def gamma_difference_hrf(
tr,
oversampling=16,
time_length=32.0,
onset=0.0,
delay=6,
undershoot=16.0,
dispersion=1.0,
u_dispersion=1.0,
ratio=0.167,
):
""" Compute an hrf as the difference of two gamma functions
Parameters
----------
tr: float, scan repeat time, in seconds
oversampling: int, temporal oversampling factor, optional
time_length: float, hrf kernel length, in seconds
onset: float, onset of the hrf
Returns
-------
hrf: array of shape(length / tr * oversampling, float),
hrf sampling on the oversampled time grid
"""
dt = tr / oversampling
time_stamps = np.linspace(0, time_length, float(time_length) / dt)
time_stamps -= onset / dt
hrf = gamma.pdf(time_stamps, delay / dispersion, dt / dispersion) - ratio * gamma.pdf(
time_stamps, undershoot / u_dispersion, dt / u_dispersion
)
hrf /= hrf.sum()
return hrf
def mcmc(N=1000, k={"t1":100, "t2":100, "t3":5}, x=[], v=[]):
chute = {"t1":[10],"t2":[10],"t3":[0.01]}
M = chute
hiper = {"t1":[0,100],"t2":[0,100],"t3":[0.1,0.1]} #VALORES DOS HIPERPARAMETROS
for i in range(N-1):
for j in M.keys():
if j == "t1" or j == "t2":
M[j].append( np.random.normal(loc = M[j][-1]-k[j]/100, scale = k[j], size = 1) )
lista = [ [ M[l][-1] for l in M.keys()] , [ M[l][-1] if l!=j else M[l][-2] for l in M.keys() ] ]
t1 = norm.pdf(M[j][-1], loc = hiper[j][0], scale = hiper[j][1]) * L(x, v, lista[0]) * norm.pdf(M[j][-2], loc = M[j][-1]-k[j]/100, scale = k[j])
t2 = norm.pdf(M[j][-2], loc = hiper[j][0], scale = hiper[j][1]) * L(x, v, lista[1]) * norm.pdf(M[j][-1], loc = M[j][-2]-k[j]/100, scale = k[j])
teste = (t1/t2)
else:
M[j].append( np.random.gamma(shape = M[j][-1]*k[j], scale = k[j], size = 1) )
lista = [ [ M[l][-1] for l in M.keys()] , [ M[l][-1] if l!=j else M[l][-2] for l in M.keys() ] ]
t1 = gamma.pdf(M[j][-1], a = hiper[j][0], scale = hiper[j][1]) * L(x, v, lista[0]) * gamma.pdf(M[j][-2], a = M[j][-1]*k[j], scale = k[j])
t2 = gamma.pdf(M[j][-2], a = hiper[j][0], scale = hiper[j][1]) * L(x, v, lista[1]) * gamma.pdf(M[j][-1], a = M[j][-2]*k[j], scale = k[j])
teste = (t1/t2)
if (min(1 , teste) < np.random.uniform(low = 0, high = 1, size = 1) ) or (np.isinf(teste)) or (np.isnan(teste)) :
M[j][-1] = M[j][-2]
return(M)
def hrf_single(value): """ Return values for HRF at single value Parameters: ----------- value: a single float or integer value Returns: -------- hrf_value: the hrf(value) evaluated Note: ----- You must change the max_value (use np.argmax) if you change the function """ if value <0 or value >30: # if outside the range of the function return 0 # Gamma pdf for the peak peak_values = gamma.pdf(value, 6) # Gamma pdf for the undershoot undershoot_values = gamma.pdf(value, 12) # Combine them values = peak_values - 0.35 * undershoot_values # Scale max to 0.6 return values / max_value * 0.6
def fast_hrf(values): """ Return values for HRF at multiple values Parameters: ----------- value: an array-like structure of integers or floats. Returns: -------- comb_values: the hrf(values) evaluated Note: ----- You must change the max_value (use np.argmax) if you change the function """ # Gamma pdf for the peak peak_values = gamma.pdf(values, 6) # Gamma pdf for the undershoot undershoot_values = gamma.pdf(values, 12) # Combine them comb_values = peak_values - 0.35 * undershoot_values # if outside the range of the function comb_values[np.logical_or(values <0, values >30)] = 0 # Scale max to 0.6 return comb_values / max_value * 0.6
def spm_hrf(times):
""" Return values for standard SPM HRF at given `times`
This is the same as SPM's ``spm_hrf.m`` function using the default input
values.
Parameters
----------
times : array
Times at which to sample hemodynamic response function
Returns
-------
values : array
Array of same length as `times` giving HRF samples at corresponding
time post onset (where onset is T==0).
"""
# Gamma only defined for x values > 0
time_gt_0 = times > 0
ok_times = times[time_gt_0]
# Output vector
values = np.zeros(len(times))
# Gamma pdf for the peak
peak_values = gamma.pdf(ok_times, 6)
# Gamma pdf for the undershoot
undershoot_values = gamma.pdf(ok_times, 16)
# Combine them
values[time_gt_0] = peak_values - undershoot_values / 6.
# Divide by sum
return values / np.sum(values)
def test_hrf():
time = np.arange(0,24, 1.0/100)
peak_values = gamma.pdf(time,6)
undershoot_values = gamma.pdf(time, 12)
values = peak_values - 0.35 * undershoot_values
hrf_totest = values/np.max(values) * 0.6
npt.assert_array_equal(hrf_totest,stimuli.hrf(np.arange(0,24,1.0/100)))
def hrf(times): """Produce hemodynamic response function for 'times' Parameters ---------- times : times in seconds for the events Returns ------- nparray of length == len(times) with hemodynamic repsonse values for each time course Example ------- >>> tr_times = np.arange(240) * 2 >>> hrf(tr_times)[:5] array([ 0. , 0.13913511, 0.6 , 0.58888885, 0.25576589]) """ # Gamma pdf for the peak peak_values = gamma.pdf(times, 6) # Gamma pdf for the undershoot undershoot_values = gamma.pdf(times, 12) # Combine them values = peak_values - 0.35 * undershoot_values # Scale max to 0.6 return values / np.max(values) * 0.6
def hrf(times):
"""
Computes values for the canonical hemodynamic response function at the
specified times
Parameters
----------
times : np.ndarray
1-D array of time points
Return:
------
hrf : np.ndarray
Array of shape (len(times),) that represents the hemodynamic response
function for the specified time points
"""
# Gamma pdf for the peak
peak_values = gamma.pdf(times, 6)
# Gamma pdf for the undershoot
undershoot_values = gamma.pdf(times, 12)
# Combine them
values = peak_values - 0.35 * undershoot_values
# Scale max to 0.6
return values / np.max(values) * 0.6
def hrf(times):
"""
Return values for HRF at given times
Used to get the convolved parameters
"""
peak_values=gamma.pdf(times,6)
undershoot_values=gamma.pdf(times,12)
values=peak_values-0.35*undershoot_values
return values/np.max(values)*0.6
def hrf(times):
# Gamma pdf for the peak
peak_values = gamma.pdf(times, 6)
# Gamma pdf for the undershoot
undershoot_values = gamma.pdf(times, 12)
# Combine them
values = peak_values - 0.35 * undershoot_values
# Scale max to 0.06
return values / np.max(values) * 0.06
def hrf(times):
""" Return values for HRF at given times """
# Gamma pdf for the peak
peak_values = gamma.pdf(times, 6)
# Gamma pdf for the undershoot
undershoot_values = gamma.pdf(times, 12)
# Combine them
values = peak_values - 0.35 * undershoot_values
# Scale max to 0.6
return values / np.max(values) * 0.6
def _gamma_difference_hrf(tr, oversampling=50, time_length=32., onset=0.,
delay=6, undershoot=16., dispersion=1.,
u_dispersion=1., ratio=0.167):
""" Compute an hrf as the difference of two gamma functions
Parameters
----------
tr : float
scan repeat time, in seconds
oversampling : int, optional (default=16)
temporal oversampling factor
time_length : float, optional (default=32)
hrf kernel length, in seconds
onset: float
onset time of the hrf
delay: float, optional
delay parameter of the hrf (in s.)
undershoot: float, optional
undershoot parameter of the hrf (in s.)
dispersion : float, optional
dispersion parameter for the first gamma function
u_dispersion : float, optional
dispersion parameter for the second gamma function
ratio : float, optional
ratio of the two gamma components
Returns
-------
hrf : array of shape(length / tr * oversampling, dtype=float)
hrf sampling on the oversampled time grid
"""
from scipy.stats import gamma
dt = tr / oversampling
time_stamps = np.linspace(0, time_length, np.rint(float(time_length) / dt).astype(np.int))
time_stamps -= onset
hrf = gamma.pdf(time_stamps, delay / dispersion, dt / dispersion) -\
ratio * gamma.pdf(
time_stamps, undershoot / u_dispersion, dt / u_dispersion)
hrf /= hrf.sum()
return hrf
def test_hrf():
# create test array of times
hrf_times = np.arange(0,20,0.2)
# Gamma pdf for the peak
peak_values = gamma.pdf(hrf_times, 6)
# Gamma pdf for the undershoot
undershoot_values = gamma.pdf(hrf_times, 12)
# Combine them
test_values = peak_values - 0.35 * undershoot_values
# Scale max to 0.6
test_values = test_values/np.max(test_values)*0.6
# my values from function
my_values = hrf(hrf_times)
# assert
assert_almost_equal(test_values, my_values)
def glover_hrf(timepoints): """ Canonical (Glover) HRF. Based on the nipy implementation (github.com/nipy/nipy/blob/master/nipy/ modalities/fmri/hrf.py). Peaks at 5.4 with 5.2 FWHM, undershoot peak at 10.8 with FWHM of 7.35 and amplitude of -0.35. Args: timepoints: Array of floats. Time points (in seconds, onset is 0). """ # Compute HRF as a difference of gammas and normalize hrf = gamma.pdf(timepoints, 7, scale=0.9) - 0.35 * gamma.pdf(timepoints, 13, scale=0.9) hrf /= hrf.sum() return hrf
def get_probability(self, shared_length, query_node, labeled_node):
"""
Returns the probability that query_node and labeled_node have total
shared segment length shared_length
"""
shape, scale = self._distributions[query_node, labeled_node]
return gamma.pdf(shared_length, a = shape, scale = scale)
def fit_gamma_distribution(self, desorption_thresh=5, plot=False, bins=15, normed=True):
# first get the detachment time
dt = self.get_desorption_distribution(thresh=desorption_thresh)
# you need to invert the data - to be able to fit gamma
# dt = dt.max() - dt
fit_alpha, fit_loc, fit_beta = gamma.fit(dt)
x = np.linspace(0, dt.max(), 100)
pdf_fitted = gamma.pdf(x, fit_alpha, fit_loc, fit_beta)
# normalize
# pdf_fitted = pdf_fitted / pdf_fitted.max()
# this is the maximum of the distribution
mode = x[pdf_fitted.argmax()]
if plot:
x = np.linspace(0, dt.max(), 100)
plt.hist(dt, bins=bins, normed=normed)
plt.plot(x, pdf_fitted)
plt.show()
return fit_alpha, fit_loc, fit_beta
def result_N_sub(path):
fig, ax = plt.subplots()
for result_data_path in path:
data = np.load(result_data_path)
beta = data['beta']
num_of_strings = data['num_of_strings']
L = data['L']
frames = data['frames']
Ls = data['Ls'].astype(np.float)
N_sub = data['N_sub']
# M = N_sub / 3 * Ls * (Ls + 1) + 1
M = N_sub
M_ave = M / np.sum(M)
popt = curve_fit(gamma.pdf, xdata=Ls, ydata=M_ave, p0=[2.5, -5., 30])[0]
print beta, popt
ax.plot(Ls, M_ave, '.-', label=r'$\beta = %2.2f$' % beta)
x = np.linspace(1., max(Ls), num=5*max(Ls))
ax.plot(x, gamma.pdf(x, a=popt[0], loc=popt[1], scale=popt[2]),
'-', label=r'fitted $\beta = %2.2f$' % beta)
ax.legend(loc='best')
ax.set_ylim((0., 0.1))
ax.set_title('Strings in hexagonal region' +
' (sample: {})'.format(num_of_strings))
ax.set_xlabel(r'Cutting size $L$')
ax.set_ylabel('Average number of the sub-clusters in the hexagonal region of size L')
plt.show()
def lowerbound(self, lnjoint):
#probability of these targets is 1 as they are training labels
lnpCT = self.post_lnjoint_ct(lnjoint)
lnpPi = np.sum(norm.pdf(self.mu, loc=self.m0, scale=1 / (self.lamb0 * self.prec)) \
* gamma.pdf(self.prec, shape=self.gam_alpha0, scale=1 / self.gam_beta0))
lnpKappa = self.post_lnkappa()
EEnergy = lnpCT + lnpPi + lnpKappa
lnqT = self.q_ln_t()
lnqPi = np.sum(norm.pdf(self.mu, loc=self.m, scale=1 / (self.lamb * self.prec)) \
* gamma.pdf(self.prec, shape=self.gam_alpha, scale=1 / self.gam_beta))
lnqKappa = self.q_lnkappa()
H = - lnqT - lnqPi - lnqKappa
L = EEnergy + H
#logging.debug('EEnergy ' + str(EEnergy) + ', H ' + str(H))
return L
def _fit_gamma(sampleses, filename):
"""Fits a gamma distribution to the first 16 samples and plots the results
Assuming that filename ends with ".pdf"
"""
for i, samples in enumerate(sampleses[:16]):
sample_mean = np.mean(samples)
sample_var = np.var(samples)
sample_median = np.median(samples)
shape, loc, scale = gamma.fit(samples)
stat, pval = kstest(
samples,
'gamma',
args=(shape, loc, scale))
fig, axis = plt.subplots(1, 1)
axis.hist(samples, normed=True)
if i == 15:
fig.savefig('last.pdf')
plotx = np.linspace(np.min(samples), np.max(samples))
axis.plot(
plotx,
gamma.pdf(plotx, shape, loc=loc, scale=scale),
linewidth=3)
axis.set_title(
'shape='+str(shape)+'; loc='+str(loc) +
'; scale='+str(scale)+'\n' +
'stat='+str(stat)+'; pval='+str(pval)+'\n' +
'mean='+str(shape*scale)+'; var='+str(shape*scale*scale)+'\n' +
's_mean='+str(sample_mean)+'; s_var='+str(sample_var)+'\n' +
's_median='+str(sample_median))
fig.savefig(
filename[:-4]+'_fit_'+_pad_num(i+1)+'.pdf',
bbox_inches='tight')
plt.close()
def params_of(strings):
strings_logprobs = np.empty(len(strings))
for i, string in enumerate(strings):
strings_logprobs[i] = sum(old_logprobs[state, symbol] for state, symbol in of(string))
strings_params = gamma.fit(strings_logprobs[strings_logprobs != np.inf])
_, bins, _ = plt.hist(strings_logprobs[strings_logprobs != np.inf], 500, histtype = 'step', normed = True)
plt.plot(bins, gamma.pdf(bins, *strings_params))
return strings_params
def plot_gamma(ax, shape, scale):
"""plot a gamma distribution on the supplied axis"""
tmin = max(0, ax.get_xlim()[0])
tmax = ax.get_xlim()[1]
t = np.linspace(tmin, tmax)
ax.plot(t, gamma.pdf(t, a=shape, scale=scale), 'r',
label="gamma pdf, $shape=%.1f, scale=%f$"%(shape, scale))
xlims = ax.set_xlim(tmin, tmax)
return ax
def _recall(m, l, gamma_params, max_x):
k = len(gamma_params)
s = 0.0
for i in range(1, k):
shape, loc, scale = gamma_params[i]
join_prob_func = lambda x : _hash_probability(m, l, np.sqrt(x)) * gamma.pdf(x, shape, loc, scale)
prob, _ = quad(join_prob_func, 0.0, max_x)
s += prob
return s / float(k - 1)
def gamma(sample, alpha, beta):
"""
https://en.wikipedia.org/wiki/Gamma_distribution#Parameterizations
https://stackoverflow.com/a/16964743/3052112
"""
x = sample
k = alpha
theta = 1.0 / beta
return gamma.pdf(x, a=k, scale=theta)
def calc_weight(weight, period, similarity):
"""
:descption
Before answer we add this five content.
1. more is different.
2. rare is beautiful.
3. new is good.
4. refractory period
5. key word
"""
return gamma.pdf(period, GAMMA) + similarity + more_or_rare(weight)
def hrf(times): """ Return values for canonical HRF at given times Parameter: --------- times: array an array of times points Return: ------ an array (len(times),) hemodynamic response """ # Gamma pdf for the peak peak_values = gamma.pdf(times, 6) # Gamma pdf for the undershoot undershoot_values = gamma.pdf(times, 12) # Combine them values = peak_values - 0.35 * undershoot_values # Scale max to 0.6 return values / np.max(values) * 0.6
def simulate_gamma(psth, trials, duration, num_trials=20):
#rescale the ISIs
dt = 0.001
rs_isis = []
for trial in trials:
if len(trial) < 1:
continue
csum = np.cumsum(psth)*dt
for k,ti in enumerate(trial[1:]):
tj = trial[k]
if ti > duration or tj > duration or ti < 0.0 or tj < 0.0:
continue
ti_index = int((ti / duration) * len(psth))
tj_index = int((tj / duration) * len(psth))
#print 'k=%d, ti=%0.6f, tj=%0.6f, duration=%0.3f' % (k, ti, tj, duration)
#print ' ti_index=%d, tj_index=%d, len(psth)=%d, len(csum)=%d' % (ti_index, tj_index, len(psth), len(csum))
#get rescaled time as difference in cumulative intensity
ui = csum[ti_index] - csum[tj_index]
if ui < 0.0:
print 'ui < 0! ui=%0.6f, csum[ti]=%0.6f, csum[tj]=%0.6f' % (ui, csum[ti_index], csum[tj_index])
else:
rs_isis.append(ui)
rs_isis = np.array(rs_isis)
rs_isi_x = np.arange(rs_isis.min(), rs_isis.max(), 1e-5)
#fit a gamma distribution to the rescaled ISIs
gamma_alpha,gamma_loc,gamma_beta = gamma.fit(rs_isis)
gamma_pdf = gamma.pdf(rs_isi_x, gamma_alpha, loc=gamma_loc, scale=gamma_beta)
print 'Rescaled ISI Gamma Fit Params: alpha=%0.3f, beta=%0.3f, loc=%0.3f' % (gamma_alpha, gamma_beta, gamma_loc)
#simulate new trials using rescaled ISIs
new_trials = []
for nt in range(num_trials):
ntrial = []
next_rs_time = gamma.rvs(gamma_alpha, loc=gamma_loc,scale=gamma_beta)
csum = 0.0
for t_index,pval in enumerate(psth):
csum += pval*dt
if csum >= next_rs_time:
#spike!
t = t_index*dt
ntrial.append(t)
#reset integral and generate new rescaled ISI
csum = 0.0
next_rs_time = gamma.rvs(gamma_alpha, loc=gamma_loc,scale=gamma_beta)
new_trials.append(ntrial)
#plt.figure()
#plt.hist(rs_isis, bins=20, normed=True)
#plt.plot(rs_isi_x, gamma_pdf, 'r-')
#plt.title('Rescaled ISIs')
return new_trials
def posterior(m , t):
xbar , s = np.mean(data) , np.var(data)
hyper_t = 1./hyper_sigma**2.
sigma_pos = (n*t + hyper_t)**-.5
mean_pos = (n*xbar*t + hyper_mu*hyper_t)/(n*t + hyper_t)
a_pos = n/2. + hyper_a
scale_pos = 1./(1 + n*s/2.)
#print mean_pos
#print sigma_pos
return gamma.pdf(t , a_pos , loc=0 , scale=scale_pos) * norm.pdf(m , loc = mean_pos , scale=sigma_pos)
def _pdf(self, value: float):
"""
Defines the gamma distribution
:param value: x-value
:return: Function value at point x
"""
if self._research_mode:
return gamma.pdf(value, a=self._alpha, scale=self._beta)
else:
if value > 0:
return (math.pow(self.beta, -self.alpha) * math.pow(value, self.alpha-1) * math.exp(-value/self.beta)) / \
math.gamma(self.alpha)
else:
return 0
def main():
model=pymc.MCMC(gamma_model)
model.sample(iter=1000, burn=500, thin=2)
alpha = mean(model.trace('alpha')[:])
beta = mean(model.trace('beta')[:])
print('alpha: %s' % alpha)
print('beta: %s' % beta )
x = np.linspace(0, 100, 0.001)
y = gamma.pdf(x, alpha, scale= 1.0 / beta)
plt.plot(x,y)
plt.xlim([0,100])
plt.ylim([0,0.001])
plt.show()
def fit_a_x0_scale(path):
betas = []
a = []
loc = []
scale = []
fig, ax = plt.subplots()
for i, result_data_path in enumerate(path):
globals().update(load_data(result_data_path))
ax.plot(Ls, M_ave, '.', label=r'$\beta = %2.2f$' % beta,
color=cm.viridis(float(i) / len(path)))
popt = curve_fit(gamma.pdf, xdata=Ls, ydata=M_ave, p0=[2.5, -5., 10.])[0]
print beta, popt
betas.append(beta)
a.append(popt[0])
loc.append(popt[1])
scale.append(popt[2])
x = np.linspace(0, max(Ls), num=5*max(Ls))
ax.plot(x, gamma.pdf(x, a=popt[0], loc=popt[1], scale=popt[2]),
'-', label=r'fitted $\beta = %2.2f$' % beta,
color=cm.viridis(float(i) / len(path)))
show_plot1(ax, num_of_strings)
plt.show()
betas = np.array(betas)
a = np.array(a)
loc = np.array(loc)
scale = np.array(scale)
fig, (ax1, ax2, ax3) = plt.subplots(3, 1)
ax1.plot(betas, a, 'o')
[ax.set_xlabel(r'$\beta$') for ax in [ax1, ax2, ax3]]
[ax.set_xlim((0, max(betas))) for ax in [ax1, ax2, ax3]]
ax1.set_ylabel(r'Shape parameter: $a$')
ax2.plot(betas, loc, 'o')
ax2.set_ylabel(r'Translation parameter: $x_{0}$')
# ax3.plot(-betas, -scale) # お試し
ax3.plot(betas, scale, 'o')
ax3.set_ylabel(r'Scale parameter: $\theta$')
plt.show()
def compute_gamma_prob(tau, a, b):
dist = gamma.pdf(tau, a, loc=0, scale=(1/b))
return dist
def g(x):
return gamma.pdf(x, C) * abs(np.cos(R * x))
def prob_gamma(x, shape, scale):
p = gamma.pdf(x,shape, loc=0, scale=scale)
return p
def dgamma(x, a):
""" Probability of a gamma continuous random variable. """
g2 = gamma.pdf(x, a)
return g2
areas = np.array([float(x) for x in line.rsplit(",")[0:-1]])
i+=1
nonzero_areas = areas[areas.nonzero()]
curved_core_cell_areas_sep[name]=nonzero_areas/nonzero_areas.mean()
pop_areas = list()
for n in names:
pop_areas.extend(curved_core_cell_areas_sep[n])
pop_areas=remove_zeros(pop_areas)
# =============================================================================
# FITS
# =============================================================================
x = np.linspace(0,xmax,1000)
fit_pop = gamma.pdf(x,*pdr_params)
if floc:
neo_params = gamma.fit(curved_neovascularized_areas,floc=0)
fit_neo = gamma.pdf(x,*neo_params)
# =============================================================================
# PLOT
# =============================================================================
fig = plt.figure()
ax = plt.subplot(111)
#plot_linear_distribution(pop_areas,"DR population", density=True,n="auto",fig=fig,ax=ax)
plt.plot(x,fit_pop,label="PDR whole image",c="red")
plt.plot(x,fit_neo,label="Neovascularized region only",c="#411900")
plot_linear_distribution(pop_areas,"PDR", density=True,n="auto",fig=fig,ax=ax,formatting=formatting)
}
# Proposed values are a Gaussian peturbation away from the previous values.
# This is controlled by the sigma of the gaussian, which is defined for each variable
proposal_sigma = {
'missing': 0.025,
'shape': 0.05,
'scale': 2,
'mixture': 0.025,
}
# PRIORS
priors = (lambda x: {
'missing': beta.pdf(x['missing'], a=3, b=15),
'mixture': beta.pdf(x['mixture'], a=1.1, b=1.1),
'shape': gma.pdf(x['shape'], a=10, scale=1 / 5),
'scale': gma.pdf(x['scale'], a=6, scale=50)
})
def test_mcmc():
folder = os.path.dirname(os.path.abspath(__file__))
file = "/mcmc_test_chain"
chain = mcmc.run_MCMC(data=am_data,
initial_parameters=initial_parameters,
proposal_sigma=proposal_sigma,
priors=priors,
thin=1,
nreps=3,
output_dir=folder,
def gps_function(treatment_val):
return gamma.pdf(treatment_val, a=shape, loc=0, scale=scale)
def main():
assert exists(SDCIT_RESULT_DIR + '/kcipt_chaotic_5000.csv'), 'run_SDCIT first'
assert exists(SDCIT_RESULT_DIR + '/kcipt_chaotic_20000.csv'), 'run_SDCIT first'
from experiments.draw_figures import color_palettes, method_color_codes
obj_filename = SDCIT_RESULT_DIR + '/right_power.pickle'
experiment(obj_filename)
time.sleep(3)
with open(obj_filename, 'rb') as f: # Python 3: open(..., 'rb')
sdcit_mmd, sdcit_null, mmds100, outer_null100, desired_B, mmds_B, outer_null_B, distr_boot = pickle.load(f)
print(desired_B)
print('SKEW SDCIT NULL: {}'.format(scipy.stats.skew(sdcit_null)))
print('SKEW KCIPT NULL: {}'.format(scipy.stats.skew(outer_null_B)))
names_kcipt_chaotic = ['independent', 'gamma', 'trial', 'N', 'statistic', 'pvalue', 'B']
names_sdcit_chaotic = ['independent', 'gamma', 'trial', 'N', 'statistic', 'pvalue']
df_kcipt_desired_B = pd.read_csv(SDCIT_RESULT_DIR + '/kcipt_chaotic_{}.csv'.format(desired_B), names=names_kcipt_chaotic, )
df_kcipt_5000 = pd.read_csv(SDCIT_RESULT_DIR + '/kcipt_chaotic_5000.csv', names=names_kcipt_chaotic, )
df_kcipt_20000 = pd.read_csv(SDCIT_RESULT_DIR + '/kcipt_chaotic_20000.csv', names=names_kcipt_chaotic, )
df_sdcit = pd.read_csv(SDCIT_RESULT_DIR + '/sdcit_chaotic.csv', names=names_sdcit_chaotic, )
df_sdcit = df_sdcit[df_sdcit['N'] == 400]
df_sdcit = df_sdcit[df_sdcit['independent'] == 1]
df_sdcit = df_sdcit[df_sdcit['gamma'] == 0.0]
assert len(df_sdcit) == 300
xs_sdcit = np.linspace(1.3 * sdcit_null.min(), 1.3 * sdcit_null.max(), 1000)
ys_sdcit_pearson3 = pearson3.pdf(xs_sdcit, *pearson3.fit(sdcit_null))
xs_kcipt = np.linspace(1.3 * outer_null_B.min(), 1.3 * outer_null_B.max(), 1000)
ys_kcipt_pearson3 = pearson3.pdf(xs_kcipt, *pearson3.fit(outer_null_B))
# 20000's null is inferred from known one...
factor_20000 = np.sqrt(20000 / desired_B)
ys_kcipt_20000_gamma = gamma.pdf(xs_kcipt, *gamma.fit(outer_null_B / factor_20000))
sns.set(style='white', font_scale=1.2)
paper_rc = {'lines.linewidth': 0.8, 'lines.markersize': 2, 'patch.linewidth': 1}
sns.set_context("paper", rc=paper_rc)
plt.rc('text', usetex=True)
plt.rc('text.latex', preamble=r'\usepackage{cmbright}')
if True:
fig = plt.figure(figsize=[5, 3.5])
##################################
fig.add_subplot(2, 2, 1, adjustable='box')
plt.plot(xs_sdcit, ys_sdcit_pearson3, label='SDCIT null', lw=1.5, color=color_palettes[method_color_codes['SDCIT']])
plt.plot([sdcit_mmd, sdcit_mmd], [0, 1000], label='SDCIT TS', color=color_palettes[method_color_codes['SDCIT']])
plt.plot(xs_kcipt, ys_kcipt_pearson3, label='KCIPT null', lw=1.5, color=color_palettes[method_color_codes['KCIPT']])
sns.distplot(distr_boot, hist=True, kde=False, hist_kws={'histtype': 'stepfilled'}, norm_hist=True, label='KCIPT TS', color=color_palettes[method_color_codes['KCIPT']])
plt.gca().set_xlim([-0.0003, 0.0005])
plt.ticklabel_format(style='sci', axis='x', scilimits=(0, 0))
plt.gca().set_ylabel('density')
plt.setp(plt.gca(), 'yticklabels', [])
plt.legend(loc=1)
##################################
fig.add_subplot(2, 2, 2, adjustable='box')
pvals_B = [p_value_of(t, outer_null_B) for t in distr_boot]
pval_sdcit = p_value_of(sdcit_mmd, sdcit_null)
sns.distplot(pvals_B, bins=20, hist=True, kde=False, hist_kws={'histtype': 'stepfilled'}, norm_hist=True, color=color_palettes[method_color_codes['KCIPT']], label='KCIPT p-values')
plt.plot([pval_sdcit, pval_sdcit], [0, 1], label='SDCIT p-value', color=color_palettes[method_color_codes['SDCIT']])
plt.gca().set_ylim([0, 2.2])
plt.gcf().subplots_adjust(wspace=0.3)
plt.legend(loc=2)
sns.despine()
##################################
fig.add_subplot(2, 2, 3, adjustable='box')
sns.distplot(df_sdcit['statistic'], hist=True, bins=20, kde=False, color=color_palettes[method_color_codes['SDCIT']], label='SDCIT TS')
sns.distplot(df_kcipt_desired_B['statistic'], hist=True, bins=20, kde=False, color=color_palettes[method_color_codes['KCIPT']], label='KCIPT TS')
plt.legend()
plt.gca().set_xlim([-0.0003, 0.0005])
plt.gca().set_xlabel('MMD')
plt.ticklabel_format(style='sci', axis='x', scilimits=(0, 0))
plt.gca().set_ylabel('density')
plt.setp(plt.gca(), 'yticklabels', [])
##################################
fig.add_subplot(2, 2, 4, adjustable='box')
sns.distplot(df_sdcit['pvalue'], hist=True, bins=20, kde=False, color=color_palettes[method_color_codes['SDCIT']], norm_hist=True, label='SDCIT p-values')
sns.distplot(df_kcipt_desired_B['pvalue'], hist=True, bins=20, kde=False, color=color_palettes[method_color_codes['KCIPT']], norm_hist=True, label='KCIPT p-values')
plt.gca().set_xlabel('p-value')
plt.gcf().subplots_adjust(wspace=0.3, hspace=0.3)
plt.gca().set_ylim([0, 2.2])
plt.legend(loc=0)
sns.despine()
plt.savefig(SDCIT_FIGURE_DIR + '/kcipt_{}_ps.pdf'.format(desired_B), transparent=True, bbox_inches='tight', pad_inches=0.02)
plt.close()
###############################################
###############################################
###############################################
###############################################
###############################################
###############################################
if True:
sns.set(style='white', font_scale=1.2)
paper_rc = {'lines.linewidth': 0.8, 'lines.markersize': 2, 'patch.linewidth': 1}
sns.set_context("paper", rc=paper_rc)
plt.rc('text', usetex=True)
plt.rc('text.latex', preamble=r'\usepackage{cmbright}')
fig = plt.figure(figsize=[5, 1.6])
##################################
fig.add_subplot(1, 2, 1, adjustable='box')
sns.distplot(df_kcipt_5000['statistic'], hist=True, bins=20, kde=False, color=color_palettes[method_color_codes['KCIPT']], label='TS')
plt.legend()
plt.gca().set_xlabel('MMD')
plt.ticklabel_format(style='sci', axis='x', scilimits=(0, 0))
plt.gca().set_ylabel('density')
plt.gca().set_xlim([-0.0002, 0.0003])
plt.setp(plt.gca(), 'yticklabels', [])
##
fig.add_subplot(1, 2, 2, adjustable='box')
sns.distplot(df_kcipt_5000['pvalue'], hist=True, bins=20, kde=False, color=color_palettes[method_color_codes['KCIPT']], norm_hist=True, label='p-value')
plt.gca().set_xlabel('p-value')
plt.gcf().subplots_adjust(wspace=0.3, hspace=0.3)
plt.legend(loc=0)
sns.despine()
plt.savefig(SDCIT_FIGURE_DIR + '/kcipt_5000_ps.pdf', transparent=True, bbox_inches='tight', pad_inches=0.02)
plt.close()
if True:
sns.set(style='white', font_scale=1.2)
paper_rc = {'lines.linewidth': 0.8, 'lines.markersize': 2, 'patch.linewidth': 1}
sns.set_context("paper", rc=paper_rc)
plt.rc('text', usetex=True)
plt.rc('text.latex', preamble=r'\usepackage{cmbright}')
fig = plt.figure(figsize=[5, 1.6])
# left subplot
fig.add_subplot(1, 2, 1, adjustable='box')
plt.plot(xs_sdcit, ys_sdcit_pearson3, label='SDCIT null', lw=1.5, color=color_palettes[method_color_codes['SDCIT']])
plt.plot(xs_kcipt, ys_kcipt_20000_gamma, label='KCIPT null', lw=1.5, color=color_palettes[method_color_codes['KCIPT']])
sns.distplot(df_kcipt_20000['statistic'], hist=True, bins=20, kde=False, norm_hist=True, color=color_palettes[method_color_codes['KCIPT']], label='KCIPT TS')
plt.legend(loc=1)
plt.gca().set_xlabel('MMD')
plt.ticklabel_format(style='sci', axis='x', scilimits=(0, 0))
plt.gca().set_ylabel('density')
plt.gca().set_xlim([-0.0002, 0.0003])
plt.setp(plt.gca(), 'yticklabels', [])
# right subplot
fig.add_subplot(1, 2, 2, adjustable='box')
sns.distplot(df_kcipt_20000['pvalue'], hist=True, bins=20, kde=False, color=color_palettes[method_color_codes['KCIPT']], norm_hist=True, label='KCIPT p')
sns.distplot([p_value_of(ss, sdcit_null) for ss in df_kcipt_20000['statistic']], hist=True, bins=20, kde=False, color='k', norm_hist=True, label='KCIPT p on SDCIT null')
plt.gca().set_xlabel('p-value')
plt.gcf().subplots_adjust(wspace=0.3, hspace=0.3)
plt.legend(loc=0)
sns.despine()
plt.savefig(SDCIT_FIGURE_DIR + '/kcipt_20000_ps.pdf', transparent=True, bbox_inches='tight', pad_inches=0.02)
plt.close()
def iet_plot(obj1,
Norm=None,
model=None,
t_lims=None,
lon_lims=None,
lat_lims=None,
z_lims=None,
Mc=None):
"""
Plot a histogram of interevent times and a pdf of normalized IETs
Args:
obj1: a varpy object containing event catalogue data
Norm: if True, normalize the IET histogram
model: option to fit and bootstrap CoIs for model. Existing options: Poisson, Gamma
t_lims: [t_min, t_max] defining time axis limits
lon_lims: [lon_min, lon_max] defining x-axis limits
lat_lims: [lat_min, lat_max] defining y-axis limits
z_lims: [z_min, z_max] defining depth range
Mc: magnitude cut-off
Returns:
fig1: a png image of the resulting plot
"""
if obj1.type == 'volcanic':
data = obj1.ecvd.dataset
header = obj1.ecvd.header
else:
data = obj1.ecld.dataset
header = obj1.ecld.header
if t_lims is not None:
try:
t_min = conversion.date2int(t_lims[0])
t_max = conversion.date2int(t_lims[1])
except:
t_min = float(t_lims[0])
t_max = float(t_lims[1])
pass
data = data[logical_and(data[:, header.index('datetime')] >= t_min,
data[:, header.index('datetime')] < t_max), :]
if lon_lims is not None:
data = data[
logical_and(data[:, header.index('longitude')] >= lon_lims[0],
data[:, header.index('longitude')] < lon_lims[1]), :]
if lat_lims is not None:
data = data[
logical_and(data[:, header.index('latitude')] >= lat_lims[0],
data[:, header.index('latitude')] < lat_lims[1]), :]
if z_lims is not None:
data = data[logical_and(data[:, header.index('depth')] >= z_lims[0],
data[:, header.index('depth')] < z_lims[1]), :]
if Mc is not None:
data = data[data[:, header.index('magnitude')] >= Mc, :]
dt_data = data[:, header.index('datetime')]
iets = diff(dt_data, n=1)
iet_mean = mean(iets)
iet_bins = logspace(-5.0, 2.0, num=50)
mid_iet_bins = iet_bins[:-1] + diff(iet_bins) / 2
iet_counts, iet_bes = histogram(iets, iet_bins)
##########
fig1 = plt.figure(1, figsize=(12, 6))
ax1 = fig1.add_subplot(121, axisbg='lightgrey')
ax1.semilogx(mid_iet_bins, iet_counts, '-s', color='blue')
ax2 = fig1.add_subplot(122, axisbg='lightgrey')
ax2.loglog(mid_iet_bins / iet_mean,
(iet_mean * iet_counts) / (diff(iet_bins) * len(iets)),
'-s',
color='blue')
if Norm is True:
norm = iet_mean
else:
norm = 1.
if model is not None:
#Bootstrap 95% COIs
iet_bstps = 1000
rates_bstps = zeros((len(iet_bins) - 1, iet_bstps))
if model is 'Gamma':
#fit gamma model
fit_alpha, fit_loc, fit_beta = gamma.fit(iets, loc=0.0)
for j in range(iet_bstps):
model_sim = gamma.rvs(fit_alpha,
loc=fit_loc,
scale=fit_beta,
size=len(iets))
rates_bstps[:, j], model_bes = histogram(model_sim, iet_bins)
coi_95 = scoreatpercentile(rates_bstps.transpose(), 95, axis=0)
coi_5 = scoreatpercentile(rates_bstps.transpose(), 5, axis=0)
ax1.semilogx(
mid_iet_bins / norm,
gamma.pdf(mid_iet_bins, fit_alpha, fit_loc, fit_beta) *
diff(iet_bins) * len(iets), 'r')
ax1.semilogx(mid_iet_bins / norm, coi_95, 'r:')
ax1.semilogx(mid_iet_bins / norm, coi_5, 'r:')
ax2.loglog(mid_iet_bins / iet_mean,
(iet_mean *
gamma.pdf(mid_iet_bins, fit_alpha, fit_loc, fit_beta)),
'r')
ax2.loglog(mid_iet_bins / iet_mean,
(iet_mean * coi_95) / (diff(iet_bins) * len(iets)),
'r:')
ax2.loglog(mid_iet_bins / iet_mean,
(iet_mean * coi_5) / (diff(iet_bins) * len(iets)), 'r:')
elif model is 'Poisson':
#fit exponential model
for j in range(iet_bstps):
model_sim = expon.rvs(scale=iet_mean, size=len(iets))
rates_bstps[:, j], model_bes = histogram(model_sim, iet_bins)
coi_95 = scoreatpercentile(rates_bstps.transpose(), 95, axis=0)
coi_5 = scoreatpercentile(rates_bstps.transpose(), 5, axis=0)
ax1.semilogx(
mid_iet_bins / norm,
expon.pdf(mid_iet_bins, loc=0, scale=iet_mean) *
diff(iet_bins) * len(iets), 'r')
ax1.semilogx(mid_iet_bins / norm, coi_95, 'r:')
ax1.semilogx(mid_iet_bins / norm, coi_5, 'r:')
ax2.loglog(
mid_iet_bins / iet_mean,
(iet_mean * expon.pdf(mid_iet_bins, loc=0, scale=iet_mean)),
'r')
ax2.loglog(mid_iet_bins / iet_mean,
(iet_mean * coi_95) / (diff(iet_bins) * len(iets)),
'r:')
ax2.loglog(mid_iet_bins / iet_mean,
(iet_mean * coi_5) / (diff(iet_bins) * len(iets)), 'r:')
if Norm is True:
ax1.set_xlabel(r'$\tau \backslash \bar\tau$ (days)')
else:
ax1.set_xlabel(r'$\tau$ (days)')
ax1.set_ylabel('Frequency')
ax1.xaxis.set_ticks_position('bottom')
ax2.set_xlim(0.00008, 200)
ax2.set_ylim(0.00001, 1000)
ax2.set_xlabel(r'$\tau \backslash \bar\tau$ (days)')
ax2.set_ylabel('pdf')
ax2.xaxis.set_ticks_position('bottom')
png_name = obj1.figure_path + '/iet_plots.png'
eps_name = obj1.figure_path + '/iet_plots.eps'
plt.savefig(png_name)
plt.savefig(eps_name)
from scipy.stats import expon
from scipy.stats import gamma
from scipy.stats import logistic
import matplotlib.pyplot as plt
import numpy as np
fig, ((ax1, ax2), (ax3, ax4), (ax5, ax6)) = plt.subplots(3, 2)
# gamma
a = 1.99
mean, var, skew, kurt = gamma.stats(a, moments = 'mvsk')
x = np.linspace(gamma.ppf(0.01, a),
gamma.ppf(0.99, a), 100)
ax1.plot(x, gamma.pdf(x, a),
'r-', lw=5, alpha=0.6, label='gamma pdf')
ax1.set_title('gamma pdf')
ax2.plot(x, gamma.cdf(x, a),
'r-', lw=5, alpha=0.6, label='gamma cdf')
ax2.set_title('gamma cdf')
# logistic
b = 0.5
mean, var, skew, kurt = logistic.stats(b, moments = 'mvsk')
x = np.linspace(logistic.ppf(0.01, b),
logistic.ppf(0.99, b), 100)
ax3.plot(x, logistic.pdf(x, b),
'g-', lw=5, alpha=0.6, label='gamma pdf')
ax3.set_title('logistic pdf')
ax4.plot(x, logistic.cdf(x, b),
'g-', lw=5, alpha=0.6, label='gamma cdf')
m2list = []
m3list = []
m4list = []
m5list = []
for i in range(len(state["rews"])):
m1list.append(m1(state))
m2list.append(m2(state))
m3list.append(m3(state))
m4list.append(m4(state))
m5list.append(m5(state))
state["t"] += 1
x = np.linspace(0, 1, 100)
dist = gamma.pdf(1, 4, x)
plt.plot(x, dist)
plt.title("Gamma prior")
plt.xlabel('N0')
plt.ylabel('Probability Mass')
plt.show()
plt.figure()
# plt.plot(np.array(m1list) / sum(m1list))
# plt.title('Standardized Reward Integration for Sequence: [1,0,0,0,1,0,0,1,0,1,0,1,0]')
# plt.plot(np.array(m1list) / np.std(m1list),label = "Time")
# plt.plot(-np.array(m2list) / np.std(m2list),label = "Memoryless Integrator")
# plt.plot(np.array(m3list) / np.std(m3list),label = "Basic Integrator (a=3, b=1)")
# plt.plot(np.array(m4list) / np.std(m4list),label = "Bayesian Estimation of N0 (a0=1, b0=4)")
# plt.plot(np.array(m5list) / np.std(m5list),label = "Recency-Biased Integrator (a=1, b=2, x=3)")
plt.title(
def NG(mu, precision, mu0, kappa0, alpha0, beta0):
'''
PDF of a Normal-Gamma distribution.
'''
return norm.pdf(mu, mu0, 1. / (precision * kappa0)) * gamma.pdf(
precision, alpha0, scale=1. / beta0)
from scipy.stats import gamma
import matplotlib.pyplot as plt
import numpy as np
fig, ax = plt.subplots(1, 1)
a = 0.01
mean, var, skew, kurt = gamma.stats(a, moments='mvsk')
x = np.linspace(gamma.ppf(0.01, a), gamma.ppf(0.99, a), 100)
ax.plot(x,
gamma.pdf(x, a, loc=0.0, scale=2.0),
'r-',
lw=5,
alpha=0.6,
label='gamma pdf')
# ax.plot(x, gamma.pdf(x, a),
# 'r-', lw=5, alpha=0.6, label='gamma pdf')
rv = gamma(a, loc=0.0, scale=2.0)
# rv = gamma(a)
ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
vals = gamma.ppf([0.001, 0.5, 0.999], a)
np.allclose([0.001, 0.5, 0.999], gamma.cdf(vals, a))
r = gamma.rvs(a, size=1000, loc=0.0, scale=2.0)
# r = gamma.rvs(a, size=1000)
# ax.hist(r, density='True', histtype='stepfilled', alpha=0.2)
# ax.legend(loc='best', frameon=False)
plt.show()
def analysis_1_generax_withgamma(lang_fr=True, dark=False):
# First analyse output from GeneRax (1by1)
with HtmlReport(str(workdir / 'familyrates.html'),
style=(css_dark_style if dark else None)) as hr:
# Invalid values:
df, nodup = filter_invalid_generax(load_generax_familyrates(), out=hr)
fig, ((ax0top, ax1top), (ax0bottom, ax1bottom)) = plt.subplots(2, ncols=2)
# Y axis with a broken scale : ---//---
fig.subplots_adjust(hspace=0.1)
axes_dup = brokenAxes(ax0bottom, ax0top)
(heights, _, _), _ = axes_dup.hist(df.duprate, bins=100, density=True)
axes_dup.dobreak(max(heights[1:]))
logger.info('Plotted dup rates')
axes_loss = brokenAxes(ax1bottom, ax1top)
((_,heights), _, _), _ = axes_loss.hist((df.lossrate[nodup], df.lossrate[~nodup]),
#label=['No dup', 'dup > 0'],
label=[r'$\delta=0$', r'$\delta>0$'],
bins=100, density=True, stacked=True)
ymax = heights.max()
axes_loss.dobreak(max(heights[heights<ymax]))
logger.info('Plotted loss rates')
dup_gamma = gamma.fit(df.duprate.values)
dup_gamma_nonzero = gamma.fit(df.duprate[~nodup].values)
loss_gamma = gamma.fit(df.lossrate.values)
loss_gamma_nodup = gamma.fit(df.lossrate[nodup].values)
loss_gamma_dup = gamma.fit(df.lossrate[~nodup].values)
xdup = np.linspace(*ax0bottom.get_xlim(), num=100)
xloss = np.linspace(*ax1bottom.get_xlim(), num=100)
axes_dup.plot(xdup, gamma.pdf(xdup, *dup_gamma),
label=r'$\Gamma(%g, %g, %g)$' % inverse_scale(dup_gamma))
#ax0.annotate('Gamma(%g, %g, %g)' % dup_gamma, (1,1), (-2,-2),
# xycoords='axes fraction', textcoords='offset points',
# va='top', ha='right')
axes_dup.plot(xdup, gamma.pdf(xdup, *dup_gamma_nonzero),
#label='dup>0 Gamma(%g, %g, %g)' % dup_gamma_nonzero)
label=r'$\delta>0$ $\Gamma(%g, %g, %g)$' % inverse_scale(dup_gamma_nonzero))
ax0top.legend()
ax0bottom.set_ylabel("% d'arbres de gènes" if lang_fr else '% of gene trees')
ax0top.set_title(('Taux de duplication' if lang_fr else 'Duplication rates') + r' $\delta$')
axes_loss.plot(xloss, gamma.pdf(xloss, *loss_gamma),
label=r'$\Gamma(%g, %g, %g)$' % loss_gamma)
axes_loss.plot(xloss, gamma.pdf(xloss, *loss_gamma_nodup),
label=r'$\delta=0$ $\Gamma(%g, %g, %g)$' % inverse_scale(loss_gamma_nodup))
axes_loss.plot(xloss, gamma.pdf(xloss, *loss_gamma_dup),
label=r'$\delta>0$ $\Gamma(%g, %g, %g)$' % inverse_scale(loss_gamma_dup))
#ax1.annotate('Gamma(%g, %g, %g)' % loss_gamma, (1,1), (-2,-2),
# xycoords='axes fraction', textcoords='offset points',
# va='top', ha='right')
ax1top.legend()
ax1top.set_title(('Taux de perte' if lang_fr else 'Loss rates') + r' $\lambda$')
logger.info('Fitted gamma distribs')
fig.savefig(str(workdir / ('fit_duploss_gamma%s.pdf' % ('_darkbg' if dark else ''))),
bbox_inches='tight')
hr.show()
for dataset, data_params, data in zip(
#('dup', 'dup>0', 'loss', 'nodup loss', 'dup>0 loss'),
(r'$\delta$', r'$\delta>0$', r'$\lambda$', r'$\lambda_{\delta=0}$', r'$\lambda_{\delta>0}$'),
(dup_gamma, dup_gamma_nonzero, loss_gamma, loss_gamma_nodup, loss_gamma_dup),
(df.duprate, df.duprate[~nodup], df.lossrate, df.lossrate[nodup], df.lossrate[~nodup])):
hr.mkd(r'\\[ - lL(%s\\ params) = %g \\]' % (
dataset,
gamma.nnlf(inverse_scale(data_params), data.values)))
nonzerodup_df = df.loc[~nodup]
suggested_transforms = test_transforms(df, ['duprate', 'lossrate'],
widget=False, out=hr)
suggested_transforms_nonzerodup = test_transforms(nonzerodup_df, ['duprate', 'lossrate'],
widget=False, out=hr)
fig, axes = plt.subplots(ncols=2, squeeze=False)
scatter_density('duprate', 'lossrate', data=df, alpha=0.4, ax=axes[0,0])
axes[0,0].set_xlabel(r'$\delta$')
axes[0,0].set_ylabel(r'$\lambda$')
axes[0,0].set_title('Données complètes' if lang_fr else 'Complete dataset')
scatter_density('duprate', 'lossrate', data=nonzerodup_df, alpha=0.4, ax=axes[0,1])
axes[0,1].set_xlabel(r'$\delta$')
axes[0,1].set_ylabel(r'$\lambda$')
axes[0,1].set_title(r'Données avec $\delta>0$' if lang_fr else r'Dataset with $\delta > 0$')
hr.show()
fig.savefig(str(workdir/'scatter_duploss.pdf'), bbox_inches='tight')
logger.info('Plotted scatter of dup/loss (dup>0, untransformed)')
hr.print('\n# Regress untransformed data (dup>0)')
fit = sm.OLS(nonzerodup_df[['lossrate']],
sm.add_constant(nonzerodup_df[['duprate']])).fit()
hr.output(fit.summary())
hr.print('\n# Regress transformed data (dup>0):')
for ft, transform in suggested_transforms_nonzerodup.items():
hr.print('- %s : %s' %(ft, transform.__name__))
transformed_df = nonzerodup_df.transform(suggested_transforms_nonzerodup)
fig, ax = plt.subplots()
scatter_density('duprate', 'lossrate', data=transformed_df, alpha=0.4, ax=ax)
ax.set_ylabel(r'$\mathrm{%s}(\lambda)$' % suggested_transforms_nonzerodup['lossrate'].__name__)
ax.set_xlabel(r'$\mathrm{%s}(\delta)$' % suggested_transforms_nonzerodup['duprate'].__name__)
hr.show()
fig.savefig(str(workdir/'scatter_transformed-duploss.pdf'), bbox_inches='tight')
logger.info('Plotted scatter of dup/loss (dup>0, transformed:%s,%s)',
suggested_transforms_nonzerodup['duprate'].__name__,
suggested_transforms_nonzerodup['lossrate'].__name__
)
fit = sm.OLS(transformed_df[['lossrate']],
sm.add_constant(transformed_df[['duprate']])).fit()
hr.output(fit.summary())
variance_noise = sigma_noise**2
X_awgn = np.random.normal(mu_noise, sigma_noise, N) #noise
X = X_normal + X_awgn #a vector of observations as an example/for plotting
##########################################
#the conjugate prior of the Gaussian with known mean is Gamma (hyperparameters estimate precision)
#define parameters of initial prior
a = 10
b = .01
#plot initial prior and likelihood
fig1 = plt.figure()
ax12 = fig1.add_subplot(1, 1, 1)
x = np.linspace(precision - 1, precision + 1, N)
y2 = gamma.pdf(x, a=a, scale=1/b) #plot initial prior, scale is theta = 1/beta
prior = ax12.plot(x, y2, 'g--', label='Original Prior')
handles1, labels1 = ax12.get_legend_handles_labels()
ax12.legend(handles1, labels1)
ax12.set_title('Conjugate Prior Update - Gaussian with known mean, unknown precision = ' + str(precision), fontweight='bold')
##########################################
#update equations for Gaussian of known variance, unknown mean
#initial hyperparameters
update_a = a
update_b = b
plot_list = [0, 1, 2, 3, 4, 9, 19, 49, N-1]
for j in range(0, N): #N is the obseration in question, one index off
n_update = j + 1
sum_xn_mu_squared = sum((X[0:n_update] - mu)**2)
def tau_prior(tau, tau_rate):
return (gamma.pdf(tau / 1000, a=1, scale=1 / tau_rate))
beta = 4.67873 # Mathematica solution!
######## hospitalization times
hosp_time_dist = np.zeros(len(t))
#################### computation
for k in range(200): ### sum over geometric distribution
# determine deterministic hitting time of k infected individuals
tdet = np.log((k + 1) * alpha * beta * p_surv) / alpha
if (tdet <= 0): tdet = 0
# add hospitalisation time distribution to tdet
index = int(tdet / dt)
hosp_time_dist[index:] += geom.pmf(k + 1, p_hosp) * gamma.pdf(
t[0:(len(t) - index)], shape_hosp, scale=scale_hosp)
####### epidemic size distribution
dsize = 50
I = np.arange(dsize, 15001, dsize)
dens_I = np.zeros(len(I))
ind_old = 0
for i in range(len(I)):
tdet_index = int(
np.round(np.log(I[i] * alpha * beta * p_surv) / alpha / dt)) + 1
dens_I[i] = np.sum(hosp_time_dist[ind_old:tdet_index] * dt) / dsize
ind_old = tdet_index
def function(intensity, int_intensity_diff, shape):
return shape*intensity * gamma.pdf(x=shape*int_intensity_diff, a=shape)
# Based on https://github.com/probml/pmtk3/blob/master/demos/gammaPlotDemo.m
import numpy as np
import matplotlib.pyplot as plt
import pyprobml_utils as pml
from scipy.stats import gamma
x = np.linspace(0, 7, 100)
aa = [1.0, 1.5, 2.0, 1.0, 1.5, 2.0]
bb = [1.0, 1.0, 1.0, 2.0, 2.0, 2.0]
#props = ['b-', 'r:', 'k-.', 'g--', 'c-', 'o-']
props = ['b-', 'r-', 'k-', 'b:', 'r:', 'k:']
for a, b, p in zip(aa, bb, props):
y = gamma.pdf(x, a, scale=1 / b, loc=0)
plt.plot(x, y, p, lw=3, label='a=%.1f,b=%.1f' % (a, b))
plt.title('Gamma distributions')
plt.legend(fontsize=14)
pml.savefig('gammadist.pdf')
plt.show()
x = np.linspace(0, 7, 100)
b = 1
plt.figure()
for a in [1, 1.5, 2]:
y = gamma.pdf(x, a, scale=1 / b, loc=0)
plt.plot(x, y)
plt.legend(['a=%.1f, b=1' % a for a in [1, 1.5, 2]])
plt.title('Gamma(a,b) distributions')
pml.savefig('gammaDistb1.pdf')
xlabel = "time (h)"
yticks1 = [0,0.02, 0.04, 0.06]
yticks2 = [0,0.05,0.1]
yticks = [yticks1, yticks2]
alphas = [fit_gamma[0][0][0], fit_gamma[1][0][0]]
betas = [fit_gamma[0][0][1], fit_gamma[1][0][1]]
# load peine facs data to plot figure together
x_arr = [x1, x2]
gamma_arr = [gamma.pdf(x, alpha, 0, 1/beta) for x, alpha, beta in zip(x_arr, alphas, betas)]
fig, (ax1, ax2, ax3) = plt.subplots(1,3, figsize = (15,4))
ylabel = "density"
for df, ax, x, y, barwidth in zip(df_list, (ax1, ax2), x_arr, gamma_arr, width):
ax.bar(df["time"], df.val_norm, width=barwidth, color="grey", edgecolor="k")
ax.plot(x, y, color="k")
ax.set_ylabel(ylabel)
ax.set_xlabel(xlabel)
ax.set_xlim([x[0], x[-1]])
ax1.set_xticks(np.arange(0,73,24))
ax1.set_yticks(yticks1)
ax2.set_yticks(yticks2)
#plt.show()
loadfile = "../figures/fig1/peine_numpy.npz"
def A_p_prior(A_p, A_p_rate):
return (gamma.pdf(A_p, a=1, scale=1 / A_p_rate))
### effective re-production
tau = 5#13 #tau equals number of fitted days
a = 1
b = 5
n = timeSpan-tau + 1 #samples for fit
repVec = np.zeros((n,))
for d in np.arange(1,n):
ii = np.arange(d,d+tau)
y = newCases[ii]
num = a+ np.sum(y)
s = np.arange(0,d+tau)
ws = gamma.pdf(s,a=3,loc=0,scale=1) # gamma parameters to play around
ws = ws/np.sum(ws)
sum_di = 0
for i in ii:
w = np.reshape(ws[:i:],(-1,1))
w = w[::-1]
ys = np.reshape(newCases[:i:],(1,-1))
sum_di += ys@w
#unifrom dist.
#sum_di += np.mean(ys)
den = 1/b + sum_di
#A = we(part[I])
#A = we(median[I])
C = we(cases[I])
else:
I = (state == State[i])
Y = np.concatenate([Y, we(deaths[I])])
A = np.concatenate([A, we(home[I])]) # using HOME
#A = np.concatenate([A, we(work[I])])
#A = np.concatenate([A, we(part[I])])
#A = np.concatenate([A, we(median[I])])
C = np.concatenate([C, we(cases[I])])
#######################################################
l = 18
t = np.linspace(start=0, stop=l, num=l + 1)
ft = gamma.pdf(t * 7, scale=3.64, a=6.28) # a - shape parameter
ft = (ft / sum(ft)) * 0.03
x = range(1, l + 1)
pdf = PdfPages("plots/fit_optim_forecast.pdf")
_, axs = pyplot.subplots(3, 3, figsize=(8, 8))
theta = np.zeros((51, 5))
pool = mp.Pool(mp.cpu_count())
# training loop
for i in range(51):
y_true = Y[i, :l]
m = A[i, :l]
pool.apply_async(
worker,
[i, m, ft[:l], y_true],
def gamma_bnd(t = 1,
node = 1,
shape = 1.01,
scale = 1,
theta = 0):
return gamma.pdf(t - node, a = shape, scale = scale)
def plot_parameter_assumptions(df_parameters, xlimits=[0, 30], lw=3):
"""
Plot distributions of mean transition times between compartments in the parameters of the
OpenABM-Covid19 model
Arguments
---------
df_parameters : pandas.DataFrame
DataFrame of parameter values as input first input argument to the OpenABM-Covid19 model
This plotting scripts expects the following columns within this dataframe:
mean_time_to_hospital
mean_time_to_critical, sd_time_to_critical
mean_time_to_symptoms, sd_time_to_symptoms
mean_infectious_period, sd_infectious_period
mean_time_to_recover, sd_time_to_recover
mean_asymptomatic_to_recovery, sd_asymptomatic_to_recovery
mean_time_hospitalised_recovery, sd_time_hospitalised_recovery
mean_time_to_death, sd_time_to_death
mean_time_critical_survive, sd_time_critical_survive
xlimits : list of ints
Limits of x axis of gamma distributions showing mean transition times
lw : float
Line width used in plotting lines of the PDFs
Returns
-------
fig, ax : figure and axis handles to the generated figure using matplotlib.pyplot
"""
df = df_parameters # for brevity
x = np.linspace(xlimits[0], xlimits[1], num=50)
fig, ax = plt.subplots(nrows=3, ncols=3)
####################################
# Bernoulli of mean time to hospital
####################################
height1 = np.ceil(df.mean_time_to_hospital.values[0]
) - df.mean_time_to_hospital.values[0]
height2 = df.mean_time_to_hospital.values[0] - np.floor(
df.mean_time_to_hospital.values[0])
x1 = np.floor(df.mean_time_to_hospital.values[0])
x2 = np.ceil(df.mean_time_to_hospital.values[0])
ax[0, 0].bar([x1, x2], [height1, height2], color="#0072B2")
ax[0, 0].set_ylim([0, 1.0])
ax[0, 0].set_xticks([x1, x2])
ax[0, 0].set_xlabel("Time to hospital\n(from symptoms; days)")
ax[0, 0].set_ylabel("Density")
ax[0, 0].set_title("")
ax[0, 0].spines["top"].set_visible(False)
ax[0, 0].spines["right"].set_visible(False)
####################################
# Gamma of mean time to critical
####################################
a, b = gamma_params(df.mean_time_to_critical.values,
df.sd_time_to_critical.values)
ax[1, 0].plot(x,
gamma.pdf(x, a=a, loc=0, scale=b),
linewidth=lw,
color="#0072B2")
ax[1, 0].axvline(df.mean_time_to_critical.values,
color="#D55E00",
linestyle="dashed",
alpha=0.7)
ax[1, 0].set_xlabel("Time to critical\n(from hospitalised; days)")
ax[1, 0].set_title("")
ax[1, 0].spines["top"].set_visible(False)
ax[1, 0].spines["right"].set_visible(False)
ax[1, 0].text(0.9,
0.7,
'mean: {}\nsd: {}'.format(df.mean_time_to_critical.values[0],
df.sd_time_to_critical.values[0]),
ha='right',
va='center',
transform=ax[1, 0].transAxes)
################################
# Gamma of mean time to symptoms
################################
a, b = gamma_params(df.mean_time_to_symptoms.values,
df.sd_time_to_symptoms.values)
ax[0, 1].plot(x,
gamma.pdf(x, a=a, loc=0, scale=b),
linewidth=lw,
color="#0072B2")
ax[0, 1].axvline(df.mean_time_to_symptoms.values,
color="#D55E00",
linestyle="dashed",
alpha=0.7)
ax[0, 1].set_xlabel("Time to symptoms\n(from presymptomatic; days)")
ax[0, 1].set_title("")
ax[0, 1].spines["top"].set_visible(False)
ax[0, 1].spines["right"].set_visible(False)
ax[0, 1].text(0.9,
0.7,
'mean: {}\nsd: {}'.format(df.mean_time_to_symptoms.values[0],
df.sd_time_to_symptoms.values[0]),
ha='right',
va='center',
transform=ax[0, 1].transAxes)
################################
# Gamma of mean infectious period
################################
a, b = gamma_params(df.mean_infectious_period, df.sd_infectious_period)
ax[0, 2].plot(x,
gamma.pdf(x, a=a, loc=0, scale=b),
linewidth=lw,
color="#0072B2")
ax[0, 2].axvline(df.mean_infectious_period.values,
color="#D55E00",
linestyle="dashed",
alpha=0.7)
ax[0, 2].set_xlabel("Infectious period (days)")
ax[0, 2].set_title("")
ax[0, 2].spines["top"].set_visible(False)
ax[0, 2].spines["right"].set_visible(False)
ax[0,
2].text(0.9,
0.7,
'mean: {}\nsd: {}'.format(df.mean_infectious_period.values[0],
df.sd_infectious_period.values[0]),
ha='right',
va='center',
transform=ax[0, 2].transAxes)
################################
# Gamma of mean time to recover
################################
a, b = gamma_params(df.mean_time_to_recover, df.sd_time_to_recover)
ax[1, 1].plot(x,
gamma.pdf(x, a=a, loc=0, scale=b),
linewidth=lw,
color="#0072B2")
ax[1, 1].axvline(df.mean_time_to_recover.values,
color="#D55E00",
linestyle="dashed",
alpha=0.7)
ax[1,
1].set_xlabel("Time to recover\n(from hospitalised or critical; days)")
ax[1, 1].set_title("")
ax[1, 1].spines["top"].set_visible(False)
ax[1, 1].spines["right"].set_visible(False)
ax[1, 1].text(0.9,
0.7,
'mean: {}\nsd: {}'.format(df.mean_time_to_recover.values[0],
df.sd_time_to_recover.values[0]),
ha='right',
va='center',
transform=ax[1, 1].transAxes)
########################################
# Gamma of mean asymptomatic to recovery
########################################
a, b = gamma_params(df.mean_asymptomatic_to_recovery,
df.sd_asymptomatic_to_recovery)
ax[2, 0].plot(x,
gamma.pdf(x, a=a, loc=0, scale=b),
linewidth=lw,
color="#0072B2")
ax[2, 0].axvline(df.mean_asymptomatic_to_recovery.values,
color="#D55E00",
linestyle="dashed",
alpha=0.7)
ax[2, 0].set_xlabel("Time to recover\n(from asymptomatic; days)")
ax[2, 0].set_title("")
ax[2, 0].spines["top"].set_visible(False)
ax[2, 0].spines["right"].set_visible(False)
ax[2, 0].text(0.9,
0.7,
'mean: {}\nsd: {}'.format(
df.mean_asymptomatic_to_recovery.values[0],
df.sd_asymptomatic_to_recovery.values[0]),
ha='right',
va='center',
transform=ax[2, 0].transAxes)
########################################
# Gamma of mean hospitalised to recovery
########################################
a, b = gamma_params(df.mean_time_hospitalised_recovery,
df.sd_time_hospitalised_recovery)
ax[2, 1].plot(x,
gamma.pdf(x, a=a, loc=0, scale=b),
linewidth=lw,
color="#0072B2")
ax[2, 1].axvline(df.mean_time_hospitalised_recovery.values,
color="#D55E00",
linestyle="dashed",
alpha=0.7)
ax[2, 1].set_xlabel(
"Time to recover\n(from hospitalisation to hospital discharge if not ICU\nor from ICU discharge to hospital discharge if ICU; days)"
)
ax[2, 1].set_title("")
ax[2, 1].spines["top"].set_visible(False)
ax[2, 1].spines["right"].set_visible(False)
ax[2, 1].text(0.9,
0.7,
'mean: {}\nsd: {}'.format(
df.mean_time_hospitalised_recovery.values[0],
df.sd_time_hospitalised_recovery.values[0]),
ha='right',
va='center',
transform=ax[2, 1].transAxes)
#############################
# Gamma of mean time to death
#############################
a, b = gamma_params(df.mean_time_to_death.values,
df.sd_time_to_death.values)
ax[1, 2].plot(x,
gamma.pdf(x, a=a, loc=0, scale=b),
linewidth=lw,
c="#0072B2")
ax[1, 2].axvline(df.mean_time_to_death.values,
color="#D55E00",
linestyle="dashed",
alpha=0.7)
ax[1, 2].set_xlabel("Time to death\n(from critical; days)")
ax[1, 2].set_title("")
ax[1, 2].spines["top"].set_visible(False)
ax[1, 2].spines["right"].set_visible(False)
ax[1, 2].text(0.9,
0.7,
'mean: {}\nsd: {}'.format(df.mean_time_to_death.values[0],
df.sd_time_to_death.values[0]),
ha='right',
va='center',
transform=ax[1, 2].transAxes)
########################################
# Gamma of mean time to survive if critical: FIXME - definitions
########################################
a, b = gamma_params(df.mean_time_critical_survive,
df.sd_time_critical_survive)
ax[2, 2].plot(x,
gamma.pdf(x, a=a, loc=0, scale=b),
linewidth=lw,
color="#0072B2")
ax[2, 2].axvline(df.mean_time_critical_survive.values,
color="#D55E00",
linestyle="dashed",
alpha=0.7)
ax[2, 2].set_xlabel("Time to survive\n(if ICU; days)")
ax[2, 2].set_title("")
ax[2, 2].spines["top"].set_visible(False)
ax[2, 2].spines["right"].set_visible(False)
ax[2, 2].text(0.9,
0.7,
'mean: {}\nsd: {}'.format(
df.mean_time_critical_survive.values[0],
df.sd_time_critical_survive.values[0]),
ha='right',
va='center',
transform=ax[2, 2].transAxes)
plt.subplots_adjust(hspace=0.5)
return (fig, ax)
from diafunc import linearfunc
from scipy.integrate import quad
import scipy.stats as st
import matplotlib.pyplot as plt
from scipy.integrate import quad
from scipy.stats import gamma
def myf(maxmmol, maxgoing, endgoing, typebranch1, typebranch2):
pass
norm = st.norm(loc=1, scale=0.25)
x = np.linspace(norm.ppf(0.0001), norm.ppf(0.9999), 50)
a = 2
#erl = st.erlang.stats(a)
mean, var, skew, kurt = gamma.stats(a, moments='mvsk')
print(mean, var, skew, kurt)
x2 = np.linspace(0, 6, 100)
#x2 = np.linspace(erl.ppf(0.0001, a), erl.ppf(0.9999, a), 50)
res, err = quad(gamma.pdf, 0, 6, args=(a))
print(res)
print(x2)
fig, ax = plt.subplots()
ax.plot(x, norm.pdf(x))
ax.plot(x2, gamma.pdf(x2, a))
plt.show()
##### PDE solution
fx = np.zeros((int(tfin / dt) + 1, int(tfin / dt) + 1))
tot = [1]
# initialize with 1 individual at time 0 with age 0
fx[0, 0] = 1
k = 2
mu_adj = (1 + pext[0])
inf_times = [0]
# infectiousness vector
mu = []
x = 0
for i in range(int(tfin / dt) + 1):
mu.append(R0 * (gamma.pdf(x + dt / 2, shape_inf, scale=scale_inf)))
x = x + dt
mu = np.asarray(mu)
for i in range(int(tfin / dt)):
# move up age
fx[i + 1, 1:] = fx[i, 0:-1]
# add infections
# adjusted mu
if (tot[-1] >= k):
prod = 1
for j in range(len(inf_times)):
prod = pext[i - inf_times[j]] * prod
def gamma(scale, prior_shape):
x = np.linspace(gamma.ppf(0.001, prior_shape, loc=0, scale=scale),
gamma.ppf(0.999, prior_shape, loc=0, scale=scale))
y = gamma.pdf(x, prior_shape, loc=0, scale=scale)
return x, y
P = [1 - i for i in Q]
lambdat = [F[i] / P[i] for i in range(len(F))]
print("normal")
if min(chi_exp, chi_normal, chi_uniform, chi_gamma) == chi_uniform:
F = uniform.pdf(range(int(min(array)), int(max(array))), min(array),
max(array))
Q = uniform.cdf(range(int(min(array)), int(max(array))), min(array),
max(array))
P = [1 - i for i in Q]
lambdat = [F[i] / P[i] for i in range(len(F))]
print("uni")
if min(chi_exp, chi_normal, chi_uniform, chi_gamma) == chi_gamma:
F = gamma.pdf(range(int(min(array)), int(max(array))),
a=alpha,
scale=1 / beta)
Q = gamma.cdf(range(int(min(array)), int(max(array))),
a=alpha,
scale=1 / beta)
P = [1 - i for i in Q]
lambdat = [F[i] / P[i] for i in range(len(F))]
print("gamma")
h = (max(array) - min(array)) / n_cells
borders = [min(array) + h * i for i in range(n_cells)]
qt = [0 for i in range(n_cells)]
for i in range(len(array)):
for j in range(len(borders)):
if array[i] <= borders[j] + h:
qt[j] += 1
y[np.logical_or(np.kron(d_star, np.ones(T,)) == 0,y < 0)] = 0.
y = y.reshape(N,T)
X = X.reshape(N,T,2)
i=0
H=10000
resample_type = 'multinomial'
K1 = 2
K2 = 2
K3 = 1
K4 = 1
### initialization
theta = np.concatenate([np.random.normal(0,5,[H,K1]), np.random.normal(0,5,[H,K2]),np.random.gamma(1,1,[H,K3]), np.random.gamma(1,1,[H,K4])], axis=1)
w = np.concatenate([norm.pdf(theta[:,:K1],0,5), norm.pdf(theta[:,K1:K1+K2],0,5), gamma.pdf(theta[:,K1+K2+K3-1],1).reshape(-1,1), gamma.pdf(theta[:,K1+K2+K3+K4-1],1).reshape(-1,1)],axis=1)
w = w / w.sum(axis=0) # ini_weights
### run sequential monte carlo
all_mu_theta = []
all_std_theta = []
for i in range(N):
print(i)
### run sequential monte carlo
###reweight
#parallel computing
w = reweight(theta, w, y, i, X, Z, K1, K2, K3, K4)
### resampling-np.random.choice
all_theta_ = []
all_w_ = []
