def estimate_kappa(N, ssx, scx):
if N == 0:
return 10.0**-6
elif N == 1:
return 10*math.pi
else:
rbar2 = (ssx/N)**2. + (scx/N)**2.
rbar = rbar2**.5
kappa = rbar*(2.-rbar2)/(1.-rbar2)
A_p = lambda k : bessel_1(k)/bessel_0(k)
Apk = A_p(kappa)
kappa_1 = kappa - (Apk - rbar)/(1.0-Apk**2-(1.0/kappa)*Apk)
Apk = A_p(kappa_1)
kappa = kappa_1 - (Apk - rbar)/(1.0-Apk**2-(1.0/kappa_1)*Apk)
Apk = A_p(kappa)
kappa_1 = kappa - (Apk - rbar)/(1.0-Apk**2-(1.0/kappa)*Apk)
Apk = A_p(kappa_1)
kappa = kappa_1 - (Apk - rbar)/(1.0-Apk**2-(1.0/kappa_1)*Apk)
if numpy.isnan(kappa):
return 10.0**-6
else:
return numpy.abs(kappa)
def estimate_kappa(N, ssx, scx):
if N == 0:
return 10.**-6
elif N == 1:
return 10 * pi
else:
rbar2 = (ssx / N)**2. + (scx / N)**2.
rbar = rbar2**.5
kappa = rbar * (2. - rbar2) / (1. - rbar2)
A_p = lambda k: bessel_1(k) / bessel_0(k)
Apk = A_p(kappa)
kappa_1 = kappa - (Apk - rbar) / (1. - Apk**2 - (1. / kappa) * Apk)
Apk = A_p(kappa_1)
kappa = kappa_1 - (Apk - rbar) / (1. - Apk**2 - (1. / kappa_1) * Apk)
Apk = A_p(kappa)
kappa_1 = kappa - (Apk - rbar) / (1. - Apk**2 - (1. / kappa) * Apk)
Apk = A_p(kappa_1)
kappa = kappa_1 - (Apk - rbar) / (1. - Apk**2 - (1. / kappa_1) * Apk)
if isnan(kappa):
return 10.**-6
else:
return abs(kappa)
def log_bessel_0(x):
besa = bessel_0(x)
# If bessel_0(a) is inf, then use the exponential approximation to
# prevent numerical overflow.
if isinf(besa):
I0 = x - .5 * log(2 * pi * x)
else:
I0 = log(besa)
return I0
def log_bessel_0(x):
besa = bessel_0(x)
# if bessel_0(a) is inf, then use the eponential approximation to
# prevent numericala overflow
if math.isinf(besa):
I0 = x - .5*log(2*math.pi*x)
else:
I0 = log(besa)
return I0
