def de_fun(state, control, params, noise):
'''
Inputs:
state: array of state variables [x,y]
control: control parameter that is to be varied
params: list of parameter values [kb, knb, rnb, a, eps1, eps2]
Output:
array for subsequent state
'''
[x, y] = state # x (y) population after breeding (non-breeding) period
[kb, knb, rnb, a] = params
[eps1, eps2] = noise
rb = control
# Compute pop size after breeding period season t+1
# Parameters for negative binomial distribution
mu = y * np.exp((rb - a * x) * (1 - y / kb))
p = ke / (ke + mu)
# Compute pop size
xnew = nbinom.rvs(ke, p)
# Compute pop size after non-breeding period season t+1
## Parameters for negative binomial distribution
mu = xnew * np.exp(rnb * (1 - xnew / knb))
p = ke / (ke + mu)
ynew = nbinom.rvs(ke, p)
# Ouput updated state
return np.array([xnew, ynew])
def c19_nbinom_rvs(r0, k, size=0):
"""Generates random variates"""
n, p = c19_nbinom_transform(r0, k)
if size > 1:
r = nbinom.rvs(n, p, size=size)
else:
r = nbinom.rvs(n, p)
return r
def simulate(self, length: int) -> pd.DataFrame:
r"""Simulate outbreaks.
Parameter
---------
length
Number of weeks to model.
Returns
-------
A ``DataFrame`` of an endemic time series where each row contains the case counts ot this week.
"""
if self.seed:
np.random.seed(self.seed)
mu_s = [
np.exp(self.baseline_frequency + self.trend * week +
self._seasonality(week)) for week in range(length)
]
if self.dispersion == 1:
cases = [poisson.rvs(mu, size=1)[0] for mu in mu_s]
else:
cases = []
for mu in mu_s:
r = np.float(mu / (self.dispersion - 1))
p = r / (r + mu)
cases.append(nbinom.rvs(r, p, size=1)[0])
return (pd.DataFrame({
"n_cases": cases
}).pipe(add_date_time_index_to_frame).assign(
timestep=list(range(1, length + 1))))
def sample(self,n):
data = np.zeros(n,dtype=np.int32)
U = uniform.rvs(size=n)
poisson_index = U <= self.pi
data[poisson_index] = poisson.rvs(mu=self.lambda_0,loc=1,size=np.sum(poisson_index))
data[np.invert(poisson_index)] = nbinom.rvs(n=self.r,p=1-self.p,loc=1,size=n-np.sum(poisson_index))
return data
def randnegbinom(self, mu, sd, size):
mu = float(mu)
sd = float(sd)
r = (mu * mu) / (sd * sd - mu)
p = 1 - mu / (r + mu)
result = nbinom.rvs(r, p, size=size)
return result
def count_regression(n):
X = [norm.rvs(.4, 1 / 9) for i in range(n)]
U = [np.exp(1 * x) for x in X]
p = 1 / 2
Y = [nbinom.rvs(p / (1 - p) * u, p) for u in U]
data = [[Y[i], X[i]] for i in range(n)]
def g(x, theta):
return (X[0] - np.exp(X[1] * theta)) * X[1]
def prior(theta):
return t.pdf(x=theta, df=2.5, loc=0, scale=5)
x_list = np.arange(-3, 3, .01)
y_list = [prior(x) for x in x_list]
plt.plot(x_list, y_list)
plt.show()
mh_block_sampler = MH_block_sampler(data, 1, 1, g, prior)
mh_block_sampler.sample(1000)
plt.hist([
mh_block_sampler.thetas[i] for i in range(len(mh_block_sampler.thetas))
],
density=True,
bins=30)
plt.show()
return
def evaluate_iterated_game(genomes):
# When using this evaluation function, a list of lists of genomes
# should be provided to the main 'evaluate' function.
agents = []
for g in genomes:
net = NEAT.NeuralNetwork()
g.BuildPhenotype(net)
agents.append(NeuralNetworkAgent(net))
fitness = 0
n_total_rounds = 0.0
p1 = agents[0]
for p2 in agents[1:]:
n_rounds = nbinom.rvs(1, 0.02, 1) + 1
p1.flush()
p2.flush()
p1_payoff = 0
p2_payoff = 0
for i in range(n_rounds):
p1_decision = p1.get_action([p1_payoff, p2_payoff]);
p2_decision = p2.get_action([p2_payoff, p1_payoff]);
p1_payoff = PAYOFFS[p1_decision][p2_decision]
p2_payoff = PAYOFFS[p2_decision][p1_decision]
p1.add_payoff(p1_payoff)
n_total_rounds += 1.0
fitness = p1.get_total_payoff() / n_total_rounds
fitness -= INTEL_PENALTY*(len(p1.net.neurons))
return fitness
def randnegbinom(self, mu, sd, size):
mu = float(mu)
sd = float(sd)
r = (mu * mu) / (sd * sd - mu)
p = 1 - mu / (r + mu)
result = nbinom.rvs(r, p, size=size)
return result
def RandSFCorr(NumShow, SF=None, sfp=None,date=None,CalcNumDuck=True,Randomize=True):
'''RandSFCorr(NumShow, SF=None, sfp=None,date=None,CalcNumDuck=True)
Make a random-correction to the number of shows in order to get the number of geoducks.
*SF is the show-factor. zero to one. It takes precedent over show-factor plot.
*sfp is an instance of SFplot. It represents a show-factor plot or a list of show-factor plots.
*date is only relevent if SF is undefined.
*CalcNumDuck indicates that the number of geoducks in the show-factor plot(s) needs to be re-calculated
'''
if SF==1: return(NumShow)
if (SF==None) and (sfp==None):#ignore show-factor effect if there is no indication of value to use.
return(NumShow)
if isinstance(SF,(list,ndarray)): return(list(map(lambda sf: RandSFCorr(NumShow, SF=sf, ,CalcNumDuck=CalcNumDuck,Randomize=Randomize) ,SF)))
if not(SF==None):#A single deterministic value for show-factor
if not(Randomize):#deterministic
return(float(NumShow)/SF)
#Probabilistic
result=NumShow+nbinom.rvs(NumShow,SF)
return(result)
#Get the show-factor from a set of show-factor data
sf=sfp.RandSF(date=date,CalcNumDuck=CalcNumDuck)
result=RandSFCorr(NumShow, SF=sf, CalcNumDuck=CalcNumDuck,Randomize=Randomize)
return(result)
def neg_bin(mean, var):
# Where does this is explained?
p = mean / var
n = mean * p / (1 - p)
while(True):
yield nbinom.rvs(n, p)
def Mod_NB(x):
theta = x[:-1]
r = 1 / x[-1]
FM = Mod(theta, time_f)
mu = np.diff(FM)
p = r / (mu + r) #mu/(mu+r)
FM_error = nbinom.rvs(r, p)
return FM_error
def generate_negbin(N, r, prior):
# sample from prior
theta = prior.rvs()
# generate samples
x = nbinom.rvs(r, theta, size=N)
return theta, x
def modelrvs(self, spec):
# simulate seed data under model
r_loc = self.get_r(spec, sim=True)
for i in range(len(self.sim_data[spec][self.sc])):
if np.random.random() > self.q0:
self.data[spec][self.sc][i] = nbinom.rvs(n=r_loc[i], p=self.p0)
else:
self.data[spec][self.sc][i] = 0
def randnegbinom(self, mu, sd, size):
mu = float(mu)
sd = float(sd)
r = (mu * mu) / (sd * sd - mu)
p = 1 - mu / (r + mu)
result = nbinom.rvs(r, p, size=size)
#print('nbinom', describe(result))
return result
def simulator(home_mean, away_mean, niterations):
# estimates probability of home team win
home_game_score = [0] * niterations
away_game_score = [0] * niterations
home_win = [0] * niterations
i = 0
while (i < niterations):
home_game_score[i] = \
nbinom.rvs(n = 4.0, p = 4.0/(4.0 + home_mean), size = 1)[0]
away_game_score[i] = \
nbinom.rvs(n = 4.0, p = 4.0/(4.0 + away_mean), size = 1)[0]
if (home_game_score[i] > away_game_score[i]):
home_win[i] = 1
if ((away_game_score[i] > home_game_score[i]) or \
(away_game_score[i] < home_game_score[i])):
i = i + 1
n_home_win = sum(home_win)
return n_home_win / niterations
def simulator(home_mean, away_mean, niterations):
# estimates probability of home team win
home_game_score = [0] * niterations
away_game_score = [0] * niterations
home_win = [0] * niterations
i = 0
while (i < niterations):
home_game_score[i] = \
nbinom.rvs(n = 4.0, p = 4.0/(4.0 + home_mean), size = 1)[0]
away_game_score[i] = \
nbinom.rvs(n = 4.0, p = 4.0/(4.0 + away_mean), size = 1)[0]
if (home_game_score[i] > away_game_score[i]):
home_win[i] = 1
if ((away_game_score[i] > home_game_score[i]) or \
(away_game_score[i] < home_game_score[i])):
i = i + 1
n_home_win = sum(home_win)
return n_home_win / niterations
def samples_deaths(self, new_infections, fatality_ratio, time_to_death,
niu, k):
r"""
Computes samples for the number of deaths at time step
:math:`k` in specified region, given the simulated timeline of
susceptible number of individuals, for all age groups in the model.
The number of deaths is assumed to be distributed according to
a negative binomial distribution with mean
.. math::
\mu_{r,t_k,i} = p_i \sum_{l=0}^{k} f_{k-l} \delta_{r,t_l,i}^{infec}
and variance :math:`\mu_{r,t_k,i} (\nu + 1)`, where :math:`p_i` is the
age-specific fatality ratio for age group :math:`i`, :math:`f_{k-l}`
is the probability of demise :math:`k-l` days after infection and
:math:`\delta_{r,t_l,i}^{infec}` is the number of new infections
in specified region, for age group :math:`i` on day :math:`t_l`.
It uses an output of the simulation method for the PheSEIRModel,
taking all the rest of the parameters necessary for the computation
from the way its simulation has been fitted.
Parameters
----------
new_infections
(numpy.array) Number of new infections from the simulation method
for the PheSEIRModel.
fatality_ratio
List of age-specific fatality ratios.
time_to_death
List of probabilities of death of individual d days after
infection.
niu
Dispesion factor for the negative binomial distribution.
k
Index of day for which we intend to sample the number of deaths for
by age group.
Returns
-------
Array of log-likelihoods for the obsereved number of deaths for
each age group in specified region at time :math:`t_k`.
Notes
-----
Always run :meth:`PheSEIRModel.new_infections` and
:meth:`PheSEIRModel.check_death_format` before running this one.
"""
self._check_time_step_format(k)
# Compute mean of negative-binomial
return nbinom.rvs(
n=niu *
self.mean_deaths(fatality_ratio, time_to_death, k, new_infections),
p=niu / (1 + niu))
def draw_nbinom_dataset(draw, n_samples):
"""
Generate random samples from a negative binomial model. Assumes that
draw is a sample from the model parameter space (probably posterior
but could be prior) and that the 1st element of the draw is
the burst rate and the 2nd element is the mean burst size.
"""
pp_samples = neg_binom.rvs(draw[0], (1 + draw[1])**(-1), size=n_samples)
return np.unique(pp_samples, return_counts=True)
def simulate_ge(self, negative_binomial):
# dimension of initial space (i.e number of genes)
self.W = np.random.normal(loc=0,
scale=0.5,
size=(self.dim, self.latent))
self.beta = np.random.normal(loc=0, scale=0.5, size=self.dim)
#self.W = np.random.normal(loc=0, scale=1.0, size=(self.latent, self.dim))
#self.beta = np.random.normal(loc=0, scale=1.0, size=self.dim)
self.mu = np.clip(a=np.exp(self.z @ self.W.T + self.beta),
a_min=0,
a_max=1e5)
if negative_binomial:
print('=== Negative Binomial simulations ===')
#g = gamma.rvs(self.alpha, scale=self.mu / self.alpha)
#self.X = np.asarray(poisson(g), dtype=np.float64)
r, p = convert_params_NB(mu=self.mu, alpha=self.alpha)
self.X = nbinom.rvs(n=r, p=p)
else:
self.X = np.asarray(poisson(self.mu), dtype=np.float64)
if self.vis:
## Poissson distribution
fig, axes = plt.subplots(
1,
1,
figsize=(14, 8),
sharey=True,
)
bins = np.arange(0, 30, 5)
cm = plt.cm.get_cmap('RdYlBu_r')
n, binss, patches = axes.hist(
self.X,
bins=bins,
edgecolor='black',
)
# set color of patches
# scale values to interval [0,1]
bin_centers = 0.5 * (binss[:-1] + binss[1:])
col = bin_centers - min(bin_centers)
col /= max(col)
for c, p in zip(col, patches):
plt.setp(p, 'facecolor', cm(c))
axes.set_title('Histogram of simulated gene expression data')
plt.ylabel('Counts')
plt.xlabel('Gene Expression value')
plt.legend(['gene_' + str(i) for i in list(range(self.dim))],
loc='best')
plt.show()
def C1(self):
print('Subsampling C1.')
snv = nbinom.rvs(
self.size, self.size /
(self.size + self.snv.reshape(3, 3, -1, self.p, self.samples)))
self._C1 = tf.constant(snv, dtype=self.dtype)
if self.verbose:
print('C1:', self._C1.shape)
return self._C1
def corner_spread(home_corners, away_corners, corner_mean, niterations):
random.seed(1234)
game_home_mean = [0] * niterations
game_away_mean = [0] * niterations
game_corner_mean = [0] * niterations
over_corner_mean_counter = [0] * niterations
i = 0
n_count = 4.0
while i < niterations:
game_home_mean[i] = nbinom.rvs(n=n_count, p=n_count / (n_count + home_corners), size=1)[0]
game_away_mean[i] = nbinom.rvs(n=n_count, p=n_count / (n_count + away_corners), size=1)[0]
game_corner_mean[i] = nbinom.rvs(n=n_count, p=n_count / (n_count + corner_mean), size=1)[0]
home_plus_away = game_home_mean[i] + game_away_mean[i]
if home_plus_away > game_corner_mean[i]:
over_corner_mean_counter[i] = 1
if (game_corner_mean[i] > home_plus_away) or (game_corner_mean[i] < home_plus_away):
i += 1
n_over_corner_mean_count = sum(over_corner_mean_counter)
return n_over_corner_mean_count / float(niterations)
def sample_usage():
t_arr = np.ones(100)
m = 10
theta = .7
ps = t_arr / (t_arr + theta)
n_arr = nbinom.rvs(m, ps)
NBinom.loglik(n_arr, t_arr, m, theta)
NBinom.numeric_grad(n_arr, t_arr, m, theta)
nb2 = NBinom2(n_arr, t_arr)
params = nb2.gradient_descent(verbose=True)
return sum(params - np.array([m, theta])) < 1e-1
def observationGenerator(states, parameters):
#input states is 2D: numStates x dimObs, parameters is 1D
obs = zeros((states.shape[0], 2))
for i in range(states.shape[0]):
#obs[i,:] = transpose(random.multivariate_normal(repeat(states[i,0],1), [[parameters[0] * states[i,0] ** 2]], size = 2))
p = 1 / (1 + parameters[0] * states[i,0])
p = minimum(p, 1-1e-7)
p = maximum(p, 1e-7)
n = maximum(1, floor( states[i,0] * p / (1-p) ) ).astype(int32)
obs[i,:] = nbinom.rvs(n, p, 2)
return obs
def C2(self):
sub_set = np.ones_like(self.other)
sub_set[np.where(np.isnan(self.other))] = 0
self.other[np.where(np.isnan(self.other))] = 0
self.C2_nans = tf.constant(sub_set, dtype=self.dtype)
print('Subsampling C2')
other = nbinom.rvs(self.size, self.size / (self.size + self.other))
self._C2 = tf.constant(other, dtype=self.dtype)
if self.verbose:
print('C2:', self._C2.shape)
return self._C2
def __init__(self):
# total sessions this user will have:
self.num_sessions = 1 + int(uniform.rvs() > sessions_zero_inflation
) * nbinom.rvs(4, beta.rvs(12, 10))
self.first_session = fuzz_time(local_epoch)
self.session_starts = [
fuzz_time(self.first_session) for i in range(self.num_sessions - 1)
] + [self.first_session]
self.next_session = self.first_session
self.guid = uuid4()
self._current_cart = 0 # num items currently in cart
def gentestcase2(nsg=10):
'''
The second testcase, 2 samples, control and treatment
'''
vark = 0.01
# desmat=np.matrix([[0,0],[0,1],[1,0],[1,1]])
desmat = np.matrix([[1, 0, 0], [0, 1, 0], [0, 1, 1], [1, 1, 1]])
(nsample, nbeta) = desmat.shape
# basic parameters
sks = SimCaseSimple()
sks.prefix = 'sample2'
sks.design_mat = desmat
sks.beta0 = [random.uniform(3, 10)
for i in range(nsg)] # these are the base
sks.beta1 = [random.random() * 5
for i in range(nbeta)] # treatments;size: nbeta
print('beta_0:' + '\t'.join([decformat(x) for x in sks.beta0]))
print('beta_1:' + '\t'.join([decformat(x) for x in sks.beta1]))
# mean and variance
mu0 = [math.exp(t) for t in sks.beta0] # size: nsg
tprod = desmat * np.matrix(sks.beta1).getT() # size: nsample*1
tprodlist = [x[0] for x in tprod.tolist()] # size: nsample*1
sks.mu = [mu0]
for nr in range(nsample):
sgi = [math.exp(t + tprodlist[nr]) for t in sks.beta0]
sks.mu += [sgi]
# sks.var0=[t+vark*(t*t) for t in sks.mu0]
sks.var = [[t + vark * (t * t) for t in tl] for tl in sks.mu]
for i in range(nsample + 1): # including 1 base and n samples
print('mu_:' + str(i) + '\t'.join([decformat(x) for x in sks.mu[i]]))
print('var_:' + str(i) + '\t'.join([decformat(x) for x in sks.var[i]]))
# parameters for generating NB counts
#sks.nb_p0=[sks.mu0[i]/sks.var0[i] for i in range(nsg)]
#sks.nb_r0=[sks.mu0[i]*sks.mu0[i]/(sks.var0[i]-sks.mu0[i]) for i in range(nsg)]
#sks.nb_p1=[[sks.mu1[t][i]/sks.var1[t][i] for i in range(nsg)] for t in range(nsample)]
#sks.nb_r1=[[sks.mu1[t][i]*sks.mu1[t][i]/(sks.var1[t][i]-sks.mu1[t][i]) for i in range(nsg)] for t in range(nsample)]
sks.nb_p = [[sks.mu[t][i] / sks.var[t][i] for i in range(nsg)]
for t in range(nsample + 1)]
sks.nb_r = [[
sks.mu[t][i] * sks.mu[t][i] / (sks.var[t][i] - sks.mu[t][i])
for i in range(nsg)
] for t in range(nsample + 1)]
#
#sks.nb_count0=[nbinom.rvs(sks.nb_r0[i],sks.nb_p0[i]) for i in range(nsg)]
#sks.nb_count1=[[nbinom.rvs(sks.nb_r1[t][i],sks.nb_p1[t][i]) for i in range(nsg)] for t in range(nsample)]
sks.nb_count = [[
nbinom.rvs(sks.nb_r[t][i], sks.nb_p[t][i]) for i in range(nsg)
] for t in range(nsample + 1)]
return (sks)
def gentestcase3(nsg=10,desmat=None):
'''
The third testcase, with efficient
'''
vark=0.01
effiprob=0.5 # the probability that a sgRNA is efficient
# desmat=np.matrix([[0,0],[0,1],[1,0],[1,1]])
if desmat==None:
# desmat=np.matrix([[1,0,0],[0,1,0],[0,1,1],[1,1,1]])
desmat=np.matrix([[1,0,0,1],[0,1,1,1],[1,0,1,0]]).getT()
(nsample,nbeta)=desmat.shape
# basic parameters
sks=SimCaseSimple()
sks.prefix='sample3'
sks.design_mat=desmat
#sks.beta0=[random.uniform(3,10) for i in range(nsg)] # these are the base
#sks.beta1=[(random.random())*5 for i in range(nbeta)] # treatments;size: nbeta
sks.beta0=[random.uniform(5,10) for i in range(nsg)] # these are the base
sks.beta1=[(random.random()*2-1)*5 for i in range(nbeta)] # treatments;size: nbeta
print('beta_0:'+'\t'.join([decformat(x) for x in sks.beta0]))
print('beta_1:'+'\t'.join([decformat(x) for x in sks.beta1]))
# efficiency
sks.isefficient=[ (lambda x: 1 if x>=effiprob else 0)(random.random()) for i in range(nsg)]
# mean and variance
mu0=[math.exp(t) for t in sks.beta0] # size: nsg
tprod=desmat*np.matrix(sks.beta1).getT() # size: nsample*1
tprodlist=[x[0] for x in tprod.tolist()] # size: nsample*1
sks.mu=[mu0]
for nr in range(nsample):
sgi=[math.exp(sks.beta0[ti]+tprodlist[nr]*sks.isefficient[ti]) for ti in range(nsg)]
sks.mu+=[sgi]
# sks.var0=[t+vark*(t*t) for t in sks.mu0]
sks.var=[[t+vark*(t*t) for t in tl] for tl in sks.mu]
for i in range(nsample+1): # including 1 base and n samples
print('mu_:'+str(i)+'\t'.join([decformat(x) for x in sks.mu[i]]))
print('var_:'+str(i)+'\t'.join([decformat(x) for x in sks.var[i]]))
# parameters for generating NB counts
#sks.nb_p0=[sks.mu0[i]/sks.var0[i] for i in range(nsg)]
#sks.nb_r0=[sks.mu0[i]*sks.mu0[i]/(sks.var0[i]-sks.mu0[i]) for i in range(nsg)]
#sks.nb_p1=[[sks.mu1[t][i]/sks.var1[t][i] for i in range(nsg)] for t in range(nsample)]
#sks.nb_r1=[[sks.mu1[t][i]*sks.mu1[t][i]/(sks.var1[t][i]-sks.mu1[t][i]) for i in range(nsg)] for t in range(nsample)]
sks.nb_p=[[sks.mu[t][i]/sks.var[t][i] for i in range(nsg)] for t in range(nsample+1)]
sks.nb_r=[[sks.mu[t][i]*sks.mu[t][i]/(sks.var[t][i]-sks.mu[t][i]) for i in range(nsg)] for t in range(nsample+1)]
#
#sks.nb_count0=[nbinom.rvs(sks.nb_r0[i],sks.nb_p0[i]) for i in range(nsg)]
#sks.nb_count1=[[nbinom.rvs(sks.nb_r1[t][i],sks.nb_p1[t][i]) for i in range(nsg)] for t in range(nsample)]
sks.nb_count=[[nbinom.rvs(sks.nb_r[t][i],sks.nb_p[t][i]) for i in range(nsg)] for t in range(nsample+1)]
print('efficient: '+' '.join([str(x) for x in sks.isefficient]))
return (sks)
def gentestcase3(nsg=10,desmat=None):
'''
The third testcase, with efficient
'''
vark=0.01
effiprob=0.5 # the probability that a sgRNA is efficient
# desmat=np.matrix([[0,0],[0,1],[1,0],[1,1]])
if desmat==None:
# desmat=np.matrix([[1,0,0],[0,1,0],[0,1,1],[1,1,1]])
desmat=np.matrix([[1,0,0,1],[0,1,1,1],[1,0,1,0]]).getT()
(nsample,nbeta)=desmat.shape
# basic parameters
sks=SimCaseSimple()
sks.prefix='sample3'
sks.design_mat=desmat
#sks.beta0=[random.uniform(3,10) for i in range(nsg)] # these are the base
#sks.beta1=[(random.random())*5 for i in range(nbeta)] # treatments;size: nbeta
sks.beta0=[random.uniform(5,10) for i in range(nsg)] # these are the base
sks.beta1=[(random.random()*2-1)*5 for i in range(nbeta)] # treatments;size: nbeta
print('beta_0:'+'\t'.join([decformat(x) for x in sks.beta0]))
print('beta_1:'+'\t'.join([decformat(x) for x in sks.beta1]))
# efficiency
sks.isefficient=[ (lambda x: 1 if x>=effiprob else 0)(random.random()) for i in range(nsg)]
# mean and variance
mu0=[math.exp(t) for t in sks.beta0] # size: nsg
tprod=desmat*np.matrix(sks.beta1).getT() # size: nsample*1
tprodlist=[x[0] for x in tprod.tolist()] # size: nsample*1
sks.mu=[mu0]
for nr in range(nsample):
sgi=[math.exp(sks.beta0[ti]+tprodlist[nr]*sks.isefficient[ti]) for ti in range(nsg)]
sks.mu+=[sgi]
# sks.var0=[t+vark*(t*t) for t in sks.mu0]
sks.var=[[t+vark*(t*t) for t in tl] for tl in sks.mu]
for i in range(nsample+1): # including 1 base and n samples
print('mu_:'+str(i)+'\t'.join([decformat(x) for x in sks.mu[i]]))
print('var_:'+str(i)+'\t'.join([decformat(x) for x in sks.var[i]]))
# parameters for generating NB counts
#sks.nb_p0=[sks.mu0[i]/sks.var0[i] for i in range(nsg)]
#sks.nb_r0=[sks.mu0[i]*sks.mu0[i]/(sks.var0[i]-sks.mu0[i]) for i in range(nsg)]
#sks.nb_p1=[[sks.mu1[t][i]/sks.var1[t][i] for i in range(nsg)] for t in range(nsample)]
#sks.nb_r1=[[sks.mu1[t][i]*sks.mu1[t][i]/(sks.var1[t][i]-sks.mu1[t][i]) for i in range(nsg)] for t in range(nsample)]
sks.nb_p=[[sks.mu[t][i]/sks.var[t][i] for i in range(nsg)] for t in range(nsample+1)]
sks.nb_r=[[sks.mu[t][i]*sks.mu[t][i]/(sks.var[t][i]-sks.mu[t][i]) for i in range(nsg)] for t in range(nsample+1)]
#
#sks.nb_count0=[nbinom.rvs(sks.nb_r0[i],sks.nb_p0[i]) for i in range(nsg)]
#sks.nb_count1=[[nbinom.rvs(sks.nb_r1[t][i],sks.nb_p1[t][i]) for i in range(nsg)] for t in range(nsample)]
sks.nb_count=[[nbinom.rvs(sks.nb_r[t][i],sks.nb_p[t][i]) for i in range(nsg)] for t in range(nsample+1)]
print('efficient: '+' '.join([str(x) for x in sks.isefficient]))
return (sks)
def get_num_random_interactions(age, random_network_params_dict,
child_upper_ix, adult_upper_ix):
if age <= child_upper_ix:
mean = random_network_params_dict['CHILD']['mu']
sd = random_network_params_dict['CHILD']['sigma']
elif age <= adult_upper_ix:
mean = random_network_params_dict['ADULT']['mu']
sd = random_network_params_dict['ADULT']['sigma']
else:
mean = random_network_params_dict['ELDERLY']['mu']
sd = random_network_params_dict['ELDERLY']['sigma']
p = mean / (sd * sd)
n = mean * mean / (sd * sd - mean)
num_interactions = nbinom.rvs(n, p)
return num_interactions
def bin_neg_simulation(k, p, n=10000, odd=99):
"""
Funcao que retorna o valor de uma distribuicao binomial negativa frente aos parametros dados
"""
if k <= 0:
return None
a = 100 - odd
b = odd + (100 - odd)
r = nbinom.rvs(k, p, size=n)
return int(
scipy.stats.tmean(
r,
(scipy.stats.scoreatpercentile(
r, a), scipy.stats.scoreatpercentile(r, b)),
))
def negbinomial_dist(n,
mu,
max_value=10,
min_value=0,
num_values=10000,
integers=False):
""" generate a negative binomial distribution """
p = 1 / ((mu / n) + 1)
random_list = nbinom.rvs(n=n, p=p,
size=num_values) # Negative binomial function
return scale_a_distribution(random_list,
integers=integers,
max_value=max_value,
min_value=min_value)
def _random_noise(df, noise_factor):
r"""
Generates random noise on an observable by a Negative Binomial :math:`NB`.
References to the negative binomial can be found `here <https://ncss-wpengine.netdna-ssl.com/wp-content/themes/ncss/pdf/Procedures/NCSS/Negative_Binomial_Regression.pdf>`_
.
.. math::
O &\sim NB(\mu=datapoint,\alpha)
We keep the alpha parameter low to obtain a small variance which should than always be approximately the size of the mean.
Parameters
----------
df : new_cases , pandas.DataFrame
Observable on which we want to add the noise
noise_factor: :math:`\alpha`
Alpha factor for the random number generation
Returns
-------
array : 1-dim
observable with added noise
"""
def convert(mu, alpha):
r = 1 / alpha
p = mu / (mu + r)
return r, 1 - p
# Apply noise on every column
for column in df:
# Get values
array = df[column].to_numpy()
for i in range(len(array)):
if (array[i] == 0) or (np.isnan(array[i])):
continue
log.debug(f"Data {array[i]}")
r, p = convert(array[i], noise_factor)
log.info(f"n {r}, p {p}")
mean, var = nbinom.stats(r, p, moments="mv")
log.debug(f"mean {mean} var {var}")
array[i] = nbinom.rvs(r, p)
log.debug(f"Drawn {array[i]}")
df[column] = array
return df
def play(self, player1, player2, n_rounds=None):
if n_rounds is None:
n_rounds = nbinom.rvs(1,0.2,1) + 1
player1.reset()
player2.reset()
total_payoffs = np.zeros((1,2))
p1_payoff = 0
p1_action = None
p1_results = {}
p2_payoff = 0
p2_action = None
p2_results = {}
payoffs = np.zeros((1,2))
p1_trace = []
p2_trace = []
for i in range(0, n_rounds):
if i == 0:
p1_action = player1.get_initial_action()
p2_action = player2.get_initial_action()
else:
p1_results['payoff'] = p1_payoff
p1_results['action'] = p1_action
p2_results['payoff'] = p2_payoff
p2_results['action'] = p2_action
p1_action = player1.get_action([p1_results, p2_results])
p2_action = player2.get_action([p2_results, p1_results])
p1_trace.append(p1_action)
p2_trace.append(p2_action)
p1_payoff = self.payoff_matrix[p1_action, p2_action]
p2_payoff = self.payoff_matrix[p2_action, p1_action]
total_payoffs += [[p1_payoff, p2_payoff]]
traces = (p1_trace, p2_trace)
avg_payoffs = total_payoffs / float(n_rounds)
return avg_payoffs, traces
def inversion(self):
if (len(self.sequence) <= 1):
pos = 0
else:
pos = random.randint(0, len(self.sequence) - 1)
cfg = AppSettings()
p = cfg.genetics.mutation_length / (1 + cfg.genetics.mutation_length)
length = nbinom.rvs(
1,
cfg.genetics.mutation_length / (1 + cfg.genetics.mutation_length))
self.sequence = self.sequence[:pos] + \
self.sequence[pos:(pos + length)][::-1] + \
self.sequence[(pos + length):]
def update_state(self, state, rolling_time):
# land, land_item, add_to_cart, enter_checkout, enter_address, enter_ccard, complete
r = uniform.rvs()
new_state = ''
if state == 'land_homepage':
if r < .8:
new_state = 'land_item'
rolling_time += timedelta(minutes=1 + nbinom.rvs(1, .5))
elif state == 'land_item':
if r < .3:
new_state = 'land_item'
rolling_time += timedelta(minutes=1 + nbinom.rvs(2, .5))
elif r < .7:
new_state = 'add_to_cart'
rolling_time += timedelta(minutes=1 + nbinom.rvs(2, .5))
elif self._current_cart > 0 and r < .8:
new_state = 'enter_checkout'
rolling_time += timedelta(minutes=1 + nbinom.rvs(4, .5))
elif state == 'add_to_cart':
if r < .6:
new_state = 'enter_checkout'
rolling_time += timedelta(minutes=1 + nbinom.rvs(1, .5))
elif r < .9:
new_state = 'land_item'
rolling_time += timedelta(minutes=1 + nbinom.rvs(4, .5))
elif state == 'enter_checkout':
if r < .98:
new_state = 'enter_address'
rolling_time += timedelta(minutes=1 + nbinom.rvs(1, .8))
elif state == 'enter_address':
if r < .97:
new_state = "enter_ccard"
rolling_time += timedelta(minutes=1 + nbinom.rvs(1, .9))
elif state == 'enter_ccard':
if r < .9:
new_state = 'complete'
rolling_time += timedelta(minutes=1 + nbinom.rvs(1, .8))
return new_state, rolling_time
def gentestcase1(nsg=10):
'''
The first testcase, 2 samples, control and treatment
'''
vark = 0.01
# basic parameters
sks = SimCaseSimple()
sks.beta0 = [random.uniform(3, 10)
for i in range(nsg)] # these are the base
sks.beta1 = [random.random() * 5] # treatment
print('beta_0:' + '\t'.join([decformat(x) for x in sks.beta0]))
print('beta_1:' + decformat(sks.beta1[0]))
# mean and variance
sks.mu = [[math.exp(t) for t in sks.beta0]]
for t in sks.beta0:
sks.mu += [[math.exp(t + sks.beta1[0]) for t in sks.beta0]]
#sks.var0=[t+vark*(t*t) for t in sks.mu0]
#sks.var1=[[t+vark*(t*t) for t in sks.mu1[0]]]
sks.var = [[t + vark * (t * t) for t in sks.mu[i]] for i in range(2)]
#print('mu_0:'+'\t'.join([decformat(x) for x in sks.mu0]))
#print('var_0:'+'\t'.join([decformat(x) for x in sks.var0]))
#print('mu_1:'+'\t'.join([decformat(x) for x in sks.mu1[0]]))
#print('var_1:'+'\t'.join([decformat(x) for x in sks.var1[0]]))
# parameters for generating NB counts
#sks.nb_p0=[sks.mu0[i]/sks.var0[i] for i in range(nsg)]
#sks.nb_p1=[[sks.mu1[0][i]/sks.var1[0][i] for i in range(nsg)]]
sks.nb_p = [[sks.mu[j][i] / sks.var[j][i] for i in range(nsg)]
for j in range(2)]
#sks.nb_r0=[sks.mu0[i]*sks.mu0[i]/(sks.var0[i]-sks.mu0[i]) for i in range(nsg)]
#sks.nb_r1=[[sks.mu1[0][i]*sks.mu1[0][i]/(sks.var1[0][i]-sks.mu1[0][i]) for i in range(nsg)]]
sks.nb_r = [[
sks.mu[j][i] * sks.mu[j][i] / (sks.var[j][i] - sks.mu[j][i])
for i in range(nsg)
] for j in range(2)]
#
#sks.nb_count0=[nbinom.rvs(sks.nb_r0[i],sks.nb_p0[i]) for i in range(nsg)]
#sks.nb_count1=[[nbinom.rvs(sks.nb_r1[0][i],sks.nb_p1[0][i]) for i in range(nsg)]]
sks.nb_count = [[
nbinom.rvs(sks.nb_r[j][i], sks.nb_p[j][i]) for i in range(nsg)
] for j in range(2)]
# design matrix
# sks.design_mat=getsimpledesignmat(nsg)
sks.design_mat = np.matrix([[1]])
return (sks)
def gentestcase2(nsg=10):
'''
The second testcase, 2 samples, control and treatment
'''
vark=0.01
# desmat=np.matrix([[0,0],[0,1],[1,0],[1,1]])
desmat=np.matrix([[1,0,0],[0,1,0],[0,1,1],[1,1,1]])
(nsample,nbeta)=desmat.shape
# basic parameters
sks=SimCaseSimple()
sks.prefix='sample2'
sks.design_mat=desmat
sks.beta0=[random.uniform(3,10) for i in range(nsg)] # these are the base
sks.beta1=[random.random()*5 for i in range(nbeta)] # treatments;size: nbeta
print('beta_0:'+'\t'.join([decformat(x) for x in sks.beta0]))
print('beta_1:'+'\t'.join([decformat(x) for x in sks.beta1]))
# mean and variance
mu0=[math.exp(t) for t in sks.beta0] # size: nsg
tprod=desmat*np.matrix(sks.beta1).getT() # size: nsample*1
tprodlist=[x[0] for x in tprod.tolist()] # size: nsample*1
sks.mu=[mu0]
for nr in range(nsample):
sgi=[math.exp(t+tprodlist[nr]) for t in sks.beta0]
sks.mu+=[sgi]
# sks.var0=[t+vark*(t*t) for t in sks.mu0]
sks.var=[[t+vark*(t*t) for t in tl] for tl in sks.mu]
for i in range(nsample+1): # including 1 base and n samples
print('mu_:'+str(i)+'\t'.join([decformat(x) for x in sks.mu[i]]))
print('var_:'+str(i)+'\t'.join([decformat(x) for x in sks.var[i]]))
# parameters for generating NB counts
#sks.nb_p0=[sks.mu0[i]/sks.var0[i] for i in range(nsg)]
#sks.nb_r0=[sks.mu0[i]*sks.mu0[i]/(sks.var0[i]-sks.mu0[i]) for i in range(nsg)]
#sks.nb_p1=[[sks.mu1[t][i]/sks.var1[t][i] for i in range(nsg)] for t in range(nsample)]
#sks.nb_r1=[[sks.mu1[t][i]*sks.mu1[t][i]/(sks.var1[t][i]-sks.mu1[t][i]) for i in range(nsg)] for t in range(nsample)]
sks.nb_p=[[sks.mu[t][i]/sks.var[t][i] for i in range(nsg)] for t in range(nsample+1)]
sks.nb_r=[[sks.mu[t][i]*sks.mu[t][i]/(sks.var[t][i]-sks.mu[t][i]) for i in range(nsg)] for t in range(nsample+1)]
#
#sks.nb_count0=[nbinom.rvs(sks.nb_r0[i],sks.nb_p0[i]) for i in range(nsg)]
#sks.nb_count1=[[nbinom.rvs(sks.nb_r1[t][i],sks.nb_p1[t][i]) for i in range(nsg)] for t in range(nsample)]
sks.nb_count=[[nbinom.rvs(sks.nb_r[t][i],sks.nb_p[t][i]) for i in range(nsg)] for t in range(nsample+1)]
return (sks)
def nextGenStoch(self,inf=True,BFOD=True):
# this function is currently depricated
# some of these seeds die from BFOD
if BFOD:
self.numSeeds = binom.rvs(n=self.numSeeds,p=self.BFODmat)[:]
# some of remaining seeds get pathogen infected
germ = []
if inf:
infSeeds = binom.rvs(n=self.numSeeds,p=self.pInf)[:]
unInfSeeds = np.subtract(self.numSeeds,infSeeds)[:]
# some of seeds germinate
germ = binom.rvs(p=self.germMatUninf,n=unInfSeeds)[:]
germ = np.add(germ,binom.rvs(p=self.germMatInf,n=infSeeds)[:])[:]
else:
germ = binom.rvs(p=self.germMatUninf,n=self.numSeeds)[:]
# subtract out germinated seeds from total number of seeds to keep in seed bank
self.numSeeds = np.subtract(self.numSeeds,germ)[:]
# incorporate perennials that survived
self.species = np.add(binom.rvs(p=self.perSurv,n=self.species.astype(int)).astype(int),binom.rvs(p=self.annuals,n=germ.astype(int).astype(int))).astype(int)[:]
# competition
compMat = np.exp(-1.*np.dot(self.compParams,self.species))
num_seeds_this_gen = np.zeros(self.numSpec)
for i in range(self.numSpec):
num_seeds_this_gen[i] += np.sum(nbinom.rvs(n=self.get_r(compMat,i),p=self.negBinP[i],size=self.species[i]))
# infection
if inf:
num_seeds_this_gen = binom.rvs(p=self.infMat,n=num_seeds_this_gen.astype(int))[:]
# add in new seeds to model
self.numSeeds = np.add(self.numSeeds,num_seeds_this_gen.astype(int))[:]
# add seedlings from perrenials to seedlings, and ones that survived from last year to adults
self.seedlings = np.array([germ[0],germ[1],0,0,0])[:]
self.species = np.add(self.species,binom.rvs(p=self.perTrans[3]/(1.+(self.seedlings[0]+self.seedlings[1])*self.perTrans[0]+(self.species[0]+self.species[1])*self.perTrans[2]
+(self.species[2]+self.species[3]+self.species[4])*self.perTrans[1]),n=self.seedlings.astype(int)).astype(int))[:]
#i = 0
#for spec in num_seeds_this_gen:
# print spec,self.species[i], " ",
# i += 1
#print
return (self.species,self.numSeeds)
def gentestcase1(nsg=10):
'''
The first testcase, 2 samples, control and treatment
'''
vark=0.01
# basic parameters
sks=SimCaseSimple()
sks.beta0=[random.uniform(3,10) for i in range(nsg)] # these are the base
sks.beta1=[random.random()*5] # treatment
print('beta_0:'+'\t'.join([decformat(x) for x in sks.beta0]))
print('beta_1:'+decformat(sks.beta1[0]))
# mean and variance
sks.mu=[[math.exp(t) for t in sks.beta0]]
for t in sks.beta0:
sks.mu+=[[math.exp(t+sks.beta1[0]) for t in sks.beta0]]
#sks.var0=[t+vark*(t*t) for t in sks.mu0]
#sks.var1=[[t+vark*(t*t) for t in sks.mu1[0]]]
sks.var=[[t+vark*(t*t) for t in sks.mu[i]] for i in range(2)]
#print('mu_0:'+'\t'.join([decformat(x) for x in sks.mu0]))
#print('var_0:'+'\t'.join([decformat(x) for x in sks.var0]))
#print('mu_1:'+'\t'.join([decformat(x) for x in sks.mu1[0]]))
#print('var_1:'+'\t'.join([decformat(x) for x in sks.var1[0]]))
# parameters for generating NB counts
#sks.nb_p0=[sks.mu0[i]/sks.var0[i] for i in range(nsg)]
#sks.nb_p1=[[sks.mu1[0][i]/sks.var1[0][i] for i in range(nsg)]]
sks.nb_p=[[sks.mu[j][i]/sks.var[j][i] for i in range(nsg)] for j in range(2)]
#sks.nb_r0=[sks.mu0[i]*sks.mu0[i]/(sks.var0[i]-sks.mu0[i]) for i in range(nsg)]
#sks.nb_r1=[[sks.mu1[0][i]*sks.mu1[0][i]/(sks.var1[0][i]-sks.mu1[0][i]) for i in range(nsg)]]
sks.nb_r=[[sks.mu[j][i]*sks.mu[j][i]/(sks.var[j][i]-sks.mu[j][i]) for i in range(nsg)] for j in range(2)]
#
#sks.nb_count0=[nbinom.rvs(sks.nb_r0[i],sks.nb_p0[i]) for i in range(nsg)]
#sks.nb_count1=[[nbinom.rvs(sks.nb_r1[0][i],sks.nb_p1[0][i]) for i in range(nsg)]]
sks.nb_count=[[nbinom.rvs(sks.nb_r[j][i],sks.nb_p[j][i]) for i in range(nsg)] for j in range(2)]
# design matrix
# sks.design_mat=getsimpledesignmat(nsg)
sks.design_mat=np.matrix([[1]])
return (sks)
def sample_negative_binomial(p, r):
return int(nbinom.rvs(r, p))
def meanVar(_files, _gff_file , _output):
NFILE=len(_files)
if NFILE == 1:
sys.stderr.write("Need at least two samples for each group.\n")
sys.exit(1)
#####
_dict_counts = dict() ## dictionary of gene counts
_genes = HTSeq.GenomicArrayOfSets("auto",stranded=False)
idx=0
if MODE == "all-genes":
for feature in _gff_file:
if feature.type in GENE:
_dict_counts[ feature.name ] = [0]*NFILE
_genes[feature.iv] += feature.name
if feature.type in TX:
if feature.attr["geneID"] not in _dict_counts:
_dict_counts[feature.attr["geneID"]] = [0]*NFILE
_genes[feature.iv] += feature.attr["geneID"]
if MODE == "AS-genes":
## Bug: Does not report last gene in gff if it has at least two transcript
transcript= set()
cur_line = None
last_gene_id = None
for feature in _gff_file:
if feature.type in GENE:
if len(transcript) >1:
_dict_counts[ cur_line.name ] = [0]*NFILE
_genes[cur_line.iv] += cur_line.name
cur_line = feature
transcript.clear()
if feature.type in TX:
key = None
if "geneID" in feature.attr:
key = "geneID"
elif "Parent" in feature.attr:
key = "Parent"
else:
sys.stderr.write("transcript line does not have Parent or geneID field\n")
if last_gene_id == feature.attr[key]:
transcript.add(feature.attr["ID"])
else:
if len(transcript) > 1:
if feature.attr[key] not in _dict_counts:
_dict_counts[feature.attr[key]] = [0]*NFILE
_genes[feature.iv] += feature.attr[key]
transcript.clear()
transcript.add(feature.attr["ID"])
last_gene_id = feature.attr[key]
if feature.type in EXON:
transcript.add(feature.attr["Parent"])
print "num of genes to simulate: ", len(_dict_counts)
_file_raw_count = open(_output+'.rawcounts','w')
_file_nb_count = open(_output+'.nbcounts','w')
## This loop read through the input list and call countSam for each input file
for f in _files:
sam_file=HTSeq.SAM_Reader(f)
_dict_counts=countSam(sam_file, _genes,_dict_counts, idx)
f.close()
idx += 1
sys.stderr.write("library %d has generated.\n" % idx)
## Print raw counts in file specified by <out>
for key, value in sorted(_dict_counts.iteritems()):
_file_raw_count.write(key+"\t"+"\t".join(map(str,value))+"\n")
_file_raw_count.close()
## calculate group mean and variance
list_mean = list()
list_var = list()
for key, value in sorted(_dict_counts.iteritems()):
list_mean.append(np.mean(np.array(value)))
list_var.append(np.var(np.array(value)))
## computer loess esimates
## The following code is using rpy2 module
a = robjects.FloatVector(list_mean)
b = robjects.FloatVector(list_var)
df = robjects.DataFrame({"mean": a, "var": b})
non0_df=df.rx(df.rx2("mean").ro > 0, True) ## subsetting if mean > 0
loess_fit = r.loess("var ~ mean", data=non0_df, degree=2)
'''
#good-of-fit test:
variance=r.predict(loess_fit, 1000)
print variance[0]
print (1000*1000)/(variance[0]-1000)
'''
var_pred = r.predict(loess_fit, a)
# This loop overwrite global variable dict_counts for recoding new count data
count_idx = 0
for key, value in sorted(_dict_counts.iteritems()):
n = math.pow(list_mean[count_idx],2)/(var_pred[count_idx]-list_mean[count_idx])
n = int(n) # n: number of failures
if n<=0:
_dict_counts[key] = [0]*NREPS
else:
p = n/float(n+list_mean[count_idx]) # p: prob of success
_dict_counts[key] = nbinom.rvs(n, p, size=NREPS).tolist()
count_idx += 1
#var_pred = r.predict(loess_fit, a)
for key, value in sorted(_dict_counts.iteritems()):
_file_nb_count.write(key+"\t"+"\t".join(map(str,value))+"\n")
_file_nb_count.close()
_file_raw_count.close()
return _dict_counts
import statsmodels.api as sm
# Data
np.random.seed(141) # set seed to replicate example
nobs= 2500 # number of obs in model
x1 = binom.rvs(1, 0.6, size=nobs) # categorical explanatory variable
x2 = uniform.rvs(size=nobs) # real explanatory variable
theta = 0.303
X = sm.add_constant(np.column_stack((x1, x2)))
beta = [1.0, 2.0, -1.5]
xb = np.dot(X, beta) # linear predictor
exb = np.exp(xb)
nby = nbinom.rvs(exb, theta)
mydata = {} # build data dictionary
mydata['N'] = nobs # sample size
mydata['X'] = X # predictors
mydata['Y'] = nby # response variable
mydata['K'] = len(beta)
# Fit
stan_code = """
data{
int N;
int K;
matrix[N,K] X;
int Y[N];
def draw_from_negative_binomial(mu, phi):
n = phi
p = 1/(1+mu/phi)
return nbinom.rvs(n, p)
print"##INFO=<ID=%s,Number=.,Type=%s,Description=\"%s\">" % (INFO.id, INFO.type, INFO.desc)
for fmat in FORMAT:
print"##FORMAT=<ID=%s,Number=.,Type=%s,Description=\"%s\">" % (fmat.id, fmat.type, fmat.desc)
print '##analysis=simulate_dp.py --lambda %f --epsilon %f --dispersion_mean %f --dispersion_sd %f --seed %s' % (args.lamb, args.epsilon, args.dmean, args.dsd, str(args.seed))
print line
continue
fields = line.split()
genotypes = fields[9:]
samples = []
for gt in genotypes:
# scipy nbinom takes (n, p) as arguments.
# Convolution: sum_{i=1}{x}nbinom(n, p) = nbinom(xn, p).
if gt.count('0')==0:
dp_ref = 0
else:
dp_ref = nbinom.rvs(lamb * gt.count('0') / ((d - 1) * 2), 1 / d)
if gt.count('1')==0:
dp_alt = 0
else:
dp_alt = nbinom.rvs(lamb * gt.count('1') / ((d - 1) * 2), 1 / d)
dp = dp_ref + dp_alt
pl = calculate_pl(dp_ref, dp_alt)
if pl:
sample = "%s:%i,%i:%i:%i,%i,%i" % (gt, dp_ref, dp_alt, dp, pl[0], pl[1], pl[2])
samples.append(sample)
else:
samples.append(gt)
info = '%s;Dispersion=%s' % (fields[7], '{0:.3f}'.format(d))
output = fields[:7] + [info] + ['GT:AD:DP:PL'] + samples
print '\t'.join(output)
def main():
### get command line options
options = parse_options(sys.argv)
### parse parameters from options object
CFG = settings.parse_args(options, identity='test')
CFG['use_exon_counts'] = False
### generate output directory
outdir = os.path.join(options.outdir, 'testing')
if options.timestamp == 'y':
outdir = '%s_%s' % (outdir, str(datetime.datetime.now()).replace(' ', '_'))
if CFG['diagnose_plots']:
CFG['plot_dir'] = os.path.join(options.outdir, 'plots')
if not os.path.exists(CFG['plot_dir']):
os.makedirs(CFG['plot_dir'])
if options.labelA != 'condA' and options.labelB != 'condB':
outdir = '%s_%s_vs_%s' % (outdir, options.labelA, options.labelB)
if not os.path.exists(outdir):
os.makedirs(outdir)
if CFG['debug']:
print "Generating simulated dataset"
npr.seed(23)
CFG['is_matlab'] = False
#cov = npr.permutation(20000-20).astype('float').reshape(999, 20)
#cov = sp.r_[cov, sp.c_[sp.ones((1, 10)) *10, sp.ones((1, 10)) * 500000] + npr.normal(10, 1, 20)]
#sf = sp.ones((cov.shape[1], ), dtype='float')
setsize = 50
### diff event counts
cov = sp.zeros((500, 2 * setsize), dtype='int')
for i in range(10):
cov[i, :setsize] = nbinom.rvs(30, 0.8, size=setsize)
cov[i, setsize:] = nbinom.rvs(10, 0.8, size=setsize)
for i in range(10, cov.shape[0]):
cov[i, :] = nbinom.rvs(30, 0.8, size=2*setsize)
### diff gene expression
cov2 = sp.zeros((500, 2 * setsize), dtype='int')
for i in range(20):
cov2[i, :setsize] = nbinom.rvs(2000, 0.2, size=setsize)
cov2[i, setsize:] = nbinom.rvs(2000, 0.3, size=setsize)
for i in range(20, cov2.shape[0]):
cov2[i, :] = nbinom.rvs(2000, 0.3, size=2*setsize)
cov = sp.c_[cov, cov2] * 10000
tidx = sp.arange(setsize)
sf = npr.uniform(0, 5, 2*setsize)
sf = sp.r_[sf, sf]
#dmatrix0 = sp.ones((cov.shape[1], 3), dtype='bool')
dmatrix1 = sp.zeros((cov.shape[1], 4), dtype='float')
dmatrix1[:, 0] = 1
dmatrix1[tidx, 1] = 1
#dmatrix1[tidx, 2] = 1
dmatrix1[tidx + (2*setsize), 2] = 1
dmatrix1[(2*setsize):, 3] = 1
#dmatrix1[:, 4] = sp.log(sf)
dmatrix0 = dmatrix1[:, [0, 2, 3]]
cov = cov * sf
#sf = sp.ones((cov.shape[1], ), dtype='float')
pvals = run_testing(cov, dmatrix0, dmatrix1, sf, CFG)
pvals_adj = adj_pval(pvals, CFG)
pdb.set_trace()
else:
val_tag = ''
if CFG['validate_splicegraphs']:
val_tag = '.validated'
if CFG['is_matlab']:
CFG['fname_genes'] = os.path.join(CFG['out_dirname'], 'spladder', 'genes_graph_conf%i.%s%s.mat' % (CFG['confidence_level'], CFG['merge_strategy'], val_tag))
CFG['fname_count_in'] = os.path.join(CFG['out_dirname'], 'spladder', 'genes_graph_conf%i.%s%s.count.mat' % (CFG['confidence_level'], CFG['merge_strategy'], val_tag))
else:
CFG['fname_genes'] = os.path.join(CFG['out_dirname'], 'spladder', 'genes_graph_conf%i.%s%s.pickle' % (CFG['confidence_level'], CFG['merge_strategy'], val_tag))
CFG['fname_count_in'] = os.path.join(CFG['out_dirname'], 'spladder', 'genes_graph_conf%i.%s%s.count.hdf5' % (CFG['confidence_level'], CFG['merge_strategy'], val_tag))
condition_strains = None
CFG['fname_exp_hdf5'] = os.path.join(CFG['out_dirname'], 'spladder', 'genes_graph_conf%i.%s%s.gene_exp.hdf5' % (CFG['confidence_level'], CFG['merge_strategy'], val_tag))
if os.path.exists(CFG['fname_exp_hdf5']):
if CFG['verbose']:
print 'Loading expression counts from %s' % CFG['fname_exp_hdf5']
IN = h5py.File(CFG['fname_exp_hdf5'], 'r')
gene_counts = IN['raw_count'][:]
gene_strains = IN['strains'][:]
gene_ids = IN['genes'][:]
IN.close()
else:
if options.subset_samples == 'y':
condition_strains = sp.unique(sp.r_[sp.array(CFG['conditionA']), sp.array(CFG['conditionB'])])
CFG['fname_exp_hdf5'] = os.path.join(CFG['out_dirname'], 'spladder', 'genes_graph_conf%i.%s%s.gene_exp.%i.hdf5' % (CFG['confidence_level'], CFG['merge_strategy'], val_tag, hash(tuple(sp.unique(condition_strains))) * -1))
if os.path.exists(CFG['fname_exp_hdf5']):
if CFG['verbose']:
print 'Loading expression counts from %s' % CFG['fname_exp_hdf5']
IN = h5py.File(CFG['fname_exp_hdf5'], 'r')
gene_counts = IN['raw_count'][:]
gene_strains = IN['strains'][:]
gene_ids = IN['genes'][:]
IN.close()
else:
gene_counts, gene_strains, gene_ids = get_gene_expression(CFG, fn_out=CFG['fname_exp_hdf5'], strain_subset=condition_strains)
gene_strains = sp.array([x.split(':')[1] if ':' in x else x for x in gene_strains])
### estimate size factors for library size normalization
sf_ge = get_size_factors(gene_counts, CFG)
### get index of samples for difftest
idx1 = sp.where(sp.in1d(gene_strains, CFG['conditionA']))[0]
idx2 = sp.where(sp.in1d(gene_strains, CFG['conditionB']))[0]
### for TESTING
#setsize = 100
#idx1 = sp.arange(0, setsize / 2)
#idx2 = sp.arange(setsize / 2, setsize)
### subset expression counts to tested samples
gene_counts = gene_counts[:, sp.r_[idx1, idx2]]
sf_ge = sf_ge[sp.r_[idx1, idx2]]
#sf = sp.r_[sf, sf]
### test each event type individually
for event_type in CFG['event_types']:
if CFG['verbose']:
print 'Testing %s events' % event_type
CFG['fname_events'] = os.path.join(CFG['out_dirname'], 'merge_graphs_%s_C%i.counts.hdf5' % (event_type, CFG['confidence_level']))
### quantify events
(cov, gene_idx, event_idx, event_ids, event_strains) = quantify.quantify_from_counted_events(CFG['fname_events'], sp.r_[idx1, idx2], event_type, CFG)
### estimate size factors
sf_ev = get_size_factors(sp.vstack(cov), CFG)
sf = sp.r_[sf_ev, sf_ge]
assert(sp.all(gene_strains == event_strains))
### map gene expression to event order
curr_gene_counts = gene_counts[gene_idx, :]
### filter for min expression
if event_type == 'intron_retention':
k_idx = sp.where((sp.mean(cov[0] == 0, axis=1) < CFG['max_0_frac']) | \
(sp.mean(cov[1] == 0, axis=1) < CFG['max_0_frac']))[0]
else:
k_idx = sp.where(((sp.mean(cov[0] == 0, axis=1) < CFG['max_0_frac']) | \
(sp.mean(cov[1] == 0, axis=1) < CFG['max_0_frac'])) & \
(sp.mean(sp.c_[cov[0][:, :idx1.shape[0]], cov[1][:, :idx1.shape[0]]] == 0, axis=1) < CFG['max_0_frac']) & \
(sp.mean(sp.c_[cov[0][:, idx2.shape[0]:], cov[1][:, idx2.shape[0]:]] == 0, axis=1) < CFG['max_0_frac']))[0]
if CFG['verbose']:
print 'Exclude %i of %i %s events (%.2f percent) from testing due to low coverage' % (cov[0].shape[0] - k_idx.shape[0], cov[0].shape[0], event_type, (1 - float(k_idx.shape[0]) / cov[0].shape[0]) * 100)
if k_idx.shape[0] == 0:
print 'All events of type %s were filtered out due to low coverage. Please try re-running with less stringent filter criteria' % event_type
continue
# k_idx = sp.where((sp.mean(sp.c_[cov[0], cov[1]], axis=1) > 2))[0]
# k_idx = sp.where((sp.mean(cov[0], axis=1) > 2) & (sp.mean(cov[1], axis=1) > 2))[0]
cov[0] = cov[0][k_idx, :]
cov[1] = cov[1][k_idx, :]
curr_gene_counts = curr_gene_counts[k_idx, :]
event_idx = event_idx[k_idx]
gene_idx = gene_idx[k_idx]
event_ids = [x[k_idx] for x in event_ids]
cov[0] = sp.around(sp.hstack([cov[0], curr_gene_counts]))
cov[1] = sp.around(sp.hstack([cov[1], curr_gene_counts]))
cov = sp.vstack(cov)
event_ids = sp.hstack(event_ids)
tidx = sp.arange(idx1.shape[0])
#if CFG['debug']:
# for i in range(cov.shape[0]):
# fig = plt.figure(figsize=(8, 6), dpi=100)
# ax = fig.add_subplot(111)
# ax.hist(cov[i, :] * sf, 50, histtype='bar', rwidth=0.8)
# #ax.plot(sp.arange(cov.shape[1]), sorted(cov[i, :]), 'bo')
# ax.set_title('Count Distribution - Sample %i' % i )
# plt.savefig('count_dist.%i.pdf' % i, format='pdf', bbox_inches='tight')
# plt.close(fig)
### build design matrix for testing
dmatrix1 = sp.zeros((cov.shape[1], 4), dtype='bool')
dmatrix1[:, 0] = 1 # intercept
dmatrix1[tidx, 1] = 1 # delta a
dmatrix1[tidx, 2] = 1 # delta g
dmatrix1[tidx + (idx1.shape[0] + idx2.shape[0]), 2] = 1 # delta g
dmatrix1[(idx1.shape[0] + idx2.shape[0]):, 3] = 1 # is g
dmatrix0 = dmatrix1[:, [0, 2, 3]]
### make event splice forms unique to prevent unnecessary tests
event_ids, u_idx, r_idx = sp.unique(event_ids, return_index=True, return_inverse=True)
if CFG['verbose']:
print 'Consider %i unique event splice forms for testing' % u_idx.shape[0]
### run testing
#pvals = run_testing(cov[u_idx, :], dmatrix0, dmatrix1, sf, CFG, r_idx)
pvals = run_testing(cov, dmatrix0, dmatrix1, sf, CFG)
pvals_adj = adj_pval(pvals, CFG)
### write output
out_fname = os.path.join(outdir, 'test_results_C%i_%s.tsv' % (options.confidence, event_type))
if CFG['verbose']:
print 'Writing test results to %s' % out_fname
s_idx = sp.argsort(pvals_adj)
header = sp.array(['event_id', 'gene', 'p_val', 'p_val_adj'])
event_ids = sp.array(['%s_%i' % (event_type, i + 1) for i in event_idx], dtype='str')
if CFG['is_matlab']:
data_out = sp.c_[event_ids[s_idx], gene_ids[gene_idx[s_idx], 0], pvals[s_idx].astype('str'), pvals_adj[s_idx].astype('str')]
else:
data_out = sp.c_[event_ids[s_idx], gene_ids[gene_idx[s_idx]], pvals[s_idx].astype('str'), pvals_adj[s_idx].astype('str')]
data_out = sp.r_[header[sp.newaxis, :], data_out]
sp.savetxt(out_fname, data_out, delimiter='\t', fmt='%s')
from scipy.stats import norm, uniform, nbinom
np.random.seed(1656) # set seed to replicate example
N = 2000 # number of obs in model
NGroups = 10
x1 = uniform.rvs(size=N)
x2 = uniform.rvs(size=N)
Groups = np.array([200 * [i] for i in range(NGroups)]).flatten()
a = norm.rvs(loc=0, scale=0.5, size=NGroups)
eta = 1 + 0.2 * x1 - 0.75 * x2 + a[list(Groups)]
mu = np.exp(eta)
y = nbinom.rvs(mu, 0.5)
# Code 8.23 Random intercept negative binomial model in Python using Stan
import pystan
X = sm.add_constant(np.column_stack((x1,x2)))
K = X.shape[1]
model_data = {}
model_data['Y'] = y
model_data['X'] = X
model_data['K'] = K
model_data['N'] = N
model_data['NGroups'] = NGroups
def generate_count(options):
numGene = options.numEntry
numSampleConA = options.numSampleConA
numSampleConB = options.numSampleConB
nParamNB = options.nParamNB
pParamNB = options.pParamNB
beta1 = options.beta1
beta2 = options.beta2
output = options.output
# First generate the mean read count for each gene. Assume this mean value follows NB distribution (Observed from real data).
mu = nbinom.rvs(nParamNB, pParamNB, loc=0.0, size=numGene)
# If the mean of certain genes are 0, change them as 1.
idx = np.nonzero(mu == 0.0)[0]
mu[idx] = 1.0
# Generate dispersions for all genes.
if not options.dispFile:
# Generate dispersions as a function of mean count for all genes.
disper = beta1 / mu + beta2
else:
# Load the dispersions to generate the count.
disper = np.loadtxt(options.dispFile, dtype=float, skiprows=0, usecols=(0,))
if disper.size != numGene:
sys.stderr.write('\nError: The number of specified dispersions is not the same with number of genes!\n\n')
sys.exit()
# Add Gaussian distributed noise to log(dispersion).
if options.addDisperError:
std = options.addDisperError
errorNorm = norm.rvs(loc=0.0, scale=std, size=numGene)
disper = np.exp(np.log(disper) + errorNorm)
muA = mu.copy()
muB = mu.copy()
# For some genes, generate read count with different mean value in different conditions.
if options.numDiff or options.diffFile:
# Fold change genes are randomly selected, or are chosen as indicated by file.
if not options.diffFile:
numDiff = options.numDiff
# The number of genes showing increased and decreased mean count is equal or 1 less.
numDiffUp = numDiff / 2
numDiffDn = numDiff - numDiffUp
idx = random.sample(range(numGene), numDiff)
idxUp = random.sample(idx, numDiffUp)
idxDn = np.setdiff1d(idx, idxUp)
else:
diffInfo = np.loadtxt(options.diffFile, dtype=int, skiprows=0, usecols=(0,))
idxUp = (diffInfo==2).nonzero()[0]
idxDn = (diffInfo==1).nonzero()[0]
numDiffUp = idxUp.size
numDiffDn = idxDn.size
numDiff = numDiffUp + numDiffDn
if numDiff > options.numEntry:
print 'numDiff should be smaller than numGene!'
sys.exit()
shapeParam = options.shapeGamma
scaleParam = options.scaleGamma
# Assume fold changes of mean count of different genes follow gamma distribution. If fold change value of increased gene set is x, the decreased set is 1/x.
foldDiffUp = gamma.rvs(a=shapeParam, scale=scaleParam, loc=1.0, size=numDiffUp)
foldDiffDn = 1.0 / gamma.rvs(a=shapeParam, scale=scaleParam, loc=1.0, size=numDiffDn)
# Change the mean count of condition A and condition B without changing the overall mean count across the two conditions.
# (MeanCountA + MeanCountB) / 2 = MeanCountOrigin & MeanCountA * FoldChange = MeanCountB
# Assume there is a negative correlation between mean count and fold change.
idxUpMem = np.searchsorted(np.sort(mu[idxUp]), mu[idxUp])
idxDnMem = np.searchsorted(np.sort(mu[idxDn]), mu[idxDn])
muAnewUp = 2 * np.sort(mu[idxUp]) / (np.sort(foldDiffUp)[::-1] + 1)
muBnewUp = muAnewUp * np.sort(foldDiffUp)[::-1]
muA[idxUp] = muAnewUp[idxUpMem]
muB[idxUp] = muBnewUp[idxUpMem]
muAnewDn = 2 * np.sort(mu[idxDn]) / (np.sort(foldDiffDn) + 1)
muBnewDn = muAnewDn * np.sort(foldDiffDn)
muA[idxDn] = muAnewDn[idxDnMem]
muB[idxDn] = muBnewDn[idxDnMem]
n = 1.0 / disper
pA = n / (n + muA)
pB = n / (n + muB)
numDigits = len(str(numGene))
with open(output, 'w') as FileOut:
FileOut.write('Entry\t' + 'conditionA\t'*numSampleConA + 'conditionB\t'*numSampleConB + 'Dispersion\t' + 'MeanCondA\t' + 'MeanCondB\t' + 'MeanFoldChange\t' + 'SetAsDiff\n')
for i in range(numGene):
z = numDigits - len(str(i+1))
name = 'G' + '0'*z + str(i+1)
# The dispersion parameter (1/n) is the same for both conditions. The probability parameters are different if there is fold change in mean count for different conditions.
countListA = nbinom.rvs(n[i], pA[i], size=numSampleConA).tolist()
countListB = nbinom.rvs(n[i], pB[i], size=numSampleConB).tolist()
countList = countListA + countListB
countString = '\t'.join(str(element) for element in countList)
if not options.numDiff:
setAsDiff = '-1'
elif i in idxUp:
setAsDiff = '1'
elif i in idxDn:
setAsDiff = '2'
else:
setAsDiff = '0'
FileOut.write(name + '\t' + countString + '\t' + str(disper[i]) + '\t' + str(np.mean(countListA)) + '\t' + str(np.mean(countListB)) + '\t' + str((np.mean(countListB)+1e-5)/(np.mean(countListA)+1e-5)) + '\t' + setAsDiff + '\n')
def evaluate(pop, intel_penalty=0.01, game=None):
n = len(pop)
total_payoffs = np.zeros((1, n))
rate_of_coop = np.zeros((1,n))
class NNPlayer(games.Player):
def __init__(self, nnet):
self.nnet = nnet
def reset(self):
self.nnet.reset()
def get_initial_action(self):
return self.nnet.initial_move
def get_action(self, prev_results):
prev_payoffs = [r['payoff'] for r in prev_results]
output = self.nnet.activate(prev_payoffs)
if type(output) == np.ndarray:
output = output[0,0]
else:
output = output
if np.random.rand() < output:
return 1
else:
return 0
for i in range(n):
for j in range(i+1, n):
n_rounds = nbinom.rvs(1, 0.2, 1) + 1
payoffs, traces = game.play(NNPlayer(pop[i]), NNPlayer(pop[j]), n_rounds)
total_payoffs[0,i] += payoffs[0,0]
total_payoffs[0,j] += payoffs[0,1]
rate_of_coop[0, i] += np.mean(traces[0])
rate_of_coop[0, j] += np.mean(traces[1])
total_payoffs /= float(n-1)
rate_of_coop /= float(n-1)
for i in range(n):
#pop[i].fitness.values = [total_payoffs[0,i] - intel_penalty*pop[i].get_intelligence()]
pop[i].fitness.values = [total_payoffs[0,i], pop[i].get_intelligence()]
pop[i].rate_of_coop = rate_of_coop[0, i]
# Examine the strategies in the population.
class AlwaysCooperatePlayer(games.Player):
def get_initial_action(self):
return 1
def get_action(self, prev_payoffs):
return 1
class AlwaysDefectPlayer(games.Player):
def get_initial_action(self):
return 0
def get_action(self, prev_results):
return 0
class TitForTatPlayer(games.Player):
def get_initial_action(self):
return 1
def get_action(self, prev_results):
# Default cooperate, but defect if opponent defected.
if prev_results[1]['action'] == 0:
return 0
else:
return 1
class TitForTwoTatsPlayer(games.Player):
def __init__(self):
self.opponent_defected = False
def reset(self):
self.opponent_defected = False
def get_initial_action(self):
return 1
def get_action(self, prev_results):
# Default cooperate, but defect if opponent defected twice
# in a row.
if prev_results[1]['action'] == 0 and self.opponent_defected:
return 0
elif prev_results[1]['action'] == 0:
self.opponent_defected = True
return 1
else:
self.opponent_defected = False
return 1
class PavlovPlayer(games.Player):
def get_initial_action(self):
return 1
def get_action(self, prev_results):
return prev_results[1]['action']
class ProbabilisticPlayer(games.Player):
def __init__(self, prob):
# prob -> probability of cooperating
self.prob = prob
def get_initial_action(self):
self.get_action(None)
def get_action(self, prev_results):
if np.random.rand() <= prob:
return 1
else:
return 1
probs = [0.0, 0.25, 0.5, 0.75, 1.0]
n_games = 5
n_rounds = 20
n_total = len(probs)*n_games*n_rounds
test_players = [AlwaysCooperatePlayer(),
AlwaysDefectPlayer(),
TitForTatPlayer(),
TitForTwoTatsPlayer(),
PavlovPlayer()]
test_player_moves = np.zeros((len(test_players), n_total))
pop_moves = np.zeros((len(pop), n_total))
opp_moves = np.zeros(len(probs)*n_games*n_rounds)
start_idx = 0
for p in probs:
for i in range(n_games):
stop_idx = start_idx + n_rounds
random_trace = [np.random.rand() < p for i in range(n_rounds)]
random_trace = np.array(random_trace, dtype='float')
opp_moves[start_idx:stop_idx] = random_trace
for (j, player) in enumerate(test_players):
_, traces = game.play_against_trace(player, random_trace)
test_player_moves[j, start_idx:stop_idx] = traces[0]
for (j, indiv) in enumerate(pop):
_, traces = game.play_against_trace(NNPlayer(indiv), random_trace)
pop_moves[j, start_idx:stop_idx] = traces[0]
start_idx += n_rounds
# (X - Y)^2 = X^2 - 2XY + Y^2
pop_squared = np.square(pop_moves).sum(axis=1)
test_squared = np.square(test_player_moves).sum(axis=1)
pop_test = np.dot(pop_moves, test_player_moves.T)
sq_dists = pop_squared[:,np.newaxis] - 2 * pop_test + test_squared[np.newaxis,:]
sq_dists /= n_total
closest_strat = sq_dists.argmin(axis=1)
for (i, indiv) in enumerate(pop):
indiv.closest_strategy = closest_strat[i]
indiv.strategy_dists = sq_dists[i,:]
return pop