def errprob(self, E, Ei=0, thresh=2e-9, typ='thresh'):
""" calculates error probability
Parameters
----------
E : float
Legitimate Signal Energy
Ei : float
Interferer Signal Energy
thresh : float
typ : string
'thresh'
'scale': for IEEE.802.11.6 standard
'both' : both kind of decision
Returns
-------
errp : error probability
Notes
-----
See Also
--------
scipy.stats.ncf
ED.pdf
"""
self.pdf(E, Ei=Ei)
if typ == 'thresh':
self.p10 = self.pH0.sf(thresh)
self.p01 = 1 - self.pH1.sf(thresh)
errp = 0.5 * (self.p10 + self.p01)
if typ == 'scale':
ncf = st.ncf(dfn=self.order,
dfd=self.order,
scale=1,
nc=self.E / self.scale)
errp = 1 - ncf.sf(1)
if typ == 'both':
self.p10 = self.pH0.sf(thresh)
self.p01 = 1 - self.pH1.sf(thresh)
pe1 = 0.5 * (self.p10 + self.p01)
ncf = st.ncf(dfn=self.order,
dfd=self.order,
scale=1,
nc=self.E / self.scale)
pe2 = 1 - ncf.sf(1)
errp = (pe1, pe2)
return (errp)
def errprob(self,E,Ei=0,thresh=0,typ='thresh'):
""" calculates error probability
Parameters
----------
E : float
Legitimate Signal Energy
Ei : float
Interferer Signal Energy
thresh : float
typ : string
'thresh'
'scale': for IEEE.802.11.6 standard
'both' : both kind of decision
Returns
-------
errp : error probability
Notes
-----
See Also
--------
scipy.stats.ncf
ED.pdf
"""
self.pdf(E,Ei=Ei)
if typ=='thresh':
self.p10 = self.pH0.sf(thresh)
self.p01 = 1-self.pH1.sf(thresh)
errp = 0.5*(self.p10+self.p01)
if typ=='scale':
ncf = st.ncf(dfn = self.order,
dfd = self.order,
scale = 1,
nc = self.E/self.scale)
errp = 1 - ncf.sf(1)
if typ=='both':
self.p10 = self.pH0.sf(thresh)
self.p01 = 1-self.pH1.sf(thresh)
pe1 = 0.5*(self.p10+self.p01)
ncf = st.ncf(dfn=self.order,
dfd=self.order,
scale=1,
nc=self.E/self.scale)
pe2= 1 - ncf.sf(1)
errp =(pe1,pe2)
return(errp)
def amplitude_detection(A, var, p=0.95, alpha=0.05):
sigma2 = var
C_2 = A**2 / sigma2
N = 4
while True:
lmbda = (N * C_2) / 4
f2 = f(2, N - 3, 0).ppf(1 - alpha)
F = 1 - ncf(2, N - 3, lmbda).cdf(f2)
if F >= p:
break
N += 1
return N
dfn, dfd, nc = 27, 27, 0.416 mean, var, skew, kurt = ncf.stats(dfn, dfd, nc, moments='mvsk') # Display the probability density function (``pdf``): x = np.linspace(ncf.ppf(0.01, dfn, dfd, nc), ncf.ppf(0.99, dfn, dfd, nc), 100) ax.plot(x, ncf.pdf(x, dfn, dfd, nc), 'r-', lw=5, alpha=0.6, label='ncf 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 = ncf(dfn, dfd, nc) ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf') # Check accuracy of ``cdf`` and ``ppf``: vals = ncf.ppf([0.001, 0.5, 0.999], dfn, dfd, nc) np.allclose([0.001, 0.5, 0.999], ncf.cdf(vals, dfn, dfd, nc)) # True # Generate random numbers: r = ncf.rvs(dfn, dfd, nc, size=1000) # And compare the histogram: ax.hist(r, normed=True, histtype='stepfilled', alpha=0.2)
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),
}
def make_mod_pn(snr, n):
return lambda x: np.abs(
stats.ncf(n * x[0] - 1, x[0] * (n - 1), nc=(n * x[0]) *
(snr)).cdf(stats.f(n * x[0] - 1, x[0] *
(n - 1)).ppf(0.99)) - alpha)
def make_mod_p(snr):
return lambda x: np.abs(
stats.ncf(x[1] * x[0] - 1, x[0] * (x[1] - 1), nc=(x[1] * x[0]) * (snr))
.cdf(stats.f(x[1] * x[0] - 1, x[0] * (x[1] - 1)).ppf(0.99)) - alpha)
def mod_p(m, n, snr):
c = stats.f(n * m - 1, m * (n - 1)).ppf(0.99)
p = stats.ncf(n * m - 1, m * (n - 1), nc=(n * m) * (snr)).cdf(c)
return p
m = ['r2', 'r2c', 'sig2', 'mux', 'muy', 'lam_bar', 'ci_l', 'ci_h', 'cell_id']
df = pd.DataFrame(np.zeros((nunits, len(m))), columns=m)
for i in range(ys.shape[0]):
X = [ys[i, :, 1::2].values.T, ys[i, :, ::2].values.T]
l, h = lhs[i][:2]
est = rc.r2c_b(X)
df.loc[i][1:5] = est[:4]
df.loc[i][[-3, -2]] = [l, h]
df.loc[i][0] = np.corrcoef(X[0].mean(0), X[1].mean(0))[0, 1]**2
n = len(ys.coords['trial']) / 2
m = len(ys.coords['stim'])
df['lam_bar'] = np.sqrt(lam2_bar)
df['z_lam_bar'] = df['lam_bar'] / df['sig2']**0.5
fl = n * (m - 1) * ((df['lam_bar']**2) / df['sig2'])
fl1 = stats.ncf(1, m * (n - 1), fl).mean()
c = stats.f(1, m * (n - 1)).ppf(0.999)
df['logsf_f'] = stats.f(1, m * (n - 1)).logsf(fl1) / np.log(10)
df['cell_id'] = snr.coords['w_lab'].values.astype('str')
#df.to_csv('./figs/fig_data/apc_4_trial_stats_pymc3.csv')
plt.scatter(((c / fl)), df['r2'])
plt.semilogx()
plt.xlim(1e-3, 1)
#%%
stats.ncf(1, m * (n - 1), fl).logcdf(c)
#%%
from scipy.io import loadmat
ecc = loadmat('./data/yas_inv/ecc_yas_80.mat')['ecc'].squeeze()
dia = ecc * .625 + 40
dia = dia / 39