def get_ui(self, params: List[ndarray], bounds: Tuple[float,
float]) -> ndarray:
mean = params[0] * params[1]
return [
poisson.ppf(bounds[0], mu=mean),
poisson.ppf(bounds[1], mu=mean)
]
def apply_shape_settings(self):
self._PERIOD_WITH_COMPUTED_LIMITS = int(
config.LIMITER_FULL_COLLECTION_PERIOD_S * 1.2)
self._MIN_SUBMITS_IN_TIME = \
[poisson.ppf(config.LIMITER_MIN_SUBMITS_PERCENTILE,
i * config.LIMITER_TARGET_SUBMISSION_RATE * config.LIMITER_MIN_OK_SUBMITS_RATIO) \
for i in range(self._PERIOD_WITH_COMPUTED_LIMITS + 1)]
self._MAX_SUBMITS_IN_TIME = \
[poisson.ppf(config.LIMITER_MAX_SUBMITS_PERCENTILE,
i * config.LIMITER_TARGET_SUBMISSION_RATE * config.LIMITER_MAX_OK_SUBMITS_RATIO) \
for i in range(self._PERIOD_WITH_COMPUTED_LIMITS + 1)]
# Find the first non-zero expected value of minimal submission count
for i in range(1, config.LIMITER_FULL_COLLECTION_PERIOD_S):
# At least one submit is expected in i-th second
if self._MIN_SUBMITS_IN_TIME[i] >= 1:
self._NO_SHARE_RECALCULATION_PERIOD = i
break
# If we didn't find the right spot, full collection period is used
# (should never happen)
else:
self._NO_SHARE_RECALCULATION_PERIOD = config.LIMITER_FULL_COLLECTION_PERIOD_S
log.error("Non-zero minimal submissions not found")
# Recalculate collection period
self._HALF_COLLECTION_PERIOD = int(
config.LIMITER_FULL_COLLECTION_PERIOD_S / 2)
self._FINE_TUNE_UPPER_RATE = config.LIMITER_TARGET_SUBMISSION_RATE * \
config.LIMITER_FINE_TUNE_UPPER_RATIO
self._FINE_TUNE_LOWER_RATE = config.LIMITER_TARGET_SUBMISSION_RATE * \
config.LIMITER_FINE_TUNE_LOWER_RATIO
def plot_total(
self,
kwargs: Dict = dict(ls='', marker='.'),
line_kwargs: Dict = dict(),
fill_kwargs: Dict = dict()
) -> None:
r"""Plot the SFS using matplotlib
Args:
kwargs: keyword arguments for scatter plot
line_kwargs: keyword arguments for expectation line
fill_kwargs: keyword arguments for marginal fill
"""
x = self.X.sum(1, keepdims=True)
plt.plot(range(1, len(x) + 1), x, **kwargs)
if self.η is not None:
if 'label' in kwargs:
del kwargs['label']
if self.μ is not None:
z = self.μ.Z.sum(1)
else:
z = np.ones_like(self.η.y)
ξ = self.L.dot(z)
plt.plot(range(1, self.n), ξ, **line_kwargs)
ξ_lower = poisson.ppf(.025, ξ)
ξ_upper = poisson.ppf(.975, ξ)
plt.fill_between(range(1, self.n), ξ_lower, ξ_upper, **fill_kwargs)
plt.xlabel('sample frequency')
plt.ylabel(r'variant count')
plt.tight_layout()
def rentA(self):
prob_dict = {}
x = np.arange(poisson.ppf(0.0001, 3), poisson.ppf(0.9999, 3))
for i in x:
prob_dict[i] = poisson.pmf(i, 3)
return prob_dict
def returnB(self):
prob_dict = {}
x = np.arange(poisson.ppf(0.0001, 2), poisson.ppf(0.9999, 2))
for i in x:
prob_dict[i] = poisson.pmf(i, 2)
return prob_dict
def locate_termination(samfile, chrom, strand, gene_exons):
'''
Returns the window termination location of the gene in gene_exons
'''
# Initialize params
threshold = 0.01
s_t = 75
s_w = 100
l_g = 1000
n_w = (l_g - s_w) / s_t + 1
if strand == '-':
start = gene_exons['LOC1'].iloc[0]
end = start + 1000
N = samfile.count(chrom, start=start, end=end)
N_w = N * s_w / l_g
m = poisson.ppf(threshold, N_w)
else:
end = gene_exons['LOC2'].iloc[-1]
start = end - 1000
N = samfile.count(chrom, start=start, end=end)
N_w = N * s_w / l_g
m = poisson.ppf(threshold, N_w)
if m != 0:
return slide_window(samfile, chrom, start, end, strand, n_w, m, s_w,
s_t)
else:
return 1
def apply_shape_settings(self):
self._PERIOD_WITH_COMPUTED_LIMITS = int(config.LIMITER_FULL_COLLECTION_PERIOD_S * 1.2)
self._MIN_SUBMITS_IN_TIME = \
[poisson.ppf(config.LIMITER_MIN_SUBMITS_PERCENTILE,
i * config.LIMITER_TARGET_SUBMISSION_RATE * config.LIMITER_MIN_OK_SUBMITS_RATIO) \
for i in range(self._PERIOD_WITH_COMPUTED_LIMITS + 1)]
self._MAX_SUBMITS_IN_TIME = \
[poisson.ppf(config.LIMITER_MAX_SUBMITS_PERCENTILE,
i * config.LIMITER_TARGET_SUBMISSION_RATE * config.LIMITER_MAX_OK_SUBMITS_RATIO) \
for i in range(self._PERIOD_WITH_COMPUTED_LIMITS + 1)]
# Find the first non-zero expected value of minimal submission count
for i in range(1, config.LIMITER_FULL_COLLECTION_PERIOD_S):
# At least one submit is expected in i-th second
if self._MIN_SUBMITS_IN_TIME[i] >= 1:
self._NO_SHARE_RECALCULATION_PERIOD = i
break
# If we didn't find the right spot, full collection period is used
# (should never happen)
else:
self._NO_SHARE_RECALCULATION_PERIOD = config.LIMITER_FULL_COLLECTION_PERIOD_S
log.error("Non-zero minimal submissions not found")
# Recalculate collection period
self._HALF_COLLECTION_PERIOD = int(config.LIMITER_FULL_COLLECTION_PERIOD_S / 2)
self._FINE_TUNE_UPPER_RATE = config.LIMITER_TARGET_SUBMISSION_RATE * \
config.LIMITER_FINE_TUNE_UPPER_RATIO
self._FINE_TUNE_LOWER_RATE = config.LIMITER_TARGET_SUBMISSION_RATE * \
config.LIMITER_FINE_TUNE_LOWER_RATIO
def probf_baharev(df1, df2, noncen, fcrit):
x = 1 - special.btdtri(df1, df2, fcrit)
eps = 1.0e-7
itr_cnt = 0
f = None
while itr_cnt <= 10:
mu = noncen / 2.0
ql = poisson.ppf(eps, mu)
qu = poisson.ppf(1 - eps, mu)
k = qu
c = beta.cdf(x, df1 + k, df2)
d = x * (1.0 - x) / (df1 + k - 1.0) * beta.pdf(x, df1 + k - 1, df2, 0)
p = poisson.pmf(k, mu)
f = p * c
p = k / mu * p
k = qu - 1
while k >= ql:
c = c + d
d = (df1 + k) / (x * (df1 + k + df2 - 1)) * d
f = f + p * c
p = k / mu * p
k = k - 1
itr_cnt = itr_cnt + 1
if (itr_cnt == 11):
print("newton iteration failed")
return f
def plot_poisson():
fig, ax = plt.subplots(1, 1)
# This is prediction for Wawrinka in 2014
mu = 7.869325
x = np.arange(poisson.ppf(0.01, mu), poisson.ppf(0.999, mu))
ax.plot(x, poisson.pmf(x, mu), 'wo', ms=8, label='poisson pmf')
ax.vlines(x, 0, poisson.pmf(x, mu),
colors=['b', 'b', 'b', 'b', 'b', 'r', 'r', 'r', 'g', 'g', 'g', 'g', 'g', 'g', 'g', 'g'], lw=5, alpha=0.5)
rv = poisson(mu)
ax.vlines(x, 0, rv.pmf(x), colors='k', linestyles='-', lw=1, label='frozen pmf')
plt.title("Stanislas Wawrinka")
plt.xlabel('# QF+ Finishes in 2014')
plt.ylabel('Probability')
prob0 = poisson.cdf(6, mu)
prob123 = poisson.cdf(9, mu) - poisson.cdf(6, mu)
probAbove3 = poisson.cdf(10000, mu) - poisson.cdf(9, mu)
print prob0
print prob123
print probAbove3
plt.show()
def tpoissrnd(lam):
# lam MUST be an array
if not np.isscalar(lam):
x = np.ones(len(lam))
ind = lam > 1e-5 # below this value x=1 whp
#ind = ind[:, 0]
if np.any(ind):
n_ = sum(ind)
lam_ = lam[ind]
x[ind] = poisson.ppf(
np.exp(-lam_) +
np.multiply(np.random.rand(n_), 1 - np.exp(-lam_)),
lam_) #[:, 0]
else:
x = 1
ind = lam > 1e-5
if np.any(ind):
n_ = ind
# lam_ = lam[ind]
x = poisson.ppf(
np.exp(-lam) + np.random.rand() * (1 - np.exp(-lam)), lam)
#if x == 0:
# x = 1
return x
def run(p, tMax, fBest, rateIncreaseRatio, outputFilename):
alpha = 0.005
badBlocks = genAttackBlocks(alpha, p, fBest, rateIncreaseRatio, tMax)
# for i in xrange(len(badBlocks)):
# print("Block at %.2f, bounds: (%.2f, %.2f)" %
# ((badBlocks[i],) +
# poissonInterval(i, alpha, p * badBlocks[i])))
# print("Actual rate: %.2f" % (len(badBlocks) / badBlocks[-1]))
# Generate CSV
output = ""
output += "t, GoodFreqLow, GoodFreqAvg, GoodFreqHigh, BadFreqAvg, AdvantageRatio\n"
pointCount = 100
badBlockI = 0
for t in linspace(0, badBlocks[-2], num=pointCount)[1:]:
while badBlocks[badBlockI + 1] <= t:
badBlockI += 1
output += "%.2f, %.2f, %.2f, %.2f, %.2f, %.2f\n" % (
t, # Current time
poisson.ppf(0.05,
t * fBest * p), # Number of good blocks: lower bound
round(t * fBest * p), # Rounded number of good blocks estimate
poisson.ppf(0.95,
t * fBest * p), # Number of good blocks: upper bound
round(badBlockI), # Number of bad blocks
float(badBlockI) / (t * fBest * p) # Advantage ratio
)
outputFile = open(outputFilename, "w")
outputFile.write(output)
outputFile.close()
def poisson_and_sim_events(mu, size=10000):
"""
This function is used for calculating the Poisson probabilities and for
randomnly generating new events from the Poisson distribution for a
number of years for the scenario we want to check.
:param: mu: the average annual number of storms for the scenario
size: the number of years
:return: sim_ev: the time series of new simulated events
x: array of potential numbers of hurricanes per year based on the
mu
"""
# Getting the Poisson probabilities
# Array of potential numbers of hurricanes per year
x = np.arange(poisson.ppf(0.01, mu), poisson.ppf(0.99, mu) * 2)
# Probability of each of x occuring
prob = poisson.cdf(x, mu)
# Checking accuracy of cdf and ppf
print(np.allclose(x, poisson.ppf(prob, mu))) # must be True
# GENERATING RANDOM NUMBERS FROM THE POISSON DISTRIBUTION
# size = 10000 # choosing how many years of events we want
sim_ev = poisson.rvs(mu, size=size) # getting the random numbers
return sim_ev, x
def model():
µ = 4
x = np.arange(poisson.ppf(0.01, µ), poisson.ppf(0.99, µ))
y = poisson.pmf(x, µ)
prior_hist = plot.hist(x,
np.arange(0, 10),
weights=y,
align="left",
rwidth=0.8)
def test_poisson(self):
mu = 0.6
mean, var, skew, kurt = poisson.stats(mu, moments='mvsk')
self.assertEqual(mean, 0.6)
self.assertEqual(var, 0.6)
self.assertEqual(skew, 1.2909944487358056)
self.assertEqual(kurt, 1.6666666666666667)
n = np.array([0., 1., 2.])
x = np.arange(poisson.ppf(0.01, mu), poisson.ppf(0.99, mu))
self.assertTrue(np.array_equal(n, x))
def ppf_cached(y,cache={}):
x=round(y,4)
if x==0:
return(poisson.ppf(0.99999999,y))
if x in cache: return cache[x]
ppf=poisson.ppf(0.99999999,x)
if np.isnan(ppf) or ppf==np.inf:
print("wtf:",y,x)
cache[x]=max(ppf,1)
return ppf
def test_round_poisson(self):
random_state = RandomState()
avg = 3.4
samples = 1000
rounds = [random_state.round_poisson(avg) for i in range(samples)]
obs_avg = np.mean(rounds)
min = poisson.ppf(0.001, mu=avg)
max = poisson.ppf(0.999, mu=avg)
self.assertGreater(obs_avg, min)
self.assertLess(obs_avg, max)
def generate_data(self, copulas, lambdas=None):
arr = []
if lambdas is None: # if no vars is passed, randomly generate dependence
lambdas = np.random.uniform(0.5, 6, size=len(copulas))
firstArr = self.removeNans(copulas[0])
arr_poisson = np.array(poisson.ppf(firstArr, lambdas[0]))
for i in range(len(copulas)):
poiss = np.array(
poisson.ppf(self.removeNans(copulas[i]), lambdas[i]))
arr.append(poiss)
return np.asarray(arr)
def forward_epi_step(self, dB: int = 0):
# get previous state
S, E, I, R, D, N = (vector[-1] for vector in (self.S, self.E, self.I,
self.R, self.D, self.N))
# update state
Rt = self.Rt0 * float(S) / float(N)
b = np.exp(self.gamma * (Rt - 1))
rate_T = max(0, self.b[-1] * self.dT[-1])
num_cases = poisson.rvs(rate_T)
self.upper_CI.append(poisson.ppf(self.CI, rate_T))
self.lower_CI.append(poisson.ppf(1 - self.CI, rate_T))
E += num_cases
S -= num_cases
rate_I = self.sigma * E
num_inf = poisson.rvs(rate_I)
E -= num_inf
I += num_inf
rate_D = self.m * self.gamma * I
num_dead = poisson.rvs(rate_D)
D += num_dead
rate_R = (1 - self.m) * self.gamma * I
num_recov = poisson.rvs(rate_R)
R += num_recov
I -= (num_dead + num_recov)
if S < 0: S = 0
if E < 0: E = 0
if I < 0: I = 0
if R < 0: R = 0
if D < 0: D = 0
N = S + E + I + R
beta = (num_cases * N) / (b * S * I)
# update state vectors
self.Rt.append(Rt)
self.b.append(b)
self.S.append(S)
self.E.append(E)
self.I.append(I)
self.R.append(R)
self.D.append(D)
self.N.append(N)
self.beta.append(beta)
self.dT.append(num_cases)
self.total_cases.append(E + I + R + D)
def durations(self):
"""
持続時間の分布のsdも確率的に生成させたほうが良さそう。
20msを1としたとき、20, 100, 150, 200 あたりが
ただし /u/ の「内在時間長」は「とりわけ」短い。
poisson のつかいかたは [poisson] を参照
[poisson]: https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.poisson.html
"""
eps = np.finfo(float).eps
mu_range = np.arange(poisson.ppf(eps, min(self.poisson_params)),
poisson.ppf(1 - eps, max(self.poisson_params)))
return np.array([poisson.pmf(mu_range, pa) for pa in self.poisson_params])
def poissonFunc():
mu = 10
for i in range(len(size)):
n = size[i]
fig, ax = plt.subplots(1, 1)
ax.set_title("Распределение Пуассона, n = " + str(n))
x = np.arange(poisson.ppf(0.01, mu), poisson.ppf(0.99, mu))
ax.plot(x, poisson(mu).pmf(x), 'b-', ms=8)
r = poisson.rvs(mu, size=n)
ax.hist(r, density=True, histtype='stepfilled', alpha=0.2)
plt.show()
def poisNumbers():
for size in sizes:
fig, ax = plt.subplots(1, 1)
ax.hist(poisson.rvs(10, size=size), histtype='stepfilled', alpha=0.5, color='blue', density=True)
x = np.arange(poisson.ppf(0.01, 10), poisson.ppf(0.99, 10))
ax.plot(x, poisson(10).pmf(x), '-')
ax.set_title('PoisNumbers n = ' + str(size))
ax.set_xlabel('PoisNumbers')
ax.set_ylabel('density')
plt.grid()
plt.show()
return
def Poisson():
for s in size:
den = poisson(10)
hist = poisson.rvs(10, size=s)
fig, ax = plt.subplots(1, 1)
ax.hist(hist, density=True, alpha=0.6)
x = np.arange(poisson.ppf(0.01, 10), poisson.ppf(0.99, 10))
ax.plot(x, den.pmf(x), LINE_TYPE, lw=1.5)
ax.set_xlabel("POISSON")
ax.set_ylabel("DENSITY")
ax.set_title("SIZE: " + str(s))
plt.grid()
plt.show()
def ppf_mtc(y,N,cache={}):
pp=(1.0-(args.pvalue/N))
if pp==1.0:
pp=1.0-np.finfo(float).resolution
x=round(y,4)
if x==0:
ppf=poisson.ppf(pp,y)
if np.isnan(ppf) or np.isinf(ppf):
print("wtf:",y,x,ppf,(1.0-(args.pvalue/N)),N)
return ppf
if (x) in cache: return cache[x]
ppf=poisson.ppf(pp,x)
cache[x]=max(ppf,1)
return ppf
def _get_prediction(self, rates, data, percentile):
flag = list()
for ind, rate in enumerate(rates):
if rate > 0.0:
lower = poisson.ppf(percentile, rate)
upper = poisson.ppf(1 - percentile, rate)
if data[ind] < lower or data[ind] > upper:
flag.append(1)
else:
flag.append(0)
else:
rospy.logwarn("Occurrence rate is %.2f" % rate)
flag.append(-1)
return flag
def qNBI(q: float, location: np.ndarray, scale: np.ndarray):
"""Quantile function.
"""
n = 1 / scale
p = n / (n + location)
if len(scale) > 1:
quant = np.where(scale > 1e-04, nbinom.ppf(q=q, n=n, p=p),
poisson.ppf(q=q, mu=location))
else:
quant = poisson.ppf(q=q,
mu=location) if scale < 1e-04 else nbinom.ppf(
q=q, n=n, p=p)
return quant
def _get_prediction(self, rates, data, percentile):
flag = list()
for ind, rate in enumerate(rates):
if rate > 0.0:
lower = poisson.ppf(percentile, rate)
upper = poisson.ppf(1-percentile, rate)
if data[ind] < lower or data[ind] > upper:
flag.append(1)
else:
flag.append(0)
else:
rospy.logwarn("Occurrence rate is %.2f" % rate)
flag.append(-1)
return flag
def index():
if request.method == 'GET':
if (app.vars['firstTime']):
return render_template('intro_beforeMap.html')
else:
try:
rtDF = getRealTimeDockStatusData(app.vars['url2scrapeRT'])
mergedDF = (app.vars['stations']).merge(
rtDF, 'inner', 'terminalname')
mergedDF['muBikesW'] = mergedDF['bikeDemand'] * app.vars[
'window'] / 60.
mergedDF['muDocksW'] = mergedDF['dockDemand'] * app.vars[
'window'] / 60.
mergedDF['ppf0005_B'] = 1 + poisson.ppf(
0.9995, mergedDF['muBikesW']).astype(int)
mergedDF['ppf0005_D'] = 1 + poisson.ppf(
0.9995, mergedDF['muDocksW']).astype(int)
mergedDF['pEmpty'] = mergedDF.apply(lambda x: pOutage(
x['muBikesW'], x['muDocksW'], x['nbbikes']),
axis=1)
mergedDF['pFull'] = mergedDF.apply(lambda x: pOutage(
x['muDocksW'], x['muBikesW'], x['nbemptydocks']),
axis=1)
sendGJ = df_to_geojson(mergedDF, [
'terminalname', 'name', 'nbbikes', 'nbemptydocks',
'bikeDemand', 'dockDemand', 'ppf0005_B', 'ppf0005_D',
'pEmpty', 'pFull'
],
lat='lat',
lon='long')
return render_template('withMap.html',
num=app.vars['window'],
gjFC_StationData=sendGJ)
except:
#print('fail')
return render_template('withoutMap.html',
num=app.vars['window'],
gjFC_StationData=app.vars['gjS'])
else:
#request was a POST
tempInput = request.form['myWindow']
app.vars['firstTime'] = False
try:
app.vars['window'] = min([abs(int(float(tempInput))),
60]) # limit one hour
except:
app.vars[
'window'] = 15 # default to 15 minutes, if input cannot be converted to numeric
return redirect('/')
def plot_total(
self,
kwargs: Dict = dict(ls="", marker="."),
line_kwargs: Dict = dict(),
fill_kwargs: Dict = dict(),
folded: bool = False,
) -> None:
r"""Plot the SFS using matplotlib
Args:
kwargs: keyword arguments for scatter plot
line_kwargs: keyword arguments for expectation line
fill_kwargs: keyword arguments for marginal fill
folded: if ``True``, plot the folded SFS and fit
"""
if self.X.ndim == 1:
x = self.X
else:
x = self.X.sum(1)
if folded:
x = utils.fold(x)
plt.plot(range(1, len(x) + 1), x, **kwargs)
if self.η is not None:
if "label" in kwargs:
del kwargs["label"]
if self.μ is not None:
self.η.check_grid(self.μ)
z = self.μ.Z.sum(1)
else:
z = self.mu0 * np.ones_like(self.η.y)
ξ = self.L.dot(z)
if folded:
ξ = utils.fold(ξ)
else:
if self.r is None:
raise TypeError("ancestral state misidentification rate "
"is not inferred, do you want "
"folded=True?")
ξ = (1 - self.r) * ξ + self.r * self.AM_freq @ ξ
plt.plot(range(1, len(ξ) + 1), ξ, **line_kwargs)
ξ_lower = poisson.ppf(0.025, ξ)
ξ_upper = poisson.ppf(0.975, ξ)
plt.fill_between(range(1,
len(ξ) + 1), ξ_lower, ξ_upper,
**fill_kwargs)
plt.xlabel("sample frequency")
plt.gca().xaxis.set_major_locator(MaxNLocator(integer=True))
plt.ylabel(r"variant count")
plt.tight_layout()
def parallel_forward_epi_step(self, dB: int = 0, num_sims=10000):
# get previous state
S, I, R, D, N = (vector[-1].copy()
for vector in (self.S, self.I, self.R, self.D,
self.N))
# update state
Rt = self.Rt0 * S / N
b = np.exp(self.gamma * (Rt - 1))
rate_T = (self.b[-1] * self.dT[-1]).clip(0)
num_cases = poisson.rvs(rate_T, size=num_sims)
self.upper_CI.append(poisson.ppf(self.CI, rate_T))
self.lower_CI.append(poisson.ppf(1 - self.CI, rate_T))
I += num_cases
S -= num_cases
rate_D = self.m * self.gamma * I
num_dead = poisson.rvs(rate_D, size=num_sims)
D += num_dead
rate_R = (1 - self.m) * self.gamma * I
num_recov = poisson.rvs(rate_R, size=num_sims)
R += num_recov
I -= (num_dead + num_recov)
S = S.clip(0)
I = I.clip(0)
D = D.clip(0)
N = S + I + R
beta = (num_cases * N) / (b * S * I)
# update state vectors
self.Rt.append(Rt)
self.b.append(b)
self.S.append(S)
self.I.append(I)
self.R.append(R)
self.D.append(D)
self.dR.append(num_recov)
self.dD.append(num_dead)
self.N.append(N)
self.beta.append(beta)
self.dT.append(num_cases)
self.total_cases.append(I + R + D)
def ztp(N, lambda_):
"""Zero truncated Poisson distribution"""
temp = [poisson.pmf(0, item) for item in lambda_]
p = [uniform.rvs(loc=item, scale=1-item) for item in temp]
ztp = [int(poisson.ppf(p[i], lambda_[i])) for i in range(len(p))]
return np.array(ztp)
def test_statistics(self):
# This is a statistical test that has a non-zero chance of failure
# during normal operation. Thus, we set the random seed to a value that
# creates a realization passing the test.
np.random.seed(seed=12345)
for rate in [self.rate_profile, self.rate_profile.rescale(kHz)]:
spiketrain = stgen.inhomogeneous_poisson_process(rate)
intervals = isi(spiketrain)
# Computing expected statistics and percentiles
expected_spike_count = (np.sum(rate) *
rate.sampling_period).simplified
percentile_count = poisson.ppf(.999, expected_spike_count)
expected_min_isi = (1 / np.min(rate))
expected_max_isi = (1 / np.max(rate))
percentile_min_isi = expon.ppf(.999, expected_min_isi)
percentile_max_isi = expon.ppf(.999, expected_max_isi)
# Testing (each should fail 1 every 1000 times)
self.assertLess(spiketrain.size, percentile_count)
self.assertLess(np.min(intervals), percentile_min_isi)
self.assertLess(np.max(intervals), percentile_max_isi)
# Testing t_start t_stop
self.assertEqual(rate.t_stop, spiketrain.t_stop)
self.assertEqual(rate.t_start, spiketrain.t_start)
# Testing type
spiketrain_as_array = stgen.inhomogeneous_poisson_process(
rate, as_array=True)
self.assertTrue(isinstance(spiketrain_as_array, np.ndarray))
self.assertTrue(isinstance(spiketrain, neo.SpikeTrain))
def test_statistics(self):
# This is a statistical test that has a non-zero chance of failure
# during normal operation. Thus, we set the random seed to a value that
# creates a realization passing the test.
np.random.seed(seed=12345)
for rate in [self.rate_profile, self.rate_profile.rescale(kHz)]:
spiketrain = stgen.inhomogeneous_poisson_process(rate)
intervals = isi(spiketrain)
# Computing expected statistics and percentiles
expected_spike_count = (np.sum(
rate) * rate.sampling_period).simplified
percentile_count = poisson.ppf(.999, expected_spike_count)
expected_min_isi = (1 / np.min(rate))
expected_max_isi = (1 / np.max(rate))
percentile_min_isi = expon.ppf(.999, expected_min_isi)
percentile_max_isi = expon.ppf(.999, expected_max_isi)
# Testing (each should fail 1 every 1000 times)
self.assertLess(spiketrain.size, percentile_count)
self.assertLess(np.min(intervals), percentile_min_isi)
self.assertLess(np.max(intervals), percentile_max_isi)
# Testing t_start t_stop
self.assertEqual(rate.t_stop, spiketrain.t_stop)
self.assertEqual(rate.t_start, spiketrain.t_start)
# Testing type
spiketrain_as_array = stgen.inhomogeneous_poisson_process(
rate, as_array=True)
self.assertTrue(isinstance(spiketrain_as_array, np.ndarray))
self.assertTrue(isinstance(spiketrain, neo.SpikeTrain))
def findOptimalPolicy(self):
# algorithm on Page 659
ystar = poisson.ppf(self.b / (self.b + self.h),
self.mu).astype(int) #base stock level
s = ystar - 1 #upper bound for s
S_0 = ystar + 0 #lower bound for S_0
#calculate the optimal s for S fixed at its lower bound S0
while self.c(s, S_0) > self.G(s):
s -= 1
s_0 = s # + 0 #optimal value of s for S0
c0 = self.c(s_0, S_0) #costs for this starting value
S0 = S_0 # + 0 # S0 = S^0 of the paper
S = S0 + 1
while self.G(S) <= c0:
if self.c(s, S) < c0:
S0 = S + 0
while self.c(s, S0) <= self.G(s + 1):
s += 1
c0 = self.c(s, S0)
S += 1
#print(str(s) + " " + str(S))
self.s_star = s
self.S_star = S0
return s, S0
def findOptimalPolicy(self):
# algorithm on Page 659
ystar = poisson.ppf(self.b / (self.b + self.h),
self.mu).astype(int) #base stock level
s = ystar - 1 #upper bound for s
S_0 = ystar + 0 #lower bound for S_0
#calculate the optimal s for S fixed at its lower bound S0
self.execution_path.append([s, S_0])
while self.c(s, S_0) > self.G(s):
s -= 1
self.execution_path.append([s, S_0])
s_0 = s # + 0 #optimal value of s for S0
c0 = self.c(s_0, S_0) #costs for this starting value
S0 = S_0 # + 0 # S0 = S^0 of the paper
S = S0 + 1
self.execution_path.append([s, S])
while self.G(S) <= c0:
if self.c(s, S) < c0:
S0 = S + 0
while self.c(s, S0) <= self.G(s + 1):
s += 1
self.execution_path.append([s, S0])
c0 = self.c(s, S0)
self.execution_path.append([s, S])
S += 1
#print(np.array(self.execution_path))
#self.plot()
self.s_star = s
self.S_star = S0
return s, S0
def qpois(p,mu):
"""
Calculates the quantile function of the Poisson distribution
"""
from scipy.stats import poisson
result=poisson.ppf(q=p,mu=mu)
return result
def ztpoisson(N, lambda_par):
"""Zero truncated Poisson distribution."""
temp = poisson.pmf(0, lambda_par)
p = [uniform.rvs(loc=item, scale=1-item) for item in temp]
ztp = [int(poisson.ppf(p[i],lambda_par[i])) for i in range(N)]
return np.array(ztp)
def add_gc_bias(meancoverages,targetcoverage): rand=poisson.rvs(targetcoverage) cumprob=poisson.cdf(rand,targetcoverage) # cdf(x, mu, loc=0) Cumulative density function. toret=[] for cov in meancoverages: if cov==0: toret.append(0) else: t=int(poisson.ppf(cumprob,cov)) # ppf(q, mu, loc=0) Percent point function (inverse of cdf percentiles). toret.append(t) return toret
def replenishment(stock,open_orders,quantile,sales_prog):
'''
:param stock: stock
:param open_orders: open incoming orders
:param quantile: chosen quantile
:param sales_prog: forecast for demand
:return: order
'''
sales_quant = poisson.ppf(quantile/100.,sales_prog+1.E-3)
order = max(0,(sales_quant) - (stock + open_orders))
return stochastic_round(order)
def get_num_trips(self, lam):
"""
Samples a poisson distribution with the given lambda and returns the number
of trips produced from the dist. Returns -1 if lambda = 0 -> undefined function.
"""
probability = random.random()
while probability == 0:
probability = random.random()
num_trips = poisson.ppf(probability, lam.value)
if numpy.isnan(num_trips):
#TODO: Should we do something here?
num_trips = -1
return int(num_trips)
def _V(self, price, t, n):
p = self.sales_prob(price, t)
_sum = 0
for i in range(int(poisson.ppf(0.9999, p)) + 1):
if i > n:
break
pi = poisson.pmf(i, p)
today_profit = min(n, i) * price
holding_costs = n * self.L
_, V_future = self.V(t + 1, max(0, n - i))
exp_future_profits = self.delta * V_future
_sum += pi * (today_profit - holding_costs + exp_future_profits)
return _sum
def cnv(bamfile, windowSize, probability, genomeindexfile):
bam = pysam.Samfile(bamfile, 'rb')
chr = None
allBaseSums = []
listForArray = []
zScores = []
zScoreIndex = []
giantList = []
possibleCNVList = []
upperLimit = 0
lowerLimit = 0
for col in bam.pileup():
pos = col.pos
cov = col.n
if bam.getrname(col.tid) != chr:
chr = bam.getrname(col.tid)
baseSum = cov
numw = int(pos/windowSize) #which window
else:
if int(pos/windowSize) == numw:
baseSum += cov
else:
if baseSum >= windowSize*3:
allBaseSums += [(chr, numw*windowSize, (numw+1)*windowSize, baseSum)]
listForArray += [baseSum]
numw = int(pos/windowSize)
baseSum = cov
if baseSum >= windowSize*3:
allBaseSums += [(chr, numw*windowSize, (numw+1)*windowSize, baseSum)]
listForArray += [baseSum]
average = np.mean(listForArray) #new lambda for poisson distribution
upperLimit = np.percentile(listForArray, probability*100)
lowerLimit = np.percentile(listForArray, (1-probability)*100)
cutOff = poisson.ppf(probability, average)
for (chr, start, end, baseSum) in allBaseSums:
if baseSum > cutOff:
possibleCNVList += [(chr, start, end, baseSum)]
"""
stdDev = np.std(listForArray)
for (chr, start, end, baseSum) in allBaseSums:
zScoreTemp = ((baseSum - average)/float(stdDev))
giantList += [(chr, start, end, baseSum, zScoreTemp)] #all windows' base sums and z scores
if (zScoreTemp >= determinedZScore) or (zScoreTemp <= -determinedZScore):
possibleCNVList += [(chr, start,end,baseSum,zScoreTemp)]
"""
cnvList = findThreeInARow(possibleCNVList)
return allBaseSums, cnvList, upperLimit, lowerLimit
def kleinauGP(lL, K,p,l,h,L):
"""
Calculates the reorder point and quantity parameters from [KleinauThonemann2004]_
full Genetic Programming solution.
:param lL: demand distribution expected value
:param K: order setup cost
:param p: backorder penalty
:param l: total demand
:param h: holding cost
:param L: lead time
:returns: reorder point, reorder quantity
:rtype: tuple
"""
r = poisson.ppf(1 - math.sqrt(h / p), mu = l*L)
Q = math.sqrt(L + (K / h) + math.sqrt(2.1029*l*(K + h)*math.sqrt(K/h)))
return r, Q
def _V(price, t, n):
x = np.hstack((price, competitor_prices, rank(price, competitor_prices))).reshape(1, -1)
# sales_prob = round(sales_model(x)[0])
sales_prob = sales_model(x)[0]
_sum = 0
# TODO: Check here
# for i in range(2):
# print(sales_prob)
pi_sum = 0
for i in range(int(poisson.ppf(0.9999, sales_prob)) + 1):
pi = poisson.pmf(i, sales_prob)
pi_sum += pi
today_profit = min(n, i) * price
holding_costs = n * L
_, V_future = V(t + 1, max(0, n - i))
exp_future_profits = delta * V_future
_sum += pi * (today_profit - holding_costs + exp_future_profits)
# print(pi_sum)
return _sum
temp_bin_no_spatial_outliers = temp_bin[temp_bin['cluster_label'] != -1]
temp_bin_no_spatial_outliers.rename(columns = {'created_time' : 'num_posts_per_time_slot'}, inplace = True)
posts_per_time_period = temp_bin_no_spatial_outliers.groupby(['num_posts_per_time_slot','day_of_week','hour_of_day']).count()['cluster_label'].reset_index()
def arrival_statistics(time_bin,day_of_week):
dist_posts_per_time_period = posts_per_time_period[(posts_per_time_period['hour_of_day'] == time_bin) & (posts_per_time_period['day_of_week'] == day_of_week)]['cluster_label'].reset_index()['cluster_label']
emp_dist = (dist_posts_per_time_period/dist_posts_per_time_period.sum()).values
mu = np.dot(np.array(range(0,len(emp_dist))),emp_dist)
return mu
post_threshhold = np.zeros([bins_in_day,7])
for ii in xrange(0,bins_in_day):
for jj in xrange(0,7):
post_threshhold[ii][jj] = np.ceil(poisson.ppf(0.9999, arrival_statistics(ii,jj)))
#print post_threshhold
df2 = last_day_df[['post_id','created_time','lat','longitude','stand_res_url']]
day_of_week = datetime.datetime.fromtimestamp(max(df2['created_time'])).weekday()
df2['created_time'] = df2['created_time'].apply(lambda x: int(datetime.datetime.fromtimestamp(x).hour))
# Bin by some number of hours
time_bin_hours = 4
df2['created_time'] = df2['created_time'].apply(lambda x : x / time_bin_hours)
df2['cluster_label'] = df2[['lat','longitude']].apply(lambda x: check_spatial_membership(x['lat'],x['longitude']), axis = 1)
def __call__(self,cube):
return poisson.ppf(cube,loc=self.m)
def _rvs(self, mu):
return poisson.ppf(uniform(low=poisson.pmf(0, mu)), mu)
#from https://docs.scipy.org/doc/scipy-0.18.1/reference/generated/scipy.stats.poisson.html#scipy.stats.poisson from scipy.stats import poisson import matplotlib.pyplot as plt import numpy as np fig, ax = plt.subplots(1, 1) mu = 0.6 mean, var, skew, kurt = poisson.stats(mu, moments='mvsk') x = np.arange(poisson.ppf(0.01, mu), poisson.ppf(0.99, mu)) ax.plot(x, poisson.pmf(x, mu), 'bo', ms=8, label='poisson pmf') ax.vlines(x, 0, poisson.pmf(x, mu), colors='b', lw=5, alpha=0.5) rv = poisson(mu) ax.vlines(x, 0, rv.pmf(x), colors='k', linestyles='-', lw=1,label='frozen pmf') ax.legend(loc='best', frameon=False) plt.show()
def _ppf(self, q, mu):
return poisson.ppf(poisson.sf(0, mu) * q + poisson.pmf(0, mu), mu)
###upper bounds for X
upperX = np.zeros(n1)
temBikes = bikeData[:, 2]
for i in xrange(n1):
temp = cluster[i]
indsTemp = np.array([a[0] for a in temp])
upperX[i] = np.sum(temBikes[indsTemp])
prob = 0
U = np.zeros(nDays)
L = np.zeros(nDays)
for i in xrange(nDays):
temp = poisson.ppf([0.95], poissonParameters[i])[0]
temp2 = poisson.ppf([0.001], poissonParameters[i])[0]
U[i] = temp
L[i] = temp2
print L
print U
f = open("percentilesDays.txt", "w")
np.savetxt(f, L)
np.savetxt(f, U)
f.close()
prob = 0
for i in xrange(nDays):
for j in range(int(L[i]), int(U[i]) + 1):