def __calc_tau__(self, beta, gamma, theta, data, verbose=False):
# using a nonlinear solver (fsolve)
# ToDo(1): Add derivative of gap (fprime)
# ToDo(2): Check if it is better to use args instead of lambda functions
# ToDo(3): Check if it is better to use equation (4) of Gilardoni2007 instead of special function G
kappa = data.CPM / data.CMR
G1223 = lambda z: mp.meijerg([[0, 1 - 1 / gamma], []], [[0], [1, -1 / gamma]], (z ** gamma) / theta)
gap = lambda tau: kappa + beta * tau[0] * G1223(tau[0])
x0 = [5.84] # from ModelPLP
tau = opt.fsolve(gap, x0, args=(), fprime=None)
if verbose:
(tau, info, flag, msg) = opt.fsolve(gap, x0, args=(), fprime=None, full_output=True)
print('> calc tau')
print(' message: %s after %d iterations.' % (msg[:-1], info['nfev']))
print(' x0 = %f' % x0[0])
print(' tau = %f' % tau[0])
print(' gap = %e' % gap(tau))
return tau[0]
def __gap_params__(self, data, beta, gamma, theta, verbose=False):
G1112A = lambda z: mp.meijerg([[1 - 1 / gamma], []], [[0], [-1 / gamma]], (z ** gamma) / theta)
G1112B = lambda z: mp.meijerg([[0], []], [[0], [1]], (z ** gamma) / theta)
G1223 = lambda z: mp.meijerg([[0, 1 - 1 / gamma], []], [[0], [-1 / gamma, 1]], (z ** gamma) / theta)
G1001 = lambda z: mp.meijerg([[], []], [[0], []], (z ** gamma) / theta)
G1334 = lambda z: mp.meijerg([[0, 1 - 1 / gamma, 1 - 1 / gamma], []], [[0], [-1 / gamma, -1 / gamma, 1]], (z ** gamma) / theta)
G1445 = lambda z: mp.meijerg([[0, 1 - 1 / gamma, 1 - 1 / gamma, 1 - 1 / gamma], []], [[0], [-1 / gamma, -1 / gamma, -1 / gamma, 1]], (z ** gamma) / theta)
# gap beta
si = 0
for Ti in data.censorTimes:
si += Ti * (1 - G1112A(Ti) / gamma)
gap_beta = -si + len(data.allFailures) / beta
# gap gamma
si = 0
for Ti in data.censorTimes:
si += Ti * (mp.ln(Ti) * G1334(Ti) - G1445(Ti) / gamma)
sij = 0
for tij in data.allFailures:
sij += (mp.ln(tij) * G1112B(tij)) / (1 - G1001(tij))
gap_gamma = (beta / gamma) * si - sij
# gap theta
si = 0
for Ti in data.censorTimes:
si += Ti * G1223(Ti)
sij = 0
for tij in data.allFailures:
sij += G1112B(tij) / (1 - G1001(tij))
gap_theta = (beta * theta / gamma) * si - theta * sij
if verbose:
print(' gap beta = %g' % gap_beta)
print(' gap gamma = %g' % gap_gamma)
print(' gap theta = %g' % gap_theta)
return np.array([gap_beta, gap_gamma, gap_theta], dtype=float)
def G1555(z): return mp.meijerg([[0,1-1/gamma,1-1/gamma,1-1/gamma,0], []], [[0], [-1/gamma,-1/gamma,-1/gamma,1]], (z ** gamma) / theta)
Tij = data.allFailures
def G1444(z): return mp.meijerg([[0,1-1/gamma,1-1/gamma,0], []], [[0], [-1/gamma,-1/gamma,1]], (z ** gamma) / theta) def G1555(z): return mp.meijerg([[0,1-1/gamma,1-1/gamma,1-1/gamma,0], []], [[0], [-1/gamma,-1/gamma,-1/gamma,1]], (z ** gamma) / theta)
def G1112B(z): return mp.meijerg([[0, 0], []], [[0], [1]], (z ** gamma) / theta) def G1111(z): return mp.meijerg([[0], []], [[0], []], (z ** gamma) / theta)
def G1333(z): return mp.meijerg([[0,1-1/gamma,0], []], [[0], [-1/gamma,1]], (z ** gamma) / theta) def G1112B(z): return mp.meijerg([[0, 0], []], [[0], [1]], (z ** gamma) / theta)
def G1333(z): return mp.meijerg([[0,1-1/gamma,0], []], [[0], [1,-1/gamma]], (z**gamma) / theta) def gap(tau): return kappa + beta * tau[0] * G1333(tau[0])