def memoryFunctionZ(self):
poles = self.poles()
cpoles = [p.conjugate() for p in poles]
coeff0 = conjugate(self.coeff[0])
beta = self.order * [0]
sum = 0.
for i in range(self.order):
pole = poles[i]
prod = N.Complex(self.variance, 0.)
for j in range(i):
prod *= (pole - poles[j])
for j in range(i + 1, self.order):
prod *= (pole - poles[j])
for j in range(self.order):
prod *= (pole - N.Complex(1., 0.) / cpoles[j])
beta[i] = -((pole**(self.order - 1)) * self.sigsq / coeff0) / prod
sum += beta[i]
for i in range(self.order):
beta[i] /= sum
sum = 0.
for i in range(self.order):
sum += RationalFunction([beta[i]], [-poles[i], 1.])
mz = (1. / sum + Polynomial([1., -1.])) / self.delta_t**2
if not isComplex(self.coeff[0]):
mz.numerator.coeff = [c.real for c in mz.numerator.coeff]
mz.denominator.coeff = [c.real for c in mz.denominator.coeff]
return mz
def __init__(self, model, precision=0):
self.precision = precision
self.order = model.order
self.delta_t = model.delta_t
if model.coeff.typecode() == N.Complex64:
self.coeff = [
N.Complex(mpf(x.real, precision), mpf(x.imag, precision))
for x in model.coeff
]
else:
self.coeff = [mpf(x, precision) for x in model.coeff]
self.sigsq = mpf(model.sigsq, precision)
self.sigma = mpf(model.sigma, precision)
self.variance = mpf(model.variance, precision)
self._poles = None
