def __init__(self, settings):
Trajectory.__init__(self, settings)
# setup symbolic expressions
tau, k = sp.symbols('tau, k')
gamma = self._settings["differential_order"] + 1
alpha = sp.factorial(2 * gamma + 1)
f = sp.binomial(gamma, k) * (-1) ** k * tau ** (gamma + k + 1) / (gamma + k + 1)
phi = alpha / sp.factorial(gamma) ** 2 * sp.summation(f, (k, 0, gamma))
# differentiate phi(tau), index in list corresponds to order
dphi_sym = [phi] # init with phi(tau)
for order in range(self._settings["differential_order"]):
dphi_sym.append(dphi_sym[-1].diff(tau))
# lambdify
self.dphi_num = []
for der in dphi_sym:
self.dphi_num.append(sp.lambdify(tau, der, 'numpy'))
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