def test_plot_cauchyrv(self):
def true_alpha_density_ratio(sample):
return cauchy.pdf(sample, 0, 1. / 8) / (
alpha * cauchy.pdf(sample, 0, 1. / 8) +
(1 - alpha) * cauchy.pdf(sample, 0, 1. / 2))
def estimated_alpha_density_ratio(sample):
return densratio_obj.compute_density_ratio(sample)
np.random.seed(1)
x = cauchy.rvs(size=200, loc=0, scale=1. / 8)
y = cauchy.rvs(size=200, loc=0, scale=1. / 2)
alpha = 0
densratio_obj = densratio(x, y, alpha=alpha)
sample_points = np.linspace(-1, 3, 400)
plt.plot(sample_points,
true_alpha_density_ratio(sample_points),
'b-',
label='True Alpha-Relative Density Ratio')
plt.plot(sample_points,
estimated_alpha_density_ratio(sample_points),
'r-',
label='Estimated Alpha-Relative Density Ratio')
plt.title(
"Alpha-Relative Density Ratio - Cauchy Random Variables (alpha={:03.2f})"
.format(alpha))
plt.legend()
plt.show()
assert True
def generate_point(distribution, noise, cluster_number, number_of_clusters):
max_value = number_of_clusters * 10
overlap = (noise * np.random.uniform(low=0, high=1))
min = (10 * cluster_number) - (overlap * 10)
max = 10 + (overlap * 10) + (10 * cluster_number)
if distribution == 'g':
point = [
np.random.normal(loc=(max + min) / 2, scale=(max - min) / 3),
np.random.normal(loc=(max + min) / 2),
np.random.normal(loc=(max + min) / 2, scale=(max - min) / 3),
np.random.randint(max_value),
np.random.randint(4) * (max_value / 4),
np.random.randint(2) * max_value, 12345, cluster_number * 10
]
elif distribution == 'c':
point = [
cauchy.rvs(loc=(max + min) / 2, scale=(max - min) / 100),
cauchy.rvs(loc=(max + min) / 2, scale=(max - min) / 100),
cauchy.rvs(loc=(max + min) / 2, scale=(max - min) / 100),
np.random.randint(max_value),
np.random.randint(4) * (max_value / 4),
np.random.randint(2) * max_value, 12345, cluster_number * 10
]
else:
point = [
np.random.uniform(low=(10 * cluster_number),
high=(10 * cluster_number) + 10),
np.random.uniform(low=min, high=max),
np.random.uniform(low=min, high=max),
np.random.randint(max_value),
np.random.randint(4) * (max_value / 4),
np.random.randint(2) * max_value, 12345, cluster_number * 10
]
return point
def line(N, width, line="MnKa"):
"""
Simulate Ka/Kb Line
Parameters (and their default values):
N: desired number of pulse
width: width (FWHM) of gaussian (voigt) profile
line: line to simulate (Default: MnKa)
Return (e):
e: simulated data
"""
if width == 0:
# Simulate by Cauchy (Lorentzian)
e = np.array([])
fs = np.asarray(Constants.FS[line])
for f in fs[fs.T[2].argsort()]:
e = np.concatenate((e, cauchy.rvs(loc=f[0], scale=Analysis.fwhm2gamma(f[1]), size=int(f[2]*N))))
e = np.concatenate((e, cauchy.rvs(loc=f[0], scale=Analysis.fwhm2gamma(f[1]), size=int(N-len(e)))))
else:
# Simulate by Voigt
pdf = lambda E: Analysis.line_model(E, 0, width, line=line)
Ec = np.array(Constants.FS[line])[:,0]
_Emin = np.min(Ec) - width*50
_Emax = np.max(Ec) + width*50
e = random(pdf, N, _Emin, _Emax)
return e
def line(N, width, line="MnKa"):
"""
Simulate Ka/Kb Line
Parameters (and their default values):
N: desired number of pulse
width: width (FWHM) of gaussian (voigt) profile
line: line to simulate (Default: MnKa)
Return (e):
e: simulated data
"""
if width == 0:
# Simulate by Cauchy (Lorentzian)
fs = np.asarray(Constants.FS[line])
renorm = fs.T[2].sum()**-1
e = np.concatenate([ cauchy.rvs(loc=f[0], scale=Analysis.fwhm2gamma(f[1]), size=int(f[2]*renorm*N)) for f in fs ])
if N - len(e) > 0:
e = np.concatenate((e, cauchy.rvs(loc=f[0], scale=Analysis.fwhm2gamma(f[1]), size=int(N-len(e)))))
else:
# Simulate by Voigt
pdf = lambda E: Analysis.line_model(E, 0, width, line=line)
Ec = np.array(Constants.FS[line])[:,0]
_Emin = np.min(Ec) - width*50
_Emax = np.max(Ec) + width*50
e = random(pdf, N, _Emin, _Emax)
return e[:N]
def Ridgway_generator(d, seed, cpam):
np.random.seed(seed)
X = cauchy.rvs(scale=cpam, size=(d, d))
a = cauchy.rvs(scale=cpam, size=d)
Sigma = X.T @ X
normalizer = np.diag(1 / np.sqrt(np.diag(Sigma)))
Sigma = normalizer @ Sigma @ normalizer
a = normalizer @ a
return Sigma, a
def generate(self, num_instances):
self.num_instances = num_instances
N0, N1 = self.generate_instances_numbers()
S0 = cauchy.rvs(loc=self.mu0, scale=self.scale0,
size=N0) #np.random.normal(self.mu0, self.sigma0, N0)
S1 = cauchy.rvs(loc=self.mu1, scale=self.scale1,
size=N1) #np.random.normal(self.mu1, self.sigma1, N1)
X = np.array(np.concatenate((S0, S1), axis=0))
y = np.asarray([0] * N0 + [1] * N1)
return X, y
def get_system_noise(self):
"""v_t vector"""
data_noise = np.zeros((self.ydim, self.PARTICLES_NUM), dtype=np.float64)
for i in xrange(self.ydim):
data_noise[i,:] = cauchy.rvs(loc=[0]*self.PARTICLES_NUM, scale=np.power(10,self.particles[self.ydim]),
size=self.PARTICLES_NUM)
data_noise[data_noise==float("-inf")] = -1e308
data_noise[data_noise==float("inf")] = 1e308
parameter_noises = np.zeros((self.pdim, self.PARTICLES_NUM), dtype=np.float64)
for i in xrange(self.pdim):
parameter_noises[i,:] = cauchy.rvs(loc=0, scale=self.nois_sh_parameters[i], size=self.PARTICLES_NUM)
return np.vstack((data_noise, parameter_noises))
def selectF(muF):
# randomly generate new F based on a Cauchy distribution
newF = cauchy.rvs(loc=muF, scale=0.1)
# if it is smaller than 0, try to generate a new F value that is not
# smaller than 0
if newF <= 0:
while newF <= 0:
newF = cauchy.rvs(loc=muF, scale=0.1)
# when the newly calculated F value is greater than 1 -> return 1
if newF > 1:
return 1
else:
return newF
def CauchyBoxplotTukey():
tips, result, count = [], [], 0
for size in sizes:
for i in range(NUMBER_OF_REPETITIONS):
distribution = cauchy.rvs(size=size)
distribution.sort()
count += count_out(distribution)
result.append(count / (size * NUMBER_OF_REPETITIONS))
distribution = cauchy.rvs(size=size)
distribution.sort()
tips.append(distribution)
DrawBoxplot(tips, CAUCHY)
printAnswer(result)
return
def selectF(mF):
# get a random index ri in the F memory
ri = np.random.randint(0, mF.shape[0])
# get random new F by a chauchy distribution where mF[ri] is the centre
newF = cauchy.rvs(loc=mF[ri], scale=0.1)
# if it is smaller than 0, try to generate a new F value that is not
# smaller than 0
if newF <= 0:
while newF <= 0:
newF = cauchy.rvs(loc=mF[ri], scale=0.1)
# when the newly calculated F value is greater than 1 -> return 1
if newF > 1:
return 1
else:
return newF
def __init__(self,
d,
gamma=1,
D=50,
metric='rbf',
device=torch.device('cpu')):
'''
d: dimension of input
D: number of Fourier features
metric: 'rbf' or 'laplace'
'''
self.D = D
# Sample frequencies
if metric == 'rbf':
self.w = np.sqrt(2 * gamma) * torch.empty(
(D, d), device=device).normal_().double()
elif metric == 'laplace':
self.w = cauchy.rvs(scale=gamma, size=(D, d))
self.w = torch.from_numpy(self.w).double().to(device)
self.w_inv = torch.pinverse(self.w)
# Sample offsets
self.b = 2 * np.pi * torch.empty(
(D, ), device=device, dtype=torch.double).random_(0, to=1)
def cauchy_distribution(select_size, asked=rvs, x=0):
if asked == rvs:
return cauchy.rvs(size=select_size)
elif asked == pdf:
return cauchy.pdf(x)
elif asked == cdf:
return cauchy.cdf(x)
def randwalk(lgth,
stiff,
start=[0., 0.],
step=1.,
adrift=0.,
anoise=.2,
dist="const"):
"""generates a 2d random walk with variable angular correlation and optional constant (+noise) angular drift.
Arguments: walk length "lgth", stiffness factor "stiff" - consecutive orientations are derived by adding stiff*(random number in [-1,1]).
Parameters "adrift" and "anoise" add a constant drift angle adrift modulated by a noise factor adrift*(random number in [-1,1]).
The dist parameter accepts non-constant step length distributions (right now, only cauchy/gaussian distributed random variables)"""
rw = [
list(start)
] #user provided initial coordinates: make (reasonably) sure it's a nested list type.
ang = [0]
#step lengths are precalculated for each step to account for
if dist == "cauchy": steps = cauchy.rvs(size=lgth)
elif dist == "norm": steps = norm.rvs(size=lgth)
else: steps = array([step] * lgth) #Overkill for constant step length ;)
#first generate angular progression vila cumulative sum of increments (random/stiff + drift terms)
angs = cumsum(stiff * uniform.rvs(size=lgth, loc=-1, scale=2) + adrift *
(1. + anoise * uniform.rvs(size=lgth, loc=-1, scale=2)))
#x/y trace via steplength and angle for each step, some array reshuffling (2d conversion and transposition)
rw = concatenate([
concatenate([array(start[:1]),
cumsum(steps * sin(angs)) + start[0]]),
concatenate([array(start)[1:],
cumsum(steps * cos(angs)) + start[1]])
]).reshape(2, -1).transpose()
return rw, angs
def solve(n):
x_cauchy = cauchy.rvs(size=n * M, loc=a, scale=s).reshape(M, n)
x_median = np.apply_along_axis(np.median, 1, x_cauchy)
x_mad = np.apply_along_axis(mad, 1, x_cauchy)
mu = -x_median / x_mad
ka = 1 / x_mad
ci_par = a_ci(ci_parametric(mu, gamma), x_median, x_mad)
ci_non_par = a_ci(ci_non_parametric(mu, gamma), x_median, x_mad)
x_med = mean(x_median)
empirical_cl_non_par, empirical_cl_par, sd_width_non_par, sd_width_par, width_non_par, width_par = \
test_ci(ci_non_par, ci_par, x_med)
print("LOCATION | N = {0:5}; Non-parametric: width = {1} ({2}); empirical CL = {3}".format(
n, mean(width_non_par), sd_width_non_par, empirical_cl_non_par))
print("LOCATION | N = {0:5}; Parametric: width = {1} ({2}); empirical CL = {3}".format(
n, mean(width_par), sd_width_par, empirical_cl_par))
# ---------------------------------
ci_par = s_ci(ci_parametric(ka, gamma), x_mad)
ci_non_par = s_ci(ci_non_parametric(ka, gamma), x_mad)
mad_ = np.exp(mean(np.log(np.abs(x_cauchy - x_med))))
empirical_cl_non_par, empirical_cl_par, sd_width_non_par, sd_width_par, width_non_par, width_par = \
test_ci(ci_non_par, ci_par, mad_)
print("SCALE | N = {0:5}; Non-parametric: width = {1} ({2}); empirical CL = {3}".format(
n, mean(width_non_par), sd_width_non_par, empirical_cl_non_par))
print("SCALE | N = {0:5}; Parametric: width = {1} ({2}); empirical CL = {3}".format(
n, mean(width_par), sd_width_par, empirical_cl_par))
print
print
async def iot_handler(websocket, path):
await websocket.send(motd)
# mode_query = "What kind of sensor would you like? (temperature,occupancy)"
# await websocket.send(mode_query)
# mode = await websocket.recv()
mode = "all"
rooms = get_simulated_rooms()
while True:
await asyncio.sleep(erlang.rvs(1, 0, size=1))
room = random.choice(list(rooms.keys()))
dat = {"time": datetime.now().isoformat()}
if mode.startswith(("all", "tem")):
dat["temperature"] = cauchy.rvs(loc=rooms[room]["loc"],
scale=rooms[room]["scale"],
size=1).tolist()
if mode.startswith(("all", "occ")):
dat["occupancy"] = poisson.rvs(rooms[room]["occ"], size=1).tolist()
if mode.startswith(("all", "co")):
dat["co2"] = gamma.rvs(rooms[room]["co"], size=1).tolist()
await websocket.send(json.dumps({room: dat}))
async def iot_handler(websocket, path):
"""
generate simulated data for each room and sensor
"""
await websocket.send(motd)
mode = "all"
rooms = get_simulated_rooms()
print("IoT simulator connected to", websocket.remote_address)
while True:
await asyncio.sleep(erlang.rvs(1, 0, size=1).item())
room = random.choice(list(rooms.keys()))
dat = {"time": datetime.now().isoformat()}
if mode.startswith(("all", "tem")):
dat["temperature"] = cauchy.rvs(
loc=rooms[room]["loc"], scale=rooms[room]["scale"], size=1
).tolist()
if mode.startswith(("all", "occ")):
dat["occupancy"] = poisson.rvs(rooms[room]["occ"], size=1).tolist()
if mode.startswith(("all", "co")):
dat["co2"] = gamma.rvs(rooms[room]["co"], size=1).tolist()
try:
await websocket.send(json.dumps({room: dat}))
except websockets.exceptions.ConnectionClosedOK:
print("Closing connection to", websocket.remote_address)
break
def gen_free_energy(distribution, spread=2.0, location=0.0, size=1):
"""
Generate example free energies from a specified distribution
Parameters
----------
distribution: str
the distribution from which to draw samples
size: int
number of samples to generate
spread: list or float
the spread/scale parameter of the distribution, e.g. standard deviation for gaussian
location: list of float
the center of the distribution, e.d.
Returns
-------
numpy.ndarray
samples of free energy with dimentions equal to spread and location
"""
if distribution.lower() == 'gaussian':
f_true = np.random.normal(loc=location, scale=spread, size=size)
elif distribution.lower() == 'cauchy':
from scipy.stats import cauchy
f_true = cauchy.rvs(loc=location, scale=spread, size=size)
else:
raise Exception(
'The distribution must be either "gaussain" or "cauchy".')
return f_true
def rvs(cls,
alpha: float,
beta: float,
gamma=1.,
delta=0.,
pm=1,
size: Numeric = 1):
cls._check_parameters(alpha, beta, gamma, pm)
delta, gamma = cls._parameterize(alpha, delta, gamma, beta, pm)
if np.isclose(alpha, 1) and np.isclose(beta, 0):
z = cauchy.rvs(size=size)
else:
theta = np.pi * (np.random.uniform(size=size) - 0.5)
w = np.random.standard_exponential(size)
bt = beta * tanpi2(alpha)
t0 = min(max(-PI2, np.arctan(bt) / alpha), PI2)
at = alpha * (theta + t0)
c = (1 + bt**2)**(1 / (2 * alpha))
z = (c * np.sin(at) * (np.cos(theta)**(-1 / alpha)) *
((np.cos(theta - at) / w)**((1 - alpha) / alpha)) - bt)
return z * gamma + delta
def mod_cauchy(loc,scale,size,cut):
samples=cauchy.rvs(loc=loc,scale=scale,size=3*size)
samples=samples[abs(samples)<cut]
if len(samples)>=size:
samples=samples[:size]
else:
samples=mod_cauchy(loc,scale,size,cut) ##Only added for the very unlikely case that there are not enough samples after the cut.
return samples
def distributions(size):
n = norminvgauss.rvs(1, 0, size=size)
l = laplace.rvs(size=size, scale=1 / m.sqrt(2), loc=0)
p = poisson.rvs(10, size=size)
c = cauchy.rvs(size=size)
u = uniform.rvs(size=size, loc=-m.sqrt(3), scale=2 * m.sqrt(3))
counted_distributions = [n, l, p, c, u]
return counted_distributions
def mod_cauchy(loc,scale,size,cut):
samples=cauchy.rvs(loc=loc,scale=scale,size=3*size)
samples=samples[abs(samples)<cut]
if len(samples)>=size:
samples=samples[:size]
else:
samples=mod_cauchy(loc,scale,size,cut) ##Only added for the very unlikely case that there are not enough samples after the cut.
return samples
def generate_panel(N, T, k, q, d, lam):
beta = []
rho = []
# cov_rho = []
for l in range(k):
beta.append(generate_beta(d - 1))
temp_rho = generate_rho(q, lam)
rho.append(temp_rho)
panel1 = np.array([[[1.0 for fea in range(d)] for t in range(T)]
for i in range(N)])
panel2 = np.array([[[1.0 for fea in range(d)] for t in range(T)]
for i in range(N)])
mean = [0 for i in range(d - 2)]
cov = np.identity(d - 2)
# mean vector of each individual
mean_individual = []
cluster = np.random.randint(0, k, N)
for i in range(N):
temp = np.random.multivariate_normal(mean, cov, 1)[0]
temp = temp / np.sqrt(square_sum(temp)) * np.random.uniform(0, 5)
mean_individual.append(temp)
#for i in range(N):
# l2 = square_sum(mean_individual[i])
# norm = random.uniform(0, 10)
# for dim in range(d-1):
# mean_individual[i][dim] *= math.sqrt(norm / l2)
# model of each individual
mean_error = [0 for i in range(T)]
for i in range(N):
# Gaussian error
mean_i = np.random.multivariate_normal(
mean_individual[i], cov * square_sum(mean_individual[i]), T)
error_i = []
error_basic = np.random.normal(0, 1, T)
for t in range(T):
error_i.append(error_basic[t])
for tt in range(min(t - 1, q)):
error_i[t] += rho[cluster[i]][tt] * error_i[t - tt - 1]
for t in range(T):
panel1[i][t][0:-2] = mean_i[t]
panel1[i][t][d - 1] = np.dot(panel1[i][t][0:d - 1],
beta[cluster[i]]) + error_i[t]
# Cauchy error
error_i = []
error_basic = cauchy.rvs(
0, 2, T
) # errors drawn from Cauchy distribution with x0 = 0 and gamma = 2
for t in range(T):
error_i.append(error_basic[t])
for tt in range(min(t - 1, q)):
error_i[t] += rho[cluster[i]][tt] * error_i[t - tt - 1]
for t in range(T):
panel2[i][t][0:-2] = mean_i[t]
panel2[i][t][d - 1] = np.dot(panel2[i][t][0:d - 1],
beta[cluster[i]]) + error_i[t]
return panel1, panel2
def _generate_uniform_planes(self, size, input_dim):
""" Generate uniformly distributed hyperplanes and return it as a 2D
numpy array.
"""
if (self.lazy):
self.uniform_planes = cauchy.rvs(
size=[size, self.hash_size, self.points.shape[1]])
else:
self.uniform_planes = np.random.randn(size, self.hash_size,
input_dim)
def cauchyFunc():
for i in range(len(size)):
n = size[i]
fig, ax = plt.subplots(1, 1)
ax.set_title("Распределение Коши, n = " + str(n))
x = np.linspace(cauchy.ppf(0.01), cauchy.ppf(0.99), 100)
ax.plot(x, cauchy.pdf(x), 'b-', lw=5, alpha=0.6)
r = cauchy.rvs(size=n)
ax.hist(r, density=True, histtype='stepfilled', alpha=0.2)
plt.show()
def generate_signals(self, sig, noise_type = 4):
'''
generate noises for given sig and noise type
'''
# TODO: add different noises
if noise_type == 0: #gaussian
noise = np.random.normal(size=sig.shape)
elif noise_type == 1: # cauchy
from scipy.stats import cauchy
noise = cauchy.rvs(size=sig.shape)
elif noise_type == 2: # poisson
noise = np.random.poisson(size=sig.shape)
elif noise_type == 3: # speckle: Multiplicative noise using out = image + n*image,where n is gaussion noise with specified mean & variance.
noise = np.random.randn(size=sig.shape)*sig
else:# mix of 0 & 1
from scipy.stats import cauchy
noise = np.random.normal(size=sig.shape) + cauchy.rvs(size=sig.shape)
return noise
def generate_data(room: T.Dict[str, float]) -> T.Dict[str, T.Union[str, float]]:
"""
generate simulated data
"""
return {
"time": datetime.now().isoformat(),
"temperature": cauchy.rvs(loc=room["loc"], scale=room["scale"], size=1).tolist(),
"occupancy": poisson.rvs(room["occ"], size=1).tolist(),
"co2": gamma.rvs(room["co"], size=1).tolist(),
}
def get_system_noise(self):
"""v_t vector"""
data_noise = np.zeros((self.ydim, self.PARTICLES_NUM),
dtype=np.float64)
for i in xrange(self.ydim):
data_noise[i, :] = cauchy.rvs(loc=[0] * self.PARTICLES_NUM,
scale=np.power(
10, self.particles[self.ydim]),
size=self.PARTICLES_NUM)
data_noise[data_noise == float("-inf")] = -1e308
data_noise[data_noise == float("inf")] = 1e308
parameter_noises = np.zeros((self.pdim, self.PARTICLES_NUM),
dtype=np.float64)
for i in xrange(self.pdim):
parameter_noises[i, :] = cauchy.rvs(
loc=0,
scale=self.nois_sh_parameters[i],
size=self.PARTICLES_NUM)
return np.vstack((data_noise, parameter_noises))
def cauchyNumbers():
for size in sizes:
fig, ax = plt.subplots(1, 1)
ax.hist(cauchy.rvs(size=size), histtype='stepfilled', alpha=0.5, color='blue', density=True)
x = np.linspace(cauchy().ppf(0.01), cauchy().ppf(0.99), 100)
ax.plot(x, cauchy().pdf(x), '-')
ax.set_title('CauchyNumbers n = ' + str(size))
ax.set_xlabel('CauchyNumbers')
ax.set_ylabel('density')
plt.grid()
plt.show()
return
def random_growth(self):
""" Cauchy distribution with barriers at -30 and 15 percent.
"""
growth = cauchy.rvs(size=1,
loc=self.config['growth_mu'],
scale=self.config['growth_sigma'])[0]
if growth < -0.30:
return -0.30
elif growth > 0.15:
return 0.15
else:
return growth
def dg_cauchy(n=150,
num_groups=40,
group_size=40,
p=1600,
ro=0.5,
num_non_zero_coef_per_group=8,
num_non_zero_groups=7,
loc=0,
scale=3):
"""
Generate a dataset formed by groups of variables. All the groups have the same size.
num_non_zero_coef_per_group
num_non_zero_groups
:param n: number of observations
:param num_groups: number of groups
:param group_size: size of the groups
:param p: number of variables
:param ro: correlation between variables inside a group
:param num_non_zero_coef_per_group: controls how many significant variables we want
:param num_non_zero_groups: controls how many groups we want to store significant variables
:param loc: location parameter for cauchy error
:param scale: scale parameter for cauchy error
:return: x, y index
If num_non_zero_coef_per_group=8 and num_non_zero_groups=7 we will have 8 groups with 7 significant variables,
and num_groups-num_non_zero_coef_per_group groups with all non-significant variables
The error distribution is a student t with 3 degrees of freedom
"""
p = num_groups * group_size
group_levels = np.arange(1, (num_groups + 1), 1)
num_non_zeros_per_group = [0] * num_groups
num_non_zeros_per_group[0:num_non_zero_groups] = [
num_non_zero_coef_per_group
] * num_non_zero_groups
group_index = np.repeat(group_levels, [group_size] * num_groups, axis=0)
s = np.zeros((p, p))
for level in group_levels:
s[(level - 1) * group_size:level * group_size,
(level - 1) * group_size:level * group_size] = ro
np.fill_diagonal(s, 1)
x = np.random.multivariate_normal(np.repeat(0, p), s, n)
betas = np.zeros(p)
for i in range(num_groups):
betas[(i * group_size):((i + 1) * group_size)] = np.arange(
1, group_size + 1, 1)
for i in range(num_groups):
betas[((group_levels[i] - 1) * group_size +
num_non_zeros_per_group[i]):group_levels[i] * group_size] = 0
e = cauchy.rvs(loc=loc, scale=scale, size=n)
y = np.dot(x, betas) + e
data = dict(x=x, y=y, true_beta=betas, index=group_index)
logger.debug('Function finished without errors')
return data
def selection(mu, sigma, size, distribution):
if distribution == Distribution.NORMAL:
return norm.rvs(mu, sigma, size)
elif distribution == Distribution.CAUCHY:
return cauchy.rvs(mu, sigma, size)
elif distribution == Distribution.LAPLACE:
return laplace.rvs(mu, sigma, size)
elif distribution == Distribution.POISSON:
return poisson.rvs(mu, size=size)
elif distribution == Distribution.UNIFORM:
return uniform.rvs(mu, sigma, size)
else:
return None
def make_positive_cauchy_rv(N, mean, var):
""" Makes a list of N POSITIVE random variates drawn from a cauchy dist
with given mean and var (or whatever pars define the dist).
"""
omega = []
for i in range(N):
temp = -1
while temp < 0:
temp = float(cauchy.rvs(size=1, scale=var_omega, loc=mean_omega))
omega.append(temp)
return omega
def dataGeneration(self, x1=-5, x2=5, N=100):
c = Cauchy_regression1.c
d = Cauchy_regression1.d
np.random.seed()
x = np.random.uniform(x1, x2, N)
s_rand = np.zeros(N)
for i in range(len(x)):
gamma = abs(c * x[i] + d)
s_rand[i] = cauchy.rvs(loc=0, scale=gamma, size=1)
y = self.a * x + self.b + s_rand
return np.append(x, y).reshape(2, N).transpose()
def Cauchy():
for s in size:
density = cauchy()
histogram = cauchy.rvs(size=s)
fig, ax = plt.subplots(1, 1)
ax.hist(histogram, density=True, alpha=0.6)
x = np.linspace(density.ppf(0.01), density.ppf(0.99), 100)
ax.plot(x, density.pdf(x), LINE_TYPE, lw=1.5)
ax.set_xlabel("CAUCHY")
ax.set_ylabel("DENSITY")
ax.set_title("SIZE: " + str(s))
plt.grid()
plt.show()
def make_positive_cauchy_rv(N, mean, var):
""" Makes a list of N POSITIVE random variates drawn from a cauchy dist
with given mean and var (or whatever pars define the dist).
"""
omega = []
for i in range(N):
temp = -1
while temp < 0:
temp = float(cauchy.rvs(size = 1, scale = var_omega, loc = mean_omega))
omega.append(temp)
return omega
def test_train(self): gsm = GSM(1, 10) gsm.train(laplace.rvs(size=[1, 10000]), max_iter=100, tol=-1) p = kstest(gsm.sample(10000).flatten(), laplace.cdf)[1] # test whether GSM faithfully reproduces Laplace samples self.assertTrue(p > 0.0001) gsm = GSM(1, 6) gsm.train(cauchy.rvs(size=[1, 10000]), max_iter=100, tol=-1) # test for stability of training self.assertTrue(not any(isnan(gsm.scales)))
def rvs(cls, alpha: float, beta: float, gamma=1., delta=0., pm=1, size: Numeric = 1):
cls._check_parameters(alpha, beta, gamma, pm)
delta, gamma = cls._form_parameters(alpha, delta, gamma, beta, pm)
if np.isclose(alpha, 1) and np.isclose(beta, 0):
z = cauchy.rvs(size=size)
else:
theta = np.pi * (np.random.uniform(size=size) - 0.5)
w = np.random.standard_exponential(size)
bt = beta * tanpi2(alpha)
t0 = min(max(-PI2, np.arctan(bt) / alpha), PI2)
at = alpha * (theta + t0)
c = (1 + bt ** 2) ** (1 / (2 * alpha))
z = c * np.sin(at) \
* (np.cos(theta - at) / w) ** (1 / alpha - 1) \
/ np.cos(theta) ** (1 / alpha) \
- bt
return z * gamma + delta
N = 1000
x = 4
Inf = float("inf")
# scipy.integrateでの積分
h1 = lambda t: t * norm(loc=x).pdf(t) * cauchy.pdf(t)
h2 = lambda t: norm(loc=x).pdf(t) * cauchy.pdf(t)
num = scipy.integrate.quad(h1, -Inf, Inf)[0]
den = scipy.integrate.quad(h2, -Inf, Inf)[0]
I = num / den
print("scipy.integrate:", I)
# (1) コーシー分布からサンプリングするモンテカルロ積分の収束テスト
# 分子も分母も同じサンプルを使用すると仮定
theta = cauchy.rvs(size=N)
num = theta * norm(loc=x).pdf(theta)
den = norm(loc=x).pdf(theta)
# 分母に0がくるサンプルを削除
num = num[den != 0]
den = den[den != 0]
Ndash = len(num)
y = num / den
estint = (np.cumsum(num) / np.arange(1, Ndash + 1)) / \
(np.cumsum(den) / np.arange(1, Ndash + 1))
esterr = np.sqrt(np.cumsum((y - estint) ** 2)) / np.arange(1, Ndash + 1)
plt.subplot(2, 1, 1)
plt.plot(estint, color='red', linewidth=2)
def initialize(self, X=None, method='data'):
"""
Initializes parameter values with more sensible values.
@type X: array_like
@param X: data points stored in columns
@type method: string
@param method: type of initialization ('data', 'gabor' or 'random')
"""
if self.noise:
L = self.A[:, :self.num_visibles]
if method.lower() == 'data':
# initialize features with data points
if X is not None:
if X.shape[1] < self.num_hiddens:
raise ValueError('Number of data points to small.')
else:
# whitening matrix
val, vec = eig(cov(X))
# whiten data
X_ = dot(dot(diag(1. / sqrt(val)), vec.T), X)
# sort by norm in whitened space
indices = argsort(sqrt(sum(square(X_), 0)))[::-1]
# pick 25% largest data points and normalize
X_ = X_[:, indices[:max([X.shape[1] / 4, self.num_hiddens])]]
X_ = X_ / sqrt(sum(square(X_), 0))
# pick first basis vector at random
A = X_[:, [randint(X_.shape[1])]]
for _ in range(self.num_hiddens - 1):
# pick vector with large angle to all other vectors
A = hstack([
A, X_[:, [argmin(max(abs(dot(A.T, X_)), 0))]]])
# orthogonalize and unwhiten
A = dot(sqrtmi(dot(A, A.T)), A)
A = dot(dot(vec, diag(sqrt(val))), A)
self.A = A
elif method.lower() == 'gabor':
# initialize features with Gabor filters
if self.subspaces[0].dim > 1 and not mod(self.num_hiddens, 2):
for i in range(self.num_hiddens / 2):
G = gaborf(self.num_visibles)
self.A[:, 2 * i] = real(G)
self.A[:, 2 * i + 1] = imag(G)
else:
for i in range(len(self.subspaces)):
self.A[:, i] = gaborf(self.num_visibles, complex=False)
elif method.lower() == 'random':
# initialize with Gaussian white noise
self.A = randn(num_visibles, num_hiddens)
elif method.lower() in ['laplace', 'student', 'cauchy', 'exponpow']:
if method.lower() == 'laplace':
# approximate multivariate Laplace with GSM
samples = randn(self.subspaces[0].dim, 10000)
samples = samples / sqrt(sum(square(samples), 0))
samples = laplace.rvs(size=[1, 10000]) * samples
elif method.lower() == 'student':
samples = randn(self.subspaces[0].dim, 50000)
samples = samples / sqrt(sum(square(samples), 0))
samples = t.rvs(2., size=[1, 50000]) * samples
elif method.lower() == 'exponpow':
exponent = 0.8
samples = randn(self.subspaces[0].dim, 200000)
samples = samples / sqrt(sum(square(samples), 0))
samples = gamma(1. / exponent, 1., (1, 200000))**(1. / exponent) * samples
else:
samples = randn(self.subspaces[0].dim, 100000)
samples = samples / sqrt(sum(square(samples), 0))
samples = cauchy.rvs(size=[1, 100000]) * samples
if self.noise:
# ignore first subspace
gsm = GSM(self.subspaces[1].dim, self.subspaces[1].num_scales)
gsm.train(samples, max_iter=200, tol=1e-8)
for m in self.subspaces[1:]:
m.scales = gsm.scales.copy()
else:
# approximate distribution with GSM
gsm = GSM(self.subspaces[0].dim, self.subspaces[0].num_scales)
gsm.train(samples, max_iter=200, tol=1e-8)
for m in self.subspaces:
m.scales = gsm.scales.copy()
else:
raise ValueError('Unknown initialization method \'{0}\'.'.format(method))
if self.noise:
# don't initialize noise covariance
self.A[:, :self.num_visibles] = L
def random(self,n):
if hasattr(n,'__len__'):
n = len(n)
return np.mod(cauchy.rvs(loc=self.p[-1],scale=self.p[0]/TWOPI,size=n),1)
# posterior
theta_post = theta_post_unnorm / Z
# approximate the posterior distribution
theta_mean = trapz(theta * theta_post, theta)
theta_var = trapz((theta-theta_mean)**2 * theta_post, theta)
theta_post_approx = norm(theta_mean, np.sqrt(theta_var))
# get samples from approximate posterior
theta_samples = theta_post_approx.rvs(size=N_SAMP)
# sample the posterior predictive distribution for y6
y6_samples = np.empty(N_SAMP, dtype=float)
for ith in xrange(N_SAMP):
y6_samples[ith] = cauchy.rvs(loc=theta_samples[ith], scale=1)
# plot
fig, axes = plt.subplots(1, 3)
plt.sca(axes[0])
plt.plot(theta, theta_post, label='actual')
plt.plot(theta, theta_post_approx.pdf(theta), label='approx')
plt.legend()
plt.xlabel('theta')
plt.ylabel('P(theta | y1...y5)')
plt.sca(axes[1])
plt.hist(theta_samples)
plt.xlabel('theta')
plt.sca(axes[2])
plt.hist(y6_samples)
plt.xlabel('y6')
def sample_episodes(numepisodes, physics):
episodes = []
total_events, num_reasonable_events = 0, 0
for epinum in xrange(numepisodes):
events = []
detections = []
assocs = []
# first generate all the events
numevents = poisson.rvs( physics.lambda_e * 4 * pi * physics.R ** 2
* physics.T )
for evnum in xrange(numevents):
# longitude is uniform from -180 to 180
evlon = uniform.rvs(-180, 360)
# sin(latitude) is uniform from -1 to 1
evlat = degrees(arcsin(uniform.rvs(-1, 2)))
# magnitude has an exponential distribution as per Gutenberg-Richter law
while True:
evmag = expon.rvs(physics.mu_m, physics.theta_m)
# magnitude saturates at some maximum value,
# re-sample if we exceed the max
if evmag > physics.gamma_m:
continue
else:
break
# time is uniform
evtime = uniform.rvs(0, physics.T)
event = Event(evlon, evlat, evmag, evtime)
events.append(event)
truedets = []
#print ("event mag %f" % event.mag)
# for each event generate its set of true detections
for stanum, station in enumerate(STATIONS):
dist = compute_distance((station.lon, station.lat),
(event.lon, event.lat))
sta_to_ev_az = compute_azimuth((station.lon, station.lat),
(event.lon, event.lat))
detprob = logistic(physics.mu_d0[stanum]
+ physics.mu_d1[stanum] * event.mag
+ physics.mu_d2[stanum] * dist)
#print ("stanum %d dist %f detprob %f" % (stanum, dist, detprob))
# is detected ?
if bernoulli.rvs(detprob):
dettime = laplace.rvs(event.time + compute_travel_time(dist)
+ physics.mu_t[stanum],
physics.theta_t[stanum])
# Note: the episode only has detections within the first T
# seconds. Late arriving detections will not be available.
if dettime < physics.T:
degdiff = laplace.rvs(physics.mu_z[stanum], physics.theta_z[stanum])
detaz = (sta_to_ev_az + degdiff + 360) % 360
detslow = laplace.rvs(compute_slowness(dist) + physics.mu_s[stanum],
physics.theta_s[stanum])
while True:
# resample if the detection amplitude is infinite
try:
detamp = exp(norm.rvs(physics.mu_a0[stanum]
+ physics.mu_a1[stanum] * event.mag
+ physics.mu_a2[stanum] * dist,
physics.sigma_a[stanum]))
except FloatingPointError:
continue
# disallow zero or infinite amplitudes
if detamp == 0 or isinf(detamp):
continue
break
truedets.append(len(detections))
detections.append(Detection(stanum, dettime, detaz, detslow,
detamp))
assocs.append(truedets)
total_events += 1
if len(truedets) >= 2:
num_reasonable_events += 1
# now generate the false detections
for stanum in xrange(len(STATIONS)):
numfalse = poisson.rvs(physics.lambda_f[stanum] * physics.T)
for dnum in xrange(numfalse):
dettime = uniform.rvs(0, physics.T)
detaz = uniform.rvs(0, 360)
detslow = uniform.rvs(compute_slowness(180),
compute_slowness(0) - compute_slowness(180))
while True:
# resample if the detection amplitude is infinite
try:
detamp = exp(cauchy.rvs(physics.mu_f[stanum],
physics.theta_f[stanum]))
except FloatingPointError:
continue
# disallow zero or infinite amplitudes
if detamp == 0 or isinf(detamp):
continue
break
detections.append(Detection(stanum, dettime, detaz, detslow, detamp))
episodes.append(Episode(events, detections, assocs))
print ("{:d} events generated".format(total_events))
print ("{:.1f} % events have at least two detections"
.format(100 * num_reasonable_events / total_events))
return episodes
SF = []
CR = []
F = []
p = []
u = []
alldeltaf = []
deltaf = []
for var1 in range(0, N):
r = random.randrange(0, N)
cr = rand_normal(MCR[var1], math.sqrt(0.1))
if cr > 1:
cr = 1
if cr < 0:
cr = 0
CR.append(copy.deepcopy(cr))
f = cauchy.rvs()
while True:
if f > 1:
f = 1.0
break
if f > 0:
break
f = cauchy.rvs()
# print f
F.append(copy.deepcopy(f)) #コーシー乱数発生よく分かっておらず そもそもなんでコーシー乱数？
p = random.uniform(2.0/NP, 0.2)
# generate_trial_vector(x, P, A, p, N, CR, F)
u.append(generate_trial_vector(population[var1], population, A, p, N, CR[var1], F[var1]))#current to pbest/1/bin
test_count = 0
# print len(u)