def lognormal_minmax_log(kmin, kmax, mu, sigma):
'''returns the sum( 1/k*exp(-0.5*((lnk - mu)/sigma)^2),{k,kmin,kmax} ) with kmax=None for infty
'''
# print kmin,kmax,mu,sigma
mpm.mp.dps = 15
if kmax == None:
x = mpm.log(
mpm.sumem(
lambda k: 1.0 / (k - kmin + 1.0) * mpm.exp(-0.5 * (mpm.log(
(k - kmin + 1.0)) - mu) * (mpm.log(
(k - kmin + 1.0)) - mu) / sigma / sigma),
[kmin, mpm.inf]))
if mpm.im(x) != 0:
logS = float(mpm.fabs(x))
else:
logS = float(x)
else:
logS = (float(
mpm.log(
mpm.sumem(
lambda k: 1.0 / (k - kmin + 1.0) * mpm.exp(-0.5 * (mpm.log(
(k - kmin + 1.0)) - mu) * (mpm.log(
(k - kmin + 1.0)) - mu) / sigma / sigma),
[kmin, kmax]))))
return logS
def weibull_minmax(kmin, kmax, gamma, b):
'''returns the sum( k^(gamma-1)*exp(-b*(k)^gamma),{k,kmin,kmax} ) with kmax=None for infty
'''
gamma = float(gamma)
b = float(b)
mpm.mp.dps = 15
if kmax == None:
S = (float(
mpm.sumem(lambda k: k**(gamma - 1.0) * mpm.exp(-b * k**gamma),
[kmin, mpm.inf])))
else:
S = (float(
mpm.sumem(lambda k: k**(gamma - 1.0) * mpm.exp(-b * k**gamma),
[kmin, kmax])))
return S
def zeta_minmax(gamma, kmin, kmax):
'''kmax == None means kmax --> infty
'''
# gamma = gamma[0]
if gamma <= 1.0:
if kmax == None:
print('ERROR: Series does not converge!!!')
C = 0
else:
mpm.dps = 25
# print(gamma,kmin,kmax,'huhu')
C = (float(mpm.sumem(lambda k: k**(-gamma), [kmin, kmax])))
else:
# print(kmax)
# print(type(kmax))
# print(kmax==None)
# print('')
if isinstance(kmax, (list, np.ndarray)):
C = zeta(gamma, kmin) - zeta(gamma, kmax)
elif kmax == None:
C = zeta(gamma, kmin)
else:
C = zeta(gamma, kmin) - zeta(gamma, kmax)
# print(C)
return C
def lognormal_minmax(kmin, kmax, mu, sigma):
'''returns the sum( 1/sqrt(2*pi*sigma^2)/k*exp(-0.5*((lnk - mu)/sigma)^2),{k,kmin,kmax} ) with kmax=None for infty
'''
mpm.mp.dps = 15
if kmax == None:
S = (float(
mpm.sumem(
lambda k: 1.0 / (k - kmin + 1.0) * mpm.exp(-0.5 * (mpm.log(
(k - kmin + 1.0)) - mu) * (mpm.log(
(k - kmin + 1.0)) - mu) / sigma / sigma),
[kmin, mpm.inf])))
else:
S = (float(
mpm.sumem(
lambda k: 1.0 / (k - kmin + 1.0) * mpm.exp(-0.5 * (mpm.log(
(k - kmin + 1.0)) - mu) * (mpm.log(
(k - kmin + 1.0)) - mu) / sigma / sigma),
[kmin, kmax])))
return S
def weibull_minmax_log(kmin, kmax, gamma, b):
'''returns the sum( k^(gamma-1)*exp(-b*(k)^gamma),{k,kmin,kmax} ) with kmax=None for infty
'''
gamma = float(gamma)
b = float(b)
mpm.mp.dps = 15
if kmax == None:
x = mpm.sumem(lambda k: k**(gamma - 1.0) * mpm.exp(-b * k**gamma),
[kmin, mpm.inf])
if mpm.im(x) != 0:
logS = float(mpm.fabs(x))
else:
logS = float(x)
else:
logS = float(
mpm.log(
mpm.sumem(lambda k: k**(gamma - 1.0) * mpm.exp(-b * k**gamma),
[kmin, kmax])))
return logS