def plotFilteredDataEnvelope(noisy_signal, filtData):
filtDataEnvelope = np.abs(hilbert(filtData))
noisy_signal_envelope = np.abs(hilbert(noisy_signal))
tscale = 1.0E9
f, axarr = plt.subplots(3)
axarr[0].plot(t*tscale, noisy_signal)
axarr[0].plot(t*tscale, noisy_signal_envelope)
axarr[0].set_xlabel("Time (ns)")
axarr[0].set_ylabel("Voltage (noise units)")
axarr[1].plot(t*tscale, filtData)
axarr[1].plot(t*tscale, filtDataEnvelope)
axarr[1].set_xlabel("Time (ns)")
axarr[1].set_ylabel("Voltage (noise units)")
rv=rice(3.6)
x = np.linspace(rv.ppf(0.01), rv.ppf(0.99), 100)
axarr[2].hist(filtDataEnvelope,
normed=True, histtype='stepfilled', alpha=0.2)
axarr[2].plot(x, rv.pdf(x))
axarr[2].set_title("PDF of Signal+Noise")
axarr[2].set_xlabel("Envelope amplitude (noise units)")
axarr[2].set_ylabel("Probability")
f.tight_layout()
plt.show()
def FadingModel(self, Time=1, Graphs=False, Results=False):
"""
"""
from scipy.stats import rice
from scipy import integrate
#CALCULATING THE RICE CONTINUOUS DISTIBUTION
shape = 0.775
#MeanPowerGain = (1/Time) * integrate(pow(rice.logcdf(t, shape), 2), (t, 0, Time))
h = lambda x: pow(rice.logpdf(x, shape), 2)
MeanPowerGain, err = integrate.quad(h, 0, Time)
#PLOTING THE PROBABILITY DENSITY FUNCTION
if Graphs is True:
fig, ax = plt.subplots(1, 1)
x = linspace(rice.ppf(0.01, shape), rice.ppf(0.99, shape), 100)
ax.plot(x,
rice.pdf(x, shape),
'r-',
lw=5,
alpha=0.6,
label='Rice PDF')
rv = rice(shape)
ax.plot(x, rv.pdf(x), 'k-', lw=2, label='Frozen PDF')
r = rice.rvs(shape, size=1000)
ax.hist(r, normed=True, histtype='stepfilled', alpha=0.2)
ax.legend(loc='best', frameon=False)
#PRINTING RESULTS
if Results is True:
print("Fading - Mean Power Gain: {}".format(
(1 / Time) * MeanPowerGain))
return (1 / Time) * MeanPowerGain
def test_fit(self):
data = stats.rice(5, loc=0, scale=2).rvs(size=37)
params = self.dist.fit(data)
check_params(
(params.R, 10.100674084593422),
(params.sigma, 1.759817171541185),
(params.loc, 0),
)
def test_fit(self):
data = stats.rice(5, loc=0, scale=2).rvs(size=37)
params = self.dist.fit(data)
check_params(
(params.R, 10.100674084593422),
(params.sigma, 1.759817171541185),
(params.loc, 0),
)
def get_distro(rice_b, scale):
"""Get the distribution at given parameters with normal backup."""
return (
rice(b=rice_b, scale=scale)
if rice_b < 50.0 else
norm(loc=scale * numpy.sqrt(rice_b**2 + 1.0), scale=scale)
)
def plotSignalNoiseEnvelope( sig, gaus, noisy_signal):
signal_envelope = np.abs(hilbert(sig))
noisy_signal_envelope = np.abs(hilbert(noisy_signal))
noise_envelope = np.abs(hilbert(gaus))
# OK, make our plots. Let's scale up the time.
tscale = 1.0E9
f, axarr = plt.subplots(4)
axarr[0].plot(t*tscale, sig)
axarr[0].plot(t*tscale, signal_envelope)
axarr[0].set_title("Signal")
axarr[0].set_xlabel("Time (ns)")
axarr[0].set_ylabel("Voltage (noise units)")
axarr[1].plot(t*tscale, gaus)
axarr[1].plot(t*tscale, noise_envelope)
axarr[1].set_title("Noise")
axarr[1].set_xlabel("Time (ns)")
axarr[1].set_ylabel("Voltage (noise units)")
axarr[2].plot(t, noisy_signal)
axarr[2].plot(t, noisy_signal_envelope)
axarr[2].set_title("Signal+Noise")
axarr[2].set_xlabel("Time (ns)")
axarr[2].set_ylabel("Voltage (noise units)")
# Now plot the distribution of the data plus the analytic PDF.
# Get the x-space that makes the most sense, 100 points from 1-99%
rv = rice(amplitude/noise)
x = np.linspace(rv.ppf(0.01), rv.ppf(0.99), 100)
# Histogram the data.
axarr[3].hist(noisy_signal_envelope,
normed=True, histtype='stepfilled', alpha=0.2)
# And plot the PDF on top.
axarr[3].plot(x, rv.pdf(x))
axarr[3].set_title("PDF of Signal+Noise")
axarr[3].set_xlabel("Envelope amplitude (noise units)")
axarr[3].set_ylabel("Probability")
f.tight_layout()
plt.show()
def test_rician_high_noise(self):
# Generate rician distribution with high noise
# High noise is where the correction term counts!
sigma = 20
# Try out ours
pM = rician(self.M, self.A, sigma)
# Compare to scipy implementation
rv = rice(self.A)
pM_scipy = rv.pdf(self.M / (sigma**2))
# Should fail with no correction
self.assertFalse(np.allclose(pM, pM_scipy))
# Now correct
pM_scipy *= self.correction(sigma)
self.assertTrue(np.allclose(pM, pM_scipy))
def test_rician_low_noise(self):
# Generate rician distribution with low noise
sigma = .8 # too small will blow up the correction term for scipy rice.pdf function (see sigma**4 term in denominator)
# Try out ours
pM = rician(self.M, self.A, sigma)
# Compare to scipy implementation
rv = rice(self.A)
pM_scipy = rv.pdf(self.M / (sigma**2)) * self.correction(sigma)
# # Take a gander
# plt.plot(pM,label='Rician')
# plt.plot(pM_scipy,label='Rice (scipy)')
# plt.plot(pM - pM_scipy)
# plt.legend()
# plt.show()
self.assertTrue(np.allclose(pM, pM_scipy))
def generate_rician(image):
ssim_noise = 0
if torch.is_tensor(image):
image = image.numpy()
rician_image = np.zeros_like(image)
while ssim_noise <= 0.97 or ssim_noise >= 0.99:
b = random.uniform(0, 1)
rv = rice(b)
rician_image = rv.pdf(image)
ssim_noise = ssim(image[0],
rician_image[0],
data_range=rician_image[0].max() -
rician_image[0].min())
#print('ssim : {:.2f}'.format(ssim_noise))
return rician_image
# python extraSetGen2.py | awk 'BEGIN {srand()} !/^$/ { if (rand() <= .5) print $0 > "r.train"; else print $0 > "r.test"}'
import numpy as np
from scipy.stats import rayleigh
from scipy.stats import rice
def genSequence(dist, len):
a = 0.1
x = [0]
for i in range(0,len):
x.append(x[-1] + a*dist.rvs(size=1)[0])
return x
nExamples = 500
for i in range(0,nExamples):
seq = genSequence(rice(1),10)
for e in seq:
print('{:0.3f}'.format(e),end=' ')
print('1')
seq = genSequence(rayleigh,10)
for e in seq:
print('{:0.3f}'.format(e),end=' ')
print('0')
def all_dists():
# dists param were taken from scipy.stats official
# documentaion examples
# Total - 89
return {
"alpha":
stats.alpha(a=3.57, loc=0.0, scale=1.0),
"anglit":
stats.anglit(loc=0.0, scale=1.0),
"arcsine":
stats.arcsine(loc=0.0, scale=1.0),
"beta":
stats.beta(a=2.31, b=0.627, loc=0.0, scale=1.0),
"betaprime":
stats.betaprime(a=5, b=6, loc=0.0, scale=1.0),
"bradford":
stats.bradford(c=0.299, loc=0.0, scale=1.0),
"burr":
stats.burr(c=10.5, d=4.3, loc=0.0, scale=1.0),
"cauchy":
stats.cauchy(loc=0.0, scale=1.0),
"chi":
stats.chi(df=78, loc=0.0, scale=1.0),
"chi2":
stats.chi2(df=55, loc=0.0, scale=1.0),
"cosine":
stats.cosine(loc=0.0, scale=1.0),
"dgamma":
stats.dgamma(a=1.1, loc=0.0, scale=1.0),
"dweibull":
stats.dweibull(c=2.07, loc=0.0, scale=1.0),
"erlang":
stats.erlang(a=2, loc=0.0, scale=1.0),
"expon":
stats.expon(loc=0.0, scale=1.0),
"exponnorm":
stats.exponnorm(K=1.5, loc=0.0, scale=1.0),
"exponweib":
stats.exponweib(a=2.89, c=1.95, loc=0.0, scale=1.0),
"exponpow":
stats.exponpow(b=2.7, loc=0.0, scale=1.0),
"f":
stats.f(dfn=29, dfd=18, loc=0.0, scale=1.0),
"fatiguelife":
stats.fatiguelife(c=29, loc=0.0, scale=1.0),
"fisk":
stats.fisk(c=3.09, loc=0.0, scale=1.0),
"foldcauchy":
stats.foldcauchy(c=4.72, loc=0.0, scale=1.0),
"foldnorm":
stats.foldnorm(c=1.95, loc=0.0, scale=1.0),
# "frechet_r": stats.frechet_r(c=1.89, loc=0.0, scale=1.0),
# "frechet_l": stats.frechet_l(c=3.63, loc=0.0, scale=1.0),
"genlogistic":
stats.genlogistic(c=0.412, loc=0.0, scale=1.0),
"genpareto":
stats.genpareto(c=0.1, loc=0.0, scale=1.0),
"gennorm":
stats.gennorm(beta=1.3, loc=0.0, scale=1.0),
"genexpon":
stats.genexpon(a=9.13, b=16.2, c=3.28, loc=0.0, scale=1.0),
"genextreme":
stats.genextreme(c=-0.1, loc=0.0, scale=1.0),
"gausshyper":
stats.gausshyper(a=13.8, b=3.12, c=2.51, z=5.18, loc=0.0, scale=1.0),
"gamma":
stats.gamma(a=1.99, loc=0.0, scale=1.0),
"gengamma":
stats.gengamma(a=4.42, c=-3.12, loc=0.0, scale=1.0),
"genhalflogistic":
stats.genhalflogistic(c=0.773, loc=0.0, scale=1.0),
"gilbrat":
stats.gilbrat(loc=0.0, scale=1.0),
"gompertz":
stats.gompertz(c=0.947, loc=0.0, scale=1.0),
"gumbel_r":
stats.gumbel_r(loc=0.0, scale=1.0),
"gumbel_l":
stats.gumbel_l(loc=0.0, scale=1.0),
"halfcauchy":
stats.halfcauchy(loc=0.0, scale=1.0),
"halflogistic":
stats.halflogistic(loc=0.0, scale=1.0),
"halfnorm":
stats.halfnorm(loc=0.0, scale=1.0),
"halfgennorm":
stats.halfgennorm(beta=0.675, loc=0.0, scale=1.0),
"hypsecant":
stats.hypsecant(loc=0.0, scale=1.0),
"invgamma":
stats.invgamma(a=4.07, loc=0.0, scale=1.0),
"invgauss":
stats.invgauss(mu=0.145, loc=0.0, scale=1.0),
"invweibull":
stats.invweibull(c=10.6, loc=0.0, scale=1.0),
"johnsonsb":
stats.johnsonsb(a=4.32, b=3.18, loc=0.0, scale=1.0),
"johnsonsu":
stats.johnsonsu(a=2.55, b=2.25, loc=0.0, scale=1.0),
"ksone":
stats.ksone(n=1e03, loc=0.0, scale=1.0),
"kstwobign":
stats.kstwobign(loc=0.0, scale=1.0),
"laplace":
stats.laplace(loc=0.0, scale=1.0),
"levy":
stats.levy(loc=0.0, scale=1.0),
"levy_l":
stats.levy_l(loc=0.0, scale=1.0),
"levy_stable":
stats.levy_stable(alpha=0.357, beta=-0.675, loc=0.0, scale=1.0),
"logistic":
stats.logistic(loc=0.0, scale=1.0),
"loggamma":
stats.loggamma(c=0.414, loc=0.0, scale=1.0),
"loglaplace":
stats.loglaplace(c=3.25, loc=0.0, scale=1.0),
"lognorm":
stats.lognorm(s=0.954, loc=0.0, scale=1.0),
"lomax":
stats.lomax(c=1.88, loc=0.0, scale=1.0),
"maxwell":
stats.maxwell(loc=0.0, scale=1.0),
"mielke":
stats.mielke(k=10.4, s=3.6, loc=0.0, scale=1.0),
"nakagami":
stats.nakagami(nu=4.97, loc=0.0, scale=1.0),
"ncx2":
stats.ncx2(df=21, nc=1.06, loc=0.0, scale=1.0),
"ncf":
stats.ncf(dfn=27, dfd=27, nc=0.416, loc=0.0, scale=1.0),
"nct":
stats.nct(df=14, nc=0.24, loc=0.0, scale=1.0),
"norm":
stats.norm(loc=0.0, scale=1.0),
"pareto":
stats.pareto(b=2.62, loc=0.0, scale=1.0),
"pearson3":
stats.pearson3(skew=0.1, loc=0.0, scale=1.0),
"powerlaw":
stats.powerlaw(a=1.66, loc=0.0, scale=1.0),
"powerlognorm":
stats.powerlognorm(c=2.14, s=0.446, loc=0.0, scale=1.0),
"powernorm":
stats.powernorm(c=4.45, loc=0.0, scale=1.0),
"rdist":
stats.rdist(c=0.9, loc=0.0, scale=1.0),
"reciprocal":
stats.reciprocal(a=0.00623, b=1.01, loc=0.0, scale=1.0),
"rayleigh":
stats.rayleigh(loc=0.0, scale=1.0),
"rice":
stats.rice(b=0.775, loc=0.0, scale=1.0),
"recipinvgauss":
stats.recipinvgauss(mu=0.63, loc=0.0, scale=1.0),
"semicircular":
stats.semicircular(loc=0.0, scale=1.0),
"t":
stats.t(df=2.74, loc=0.0, scale=1.0),
"triang":
stats.triang(c=0.158, loc=0.0, scale=1.0),
"truncexpon":
stats.truncexpon(b=4.69, loc=0.0, scale=1.0),
"truncnorm":
stats.truncnorm(a=0.1, b=2, loc=0.0, scale=1.0),
"tukeylambda":
stats.tukeylambda(lam=3.13, loc=0.0, scale=1.0),
"uniform":
stats.uniform(loc=0.0, scale=1.0),
"vonmises":
stats.vonmises(kappa=3.99, loc=0.0, scale=1.0),
"vonmises_line":
stats.vonmises_line(kappa=3.99, loc=0.0, scale=1.0),
"wald":
stats.wald(loc=0.0, scale=1.0),
"weibull_min":
stats.weibull_min(c=1.79, loc=0.0, scale=1.0),
"weibull_max":
stats.weibull_max(c=2.87, loc=0.0, scale=1.0),
"wrapcauchy":
stats.wrapcauchy(c=0.0311, loc=0.0, scale=1.0),
}
b = 0.775 mean, var, skew, kurt = rice.stats(b, moments='mvsk') # Display the probability density function (``pdf``): x = np.linspace(rice.ppf(0.01, b), rice.ppf(0.99, b), 100) ax.plot(x, rice.pdf(x, b), 'r-', lw=5, alpha=0.6, label='rice 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 = rice(b) ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf') # Check accuracy of ``cdf`` and ``ppf``: vals = rice.ppf([0.001, 0.5, 0.999], b) np.allclose([0.001, 0.5, 0.999], rice.cdf(vals, b)) # True # Generate random numbers: r = rice.rvs(b, size=1000) # And compare the histogram: ax.hist(r, density=True, histtype='stepfilled', alpha=0.2)
def rice_from_error_bars(value, abs_plus_error, abs_minus_error):
"""Return a Rice distribution reproducing the given mode & standard dev."""
def get_distro(rice_b, scale):
"""Get the distribution at given parameters with normal backup."""
return (
rice(b=rice_b, scale=scale)
if rice_b < 50.0 else
norm(loc=scale * numpy.sqrt(rice_b**2 + 1.0), scale=scale)
)
def lower_diff(rice_b, scale):
"""Return the error of quantile of value - abs_minus_error."""
return (
get_distro(rice_b, scale).cdf(value - abs_minus_error)
-
norm.cdf(-1.0)
)
def upper_diff(scale, rice_b):
"""Return the error of quantile of value + abs_plus_error."""
return (
get_distro(rice_b, scale).cdf(value + abs_plus_error)
-
norm.cdf(1.0)
)
def find_b(scale):
"""Return the b parameter that matches the lower bound given scale."""
b_min = 0.0
b_min_lower_diff = lower_diff(b_min, scale)
if abs(b_min_lower_diff) < 1e-8:
return b_min
_logger.debug('b_min_lower_diff(%s) = %s',
repr(scale),
repr(b_min_lower_diff))
assert b_min_lower_diff >= 0
b_max = (value + abs_plus_error) / scale
while lower_diff(b_max, scale) > 0:
b_max *= 10.0
solution = root_scalar(f=lower_diff,
args=(scale,),
bracket=(b_min, b_max))
assert solution.converged
return solution.root
def scale_equation(scale):
"""The equation to solve in order to find the scale."""
return upper_diff(scale, find_b(scale))
def find_scale():
"""Return the scale that matches the upper bound at b matching lower."""
scale_max = (value - abs_minus_error) / rice.ppf(norm.cdf(-1.0), b=0)
if scale_max <= 0 or scale_equation(scale_max) > 0:
return None
scale_min = 0.1 * min(abs_minus_error, abs_plus_error)
while scale_equation(scale_min) < 0:
scale_max = scale_min
scale_min /= 10.0
solution = root_scalar(f=scale_equation,
bracket=(scale_min, scale_max))
assert solution.converged
return solution.root
scale = find_scale()
if scale is None:
_logger.warning(
'Lower and upper limits of %s and %s cannot be matched to 16-th '
'and 84-th percentiles of a Rice distribution. Matching upper '
'limit and assuming b=0',
repr(value - abs_minus_error),
repr(value + abs_plus_error)
)
return rice(
b=0.0,
scale=((value + abs_plus_error) / rice.ppf(norm.cdf(1.0), b=0))
)
rice_b = find_b(scale)
return rice(b=rice_b, scale=scale)
