {msg.get_payload()}')
print(
f'Execution Time {self.timer.get_current_time()} > msg obj: {msg}'
)
print(err)
exit(-1)
msg = Message(MessageKind.XML_RESPONSE, mdp_file)
msg.add_bit_length(8 * len(mdp_file))
parsed_mpd = parse_mpd(msg.get_payload())
self.qi = parsed_mpd.get_qi()
increase_factor = 1
low = round(self.qi[len(self.qi) - 1] * increase_factor)
medium = round(self.qi[(len(self.qi) // 2) - 1] * increase_factor)
high = round(self.qi[0] * increase_factor)
self.traffic_shaping_values.append(
expon.rvs(scale=1,
loc=low,
size=1000,
random_state=self.traffic_shaping_seed))
self.traffic_shaping_values.append(
expon.rvs(scale=1,
loc=medium,
size=1000,
random_state=self.traffic_shaping_seed))
self.traffic_shaping_values.append(
expon.rvs(scale=1,
loc=high,
size=1000,
random_state=self.traffic_shaping_seed))
self.send_up(msg)
def rvs(self):
if not self.size:
self.size = randint.rvs(low=self.min_size,
high=self.max_size,
size=1)
if self.scale:
return expon.rvs(loc=self.loc * 0.09,
scale=self.scale,
size=self.size)
else:
return expon.rvs(loc=self.loc * 0.09,
scale=self.loc * 8.0,
size=self.size)
def __expon_churn(self):
while True:
delay = expon.rvs(scale=self.__expon_online_beta)
if delay >= self.__expon_online_threshold:
delay = float(min(self.__expon_max_online, max(self.__expon_min_online, delay)))
self.scenario_churn("online", delay)
yield delay
delay = expon.rvs(scale=self.__expon_offline_beta)
if delay >= self.__expon_offline_threshold:
delay = float(min(self.__expon_max_offline, max(self.__expon_min_offline, delay)))
self.scenario_churn("offline", delay)
yield delay
def JumpDiffusionKou(mu, sigma, lam, p, e1, e2, ts, j_):
# Simulate a double-exponential process
# INPUTS
# mu :[scalar] mean parameter of Gausian distribution
# sigma :[scalar] standard deviation of Gaussian distribution
# lam :[scalar] Poisson intensity of jumps
# p :[scalar] binomial parameter of jumps
# e1 :[scalar] exponential parameter for the up-jumps
# e2 :[scalar] exponential parameter for the down-jumps
# ts :[vector] time steps with ts[0]=0
# j_ :[scalar] number of simulations
# OPS
# x :[matrix](j_ x len(ts)) matrix of simulated paths
## Code
tau = ts[-1]
# simulate number of jumps
n_jump = poisson.rvs(lam * tau, size=(j_))
k_ = len(ts)
jumps = zeros((j_, k_))
for j in range(j_):
# simulate jump arrival time
t = tau * rand(n_jump[j], 1)
t = sort(t)
# simulate jump size
ww = binom.rvs(1, p, size=(n_jump[j], 1))
S = ww * expon.rvs(scale=e1, size=(n_jump[j], 1)) - (
1 - ww) * expon.rvs(scale=e2, size=(n_jump[j], 1))
# put things together
CumS = cumsum(S)
for k in range(1, k_):
events = npsum(t <= ts[k])
if events:
jumps[j, k] = CumS[events - 1]
#simulate the arithmetic Brownian motion component
d_BM = zeros((j_, k_))
for k in range(1, k_):
dt = ts[k] - ts[k - 1]
d_BM[:, [k]] = mu * dt + sigma * sqrt(dt) * randn(j_, 1)
#put together the arithmetic BM with the jumps
x = cumsum(d_BM, 1) + jumps
return x
def testExponManyEvents(self):
"""
generate and fit an exponential distribution with lifetime of 25
make a plot in testExponManyEvents.png
"""
tau = 25.0
nBins = 400
size = 100
taulist = []
for i in range(1000):
x = range(nBins)
timeHgValues = np.zeros(nBins, dtype=np.int64)
timeStamps = expon.rvs(loc=0, scale=tau, size=size)
ts64 = timeStamps.astype(np.uint64)
tsBinner.tsBinner(ts64, timeHgValues)
param = expon.fit(timeStamps)
fit = expon.pdf(x,loc=param[0],scale=param[1])
fit *= size
print "i=",i," param[1]=",param[1]
taulist.append(param[1])
hist,bins = np.histogram(taulist, bins=20, range=(15,25))
width = 0.7*(bins[1]-bins[0])
center = (bins[:-1]+bins[1:])/2
plt.step(center, hist, where = 'post')
plt.savefig(inspect.stack()[0][3]+".png")
def testExponaverage(self):
"""
generate and fit a histogram of an exponential distribution with many
events using the average time to find the fit. The histogram is then
saved in testExponaverage.png
"""
tau = 25.0
nBins = 400
size = 100
taulist = []
for i in range(1000):
x = range(nBins)
yPlot = funcExpon(xPlot, *popt)
timeHgValues = np.zeros(nBins, dtype=np.int64)
timeStamps = expon.rvs(loc=0, scale=tau, size=size)
ts64 = timeStamps.astype(np.uint64)
tsBinner.tsBinner(ts64, timeHgValues)
param = sum(timeStamps)/len(timeStamps)
fit = expon.pdf(x,param)
fit *= size
taulist.append(param)
hist,bins = np.histogram(taulist, bins=20, range=(15,35))
width = 0.7*(bins[1]-bins[0])
center = (bins[:-1]+bins[1:])/2
#plt.bar(center, hist, align = 'center', width = width) produces bar graph
plt.step(center, hist, where = 'post')
plt.savefig(inspect.stack()[0][3]+".png")
def generate_random_data_from_dist(param, shape, nrows, ncols):
if shape == 'normal':
data = norm.rvs(0, param, size=(nrows, ncols))
# link the two sliders and make the param for t dfs (yolked to sample size in other slider)
# elif shape=='t':
# data = t.rvs(df=ncols-1)
elif shape == 'lognormal':
data = lognorm.rvs(param, size=(nrows, ncols))
elif shape == 'contaminated chi-squared':
# data = chi2.rvs(4, 0, param, size=size)
data = chi2.rvs(4, size=(nrows, ncols))
contam_inds = np.random.randint(ncols, size=int(param * ncols))
data[:, contam_inds] *= 10
elif shape == 'contaminated normal':
sub_size = round(param * ncols)
norm_size = int(ncols - sub_size)
standard_norm_values = norm.rvs(0, 1, size=(nrows, norm_size))
contam_values = norm.rvs(0, 10, size=(nrows, sub_size))
#print(standard_norm_values.shape)
#print(contam_values.shape)
data = np.concatenate([standard_norm_values, contam_values], axis=1)
#print(data.shape)
elif shape == 'exponential':
data = expon.rvs(0, param, size=(nrows, ncols))
return data
def get_data(n):
data = np.concatenate(
(expon.rvs(scale=1, size=n // 2), skewnorm.rvs(5, loc=3, size=n // 2)))
#getting exp dist data
#now shuffle the data
np.random.shuffle(data)
return data
def testExpon(self):
"""
generate and fit an exponential distribution with lifetime of 25
make a plot in testExpon.png
"""
tau = 25.0
nBins = 400
size = 100
x = range(nBins)
timeHgValues = np.zeros(nBins, dtype=np.int64)
timeStamps = expon.rvs(loc=0, scale=tau, size=size)
ts64 = timeStamps.astype(np.uint64)
tsBinner.tsBinner(ts64, timeHgValues)
with warnings.catch_warnings():
warnings.simplefilter("ignore")
# Note: this line casus a RuntimeWarning in optimize.py:301
param = expon.fit(timeStamps)
fit = expon.pdf(x,loc=param[0],scale=param[1])
fit *= size
tvf = timeHgValues.astype(np.double)
#tvf[tvf<1] = 1e-3 # the plot looks nicer if zero values are replaced
plt.plot(x, tvf, label="data")
plt.plot(x, fit, label="fit")
plt.yscale('symlog', linthreshy=0.9)
plt.xlim(xmax=100)
plt.ylim(ymin = -0.1)
plt.legend()
plt.title("true tau=%.1f fit tau=%.1f"%(tau,param[1]))
plt.savefig(inspect.stack()[0][3]+".png")
def simulate(ks,p,tf=10):
n = len(ks)
X = [1] * n + [0] * n + [p] #state is a vector of n empty sites, n complexes, protein
t = 0
history = [(t,X[:])]
while t < tf:
p = X[-1]
print "X:",X
rates = [p*ks[i]*X[i] for i in range(n)] + [X[n + i] for i in range(n)]
print "rates:",rates
master_rate = float(sum(rates))
dt = expon.rvs(1,1/master_rate)
print "dt:",dt
print "normalized rates:",normalize(rates)
j = inverse_cdf_sample(range(len(X)),normalize(rates))
print "chose reaction:",j
if j < n:
print "forming complex"
#update state for complex formation
X[j] = 0
X[n+j] = 1
X[-1] -= 1
else:
#update state for complex dissociation
print "dissolving complex"
X[j] = 0
X[j-n] = 1
X[-1] += 1
t += dt
history.append((t,X[:]))
return history
def sample_multiple_random_variables(self, size: int):
"""Sample a number of random variables from the distribution.
Args:
size (int): Number of random variables to be sampled.
"""
return expon.rvs(scale=self.scale, size=size)
def mutation_signatures_sim_data(N, L, K, output_prefix, mloc=100, mscale=50):
# Create the signatures
p_alphas = [2./L] * L
e_alphas = [1.] * K
P = np.random.dirichlet(p_alphas, size=K)
E = np.random.dirichlet(e_alphas, size=N)
# Sample data
samples = [ 'Sample-%s' % (i+1) for i in range(N) ]
categories = [ 'C%s' % (i+1) for i in range(L) ]
M = np.zeros((N, L), dtype=np.int)
for i, (sample, e_i) in enumerate(zip(samples, E)):
# Sample the number of mutations for this sample, and the exposures
from scipy.stats import expon
n_muts = int(expon.rvs(loc=mloc, scale=mscale, size=1)[0])
e_i = np.random.dirichlet(e_alphas)
# Generate mutations
for _ in range(n_muts):
k = np.where(np.random.multinomial(1, pvals=e_i) == 1)[0][0]
j = np.where(np.random.multinomial(1, pvals=P[k]) == 1)[0][0]
M[i, j] += 1
# Add some Poisson noise
M += np.random.poisson(1, size=(N, L))
# Output to file
np.save(output_prefix + '-signatures.npy', P)
np.save(output_prefix + '-exposure.npy', E)
np.save(output_prefix + '-mutation-counts.npy', M)
with open(output_prefix + '-mutation-counts.tsv', 'w') as OUT:
OUT.write('\t%s\n' % '\t'.join(categories))
for i, sample in enumerate(samples):
OUT.write('%s\t%s\n' % (sample, '\t'.join(map(str, M[i]))))
def sim_nd_na(E,N=1000, size_mean=100):
"""Simulate an exponential-size burst distribution with binomial (nd,na)
"""
nt = np.ceil(expon.rvs(scale=size_mean, size=N)).astype(int)
na = binom.rvs(nt, E)
nd = nt - na
return nd, na
def sim_nd_na(E, N=1000, size_mean=100):
"""Simulate an exponential-size burst distribution with binomial (nd,na)
"""
nt = np.ceil(expon.rvs(scale=size_mean, size=N)).astype(int)
na = binom.rvs(nt, E)
nd = nt - na
return nd, na
def generate_data_samples(MLE_lambda_inv, no_samples):
generated_beer_visits = expon.rvs(scale=MLE_lambda_inv,
loc=0,
size=no_samples)
return generated_beer_visits
def MBdist(
n, e_photon, thick
): # n: particle number, loct: start point(x-x0), scale: sigma, wl: wavelength,thick: thickness of the cathode
assert e_photon > bandgap
if e_photon - bandgap - 0.8 <= 0:
scale = e_photon - bandgap
loct = 0
else:
scale = 0.8
loct = e_photon - bandgap - scale
data = maxwell.rvs(loc=loct, scale=scale, size=n)
data_ene = np.array(data)
params = maxwell.fit(data, floc=0)
data_v = np.sqrt(2 * data_ene * ec / me) * 10**9
p2D = []
wl = ((19.82 - 27.95 * e_photon + 11.15 * e_photon**2) * 10**-3)**-1
pens = expon.rvs(loc=0, scale=wl, size=n)
penss = filter(lambda x: x <= thick, pens)
params_exp = expon.fit(pens, floc=0)
i = 0
for n in range(len(penss)):
phi = random.uniform(0, 2 * math.pi) # initial angular
poy = random.uniform(-1 * 10**6,
1 * 10**6) # initial y direction position
p2D.append([
penss[i], poy, data_v[i] * math.cos(phi),
data_v[i] * math.sin(phi), data_v[i], data[i]
]) #p2D: (z,y,vz,vy,v,ene)
i += 1
p2D = np.array(p2D)
return params, p2D, penss, params_exp
def p_randomly(params, step, sL, s, **kwargs):
commons = s["commons"]
sentiment = s["sentiment"]
ans = {
"new_participant": False,
"new_participant_investment": None,
"new_participant_tokens": None
}
arrival_rate = (1 + sentiment) / 10
if probability(arrival_rate):
ans["new_participant"] = True
# Here we randomly generate each participant's post-Hatch
# investment, in DAI/USD.
#
# expon.rvs() arguments:
#
# loc is the minimum number, so if loc=100, there will be no
# investments < 100
#
# scale is the standard deviation, so if scale=2, investments will
# be around 0-12 DAI or even 15, if scale=100, the investments will be
# around 0-600 DAI.
ans["new_participant_investment"] = expon.rvs(loc=0.0, scale=100)
ans["new_participant_tokens"] = commons.dai_to_tokens(
ans["new_participant_investment"])
return ans
def expon_naive(n_reads=10000, scale=100, D=50):
distances = np.zeros(n_reads, dtype=np.int64)
for i in tqdm(range(n_reads)):
distance = int(expon.rvs(scale=scale))
distances[i] = distance
distances_D = distances[distances > D]
Lambda = 1 / distances.mean()
P = lambda x: Lambda * np.exp(-Lambda * x)
quad_value, _ = quad(lambda x: P(x), 0, np.inf)
print(f'quad_value: {quad_value}')
log_likelihoods = []
d_range = range(0, 2 * D)
for d in d_range:
log_likelihood = 0
quad_value, _ = quad(lambda x: P(x), d, np.inf)
P_d = lambda x: np.where(x <= d, 0, P(x) / quad_value)
for distance in distances_D:
if distance > d:
log_likelihood += np.log(P_d(distance))
else:
log_likelihood = -np.inf
log_likelihoods.append(log_likelihood)
plt.plot(d_range, log_likelihoods)
plt.title('Log likelihood for naive estimation')
plt.xlabel('d, distance estimate')
plt.ylabel('log likelihood for d')
plt.show()
def __sample_trend(self, size, bias=0):
cursor = 0.0
cum_sum = bias
trend = []
while cursor < size:
previous = cursor
cursor += expon.rvs(scale=self.__lambda)
cursor = min(cursor, size)
tan = norm.rvs(loc=self.__tan_mean, scale=self.__tan_var)
left_idx = np.int(np.floor(previous))
right_idx = np.int(np.floor(cursor))
supp = np.arange(left_idx, right_idx) - previous
if len(supp) > 0:
trend.append(tan * supp + cum_sum)
cum_sum += tan * (cursor - previous)
trend = np.hstack(trend)
return trend
def generate_dates(population, earliest_date, latest_date, rate):
"""Produce a sample of events whose frequency is geometric
(increasingly common)
"""
low = datetime.strptime(earliest_date, "%Y-%m-%d").date()
high = datetime.strptime(latest_date, "%Y-%m-%d").date()
elapsed_days = (high - low).days
if rate == "exponential_increase":
# We oversample the distribution to trim the long tail of the
# exponential function
oversample_ratio = 1.5
distribution = (expon.rvs(
loc=0, scale=0.1, size=int(population * oversample_ratio)) *
elapsed_days).astype("int")
distribution = distribution[distribution <= elapsed_days]
elif rate == "uniform":
distribution = uniform.rvs(size=int(population)) * elapsed_days
distribution = distribution.astype("int")
else:
raise ValueError(
"Only exponential_increase and uniform distributions currently supported"
)
# And then sample it back down to the requested population size
distribution = np.random.choice(distribution, population, replace=False)
df = pd.DataFrame(distribution, columns=["days"])
shifts = pd.TimedeltaIndex(df["days"], unit="D")
df["d"] = high
df["d"] = pd.to_datetime(df["d"])
df["date"] = df["d"] - shifts
return df[["date"]]
def testExponOneEvent(self):
"""
generate and fit an exponential distribution with lifetime of 25
make a plot in testExpon.png
"""
tau = 25.0
nBins = 400
size = 100
x = range(nBins)
timeHgValues = np.zeros(nBins, dtype=np.int64)
timeStamps = expon.rvs(loc=0, scale=tau, size=size)
ts64 = timeStamps.astype(np.uint64)
tsBinner.tsBinner(ts64, timeHgValues)
param = expon.fit(timeStamps)
fit = expon.pdf(x,loc=param[0],scale=param[1])
fit *= size
tvf = timeHgValues.astype(np.double)
tvf[tvf<1] = 1e-3 # the plot looks nicer if zero values are replaced
plt.plot(x, tvf, label="data")
plt.plot(x, fit, label="fit")
plt.yscale('log')
plt.xlim(xmax=100)
plt.ylim(ymin=0.09)
plt.legend()
plt.title("true tau=%.1f fit tau=%.1f"%(tau,param[1]))
plt.savefig(inspect.stack()[0][3]+".png")
def displayFits(self):
"""
generates two histograms on the same plot. One uses maximum likelihood to fit
the data while the other uses the average time.
"""
tau = 25.0
nBins = 400
size = 100
taulist = []
taulistavg = []
for i in range(1000):
x = range(nBins)
timeHgValues = np.zeros(nBins, dtype=np.int64)
timeStamps = expon.rvs(loc=0, scale=tau, size=size)
ts64 = timeStamps.astype(np.uint64)
tsBinner.tsBinner(ts64, timeHgValues)
param = sum(timeStamps)/len(timeStamps)
fit = expon.pdf(x,param)
fit *= size
taulistavg.append(param)
for i in range(1000):
x = range(nBins)
timeHgValues = np.zeros(nBins, dtype=np.int64)
timeStamps = expon.rvs(loc=0, scale=tau, size=size)
ts64 = timeStamps.astype(np.uint64)
tsBinner.tsBinner(ts64, timeHgValues)
param = expon.fit(timeStamps)
fit = expon.pdf(x,loc=param[0],scale=param[1])
fit *= size
taulist.append(param[1])
hist,bins = np.histogram(taulistavg, bins=20, range=(15,35))
width = 0.7*(bins[1]-bins[0])
center = (bins[:-1]+bins[1:])/2
plt.step(center, hist, where = 'post', label="averagetime", color='g')
hist,bins = np.histogram(taulist, bins=20, range=(15,35))
width = 0.7*(bins[1]-bins[0])
center = (bins[:-1]+bins[1:])/2
plt.step(center, hist, where = 'post', label="maxlikelihood")
plt.legend()
plt.savefig(inspect.stack()[0][3]+".png")
def _rstable0(alpha):
U = uniform.rvs(size=1)
while True:
# generate non-zero exponential random variable
W = expon.rvs(size=1)
if W != 0:
break
return np.power(_A(math.pi * U, alpha) / np.power(W, 1.0 - alpha), 1.0 / alpha)
def generate_population(mu, N=1000, max_sigma=0.5, mean_sigma=0.08): """Extract samples from a normal distribution with variance distributed as an exponetial distribution """ exp_min_size = 1./max_sigma**2 exp_mean_size = 1./mean_sigma**2 sigma = 1/np.sqrt(expon.rvs(loc=exp_min_size, scale=exp_mean_size, size=N)) return np.random.normal(mu, scale=sigma, size=N), sigma
def central_limit_theorem():
y = []
n=100
for i in range(1000):
r = expon.rvs(scale=1, size=n)
rsum=np.sum(r)
z=(rsum-n)/np.sqrt(n)
y.append(z)
plt.hist(y,color='grey')
plt.savefig('central_limit_theorem.png')
def poisson_rate(exposuretime):
'''Generate Poisson distributed times.
Parameters
----------
exposuretime : float
Returns
-------
times : `numpy.ndarray`
Poisson distributed times.
'''
# Make 10 % more numbers then we expect to need, because it's random
times = expon.rvs(scale=1./rate, size=exposuretime * rate * 1.1)
# If we don't have enough numbers right now, add some more.
while times.sum() < exposuretime:
times = np.hstack([times, expon.rvs(scale=1/rate,
size=(exposuretime - times.sum() * rate * 1.1))])
times = np.cumsum(times)
return times[times < exposuretime]
def generate_random_exponential_data(dlamb, num = 100):
"""
This function will generate some random exponential 2d data. There is
no time series information here. This is just a one-time bunch of points.
parameters:
dlamb: float - the exponential lambda parameter
num: int - total number of coordinates
returns:
numpy array of coordinates.
"""
xcoord = expon.rvs(loc=0, scale = dlamb, size = num)
ycoord = expon.rvs(loc=0, scale = dlamb, size = num)
return np.asarray(zip(xcoord, ycoord), dtype=np.float64)
def reducedChiHist(self):
def funcExpon(x, a, b, c, d):
retval = a*np.exp(-b*(x-d)) + c
retval[x < d] = 0
return retval
tau = 25.0
t0 = 40
nBins = 800
size = 10000
taulist = []
for i in range(100):
timeHgValues = np.zeros(nBins, dtype=np.int64)
timeStamps = expon.rvs(loc=0, scale=tau, size=size) + t0
ts64 = timeStamps.astype(np.uint64)
tsBinner.tsBinner(ts64, timeHgValues)
xPoints = []
yPoints = []
for x in range(nBins):
y = timeHgValues[x]
if y > 2:
xPoints.append(x)
yPoints.append(y)
bGuess = 1/(np.mean(timeStamps))
aGuess = bGuess*(size)
cGuess = 0
dGuess = t0
pGuess = [aGuess, bGuess, cGuess, dGuess]
xArray = np.array(xPoints) #must be in array for not list to use curve_fit
yArray = np.array(yPoints)
ySigma = (yArray ** 1/2)
popt, pcov = curve_fit(funcExpon, xArray, yArray, p0=pGuess, sigma=ySigma)
xPlot = np.linspace(xArray[0], xArray[-1], 1000)
yPlot = funcExpon(xPlot, *popt)
yPlotAtPoints = funcExpon(xArray, *popt)
chi_2 = sum(((yArray-yPlotAtPoints)**2)/ySigma)
red_chi_2 = chi_2/(len(yArray)-len(popt))
print red_chi_2
hist,bins = np.histogram(red_chi_2, bins=20)
width = 0.7*(bins[1]-bins[0])
center = (bins[:-1]+bins[1:])/2
plt.step(center, hist, where = 'post')
plt.savefig(inspect.stack()[0][3]+".png")
def buildMat(_M=1,_N=1,_pConJ=0.1,_pConR=1,_J=1.,_sdJ=0.,_R=10.,_sdR=0.,_dist="bernouilli",_isSym=True,_isUni=False,_type="all"):
####pick values#######
minDim=min(_N,_M);
if _dist=="bernouilli":
temp=np.triu(bernoulli.rvs(_pConJ,size=(_M,_N)));
temp[:minDim,:minDim]=temp[:minDim,:minDim]-diag(diagonal(temp))+diag(bernoulli.rvs(_pConR,size=(minDim)));
if _dist=="poisson":
temp=np.triu(poisson.rvs(_pConJ,size=(_M,_N)));
temp[:minDim,:minDim]=temp[:minDim,:minDim]-diag(diagonal(temp))+diag(poisson.rvs(_pConR,size=(minDim)));
elif _dist=="uniform":
temp=_J+_sdJ*(0.5-np.triu(uniform.rvs(size=(_M,_N))));
temp[:minDim,:minDim]=temp[:minDim,:minDim]-diag(diagonal(temp))+diag(_R+_sdR*(0.5-uniform.rvs(size=(minDim))));
elif _dist=="expon":
temp=np.triu(expon.rvs(_J,size=(_M,_N)));
temp[:minDim,:minDim]=temp[:minDim,:minDim]-diag(diagonal(temp))+diag(expon.rvs(_R,size=(minDim)));
elif _dist=="norm":
temp=_sdJ*np.triu(norm.rvs(_J,size=(_M,_N)));
temp[:minDim,:minDim]=temp[:minDim,:minDim]-diag(diagonal(temp))+diag(_sdR*norm.rvs(_R,size=(minDim)));
####symmetrize matrix###
if _isSym==True:
if _N==_M:
temp=_J*(temp.T+temp-2*diag(diagonal(temp)))+_R*diag(diagonal(temp));
else:
print("buildMat : N!=M, cannot 'symmetrize' the matrix");
####unitarize matrix###
if _isUni==True:
if _isSym==True:
print("buildMat : WARNING : isUni=True, the matrix will not be symetric...");
temp,s,VT=svd(temp);
####render dense or sparse matrix####
if _type=="all":
return temp;
elif _type=="sparse":
return scipy.sparse.lil_matrix(temp);
def testScipyExponential():
data0 = expon.rvs(scale=10, size=1000)
###################
data = data0
plt.figure()
x = np.linspace(0, 100, 100)
plt.hist(data, bins=x, normed=True)
plt.plot(x, expon.pdf(x, loc=0, scale=10), color='g')
#loc, scale = expon.fit(data, floc=0)
#plt.plot(x, expon.pdf(x, loc=loc, scale=scale), color='r')
removedHeadLength = 1.0
dataNoHead = [v for v in data if v > removedHeadLength]
loc1, scale1 = expon.fit(dataNoHead)
plt.plot(x, expon.pdf(x, loc=0, scale=scale1), color='b')
loc, scale = expon.fit(dataNoHead, floc=removedHeadLength)
plt.plot(x, expon.pdf(x, loc=0, scale=scale), color='r')
# non-normed graphs
# plt.figure()
# plt.hist(data0, bins=x, normed=False)
# plt.plot(x, expon.pdf(x, loc=0, scale=10)*len(data0), color='r')
plt.figure()
plt.hist(dataNoHead, bins=x, normed=False)
# s = len(dataNoHead) / sInvNormalisation = intergral(pdf, removedHeadLength, infty)
int_0_removedHeadLength_expon = np.exp(- float(removedHeadLength) / scale)
s = len(dataNoHead) / int_0_removedHeadLength_expon
s0 = len(data0) / 1.0
print >> sys.stderr, s0, len(dataNoHead), s
plt.plot(x, expon.pdf(x, loc=0, scale=scale)*s, color='r')
##############################################################
# deprecated
##############################################################
# non-linear fit
#A, K, C = fit_exp_nonlinear(t, noisy)
# linear fit with the constant set to 0
# C = 0
# A, K = fit_exp_linear(t, noisy, C)
# ysModel = model_func(t, A, K, C)
#plt.tight_layout()
#plt.xlim(0, 100)
#plt.title("OSB length distribution in Human-Mouse comparison \n Confidence Interval : %s*sigma around mean" % arguments["ICfactorOfSigma"] )
#plt.title("")
# #plt.legend()
#plt.savefig(sys.stdout, format='svg')
def sampling_distribution():
fig, ax = plt.subplots(1, 1)
x = np.linspace(-5,5,100)
ax.plot(x,norm.pdf(x))
# 中心极限定理，样本均值服从正态分布（当样本足够大的时候）
y = []
n = 100
for i in range(1000):
r = expon.rvs(scale = 2 , size = 100)
rsum = np.sum(r)
z = (rsum - 100*2)/np.sqrt(4*100)
y.append(z)
ax.hist(y,normed = True,alpha=0.2)
plt.show()
def poisson_rate(exposuretime, geomarea):
'''Generate Poisson distributed times.
Parameters
----------
exposuretime : float
Exposure time in sec.
geomarea : `astropy.unit.Quantity`
Geometric opening area of telescope
Returns
-------
times : `numpy.ndarray`
Poisson distributed times.
'''
fullrate = rate * geomarea.to(u.cm**2).value
# Make 10 % more numbers then we expect to need, because it's random
times = expon.rvs(scale=1./fullrate, size=int(exposuretime * fullrate * 1.1))
# If we don't have enough numbers right now, add some more.
while times.sum() < exposuretime:
times = np.hstack([times, expon.rvs(scale=1/fullrate,
size=int(exposuretime - times.sum() * fullrate * 1.1))])
times = np.cumsum(times)
return times[times < exposuretime]
def sampling_distribution():
fig, ax = plt.subplots(1, 1)
#display the probability density function
x = np.linspace(-4, 4, 100)
ax.plot(x, norm.pdf(x))
#simulate the sampling distribution
y = []
n=100
for i in range(1000):
r = expon.rvs(scale=1, size=n)
rsum=np.sum(r)
z=(rsum-n)/np.sqrt(n)
y.append(z)
ax.hist(y, normed=True, alpha=0.2)
plt.show()
def printReducedChi(self):
def funcExpon(x, a, b, c, d):
retval = a*np.exp(-b*(x-d)) + c
retval[x < d] = 0
return retval
tau = 25.0
t0 = 40
nBins = 800
size = 10000
taulist = []
for i in range(100):
timeHgValues = np.zeros(nBins, dtype=np.int64)
timeStamps = expon.rvs(loc=0, scale=tau, size=size) + t0
ts64 = timeStamps.astype(np.uint64)
tsBinner.tsBinner(ts64, timeHgValues)
xPoints = []
yPoints = []
for x in range(nBins):
y = timeHgValues[x]
if y > 2:
xPoints.append(x)
yPoints.append(y)
bGuess = 1/(np.mean(timeStamps))
aGuess = bGuess*(size)
cGuess = 0
dGuess = t0
pGuess = [aGuess, bGuess, cGuess, dGuess]
xArray = np.array(xPoints) #must be in array for not list to use curve_fit
yArray = np.array(yPoints)
ySigma = (yArray ** 1/2)
popt, pcov = curve_fit(funcExpon, xArray, yArray, p0=pGuess, sigma=ySigma)
xPlot = np.linspace(xArray[0], xArray[-1], 1000)
yPlot = funcExpon(xPlot, *popt)
yPlotAtPoints = funcExpon(xArray, *popt)
chi_2 = sum(((yArray-yPlotAtPoints)**2)/ySigma)
red_chi_2 = chi_2/(len(yArray)-len(popt))
print red_chi_2
def central_limit_theorem():
y = []
n=100
for i in range(1000):
r = expon.rvs(scale=1, size=n)
rsum=np.sum(r)
z=(rsum-n)/np.sqrt(n)
y.append(z)
plt.subplot(211)
print y
plt.hist(y,color='grey')
y2 = []
for i in range(10000):
r = poisson.rvs(3 , size = n)
rsum = np.sum(r)
z = (rsum - n)/np.sqrt(n)
y2.append(z)
plt.subplot(212)
plt.hist(y2,color='r')
plt.show()
def gillespie(rate_funcs,stop_time,init_state,updates):
n_reacts = len(rate_funcs)
t = 0
s = tuple(init_state)
path = [(t,s)]
while True:
jump_rates = [f(s) for f in rate_funcs]
exit_rate = sum(jump_rates)
if exit_rate == 0:
break
probs = [r/exit_rate for r in jump_rates]
index = np.random.choice(n_reacts,p=probs)
t = t + expon.rvs(scale=1/jump_rates[index])
if t >= stop_time:
break
s = update_state(s,updates[index])
#s = tuple(map(add,s,updates[index])) #extra tuple() for Python 3.x
#s = tuple(x+y for (x,y) in zip(s,updates[index]))
path = path + [(t,s)]
path = path + [(stop_time,s)]
return path
def _plot_correct_weights():
# draw data from an exponential distribution
from scipy.stats import expon
import pylab as P
scale = 1.0
data = expon.rvs(scale=scale, size=8000)
bandwidth = 20/np.sqrt(data.shape[0])
range = np.array([0, 7])
n = 500
y = np.linspace(range[0], range[1], num=n)
eps = 1e-5
## Use corrected samples
q = _correct_weights(data, bandwidth, range, filter=False)
target_densities1 = figtree(data, y, q, bandwidth, epsilon=eps, eval="auto", verbose=True)
# now try again with uncorrected densities
q = np.ones(data.shape)
target_densities2 = figtree(data, y, q, bandwidth, epsilon=eps, eval="auto", verbose=True)
print("Smallest sample at %g" % min(data))
# plot the exponential density with max. likelihood estimate of the scale
P.plot(y, expon.pdf(y, scale=np.mean(data)))
P.plot(y, target_densities1 , 'ro')
P.title("Gaussian Kernel Density Estimation")
# P.show()
P.savefig("KDE_50000_h-0.05.pdf")
from scipy.stats import lognorm, expon
# Trying out different broad distributions with linear and logarithmic PDFs:
n_points = 100000
# power law:
# slope = -2!
one_over_rands = 1/np.random.rand(n_points)
# http://en.wikipedia.org/wiki/Power_law
# exponential distribution
exps = expon.rvs(size=1000)
# http://en.wikipedia.org/wiki/Exponential_distribution
# lognormal (looks like a normal distribution in a log-log scale!)
lognorms = lognorm.rvs(1.0, size=1000)
# http://en.wikipedia.org/wiki/Log-normal_distribution
fig = plt.figure(figsize=(15,15))
fig.suptitle('Different broad distribution PDFs in lin-lin, log-log, and lin-log axes')
n_bins = 30
for i, (rands, name) in enumerate(zip([one_over_rands, exps, lognorms],
["power law", "exponential", "lognormal"])):
# linear-linear scale
ax = fig.add_subplot(4, 3, i+1)
ax.hist(rands, n_bins, normed=True)
