def __init__(self, a, b, U_0, U_L, eps=0):
self.a, self.b = np.asarray(a), np.asarray(b)
assert len(a) == len(b)-1, 'a and b do not have compatible lengths'
self.eps = eps # smoothing parameter for smoothed a
self.U_0, self.U_L = U_0, U_L
# Smoothing parameter must be less than half the smallest material
if eps > 0:
assert eps < 0.5*(self.b[1:] - self.b[:-1]).min(), 'too large eps'
a_data = [[bi, ai] for bi, ai in zip(self.b, self.a)]
domain = [b[0], b[-1]]
self.a_func = PiecewiseConstant(domain, a_data, eps)
# inv_a = 1/a is needed in formulas
inv_a_data = [[bi, 1./ai] for bi, ai in zip(self.b, self.a)]
self.inv_a_func = PiecewiseConstant(domain, inv_a_data, eps)
self.integral_of_inv_a_func = \
IntegratedPiecewiseConstant(domain, inv_a_data, eps)
# Denominator in the exact formula is constant
self.inv_a_0L = self.integral_of_inv_a_func(b[-1])
