def normalize_prime(self, cache=dict(), return_num_iterations=False):
"""
Returns the derivative of the normalization factor with respect
to kappa and beta.
"""
(k, b) = (self.kappa, self.beta)
if not (k, b) in cache:
G = gamma_fun
I = modified_bessel_2ndkind
dIdk = lambda v, z: modified_bessel_2ndkind_derivative(v, z, 1)
(dcdk, dcdb) = (0.0, 0.0)
j = 0
if b == 0:
dcdk = (G(j + 0.5) / G(j + 1) *
((-0.5 * j - 0.125) * k**(-2 * j - 1.5)) *
I(2 * j + 0.5, k))
dcdk += (G(j + 0.5) / G(j + 1) * (0.5 * k)**(-2 * j - 0.5) *
dIdk(2 * j + 0.5, k))
dcdb = 0.0
else:
while True:
dk = ((-1 * j - 0.25) * np.exp(
np.log(b) * 2 * j + np.og(0.5 * k) * (-2 * j - 1.5)) *
I(2 * j + 0.5, k))
dk += np.exp(
np.log(b) * 2 * j + np.log(0.5 * k) *
(-2 * j - 0.5)) * dIdk(2 * j + 0.5, k)
dk /= G(j + 1)
dk *= G(j + 0.5)
db = (2 * j * np.exp(
np.log(b) * (2 * j - 1) + np.log(0.5 * k) *
(-2 * j - 0.5)) * I(2 * j + 0.5, k))
db /= G(j + 1)
db *= G(j + 0.5)
dcdk += dk
dcdb += db
j += 1
if (abs(dk) < abs(dcdk) * 1e-12
and abs(db) < abs(dcdb) * 1e-12 and j > 5):
break
# print("dc", dcdk, dcdb, "(", k, b)
cache[k, b] = 2 * np.pi * np.array([dcdk, dcdb])
if return_num_iterations:
return (cache[k, b], j)
else:
return cache[k, b]
def normalize_prime(self, cache=dict(), return_num_iterations=False):
"""
Returns the derivative of the normalization factor with respect to kappa and beta.
"""
k, b = self.kappa, self.beta
if not (k, b) in cache:
G = gamma_fun
I = modified_bessel_2ndkind
dIdk = lambda v, z: modified_bessel_2ndkind_derivative(v, z, 1)
dcdk, dcdb = 0.0, 0.0
j = 0
if b == 0:
dcdk = ((G(j + 0.5) / G(j + 1)) * ((-0.5 * j - 0.125) *
(k)**(-2 * j - 1.5)) *
(I(2 * j + 0.5, k)))
dcdk += ((G(j + 0.5) / G(j + 1)) *
((0.5 * k)**(-2 * j - 0.5)) * (dIdk(2 * j + 0.5, k)))
dcdb = 0.0
else:
while True:
dk = ((-1 * j - 0.25) *
exp(log(b) * 2 * j + log(0.5 * k) *
(-2 * j - 1.5)) * I(2 * j + 0.5, k))
dk += (exp(log(b) * 2 * j + log(0.5 * k) *
(-2 * j - 0.5)) * dIdk(2 * j + 0.5, k))
dk /= G(j + 1)
dk *= G(j + 0.5)
db = (2 * j * exp(
log(b) * (2 * j - 1) + log(0.5 * k) * (-2 * j - 0.5)) *
I(2 * j + 0.5, k))
db /= G(j + 1)
db *= G(j + 0.5)
dcdk += dk
dcdb += db
j += 1
if abs(dk) < abs(dcdk) * 1E-12 and abs(
db) < abs(dcdb) * 1E-12 and j > 5:
break
# print "dc", dcdk, dcdb, "(", k, b
cache[k, b] = 2 * pi * array([dcdk, dcdb])
if return_num_iterations:
return cache[k, b], j
else:
return cache[k, b]
def normalize_prime(self, cache=dict(), return_num_iterations=False):
"""
Returns the derivative of the normalization factor with respect to kappa and beta.
"""
k, b = self.kappa, self.beta
if not (k, b) in cache:
G = gamma_fun
I = modified_bessel_2ndkind
dIdk = lambda v, z : modified_bessel_2ndkind_derivative(v, z, 1)
dcdk, dcdb = 0.0, 0.0
j = 0
if b == 0:
dcdk = (
( G(j+0.5)/G(j+1) )*
( (-0.5*j-0.125)*(k)**(-2*j-1.5) )*
( I(2*j+0.5, k) )
)
dcdk += (
( G(j+0.5)/G(j+1) )*
( (0.5*k)**(-2*j-0.5) )*
( dIdk(2*j+0.5, k) )
)
dcdb = 0.0
else:
while True:
dk = (
(-1*j-0.25)*exp(
log(b)*2*j +
log(0.5*k)*(-2*j-1.5)
)*I(2*j+0.5, k)
)
dk += (
exp(
log(b)*2*j +
log(0.5*k)*(-2*j-0.5)
)*dIdk(2*j+0.5, k)
)
dk /= G(j+1)
dk *= G(j+0.5)
db = (
2*j*exp(
log(b)*(2*j-1) +
log(0.5*k)*(-2*j-0.5)
) * I(2*j+0.5, k)
)
db /= G(j+1)
db *= G(j+0.5)
dcdk += dk
dcdb += db
j += 1
if abs(dk) < abs(dcdk)*1E-12 and abs(db) < abs(dcdb)*1E-12 and j > 5:
break
# print "dc", dcdk, dcdb, "(", k, b
cache[k, b] = 2*pi*array([dcdk, dcdb])
if return_num_iterations:
return cache[k, b], j
else:
return cache[k, b]