def test(self,alpha,GSNR_low,GSNR_up,interval,test_batch,num_words):
SNR_dB_start_Eb = GSNR_low
SNR_dB_stop_Eb = GSNR_up
SNR_points = interval
SNR_dB_start_Es = SNR_dB_start_Eb + 10 * np.log10(self.k / self.N)
SNR_dB_stop_Es = SNR_dB_stop_Eb + 10 * np.log10(self.k / self.N)
SNRs = np.linspace(SNR_dB_start_Eb, SNR_dB_stop_Eb, SNR_points)
sigma_start = np.sqrt(1 / (2 * 10 ** (SNR_dB_start_Es / 10)))
sigma_stop = np.sqrt(1 / (2 * 10 ** (SNR_dB_stop_Es / 10)))
sigmas = np.linspace(sigma_start, sigma_stop, SNR_points)
nb_errors = np.zeros(len(sigmas), dtype=int)
nb_bits = np.zeros(len(sigmas), dtype=int)
ber = np.zeros(len(sigmas), dtype=float)
seedrand = np.zeros(100, dtype=int)
for sr in range(1, 100):
seedrand[sr] = np.random.randint(0, 2 ** 14, size=(1)) # seedrand[sr-1]+1
for i in range(0, len(sigmas)): # different SNR
scale = CommFunc.CalScale(SNRs[i], alpha, self.R)
# print("GSNR={},scale={}".format(SNRs[i], scale))
for ii in range(0, np.round(num_words / test_batch).astype(int)):
# Source
x_test, d_test=Data.genRanData(self.k, self.N, test_batch, seedrand[ii])
# Modulator (BPSK)
s_test = -2 * x_test + 1
# Channel (alpha-stable)
y_test = s_test + levy_stable.rvs(alpha, 0, 0, scale, (test_batch, self.N))
# Decoder
nb_errors[i] += self.decoder.evaluate(y_test, d_test, batch_size=test_batch, verbose=2)[2]
nb_bits[i] += d_test.size
ber = np.float32(nb_errors/nb_bits)
return ber
def generate_series(N, return1, return10, alpha, beta, delta, gamma):
#generate random variables sequentially according to Levy alpha-stable distribution
randomvariable = np.zeros(N)
for i in range(N):
randomvariable[i] = levy_stable.rvs(alpha, beta, delta, gamma, random_state=None)
##initialize prices
price = np.zeros(N+1)
price[0] = 100.0 #arbitrary initial price
##Standard practice, as prescribed by Mandelbrot (1963)
##presumes that the daily change in natural logarithms
##of prices is represented by said random variable:
## X = log_e[P_(i+1)] - log_e[P_i] , or equivalently
## P_(i+1) = P_i * exp(X)
exprv = np.exp(randomvariable)
for i in range(N):
price[i+1] = price[i] * exprv[i]
#Use the equations given for fractional daily returns:
# r^1_i = ( P_(i+1) - P_i ) / P_i
# r^10_i = ( P_(i+10) - P_i ) / P_i
for i in range(N):
return1[i] = (price[i+1] / price[i]) - 1
#shortcut return1[i] = exprv[i] - 1
if (i < N - 9):
return10[i] = (price[i+10] / price[i]) - 1
def monte_carlo_test(mon_car_tr, overlap_per):
# input params
alpha, beta = 1.7, .0
# generate prices
price = levy_stable.rvs(
alpha,
beta,
size=mon_car_tr
)
# Generate 1 day returns
one_day_returns = [
(price[i+1]-price[i])/price[i]
for i in range(len(price)-1)
]
# Generate overlapping data
overlap_data = []
for i in range(mon_car_tr-overlap_per):
val = 0
for j in range(overlap_per):
val = val + one_day_returns[i+j]
overlap_data.append(val)
# Probability of specific value in oveerlappig data
probs = [
levy_stable.ppf(i, alpha, beta)
for i in overlap_data
]
return probs, overlap_data
def sample_new_coordinates(self, x_old, y_old, gazeDir, dV_x, dV_y):
#Distances drawn from the stable random number generator
r = levy_stable.rvs(alpha=self.alpha_stable,
beta=self.beta_stable,
loc=self.delta_stable,
scale=self.gamma_stable,
size=self.NUM_SAMPLE_LEVY)
#Generate randomly a direction theta from a uniform distribution
#between -pi and pi and as a function of previous direction
theta = 2 * np.pi * np.random.rand(
self.NUM_SAMPLE_LEVY, ) - np.pi + gazeDir
dV_x = np.reshape(dV_x, -1, order='F')
dV_y = np.reshape(dV_y, -1, order='F')
#Compute new gaze position of the FOA via Langevin equation
x_new = np.round(x_old + self.h *
(-self.k_P * dV_x[x_old] +
self.k_R * np.multiply(r, np.cos(theta))))
y_new = np.round(y_old + self.h *
(-self.k_P * dV_y[y_old] +
self.k_R * np.multiply(r, np.sin(theta))))
return x_new, y_new
def _realization(self, truncated_distribution):
if self.alpha == 2:
z = np.random.normal(0, scale=self.scale, size=self.Na)
else:
if self.truncate is not None:
if truncated_distribution is not None:
z = truncated_distribution.sample(self.Na)
else:
z = sampling.truncated_levy_distribution(
self.truncate, self.alpha, self.scale, self.Na)
else:
z = levy_stable.rvs(self.alpha,
0,
loc=0,
scale=self.scale,
size=self.Na)
z = np.fft.fft(z, self.Na)
w = np.fft.ifft(z * self.A, self.Na).real
return w[:self.N * self.m:self.m]
def draw(a, b, fig):
x = []
for i in range(1000):
w = np.random.exponential(1)
x.append(F_inv(w, a, b))
plt.figure(fig)
plt.subplot(1, 2, 1)
plt.hist(x,
bins=100,
color='r',
label='a=' + str(a) + ' b=' + str(b),
rwidth=0.8,
density=1)
r = levy_stable.rvs(a, b, size=1000, scale=1)
plt.hist(r,
bins=100,
label="Theoretical",
color='b',
rwidth=0.8,
density=1)
plt.title('Sample histogram')
plt.legend()
plt.subplot(1, 2, 2)
plt.plot(np.arange(0, 1000), x)
plt.title('time series plot')
return
def gen_batch(hps):
y_batch = np.zeros([TIMES_SLOTS_PER_BATCH, 2 * NUM_ANT, 1])
h_batch = np.zeros([TIMES_SLOTS_PER_BATCH, 2 * NUM_ANT, 2 * NUM_ANT])
s_batch = np.random.rand(TIMES_SLOTS_PER_BATCH, 2 * NUM_ANT, 1)
s_batch = np.where(s_batch < 0.5, -1 / np.sqrt(2), 1 / np.sqrt(2))
w_batch = np.zeros([TIMES_SLOTS_PER_BATCH, 2 * NUM_ANT, 1])
p = 10**(hps.snr / 10)
for i in range(PACKETS_PER_BATCH):
h = np.sqrt(p / NUM_ANT) * complex_channel()
for j in range(TIME_SLOTS_PER_PACKET):
t = i * TIME_SLOTS_PER_PACKET + j
if NOISE_TYPE == "MIXGAUSS":
w = exampl_mixture_gauss(size=[2 * NUM_ANT, 1])
elif NOISE_TYPE == "NAKA":
w = nakagami_m(m=hps.m, size=[2 * NUM_ANT, 1])
else:
w = levy_stable.rvs(alpha=hps.alpha,
beta=hps.beta,
loc=hps.mu,
scale=hps.sigma,
size=[2 * NUM_ANT, 1])
s = s_batch[t, :, :]
s = s.reshape([2 * NUM_ANT, 1])
y = h @ s + w
y_batch[t:t + 1, :, :] = y
h_batch[t:t + 1, :, :] = h
w_batch[t:t + 1, :, :] = w
return y_batch, h_batch, s_batch, w_batch
def getSlope(alpha):
x = levy_stable.rvs(alpha=alpha, beta=0.0, size=100000)
cutoffs = np.logspace(-1,4)
means = np.array([np.std(np.clip(x,-c,c)) for c in cutoffs])
slope, intercept, r_value, p_value, std_err = linregress(np.log(cutoffs), np.log(means))
plt.loglog(cutoffs, means)
return slope
def simu_gumbel(num, theta):
"""
# Gumbel copula
"""
# https://cran.r-project.org/web/packages/gumbel/gumbel.pdf
# https://cran.r-project.org/web/packages/gumbel/vignettes/gumbel.pdf
d = theta
alpha = 1 / theta
beta = 1
gamma = 1
delta = 0
X = levy_stable.rvs(alpha=1 / theta,
beta=1,
scale=(np.cos(np.pi / (2 * theta)))**theta,
loc=0,
size=num)
v1 = np.array([np.random.exponential(scale=1.0) for i in range(0, num)])
v2 = np.array([np.random.exponential(scale=1.0) for i in range(0, num)])
def phi_1(t):
return np.exp(-t**(1 / theta))
u1 = phi_1(v1 / X)
u2 = phi_1(v2 / X)
return u1, u2
def get_transmission_delay(self):
transmission_delay = levy_stable.rvs(alpha=self.levy_stable_alpha,
beta=self.levy_stable_beta,
loc=self.levy_stable_loc,
scale=self.levy_stable_scale)
return transmission_delay
def Gumbel(self, alpha, d=(1000, )):
self.alpha = alpha
x = np.random.uniform(size=d)
y = np.random.uniform(size=d)
beta = (math.cos(math.pi / (2 * alpha)))**alpha
v = levy_stable.rvs(1 / alpha, 1, loc=0, scale=beta, size=d)
u_x = self.gumbel_generator(-np.log10(x) / v)
u_y = self.gumbel_generator(-np.log10(y) / v)
return u_x, u_y
def get_transmission_delay(self):
if self.type == 0:
transmission_delay = levy_stable.rvs(alpha=self.levy_stable_alpha,
beta=self.levy_stable_beta,
loc=self.levy_stable_loc,
scale=self.levy_stable_scale)
return transmission_delay
elif self.type == 1:
return self.mean_transmission_delay
else:
return None
def estimate_phi_mh(X,
Xhat,
alpha,
Phi,
n_iter_mcmc,
n_burnin_mcmc,
random_state,
return_loglk=False,
verbose=10):
"""Estimate the expectation of 1/phi by Metropolis-Hastings"""
if n_iter_mcmc <= n_burnin_mcmc:
raise ValueError('n_iter_mcmc must be greater than n_burnin_mcmc')
n_trials, n_times = X.shape
residual = (X - Xhat)**2
tau = np.zeros((n_trials, n_times))
rng = check_random_state(random_state)
if return_loglk:
loglk_all = np.zeros((n_iter_mcmc, 1))
for i in range(n_iter_mcmc):
scale = 2 * np.cos(np.pi * alpha / 4)**(2 / alpha)
Phi_p = levy_stable.rvs(alpha / 2,
1,
loc=0,
scale=scale,
size=(n_trials, n_times),
random_state=rng)
log_acc = 0.5 * np.log(Phi / Phi_p) + residual * (1 / Phi - 1 / Phi_p)
log_u = np.log(rng.uniform(size=(n_trials, n_times)))
ix = (log_acc > log_u)
Phi[ix] = Phi_p[ix]
if return_loglk:
loglk = np.sum(-0.5 * np.log(Phi) - 0.5 * residual / Phi)
loglk_all[i] = loglk
if verbose > 5:
print("Iter: %d\t loglk:%E\t NumAcc:%d" %
(i, loglk, np.sum(ix)))
if (i >= n_burnin_mcmc):
tau += 1 / Phi
tau = tau / (n_iter_mcmc - n_burnin_mcmc)
if return_loglk:
return Phi, tau, loglk_all
return Phi, tau
def MultiDimensionalGumbel(self, d=(2, 1000)):
arr = []
beta = (math.cos(math.pi / (2 * self.alpha)))**self.alpha
v = levy_stable.rvs(1 / self.alpha,
1,
loc=0,
scale=beta,
size=(d[1], ))
for i in range(d[0]):
x = np.random.uniform(size=(d[1], ))
u_x = self.gumbel_generator(-np.log10(x) / v)
arr.append(u_x)
return np.asarray(arr)
def levyflight(x0, n, dt, alpha, beta, out=None):
"""
Generate an instance of a Levy flight:
Arguments
---------
x0 : float or numpy array (or something that can be converted to a numpy array
using numpy.asarray(x0)).
The initial condition(s) (i.e. position(s)) of the Brownian motion.
n : int
The number of steps to take.
dt : float
The time step.
alpha, beta: Levy parameters
out : numpy array or None
If `out` is not None, it specifies the array in which to put the
result. If `out` is None, a new numpy array is created and returned.
Returns
-------
A numpy array of floats with shape `x0.shape + (n,)`.
Note that the initial value `x0` is not included in the returned array.
"""
#can we really calculate the stats?
#mean, var, skew, kurt = levy_stable.stats(alpha, beta, moments='mvsk')
#print("Levy mean: ",mean," variance: ",var)
x0 = np.asarray(x0)
# For each element of x0, generate a sample of n numbers from a
# normal distribution.
r = levy_stable.rvs(alpha, beta, size=x0.shape + (n, ), scale=sqrt(dt))
# If `out` was not given, create an output array.
if out is None:
out = np.empty(r.shape)
# This computes the Brownian motion by forming the cumulative sum of
# the random samples.
np.cumsum(r, axis=-1, out=out)
# Add the initial condition.
out += np.expand_dims(x0, axis=-1)
return out
def test_sample_2(alpha, beta):
num_samples = 10000
d = dist.Stable(alpha, beta, coords="S")
# Temporarily increase radius to test hole-patching logic.
# Scipy doesn't handle values of alpha very close to 1.
try:
old = pyro.distributions.stable.RADIUS
pyro.distributions.stable.RADIUS = 0.02
actual = d.sample([num_samples])
finally:
pyro.distributions.stable.RADIUS = old
actual = d.sample([num_samples])
expected = levy_stable.rvs(alpha, beta, size=num_samples)
assert ks_2samp(expected, actual).pvalue > 0.05
def SimuGumbel(n, m, theta):
"""
# Gumbel copula
Requires:
n = number of variables to generate
m = sample size
theta = Gumbel copula parameter
"""
# https://cran.r-project.org/web/packages/gumbel/gumbel.pdf
# https://cran.r-project.org/web/packages/gumbel/vignettes/gumbel.pdf
v = [np.random.uniform(0,1,m) for i in range(0,n)]
X = levy_stable.rvs(alpha=1/theta, beta=1,scale=(np.cos(np.pi/(2*theta)))**theta,loc=0, size=m)
phi_t = lambda t: np.exp(-t**(1/theta))
u = [phi_t(-np.log(v[i])/X) for i in range(0,n)]
return u
def generator2(dataset_name,
fraction,
mu,
sigma,
SNR=None,
distribution="Gaussian"):
#print(os.getcwd())
a = np.load(
os.path.join(os.path.join('../../data', dataset_name),
r'normlized_tensor.npy'))
b = np.zeros_like(a, dtype=bool)
DIM = a.shape
sigmas = [0.01, 0.05, 0.1, 0.5, 1]
#Add noise
if SNR != None:
sigma2 = np.var(tensor_to_vec(a)) * (1 / (10**(SNR / 10)))
GN = np.sqrt(sigma2) * np.random.randn(DIM[0], DIM[1], DIM[2])
a = a + GN
for it in range(5):
#Add outliers
if distribution == "Gaussian":
outliers = np.random.randn(DIM[0], DIM[1], DIM[2]) * sqrt(
sigmas[it]) + mu
elif distribution == "levy_stable":
outliers = levy_stable.rvs(sigma,
mu,
size=(DIM[0], DIM[1], DIM[2]))
locations = list(range(np.prod(DIM)))
if fraction != 0:
sampled_locations = np.random.choice(
locations, int(len(locations) * fraction), replace=False)
# print(len(sampled_locations))
for x in sampled_locations:
k = x // (DIM[0] * DIM[1])
x %= (DIM[0] * DIM[1])
i = x // DIM[1]
j = x % DIM[1]
b[i, j, k] = 1
a[i, j, k] += outliers[i, j, k]
return a, b
def test_spectrum():
for N in [1000, 10000]:
for q_list in [6, 12, 21]:
alpha = 1.5
X = levy_stable.rvs(alpha, beta=0, size=N)
q = np.linspace(-10, 10, q_list)
q = q[q!=0.0]
print(q)
lag = np.unique(
np.logspace(
0, np.log10(X.size // 4), 55
).astype(int) + 1
)
lag, dfa = MFDFA(X, lag = lag, q = q, order = 1)
alpha, f = singspect.singularity_spectrum(lag, dfa, q = q)
_ = singspect.singularity_spectrum_plot(alpha, f);
assert alpha.shape[0] == f.shape[0], "Output shape mismatch"
assert alpha.shape[0] == q.shape[0], "Output shape mismatch"
q, tau = singspect.scaling_exponents(lag, dfa, q = q)
_ = singspect.scaling_exponents_plot(q, tau);
assert tau.shape[0] == q.shape[0], "Output shape mismatch"
q, hq = singspect.hurst_exponents(lag, dfa, q = q)
_ = singspect.hurst_exponents_plot(q, hq);
assert hq.shape[0] == q.shape[0], "Output shape mismatch"
try:
singspect._slopes(lag, dfa, q[0:3])
except Exception:
pass
def fractional_diffusion(alpha_,
beta_,
theta_,
D_,
L,
M,
use_parallel=False,
do_save=False):
L = int(L)
M = int(M)
xnt = np.zeros((L, M))
L_temp = 20 * L
tau = 1e-5
c_alpha_ = np.power(D_ * tau, 1 / alpha_)
c_beta_ = np.power(tau, 1 / beta_)
x_alpha_ = alpha_
x_beta_ = -tan(theta_ * pi / 2) / tan(alpha_ * pi / 2)
x_gamma_ = c_alpha_ * np.power(cos(theta_ * pi / 2), 1 / alpha_)
x_delta_ = -x_gamma_ * tan(theta_ * pi / 2)
t_alpha_ = beta_
t_beta_ = 1
t_gamma_ = c_beta_ * np.power(cos(beta_ * pi / 2), 1 / beta_)
t_delta_ = t_gamma_ * tan(beta_ * pi / 2)
M_thres = 200
num_processes = cpu_count()
ti = time()
if M > M_thres:
num_M = int(np.floor(M / M_thres))
if use_parallel:
pool = Pool(processes=num_processes)
results_dt = []
results_dx = []
for i in range(num_M):
results_dt.append(
apply_async(pool, get_levy_stable,
(t_alpha_, t_beta_, t_delta_, t_gamma_,
(L_temp, M_thres))))
results_dt = [p.get() for p in results_dt]
dt = np.concatenate(results_dt, axis=1)
for i in range(num_M):
results_dx.append(
apply_async(pool, get_levy_stable,
(x_alpha_, x_beta_, x_delta_, x_gamma_,
(L_temp, M_thres))))
results_dx = [p.get() for p in results_dx]
dx = np.concatenate(results_dx, axis=1)
else:
dt = np.zeros((L_temp, M))
dx = np.zeros((L_temp, M))
for i in range(num_M):
dt_temp = levy_stable.rvs(t_alpha_,
t_beta_,
t_delta_,
t_gamma_,
size=(L_temp, M_thres))
dt[:, i * M_thres:(i + 1) * M_thres] = dt_temp
dx_temp = levy_stable.rvs(x_alpha_,
x_beta_,
x_delta_,
x_gamma_,
size=(L_temp, M_thres))
dx[:, i * M_thres:(i + 1) * M_thres] = dx_temp
else:
dt = levy_stable.rvs(t_alpha_,
t_beta_,
t_delta_,
t_gamma_,
size=(L_temp, M))
dx = levy_stable.rvs(x_alpha_,
x_beta_,
x_delta_,
x_gamma_,
size=(L_temp, M))
dt_sum = np.concatenate((np.zeros((1, M)), np.cumsum(dt, axis=0)))
dx_sum = np.concatenate((np.zeros((1, M)), np.cumsum(dx, axis=0)))
T = np.linspace(0, np.min(dt_sum[-1, :]), L)
nt = np.zeros((np.size(T), M), dtype=int)
for i in range(M):
jj = 0
looping_complete = False
for k in range(1 + L_temp):
while (True):
if dt_sum[k, i] >= T[jj]:
nt[jj, i] = k
jj += 1
if jj >= np.size(T):
looping_complete = True
break
else:
break
if looping_complete:
break
for i in range(M):
xnt[:, i] = dx_sum[nt[:, i], i]
if do_save:
data_dir_name = 'data'
make_dir(data_dir_name)
file_name = 'sim_frac_diff_a_%1.2f_b_%1.2f_t_%1.2f_D_%1.2f_L_%d_M_%d.p' % (
alpha_, beta_, theta_, D_, L, M)
pk.dump({
'x': xnt,
'T': T
}, open(os.path.join(data_dir_name, file_name), 'wb'))
savemat(
open(os.path.join(data_dir_name, file_name[:-1] + 'mat'), 'wb'), {
'xnt': xnt,
'T': T
})
return {'x': xnt, 'T': T}
###############################################################################
# We can also visualize the learned activations
plot_data([z[:10] for z in z_hat], ['stem'] * n_atoms)
###############################################################################
# Note if the data is corrupted with impulsive noise, this method may not be
# the best. Check out our :ref:`example using alphacsc
# <sphx_glr_auto_examples_plot_simulate_alphacsc.py>` to learn how to deal with
# such data.
alpha = 1.2
noise_level = 0.005
X[idx_corrupted] += levy_stable.rvs(alpha,
0,
loc=0,
scale=noise_level,
size=(n_corrupted_trials, n_times),
random_state=random_state_simulate)
pobj, times, d_hat, z_hat, reg = learn_d_z(X,
n_atoms,
n_times_atom,
reg=reg,
n_iter=n_iter,
solver_d_kwargs=dict(factr=100),
random_state=random_state,
n_jobs=1,
verbose=1)
plt.figure()
plt.plot(d_hat.T)
plt.plot(ds_true.T, 'k--')
plt.show()
def Inoise(alpha_train, x1, x2, x3):
y = np.float32(levy_stable.rvs(alpha_train, 0, x1, x2, x3))
return y
x = np.linspace(levy_stable.ppf(0.01, alpha, beta),
levy_stable.ppf(0.99, alpha, beta), 100)
ax.plot(x, levy_stable.pdf(x, alpha, beta),
'r-', lw=5, alpha=0.6, label='levy_stable pdf')
# Alternatively, the distribution object can be called (as a function)
# to fix the shape, location and scale parameters. This returns a "frozen"
# RV object holding the given parameters fixed.
# Freeze the distribution and display the frozen ``pdf``:
rv = levy_stable(alpha, beta)
ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
# Check accuracy of ``cdf`` and ``ppf``:
vals = levy_stable.ppf([0.001, 0.5, 0.999], alpha, beta)
np.allclose([0.001, 0.5, 0.999], levy_stable.cdf(vals, alpha, beta))
# True
# Generate random numbers:
r = levy_stable.rvs(alpha, beta, size=1000)
# And compare the histogram:
ax.hist(r, density=True, histtype='stepfilled', alpha=0.2)
ax.legend(loc='best', frameon=False)
plt.show()
"""
from scipy.stats import levy_stable
import numpy as np
points = 1000000
#jennys_constant = 8675309
alpha = 1.7
beta = 0.0
delta = 1.0
gamma = 1.0
draw1 = levy_stable.rvs(alpha,
beta,
gamma,
delta,
size=points,
random_state=None)
draw2 = levy_stable.rvs(alpha,
beta,
gamma,
delta,
size=points,
random_state=None)
draw = np.zeros(points)
for i in range(points):
draw[i] = draw1[i] + draw2[i]
#use scipy's quantile estimator to estimate the parameters and convert to S parameterization
#pconv = lambda alpha, beta, mu, sigma: (alpha, beta, mu - sigma * beta * np.tan(np.pi * alpha / 2.0), sigma)
for a in alpha:
for b in beta:
x = []
for i in range(N):
W = np.random.exponential(1)
x.append(f(W, a, b))
plt.figure(figsize=(10, 6))
# alpha-stable simulations
plt.subplot(1, 2, 1)
plt.hist(x,
bins=100,
color='black',
density=1,
alpha=0.75,
label='Simulation: ' + chr(945) + '=' + str(a) + ',' +
chr(946) + '=' + str(b))
theo = levy_stable.rvs(a, b, size=N, scale=1)
plt.hist(theo, bins=100, color='r', density=1, label='Theoretical')
plt.title('Simulation Histogram')
plt.legend()
# plots of time series
plt.subplot(1, 2, 2)
plt.plot(np.arange(0, N), x)
plt.title('Time Series Plot')
plt.savefig('Q3_a{}_b{}.png'.format(a, b))
plt.show()
def jumps(self, N):
return levy_stable.rvs(self.params[0], beta=0, scale=self.params[-1], size=N)
def stable(self, alpha, beta, mu=0, c=1):
return levy_stable.rvs(alpha, c)
def SimuMx(n, m, combination):
v = [np.random.uniform(0, 1, m) for i in range(0, n)]
weights = [comb["weight"] for comb in combination]
#Generate m random sample of category labels
y = np.array([
np.where(ls == 1)[0][0]
for ls in np.random.multinomial(n=1, pvals=weights, size=m)
])
for i in range(0, len(combination)):
combinationsize = len(v[0][y == i])
if combination[i]["type"] == "clayton":
theta = combination[i]["theta"]
X = np.array([
np.random.gamma(theta**(-1), scale=1.0)
for i in range(0, combinationsize)
])
phi_t = lambda t: (1 + t)**(-1 / theta)
for j in range(0, len(v)):
v[j][y == i] = phi_t(-np.log(v[j][y == i]) / X)
elif combination[i]["type"] == "gumbel":
theta = combination[i]["theta"]
X = levy_stable.rvs(alpha=1 / theta,
beta=1,
scale=(np.cos(np.pi / (2 * theta)))**theta,
loc=0,
size=combinationsize)
phi_t = lambda t: np.exp(-t**(1 / theta))
for j in range(0, len(v)):
v[j][y == i] = phi_t(-np.log(v[j][y == i]) / X)
elif combination[i]["type"] == "gaussian":
corrMatrix = combination[i]["corrMatrix"]
v2 = np.random.uniform(0, 1, combinationsize)
L = linalg.cholesky(corrMatrix, lower=True)
for j in range(0, len(v)):
v[j][y == i] = np.sqrt(-2 * np.log(v[j][y == i])) * np.cos(
2 * np.pi * v2)
y = np.dot(L, [vk[y == i] for vk in v])
Y = norm.cdf(y, loc=0, scale=1)
for j in range(0, len(v)):
v[j][y == i] = np.array(Y[j])
elif combination[i]["type"] == "student":
corrMatrix = combination[i]["corrMatrix"]
k = combination[i]["k"]
v2 = np.random.uniform(0, 1, combinationsize)
L = linalg.cholesky(corrMatrix, lower=True)
r = np.random.chisquare(df=k, size=combinationsize)
for j in range(0, len(v)):
v[j][y == i] = np.sqrt(-2 * np.log(v[j][y == i])) * np.cos(
2 * np.pi * v2)
z = np.dot(L, [vk[y == i] for vk in v])
Y = t.cdf(np.sqrt(k / r) * z, df=k, loc=0, scale=1)
for j in range(0, len(v)):
v[j][y == i] = np.array(Y[j])
return v
beta = np.max([beta, -1])
gam = np.max([gam, 0])
return [alpha, alphaold], [beta, betaold], [gam, gamold], [delta, deltaold]
if __name__ == "__main__":
alphas = np.linspace(0.1, 2, 5)
betas = np.linspace(-1, 1, 2)
errorsa = np.zeros((len(alphas), len(betas)))
errorsb = np.zeros((len(alphas), len(betas)))
for i in range(len(alphas)):
alpha = alphas[i]
for j in range(len(betas)):
beta = betas[j]
r = levy_stable.rvs(alpha, beta, loc=0, scale=1, size=10000)
k = estimate(r)
errorsa[i][j] = np.absolute((k[0][0]) - alpha) / alpha
errorsb[i][j] = np.absolute(k[1][0] - beta) / beta
'''
pd.DataFrame(errorsa,index = alphas,columns = betas).to_csv('/alpha_err.csv')
pd.DataFrame(errorsb,index = alphas,columns = betas).to_csv('/beta_err.csv')
'''
np.savetxt('errorsa.csv', errorsa, fmt='%.4e', delimiter=',')
np.savetxt('errorsb.csv', errorsb, fmt='%.4e', delimiter=',')
def noise(input_shape, alpha=1.5, beta=0, scale=1):
im_noise = levy_stable.rvs(alpha, beta, 0, scale, input_shape)
return im_noise
import numpy as np from scipy.stats import levy_stable import matplotlib.pyplot as plt N = 1000 ##alpha, beta = 1.8, 0.75 ##r = levy_stable.rvs(alpha, beta, size=N, scale = 0.3) ##plt.hist(r,bins = 30,label = "α=2 and β=0.75") ##alpha, beta = 2, 0.75 ##r = levy_stable.rvs(alpha, beta, size=N, scale = 1) ##plt.hist(r,alpha= 0.5,bins = 20,label = "Theoretical and β=0.75") ##plt.legend() ##plt.show() alpha, beta = 0.5, 0 r = levy_stable.rvs(alpha, beta, size=N, scale=1) x = np.linspace(0, 999, 1000) plt.plot(x, r) plt.legend() plt.show()
