def prob_alias(self, plot=False):
"""Returns tuple (threshold, probability)"""
from scipy.stats import gamma
# scipy-ref.pdf Section 5.13 on page 390
if plot:
import matplotlib.pyplot as plt
plt.ion()
plt.clf()
nd = self.get_all_noise_dists()
a, loc, scale = gamma.fit(nd)
ndrv = gamma(a, loc, scale)
if plot:
plt.hist(nd, normed=True) # 'normed' might become 'density' later?
x = range(max(nd))
plt.plot(x, ndrv.pdf(x))
icd = self.get_all_inter_chip_dists()
a, loc, scale = gamma.fit(icd)
icdrv = gamma(a, loc, scale)
if plot:
plt.hist(icd, normed=True)
x = range(max(icd))
plt.plot(x, icdrv.pdf(x))
# Here it goes!
threshold = ndrv.ppf(0.997)
if plot:
plt.axvline(threshold)
prob = icdrv.cdf(threshold)
print 'Noise 99.7%% threshold: %f, probability of aliasing: %1.3e' % (
threshold, prob)
return threshold, prob
def rv_gama(hind, obs, fcst):
# Ajuste da distribuição gama para os dados observados
obs = np.sort(obs)
n_zeros_obs = len(np.where(obs == 0)[0])
q = n_zeros_obs / float(len(obs))
obs = obs[obs > 0]
gamma_obs = gamma.fit(obs, floc=0)
# Ajuste da distrivbuição gama para os dados do modelo
hind = np.sort(hind)
hind = hind[n_zeros_obs:]
hind = hind[hind > 0]
gamma_hind = gamma.fit(hind, floc=0)
# Correção da previsão usando função gama
if fcst < hind[0]:
corr = 0
else:
prob_mod = gamma.cdf(fcst, *gamma_hind)
H = q + (1 - q) * prob_mod
corr = gamma.ppf(H, *gamma_obs)
if str(corr) == 'inf':
print('hey there')
return corr
def prob_alias(self, plot=False):
"""Returns tuple (threshold, probability)"""
from scipy.stats import gamma
# scipy-ref.pdf Section 5.13 on page 390
if plot:
import matplotlib.pyplot as plt
plt.ion()
plt.clf()
nd = self.get_all_noise_dists()
a, loc, scale = gamma.fit(nd)
ndrv = gamma(a, loc, scale)
if plot:
plt.hist(nd, normed=True) # 'normed' might become 'density' later?
x = range(max(nd))
plt.plot(x, ndrv.pdf(x))
icd = self.get_all_inter_chip_dists()
a, loc, scale = gamma.fit(icd)
icdrv = gamma(a, loc, scale)
if plot:
plt.hist(icd, normed=True)
x = range(max(icd))
plt.plot(x, icdrv.pdf(x))
# Here it goes!
threshold = ndrv.ppf(0.997)
if plot:
plt.axvline(threshold)
prob = icdrv.cdf(threshold)
print 'Noise 99.7%% threshold: %f, probability of aliasing: %1.3e' % (threshold, prob)
return threshold, prob
def fit_gamma(self):
""" Fit a gamma distribution to each chronology, get mean stats
"""
self.gamma_alphas = []
for ie_set in self.interevent_times.T:
gamfit = gamma.fit(ie_set, floc=0)
self.gamma_alphas.append(gamfit[0])
# test fitting to all data at once
gamfit_all = gamma.fit(self.interevent_times.flatten(), floc=0)
self.gamma_alphas = np.array(self.gamma_alphas)
self.mean_gamma_alpha = np.mean(self.gamma_alphas)
self.mean_gamma_alpha_all = gamfit_all[0]
def __init__(self, wind_data): self.wind_data = wind_data #self.wind_data_long =pd.melt(wind_data) #initialize fitting model self.alpha_hat=np.empty(3) #initialize alpha estimates self.sigma_hat=np.empty(3) #initialize sigma estimates for i in range(3): self.alpha_hat[i], self.sigma_hat[i] = fmin(self.weibul_sq_error, [2,2], args=(self.wind_data.iloc[:,i].tolist(),)) #parameters for gamma distribution of alpha and sigma self.shape_alpha, self.location_alpha, self.scale_alpha = gamma.fit(self.alpha_hat) self.shape_sigma, self.location_sigma, self.scale_sigma = gamma.fit(self.sigma_hat)
def fit(self,obs_data,sim_data):
#: estimates parameters from provided data
#: dry day fraction
self.obs_param['c'] = (obs_data[obs_data==0].shape[0]) / (obs_data.shape[0])
self.sim_param['c'] = (sim_data[sim_data==0].shape[0]) / (sim_data.shape[0])
#: fit gamma with non zero values with floc=0
self.obs_param['a'], _, self.obs_param['b'] = gamma.fit(obs_data[obs_data>0], floc=0)
self.sim_param['a'], _, self.sim_param['b'] = gamma.fit(sim_data[sim_data>0], floc=0)
return self
def returnDistData(cls, self):
gammaParam = gamma.fit(10**(self.data / 10))
gammaDist = gamma.pdf(self.data, *gammaParam)
rayleighParam = rayleigh.fit(self.data)
rayleighDist = rayleigh.pdf(self.data, *rayleighParam)
normParam = norm.fit(self.data)
normDist = norm.pdf(self.data, *normParam)
logNormParam = lognorm.fit(self.data)
lognormDist = lognorm.pdf(self.data, *logNormParam)
nakagamiParam = nakagami.fit(self.data)
nakagamiDist = nakagami.pdf(self.data, *nakagamiParam)
exponParam = expon.fit(self.data)
exponDist = expon.pdf(self.data, *exponParam)
exponweibParam = exponweib.fit(self.data)
weibDist = exponweib.pdf(self.data, *exponweibParam)
distDF = pd.DataFrame(np.column_stack([
gammaDist, rayleighDist, normDist, lognormDist, nakagamiDist,
exponDist, weibDist
]),
columns=[
'gammaDist', 'rayleighDist', 'normDist',
'lognormDist', 'nakagamiDist', 'exponDist',
'weibDist'
])
self.distDF = distDF
def run_kstests(json_path, run_date, member):
try:
full_path = json_path + "/{0}/{1}/mesh_*.json".format(run_date, member)
json_files = sorted(glob(full_path))
ks_results = {"id":[], "ks":[]}
for json_file in json_files:
js = open(json_file)
mesh_track = json.load(js)
js.close()
id = mesh_track["properties"]["id"]
for m, mesh_obj in enumerate(mesh_track["features"]):
step_id = id + "_{0:03d}".format(m)
ts = np.array(mesh_obj["properties"]["timesteps"])
mask = np.array(mesh_obj["properties"]["masks"])
vals = ts[mask == 1]
gdist = gamma.fit(vals, floc=vals.min()-0.1)
sig = kstest(vals, gamma(*gdist).cdf)
ks_results["id"].append(step_id)
ks_results["ks"].append(sig)
if sig[1] < 0.01:
print(step_id,)
print(sig[1],gdist)
print(np.sort(vals))
plt.figure(figsize=(8,8))
plt.pcolormesh(ts, alpha=0.5, cmap="YlOrRd", vmin=0, vmax=100)
pc = plt.pcolormesh(np.ma.array(ts, mask=mask==0), cmap="YlOrRd", vmin=0, vmax=100)
plt.title(step_id)
plt.colorbar(pc)
plt.savefig(step_id + ".png", bbox_inches="tight", dpi=150)
plt.close()
ks_frame = pd.DataFrame(ks_results["ks"], index=ks_results["id"],columns=["D", "p-val"])
print(ks_frame.shape[0])
except Exception as e:
raise e
return ks_frame
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 match_single_track_dist(model_track, obs_track):
label_columns = ["Max_Hail_Size", "Shape", "Location", "Scale"]
obs_hail_dists = pd.DataFrame(index=obs_track.times,
columns=label_columns)
model_hail_dists = pd.DataFrame(index=model_track.times,
columns=label_columns)
for t, step in enumerate(obs_track.timesteps):
step_vals = step[(obs_track.masks[t] == 1) & (
obs_track.timesteps[t] > self.mrms_ew.min_intensity)]
min_hail = step_vals.min() - 0.1
obs_hail_dists.loc[obs_track.times[t],
["Shape", "Location", "Scale"]] = gamma.fit(
step_vals, floc=min_hail)
obs_hail_dists.loc[obs_track.times[t],
"Max_Hail_Size"] = step_vals.max()
if obs_track.times.size > 1 and model_track.times.size > 1:
normalized_obs_times = 1.0 / (obs_track.times.max() - obs_track.times.min()) \
* (obs_track.times - obs_track.times.min())
normalized_model_times = 1.0 / (model_track.times.max() - model_track.times.min()) \
* (model_track.times - model_track.times.min())
for col in label_columns:
interp_func = interp1d(normalized_obs_times,
obs_hail_dists[col],
kind="linear",
bounds_error=False,
fill_value=0)
model_hail_dists.loc[model_track.times, col] = interp_func(
normalized_model_times)
else:
for param in obs_hail_dists.columns:
model_hail_dists.loc[model_track.times,
param] = obs_hail_dists.loc[
obs_track.times[0], param]
return model_hail_dists
def estimate_gamma_dist_scipy(vals):
# shifting can happen (e.g. size selection of DNA fragments), but tentatively ignores this.
alpha_hat, loc_hat, beta_hat = gamma.fit(vals, floc=0.0)
logger.info("estimated Gamma dist params are a = %f, b = %f." % (alpha_hat, beta_hat))
return (alpha_hat, beta_hat)
def fit_gamma_param(estacion, mes, year_test='None'):
# Ajusta parametros de Gamma para precipitacion
do, dm = select_data_period(estacion, 'precip', mes)
cdf_limite = .9999999
# Minimos de precipitacion (obs fijo = 0.1, modelo el que mejor ajusta a frec)
xo_min = 0.1
minimos_pp = pd.read_excel('../datos/minimos_pp.xls', index_col=0)
xm_min = minimos_pp.loc[mes, estacion]
# Days with precipitacion
ppo_data = precipitation_days(do, xo_min)
ppm_data = precipitation_days(dm, xm_min)
# Fit a Gamma distribution over days with precipitation
obs_gamma_param = gamma.fit(ppo_data, floc=0)
mod_gamma_param = gamma.fit(ppm_data, floc=0)
return obs_gamma_param, mod_gamma_param
def get_tonicdrive_stats(self,
remove_bad_data_indices=True,
visualize=False): # Obs?
"""
Fits a normal distribution to "tonic drive" values
:param remove_bad_data_indices: True/False (default True)
:param visualize: True/False (default False)
:return: mean and SD of the fitted normal distribution
"""
tonicdrive = self.read_tonicdrive()
if remove_bad_data_indices:
good_indices = np.setdiff1d(range(self.n_cells),
self.bad_data_indices)
tonicdrive = tonicdrive[good_indices]
skew, mean, sd = gamma.fit(tonicdrive)
print(len(tonicdrive))
if visualize:
x_min, x_max = gamma.ppf([0.001, 0.999],
a=skew,
loc=mean,
scale=sd)
xs = np.linspace(x_min, x_max, 100)
plt.plot(xs, gamma.pdf(xs, a=skew, loc=mean, scale=sd))
plt.hist(tonicdrive, density=True)
plt.title(self.gc_type + ' ' + self.response_type)
plt.xlabel('Tonic drive (a.u.)')
plt.show()
return mean, sd
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 ssi_gamma(df_SM, acc_per, df_var='sm'):
# Group data by desired accumulation period and interpolate
month_values = df_SM[df_var].resample('M').mean()
month_values = month_values.interpolate()
accum_period = month_values.rolling(acc_per).mean()
SSI_gamma = accum_period.copy()
mesi = np.arange(1, 13, 1)
#npixel=np.arange(0,len(SSI.columns))
for jj in mesi:
dfM = np.where(accum_period.index.month == jj)
series = accum_period.values[dfM]
wh = ~np.isnan(series)
series1 = series[~np.isnan(series)]
bp = np.float32((np.sum(series1 == 0)) + 1) / (2 * (len(series1) + 1))
series2 = series1[np.nonzero(series1)]
alpha, loc, beta = gamma.fit(series2, floc=0)
val = gamma.cdf(series1, alpha, loc, beta)
for ii in range(len(series1)):
if series1[ii] == 0:
val[ii] = bp
# Plotting position formula Gringorten
sta_inv = norm.ppf(val)
series[wh] = sta_inv
SSI_gamma.iloc[accum_period.index.month == jj] = series
return SSI_gamma
def generate_slm_from_txt(training_rows, slm_dir, do_plot=True):
slm_fxt = os.path.join(slm_dir, "slm.fxt")
slength_counts = Counter()
slen=1
maxl=0
#print training_rows
for r in training_rows:
r = r.strip()
segs = r.split(BREAK) # chop the line up into segments
for s in segs:
slen = len(s.split())
if slen > maxl:
print "new max length = ", slen
maxl = slen
print "from seg: ", s
# print "from row: ", r
if slen:
slength_counts[slen]+=1
#_ = raw_input("hit key")
els = list( slength_counts.elements() ) #Counter.elements() returns iterator that iterates across n instances of each element e where slength_counts[e]=n .. we make this into a list for plotting
print els
x_vals = range(0, max(els)+1)
(shape, loc, scale) = gamma.fit(els, floc=0)
gam_gen = gamma(shape, loc, scale) #use these model params to build a new gamma distrib/n generator
write_slm(slm_fxt, x_vals, gam_gen)
if do_plot:
plot_graph(x_vals, gam_gen, els)
compile_slm(slm_dir) #this last step compiles the slm to binary .fst format
def test_random_vars(self):
gen = libMHCUDA.minhash_cuda_init(1000, 128, devices=1, verbosity=2)
rs, ln_cs, betas = libMHCUDA.minhash_cuda_retrieve_vars(gen)
libMHCUDA.minhash_cuda_fini(gen)
cs = numpy.exp(ln_cs)
a, loc, scale = gamma.fit(rs)
self.assertTrue(1.97 < a < 2.03)
self.assertTrue(-0.01 < loc < 0.01)
self.assertTrue(0.98 < scale < 1.02)
a, loc, scale = gamma.fit(cs)
self.assertTrue(1.97 < a < 2.03)
self.assertTrue(-0.01 < loc < 0.01)
self.assertTrue(0.98 < scale < 1.02)
bmin, bmax = uniform.fit(betas)
self.assertTrue(0 <= bmin < 0.001)
self.assertTrue(0.999 <= bmax <= 1)
def _fit(self, X):
a, loc, scale = gamma.fit(X)
self._params = {
'a': a,
'loc': loc,
'scale': scale,
}
def gamma_plot(cell, savefig = False):
data = pd.concat([speed_pair_before, speed_pair_after])
data = list(data[data[cell] > 0][cell])
x = np.linspace(0, 35, 1000)
shape, loc, scale = gamma.fit(data, floc = 0)
print (f'{cell} Expected: {shape * scale}')
if savefig:
sns.distplot(data, kde = False, norm_hist = True, color = '#3498db', bins = np.linspace(0, 8, 32))
y = gamma.pdf(x, shape, loc, scale)
plt.title(f'Distribution of {cell} cells\' speed', fontsize = 15)
plt.axvline(shape * scale, linestyle = 'dashed', color = 'black', zorder = 1,
label = 'Expectation', linewidth = 3)
plt.xlim([0, 8])
plt.xticks(fontsize = 12)
plt.yticks(fontsize = 12)
plt.xlabel(f'Velocity ({chr(956)}m/s)', fontsize = 12)
plt.plot(x, y, label = 'Fitted Gamma', linewidth = 3)
leg = plt.legend(prop = {'size': 12})
for line in leg.get_lines():
line.set_linewidth(3)
plt.tight_layout()
plt.savefig(os.path.join(N_PATH, f'{cell}-Gamma.png'), format = 'png', dpi = 300)
plt.savefig(os.path.join(N_PATH, f'{cell}-Gamma.pdf'), format = 'pdf', dpi = 500)
plt.close()
return shape * scale
def do_MLE(data, minimum, maximum):
pars = gamma.fit(data[np.where((minimum<=data)&(maximum>=data))], floc=0.0)
a1, loc1, scale1 = pars
#print minimum, maximum, a1, loc1, scale1, \
# gamma.nnlf(pars, data[np.where((minimum<=data)&(maximum>=data))]), \
# a1 * scale1, a1 * scale1**2
return a1, scale1
def fit_gamma_param(df, xmin, mes, year_test='None', option=0):
"""
"""
cdf_limite = .9999999
if mes - 1 <= 0:
cnd = [12, 1, 2]
elif mes + 1 >= 13:
cnd = [11, 12, 1]
else:
cnd = [mes - 1, mes, mes + 1]
if year_test == 'None':
datos = df.loc[df['month'].isin(cnd), 'precip'].values
else:
id_fm = np.logical_and(df.Fecha >= '01/01/'+str(year_test),
df.Fecha <= '12/31/'+str(year_test))
# generate index to work in cnd and out of year considered.
im_tot = np.logical_and(df['month'].isin(cnd), np.logical_not(id_fm))
# extract data to generate the distribution of historical data.
#print(np.unique(pd.DatetimeIndex(df.loc[im_tot, 'Fecha']).year.to_numpy()))
#print(np.unique(pd.DatetimeIndex(df.loc[im_tot, 'Fecha']).month.to_numpy()))
datos = df.loc[im_tot, 'precip'].values
# Days with precipitacion
in_dato = np.array([e > xmin if ~np.isnan(e) else False
for e in datos], dtype=bool)
precdias = datos[in_dato]
# Fit a Gamma distribution over days with precipitation
param_gamma = gamma.fit(precdias, floc=0)
gamma_cdf = gamma.cdf(np.sort(precdias), *param_gamma)
gamma_cdf[gamma_cdf > cdf_limite] = cdf_limite
if option == 0:
return param_gamma
else:
return param_gamma, precdias, gamma_cdf
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 precision_prior_params(data, num_classes, pseudo_inputs_per_class):
# load the data into RAM to support sample with replacement
x = []
y = []
for batch in data:
x.append(batch['image'])
y.append(batch['label'])
x = tf.concat(x, axis=0)
y = tf.concat(y, axis=0)
# git distribution of precision across pixel positions
variance = tf.math.reduce_variance(tf.keras.layers.Flatten()(x), axis=0)
precision = 1 / tf.clip_by_value(
variance, clip_value_min=(1 / 255), clip_value_max=np.inf)
a, _, b_inv = gamma.fit(precision, floc=0)
b = 1 / b_inv
# randomly select pseudo inputs
u = []
for i in range(num_classes):
i_choice = np.random.choice(np.where(y == i)[0],
size=pseudo_inputs_per_class,
replace=False)
u.append(tf.gather(params=x, indices=i_choice, axis=0))
u = tf.concat(u, axis=0)
return a, b, u
def maximum_likelihood_fit(data):
"""Estimate parameters from samples.
This is a wrapper around scipy's maximum likelihood estimator to
estimate the parameters of a gamma distribution from samples.
Parameters
----------
data : list or list of lists/arrays
Data to estimate parameters from. Lists of
different length may be passed.
Returns
-------
parameter : array-like, shape=[..., 2]
Estimate of parameter obtained by maximum likelihood.
"""
def is_nested(sample):
"""Check if sample contains an iterable."""
for el in sample:
try:
return iter(el)
except TypeError:
return False
if not is_nested(data):
data = [data]
parameters = []
for sample in data:
sample = gs.array(sample)
kappa, _, scale = gamma.fit(sample, floc=0)
nu = 1 / scale
parameters.append(gs.array([kappa, kappa / nu]))
return parameters[0] if len(data) == 1 else gs.stack(parameters)
def getGammaPdf(dataset, nbins, bins):
shape, loc, scale = gamma.fit(dataset, floc=0)
x = np.linspace(min(bins), max(bins), nbins)
print('GAM: shape=' + str(shape) + ', loc=' + str(loc) + ", scale=" +
str(scale))
pdf = gamma.pdf(x, shape, loc, scale)
return (x, pdf)
def gamma_correction(obs_data,
mod_data,
sce_data,
lower_limit=0.1,
cdf_threshold=0.9999999):
obs_raindays, mod_raindays, sce_raindays = [
x[x >= lower_limit] for x in [obs_data, mod_data, sce_data]
]
obs_gamma, mod_gamma, sce_gamma = [
gamma.fit(x) for x in [obs_raindays, mod_raindays, sce_raindays]
]
obs_cdf = gamma.cdf(np.sort(obs_raindays), *obs_gamma)
mod_cdf = gamma.cdf(np.sort(mod_raindays), *mod_gamma)
sce_cdf = gamma.cdf(np.sort(sce_raindays), *sce_gamma)
obs_cdf[obs_cdf > cdf_threshold] = cdf_threshold
mod_cdf[mod_cdf > cdf_threshold] = cdf_threshold
sce_cdf[sce_cdf > cdf_threshold] = cdf_threshold
obs_cdf_intpol = np.interp(
np.linspace(1, len(obs_raindays), len(sce_raindays)),
np.linspace(1, len(obs_raindays), len(obs_raindays)), obs_cdf)
mod_cdf_intpol = np.interp(
np.linspace(1, len(mod_raindays), len(sce_raindays)),
np.linspace(1, len(mod_raindays), len(mod_raindays)), mod_cdf)
obs_inverse, mod_inverse, sce_inverse = [
1. / (1. - x) for x in [obs_cdf_intpol, mod_cdf_intpol, sce_cdf]
]
adapted_cdf = 1 - 1. / (obs_inverse * sce_inverse / mod_inverse)
adapted_cdf[adapted_cdf < 0.] = 0.
initial = gamma.ppf(np.sort(adapted_cdf), *obs_gamma) * gamma.ppf(
sce_cdf, *sce_gamma) / gamma.ppf(sce_cdf, *mod_gamma)
obs_frequency = 1. * obs_raindays.shape[0] / obs_data.shape[0]
mod_frequency = 1. * mod_raindays.shape[0] / mod_data.shape[0]
sce_frequency = 1. * sce_raindays.shape[0] / sce_data.shape[0]
days_min = len(sce_raindays) * sce_frequency / mod_frequency
expected_sce_raindays = int(min(days_min, len(sce_data)))
sce_argsort = np.argsort(sce_data)
correction = np.zeros(len(sce_data))
if len(sce_raindays) > expected_sce_raindays:
initial = np.interp(
np.linspace(1, len(sce_raindays), expected_sce_raindays),
np.linspace(1, len(sce_raindays), len(sce_raindays)), initial)
else:
initial = np.hstack(
(np.zeros(expected_sce_raindays - len(sce_raindays)), initial))
correction[sce_argsort[:expected_sce_raindays]] = initial
#correction = pd.Series(correction, index=sce_data.index)
return correction
def plot_time(time: pandas.Series):
"""
make a probability density function estimate based on the data
in this simulation, time interval is same distribution for all sensors and rooms
https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.fit.html
"""
intervals = time.diff().dropna().dt.total_seconds()
Nbin = 100
Fa, Floc, Fscale = gamma.fit(intervals)
ti = np.arange(0.01, 5, 0.01) # arbitrary time interval range to plot over
pd = gamma.pdf(ti, Fa, loc=Floc, scale=Fscale) # fit
ax = plt.figure().gca()
ax.plot(ti, pd)
ax.set_xlabel("Time Interval (seconds)")
ax.set_ylabel("Probability")
ax.set_title("Time interval observed")
# add the measured data to the plot
ax.hist(intervals, bins=Nbin)
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 train_gamma(X, y):
"""
Description: This is trained by the density of gamma-distributions for each features.
@params:
X: training features
y: training y
@return:
model:
"""
m, n = X.shape
model = {}
## calculate prob of spam and nonspam
p_spam = sum(y == 1) * 1.0 / m
p_nonspam = sum(y == 0) * 1.0 / m
model["p_spam"] = p_spam
model["p_nonspam"] = p_nonspam
index_spam = y == 1
index_nonspam = y == 0
gammas_spam = []
gammas_nonspam = []
for i in range(n):
ga = {}
x_spam = asarray(X[index_spam, i])
a, floc, scale = gamma.fit(x_spam)
ga["a"] = a
ga["floc"] = floc
ga["scale"] = scale
gammas_spam.append(ga)
ga = {}
x_nonspam = asarray(X[index_nonspam, i])
a, floc, scale = gamma.fit(x_nonspam)
ga["a"] = a
ga["floc"] = floc
ga["scale"] = scale
gammas_nonspam.append(ga)
model["gammas_spam"] = gammas_spam
model["gammas_nonspam"] = gammas_nonspam
return model
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 HSIC_pval(X,
Y,
N_samp=500,
kernelX="Gaussian",
kernelY="Gaussian",
eta=0.001,
sigmaX=None,
sigmaY=None,
p_method="boots",
return_boots=False):
""" Calculates HSIC and p-value
Gram matrices are approximated using incomplete Cholesky decomposition.
X: Data. Each row is a datapoint.
Y: Data. Each row is a datapoint.
N_samp: Number of samples
kernelX: Kernel to use (Gaussian, Linear, Delta)
kernelY: Kernel to use (Gaussian, Linear, Delta)
eta: Threshold for incomplete Cholesky decomposition
sigmaX: sigma for X when using Gaussian kernel
sigmaY: sigma for Y when using Gaussian kernel
"""
timeA = time.time()
m, _ = X.shape
sigmaX = getSigmaGaussian(X, X, 200) if sigmaX is None else sigmaX
sigmaY = getSigmaGaussian(Y, Y, 200) if sigmaY is None else sigmaY
A, max_rankA = incompleteCholeskyKernel(X, m, kernelX, sigmaX, eta)
B, max_rankB = incompleteCholeskyKernel(Y, m, kernelY, sigmaY, eta)
centered_A = A.T - A.T.mean(axis=0)
tmp = B * np.mat(centered_A)
HSIC = np.trace(tmp * tmp.T) / m**2
boots = []
Yrand = np.copy(Y)
for _ in xrange(N_samp):
np.random.shuffle(Yrand)
B, max_rankB = incompleteCholeskyKernel(Yrand, m, kernelY, sigmaY, eta)
tmp = np.mat(B) * np.mat(centered_A)
boots.append(np.trace(tmp * tmp.T) / m**2)
boots = np.array(boots)
if p_method == "boots":
pval = (sum(b >= HSIC for b in boots) + 1) / float(len(boots) + 1)
else: #gamma
fit_alpha, fit_loc, fit_beta = gamma.fit(boots)
pval = 1 - gamma.cdf(HSIC, fit_alpha, scale=fit_beta, loc=fit_loc)
if return_boots:
return HSIC, pval, boots
else:
return HSIC, pval
def __init__(self, mode=0, elem=None, sample=None):
if mode == 0:
self.a = elem[0]
self.mu = elem[1]
self.sigma = elem[2]
else:
self.a, self.mu, self.sigma = gamma.fit(sample)
self.math_average = gamma.mean(self.a, loc=self.mu, scale=self.sigma)
self.dispersion = gamma.var(self.a, loc=self.mu, scale=self.sigma)
def fit_gamma_expon_Q(trace,gammafactor=20,exponfactor=2,plot=False):
params = []
for i in range(1,len(trace[0])):
if i < 4:
a,loc,theta = gamma.fit(trace[:,i],floc = 0)
params.append([a/gammafactor,loc,theta*gammafactor])
if i == 4:
loc,scale = expon.fit(trace[:,i],floc = 0)
params.append([loc,scale*exponfactor])
return params
def get_outliers(data, filter, plotting):
if plotting:
for x, r in [("x1", (0, 1)), ("x2", (0, 30)), ("x3", (0, 1))]:
plt.violinplot(data[x], vert=False)
plt.xlim(r)
plt.savefig("plots/violin/%s.png" % x)
plt.clf()
if filter:
data_fl = data[data["class"] == 0]
else:
data_fl = data
pdf = pd.DataFrame({})
a, b, loc, scale = beta.fit(data_fl["x1"])
pdf["x1"] = beta.logpdf(data["x1"], a, b, loc=loc, scale=scale)
a, loc, scale = gamma.fit(data_fl["x2"])
pdf["x2"] = gamma.logpdf(data["x2"], a, loc=loc, scale=scale)
a, b, loc, scale = beta.fit(data_fl["x3"])
pdf["x3"] = beta.logpdf(data["x3"], a, b, loc=loc, scale=scale)
pdfs = pdf["x1"] + pdf["x2"] + pdf["x3"]
if plotting:
sns.boxplot(y=pdfs, x="class", data=data)
plt.savefig("plots/boxplot.png")
plt.clf()
if plotting:
plt.plot(np.sort(pdfs))
splits = [40, 45, 50, 60]
for split in splits:
split = np.sort(pdfs)[60]
plt.plot((0, 1000), (split, split), 'k-', lw=0.5)
split = np.sort(pdfs)[50]
plt.plot((0, 1000), (split, split), 'k.', lw=0.5)
split = np.sort(pdfs)[45]
plt.plot((0, 1000), (split, split), 'k--', lw=0.5)
split = np.sort(pdfs)[40]
plt.plot((0, 1000), (split, split), 'k--', lw=0.5)
plt.savefig("plots/thresholds.png")
plt.clf()
outliers = np.argsort(pdfs)
final = []
for outlier in outliers:
if data["class"][outlier] == -1:
final.append(outlier)
return np.array(final[:100])
def continuous():
"""Fit distributions to symptoms' duration data."""
# fetch data
x = _symptoms_data()
# fit distributions
return {
'x': x,
'norm': norm.fit(x),
'lognorm': lognorm.fit(x, floc=0),
'gamma': gamma.fit(x, floc=0)
}
def fit_gamma_sp(trace,factor=5,plot=False):
a,loc,theta = gamma.fit(trace[:,4],floc=0)
if plot == True:
xmax = max(trace[:,4])
xmin = min(trace[:,4])
xdata = np.linspace(0,xmax*2,num=500)
#plt.plot(xdata,gamma.pdf(xdata,a,loc,theta))
plt.plot(xdata,gamma.pdf(xdata,a/factor,loc,theta*factor))
plt.hist(trace[:,4],bins=50,density=True)
plt.show()
return a/factor, loc, theta*factor
def gbmodelpredictrv(rvinput, rvhandperc):
prediction = modelefftr.predict(rvinput)
distribution = probdensityrv[(probdensityrv[0] > prediction - .025) & (
probdensityrv[0] < prediction + .025)]['test actual']
fit_alpha, fit_loc, fit_beta = gamma.fit(distribution)
#flhandperc = tools.handprobability()
#flhandperc = flhandperc.sort_values('rank')
for i in rvhandperc.index:
rvhandperc.at[i, 'rank'] = rvhandperc.at[i, 'rank'] * gamma.pdf(
rvhandperc.at[i, 'rank'], fit_alpha, loc=fit_loc, scale=fit_beta)
return rvhandperc
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 _test_fit_trans(self):
filename = "../../../bridge/cfg/detection.dat"
dat = np.loadtxt(filename)
fit_shape, fit_loc, fit_scale = gamma.fit(self.trans_conc_particle(dat[77:, 1]))
print fit_shape, fit_loc, fit_scale
mean = fit_shape * fit_scale
variance = mean * fit_scale
print mean, variance
x = np.linspace(1, 250, 10000)
# ax.plot(x, gamma.pdf(x, shape), 'r-', lw=5, alpha=0.6, label='gamma pdf')
rv = gamma(fit_shape, scale=fit_scale)
fig, ax = plt.subplots(1, 1)
ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
plt.show()
def calcSPI(duration, model, cid):
"""Calculate Standardized Precipitation Index for specified month
*duration*. Need a climatology of precipitation stored in the database
used in a VIC *model* simulation."""
nt = (date(model.endyear, model.endmonth, model.endday) -
date(model.startyear + model.skipyear, model.startmonth, model.startday)).days + 1
# tablename = "precip."+model.precip
if duration < 1:
print(
"WARNING! Cannot calculate SPI with {0} months duration.".format(duration))
spi = np.zeros(nt)
else:
p = np.loadtxt("{0}/forcings/data_{1:.{3}f}_{2:.{3}f}".format(model.model_path,
model.gid[cid][0], model.gid[cid][1], model.grid_decimal))[:, 0]
p = pandas.Series(p, [date(model.startyear, model.startmonth,
model.startday) + timedelta(t) for t in range(len(p))])
p[duration:] = pandas.rolling_mean(p.resample(
'M', how='mean'), duration).values[duration:]
p[:duration] = 0.0
g1, g2, g3 = gamma.fit(p)
cdf = gamma.cdf(p, g1, g2, g3)
spi = norm.ppf(cdf)
return spi
def generate_slm(training_rows, slm_dir, do_plot=True):
slm_fxt = os.path.join(slm_dir, "slm.fxt")
slength_counts = Counter()
slen=1
for r in training_rows:
#print r
is_boundary = int(r[6])
if(not is_boundary):
slen += 1
else:
# print "adding slen=",(slen+1)
slength_counts[slen]+=1
slen = 1
els = list( slength_counts.elements() ) #Counter.elements() returns iterator that iterates across n instances of each element e where slength_counts[e]=n .. we make this into a list for plotting
#print els
x_vals = range(0, max(els)+1)
(shape, loc, scale) = gamma.fit(els, floc=0)
gam_gen = gamma(shape, loc, scale) #use these model params to build a new gamma distrib/n generator
write_slm(slm_fxt, x_vals, gam_gen)
if do_plot:
plot_graph(x_vals, gam_gen, els)
compile_slm(slm_dir) #this last step compiles the slm to binary .fst format
with open("lengths_file.pickle", "rb") as lengths_file:
lengths = load(lengths_file)
plot_count = len(list(filter(lambda x: LENGTH_CUTOFF < len(x),
lengths.values())))
num_col = int(floor(sqrt(plot_count)))
num_row = int(ceil(plot_count / num_col))
sorted_relationships = sorted(lengths.keys(), key = sum)
plt.figure(1)
subplot_num = 1
for relationship in sorted_relationships:
length_data = lengths[relationship]
length_data.sort()
if LENGTH_CUTOFF > len(length_data):
continue
plt.subplot(num_row, num_col, subplot_num)
plt.hist(length_data, bins = 200, normed = True)
plt.title(str(relationship))
fit = gamma.fit(length_data)
pdf = gamma(*fit).pdf(length_data)
plt.plot(length_data, pdf)
subplot_num += 1
plt.tight_layout()
plt.show()
def compile(alphabet, words, nonwords):
print(' Generating all possible transitions...')
from itertools import product
all = []
for state_size in range(args.max_state_size + 1):
all += product(product(alphabet, repeat = state_size), [*alphabet, None])
def of(string):
for i in range(len(string)):
yield string[max(0, i - args.max_state_size):i], string[i]
yield string[max(0, len(string) - args.max_state_size):], None
from collections import Counter
counts = Counter()
for word in tqdm(words, ' Counting transitions', leave = True):
for state, symbol in of(word):
counts[state, symbol] += 1
state_counts = Counter()
for state, symbol in tqdm(counts, ' Counting states', leave = True):
state_counts[state] += counts[state, symbol]
import numpy as np
logprobs = np.empty(len(all))
for i, (state, symbol) in enumerate(tqdm(all, ' Computing conditional transition probabilities', leave = True)):
try:
logprobs[i] = np.log(state_counts[state] / counts[state, symbol])
except ZeroDivisionError:
logprobs[i] = np.inf
print(' Fitting flattening distribution...')
from scipy.stats import gamma
params = gamma.fit(logprobs[logprobs != np.inf])
print(' Flattening...')
logprobs = gamma.cdf(logprobs, *params)
lower_bound = np.min(logprobs)
upper_bound = np.max(logprobs[logprobs != 1])
new_logprobs = np.empty(len(logprobs), int)
for i, logprob in enumerate(tqdm(logprobs, ' Discretizing', leave = True)):
if logprob == 1:
new_logprobs[i] = 2 ** args.transition_bits - 1
else:
new_logprobs[i] = round((logprob - lower_bound) * ((2 ** args.transition_bits - 2) / (upper_bound - lower_bound)))
logprobs = new_logprobs
data = bytearray()
bit_buffer = 0
bit_buffer_size = 0
for logprob in tqdm(logprobs, ' Packing', leave = True):
bit_buffer = bit_buffer << args.transition_bits | int(logprob)
bit_buffer_size += args.transition_bits
if bit_buffer_size % 8 == 0:
data += bit_buffer.to_bytes(bit_buffer_size // 8, 'big')
bit_buffer = 0
bit_buffer_size = 0
while bit_buffer_size % 8 != 0:
bit_buffer = bit_buffer << args.transition_bits
bit_buffer_size += args.transition_bits
data += bit_buffer.to_bytes(bit_buffer_size // 8, 'big')
old_logprobs = np.empty(len(logprobs))
for i, logprob in enumerate(tqdm(logprobs, ' Undiscretizing...', leave = True)):
if logprob == 2 ** args.transition_bits - 1:
old_logprobs[i] = 1
else:
old_logprobs[i] = lower_bound + logprob * ((upper_bound - lower_bound) / (2 ** args.transition_bits - 2))
print(' Unflattening...')
old_logprobs = gamma.ppf(old_logprobs, *params)
old_logprobs = dict(zip(all, old_logprobs))
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
print(' Fitting words distribution...')
words_params = params_of(words)
print(' Fitting nonwords distribution...')
nonwords_params = params_of(nonwords)
def minify(code):
if args.minify:
import subprocess
p = subprocess.run([str(Path(__file__).parent / 'node_modules/uglify-js/bin/uglifyjs'),
'--screw-ie8',
'--mangle', 'sort,toplevel',
'--compress',
'--bare-returns',
], input = code.encode(),
stdout = subprocess.PIPE,
stderr = subprocess.PIPE)
if p.returncode != 0:
import sys
sys.stderr.buffer.write(p.stderr)
p.check_returncode()
code = p.stdout.decode()
return code
print(' Generating JS code...')
code = minify(r'''
exports.init = function(buffer) {
exports.test = (new Function('buffer', buffer.utf8Slice(''' + str(len(data)) + r''')))(buffer);
};
''').encode()
data += minify(r'''
var abs = Math.abs;
var min = Math.min;
var max = Math.max;
var alphabet = [
''' + r'''
'''.join('"' + symbol + '",' for symbol in alphabet) + r'''
];
var of; (function() {
function fold(string) {
string = Array.from(string);
for (var i = alphabet.length - 1; alphabet[i].length > 1; --i) {
for (var j = 0; j <= string.length - alphabet[i].length; ++j) {
if (string.slice(j, j + alphabet[i].length).join('') == alphabet[i]) {
string.splice(j, alphabet[i].length, alphabet[i]);
}
}
}
return string;
}
of = function(string) {
string = fold(string);
var ofString = [];
for (var i = 0; i < string.length; ++i) {
ofString.push([string.slice(max(0, i - ''' + str(args.max_state_size) + r'''), i), string[i]]);
}
ofString.push([string.slice(max(0, string.length - ''' + str(args.max_state_size) + r''')), null]);
return ofString;
};
})();
var all; (function() {
function product(xs, ys) {
var result = [];
for (var i = 0; i < xs.length; ++i) {
for (var j = 0; j < ys.length; ++j) {
result.push([xs[i], ys[j]]);
}
}
return result;
}
function power(a, k) {
if (k == 0) {
return [[]];
}
var result = [];
for (var i = 0; i < a.length; ++i) {
var b = power(a, k - 1);
for (var j = 0; j < b.length; ++j) {
result.push([a[i]].concat(b[j]));
}
}
return result;
}
all = [];
for (var stateSize = 0; stateSize <= ''' + str(args.max_state_size) + r'''; ++stateSize) {
all = all.concat(product(power(alphabet, stateSize), alphabet.concat([null])));
}
})();
var gammaPdf, gammaPpf; (function() {
var pow = Math.pow;
var exp = Math.exp;
var log = Math.log;
var sqrt = Math.sqrt;
var cof = [
76.18009172947146,
-86.50532032941677,
24.01409824083091,
-1.231739572450155,
0.1208650973866179e-2,
-0.5395239384953e-5,
];
function ln(x) {
var j = 0;
var ser = 1.000000000190015;
var xx, y, tmp;
tmp = (y = xx = x) + 5.5;
tmp -= (xx + 0.5) * log(tmp);
for (; j < 6; j++)
ser += cof[j] / ++y;
return log(2.5066282746310005 * ser / xx) - tmp;
}
gammaPdf = function(x, a) {
if (x < 0)
return 0;
if (x === 0 && a === 1)
return 1;
return exp((a - 1) * log(x) - x - ln(a));
};
function lowReg(a, x) {
var aln = ln(a);
var ap = a;
var sum = 1 / a;
var del = sum;
var b = x + 1 - a;
var c = 1 / 1.0e-30;
var d = 1 / b;
var h = d;
var i = 1;
var ITMAX = -~(log((a >= 1) ? a : 1 / a) * 8.5 + a * 0.4 + 17);
var an, endval;
if (x < 0 || a <= 0) {
return NaN;
} else if (x < a + 1) {
for (; i <= ITMAX; i++) {
sum += del *= x / ++ap;
}
return sum * exp(-x + a * log(x) - aln);
}
for (; i <= ITMAX; i++) {
an = -i * (i - a);
b += 2;
d = an * d + b;
c = b + an / c;
d = 1 / d;
h *= d * c;
}
return 1 - h * exp(-x + a * log(x) - aln);
}
gammaPpf = function(p, a) {
var j = 0;
var a1 = a - 1;
var EPS = 1e-8;
var gln = ln(a);
var x, err, t, u, pp, lna1, afac;
if (p > 1)
return NaN;
if (p == 1)
return Infinity;
if (p < 0)
return NaN;
if (p == 0)
return 0;
if (a > 1) {
lna1 = log(a1);
afac = exp(a1 * (lna1 - 1) - gln);
pp = (p < 0.5) ? p : 1 - p;
t = sqrt(-2 * log(pp));
x = (2.30753 + t * 0.27061) / (1 + t * (0.99229 + t * 0.04481)) - t;
if (p < 0.5)
x = -x;
x = max(1e-3, a * pow(1 - 1 / (9 * a) - x / (3 * sqrt(a)), 3));
} else {
t = 1 - a * (0.253 + a * 0.12);
if (p < t)
x = pow(p / t, 1 / a);
else
x = 1 - log(1 - (p - t) / (1 - t));
}
for(; j < 12; j++) {
if (x <= 0)
return 0;
err = lowReg(a, x) - p;
if (a > 1)
t = afac * exp(-(x - a1) + a1 * (log(x) - lna1));
else
t = exp(-x + a1 * log(x) - gln);
u = err / t;
x -= (t = u / (1 - 0.5 * min(1, u * ((a - 1) / x - 1))));
if (x <= 0)
x = 0.5 * (x + t);
if (abs(t) < EPS * x)
break;
}
return x;
};
})();
var logprobs = {};
var bitBuffer = 0, bitBufferSize = 0;
var bufferOffset = 0;
for (var i = 0; i < all.length; ++i) {
while (bitBufferSize < ''' + str(args.transition_bits) + r''') {
bitBuffer = bitBuffer << 8 | buffer.readUInt8(bufferOffset++); bitBufferSize += 8;
}
var logprob = bitBuffer >> (bitBufferSize - ''' + str(args.transition_bits) + r''') & ''' + hex(2 ** args.transition_bits - 1) + r'''; bitBufferSize -= ''' + str(args.transition_bits) + r''';
if (logprob == ''' + str(2 ** args.transition_bits - 1) + r''') {
logprob = 1;
} else {
logprob = ''' + str(lower_bound) + r''' + logprob * ''' + str((upper_bound - lower_bound) / (2 ** args.transition_bits - 2)) + r''';
}
logprob = ''' + str(params[1]) + r''' + gammaPpf(logprob, ''' + str(params[0]) + r''') * ''' + str(params[2]) + r''';
logprobs[all[i]] = logprob;
}
return function(string) {
var stringLogprob = 0;
var ofString = of(string);
for (var i = 0; i < ofString.length; ++i) {
stringLogprob += logprobs[ofString[i]];
}
if (stringLogprob == Infinity) {
return false;
}
var wordsDensity = gammaPdf((stringLogprob - ''' + str(words_params[1]) + r''') / ''' + str(words_params[2]) + r''', ''' + str(words_params[0]) + r''') / ''' + str(words_params[2]) + r''';
var nonwordsDensity = gammaPdf((stringLogprob - ''' + str(nonwords_params[1]) + r''') / ''' + str(nonwords_params[2]) + r''', ''' + str(nonwords_params[0]) + r''') / ''' + str(nonwords_params[2]) + r''';
if (wordsDensity > nonwordsDensity) {
return true;
}
if (wordsDensity < nonwordsDensity) {
return false;
}
return Math.random() >= 0.5;
};
''').encode()
data, is_gzipped = bytes(data), False
if args.gzip:
import gzip
print(' Gzipping...')
gzipped_data = gzip.compress(data)
if len(gzipped_data) < len(data):
data, is_gzipped = gzipped_data, True
return code, data, is_gzipped
print(x.mean(), x.var())
m = 0 # Number of current step
print('m', m)
# Initial values TODO
p_m = [0.9, 0.1] # [1 / k for i in k_underline]
alpha_m =[0.2, 0.3]
beta_m = [0.0002, 0.0001]
print('p_m', p_m)
print('alpha_m', alpha_m)
print('beta_m', beta_m)
# Initial values TODO
s, loc, t = gamma.fit(x, loc = 0)
alpha_est = s
beta_est = 1 / t
print(alpha_est, loc, beta_est)
p_m = [0.4, 0.6]
alpha_m = [alpha_est ** (random() * 2) for i in k_underline]
beta_m = [beta_est ** (random() * 2) for i in k_underline]
theta_m = p_m + alpha_m + beta_m
print('p_m', p_m)
print('alpha_m', alpha_m)
print('beta_m', beta_m)
while True:
# Prepare for next step
m += 1
print('m', m)
plt.plot(taille_A, lw=2)
plt.plot(taille_B, lw=2)
plt.xlabel('Nombre de manches')
plt.grid(True)
# fait un nombre N de partie et affiche les statistiques
def play_N_batailles(N):
nb_manches = []
for idx in range(N):
cards = new_card_set()
A, B = sort_cards(cards)
taille_A, taille_B = play_bataille(A, B)
nb_manches.append(len(taille_A))
return nb_manches
N = 10000
nb_manches = np.array(play_N_batailles(N))
plt.figure(2)
plt.hist(nb_manches, bins=500, color='b', alpha=0.5)
from scipy.stats import gamma
params = gamma.fit(nb_manches)
x = np.arange(1, N)
#plt.figure(3)
plt.plot(x, 2*N*gamma.pdf(x, *params[:-2], loc=params[-2], scale=params[-1]),
lw=2, color='r')
plt.xlim(0, 300)
23304334, 130258928, 18452922, 42620009, 77351045, 76032324, 44196273, 49036974, 23245119, 50656670, 84837088, 2089074, 52517589, 21469409, 106694589, 67063796, 16053222, 101270899, 15620252, 18355964, 839197, 31083111, 66698677] # mean = np.mean(data) # var = np.var(data) # fit = truncnorm.fit(data, 0, 2866387308, loc = mean, scale = var) # print(fit) # print(truncnorm(*fit).rvs(100)) # vector = lengths[(2, 2)] vector = np.array(sorted(lengths[(5, 5)])) mean = np.mean(vector) var = np.var(vector) std = np.std(vector) # fit = truncnorm.fit(vector, a = 0, b = 2866387308, loc = mean, scale = var) fit = gamma.fit(vector) print(fit) # pdf = gamma.pdf(vector, *fit[:-2], loc = fit[-2], scale = fit[-1]) pdf = gamma(*fit).pdf(vector) print(pdf) # print(gamma.pdf(vector, alpha)) plt.figure() plt.hist(vector, bins = 20, normed = True) # plt.hist(truncnorm(*fit).rvs(10000), bins = 20, normed = True, alpha = 0.5) plt.plot(vector, pdf) # plt.hist(gamma(*fit).rvs(10000), bins = 20, normed = True, alpha = 0.5) plt.show()
def match_single_track_dist(model_track, obs_track):
label_columns = ["Max_Hail_Size", "Shape", "Location", "Scale"]
obs_hail_dists = pd.DataFrame(index=obs_track.times,
columns=label_columns)
model_hail_dists = pd.DataFrame(index=model_track.times,
columns=label_columns)
for t, step in enumerate(obs_track.timesteps):
step_vals = step[(obs_track.masks[t] == 1) & (obs_track.timesteps[t] > self.mrms_ew.min_thresh)]
min_hail = step_vals.min() - 0.1
obs_hail_dists.loc[obs_track.times[t], ["Shape", "Location", "Scale"]] = gamma.fit(step_vals,
floc=min_hail)
obs_hail_dists.loc[obs_track.times[t], "Max_Hail_Size"] = step_vals.max()
if obs_track.times.size > 1 and model_track.times.size > 1:
normalized_obs_times = 1.0 / (obs_track.times.max() - obs_track.times.min()) \
* (obs_track.times - obs_track.times.min())
normalized_model_times = 1.0 / (model_track.times.max() - model_track.times.min()) \
* (model_track.times - model_track.times.min())
for col in label_columns:
interp_func = interp1d(normalized_obs_times, obs_hail_dists[col], kind="linear",
bounds_error=False, fill_value=0)
model_hail_dists.loc[model_track.times, col] = interp_func(normalized_model_times)
else:
for param in obs_hail_dists.columns:
model_hail_dists.loc[model_track.times, param] = obs_hail_dists.loc[obs_track.times[0], param]
return model_hail_dists
'''
import json, sys, collections
import numpy as np
import scipy
from scipy.stats import gamma
import matplotlib
matplotlib.use("Agg")
import matplotlib.pyplot as plt
with open("ALL_PAIR_JACCARD.json") as f:
all_pairs = json.load(f)
print("Get all pairs distribution")
all_pair_dists = np.square(np.array(all_pairs).flatten())
gamma_x = gamma.fit(all_pair_dists)
print("Get top k distance distribution")
k = 50
topk_dists = np.square(np.sort(all_pairs, axis=1))
gamma_xk = []
for i in range(k):
dists = topk_dists[:,i]
gamma_xk.append(gamma.fit(dists))
max_x = np.max(all_pair_dists)
with open("JACCARD_DIST_DIST.json", "w") as f:
d = [gamma_x, gamma_xk, max_x]
json.dump(d, f)
print("Output file")
def match_hail_size_step_distributions(self, model_tracks, obs_tracks, track_pairings):
"""
Given a matching set of observed tracks for each model track,
Args:
model_tracks:
obs_tracks:
track_pairings:
Returns:
"""
label_columns = ["Matched", "Max_Hail_Size", "Num_Matches", "Shape", "Location", "Scale"]
s = 0
for m, model_track in enumerate(model_tracks):
model_track.observations = pd.DataFrame(index=model_track.times, columns=label_columns, dtype=np.float64)
model_track.observations.loc[:, :] = 0
model_track.observations["Matched"] = model_track.observations["Matched"].astype(np.int32)
for t, time in enumerate(model_track.times):
model_track.observations.loc[time, "Matched"] = track_pairings.loc[s, "Matched"]
if model_track.observations.loc[time, "Matched"] > 0:
all_hail_sizes = []
step_pairs = track_pairings.loc[s, "Pairings"]
for step_pair in step_pairs:
obs_step = obs_tracks[step_pair[0]].timesteps[step_pair[1]].ravel()
obs_mask = obs_tracks[step_pair[0]].masks[step_pair[1]].ravel()
all_hail_sizes.append(obs_step[(obs_mask == 1) & (obs_step >= self.mrms_ew.min_thresh)])
combined_hail_sizes = np.concatenate(all_hail_sizes)
min_hail = combined_hail_sizes.min() - 0.1
model_track.observations.loc[time, "Max_Hail_Size"] = combined_hail_sizes.max()
model_track.observations.loc[time, "Num_Matches"] = step_pairs.shape[0]
model_track.observations.loc[time, ["Shape", "Location", "Scale"]] = gamma.fit(combined_hail_sizes,
floc=min_hail)
s += 1