import numpy as np import scipy.optimize from autograd import jacobian from .obs import derived_observable def find_root(d, func, guess=1.0, **kwargs): r'''Finds the root of the function func(x, d) where d is an `Obs`. Parameters ----------------- d : Obs Obs passed to the function. func : object Function to be minimized. Any numpy functions have to use the autograd.numpy wrapper. Example: ```python import autograd.numpy as anp def root_func(x, d): return anp.exp(-x ** 2) - d ``` guess : float Initial guess for the minimization. Returns ------- Obs `Obs` valued root of the function. ''' root = scipy.optimize.fsolve(func, guess, d.value) # Error propagation as detailed in arXiv:1809.01289 dx = jacobian(func)(root[0], d.value) da = jacobian(lambda u, v: func(v, u))(d.value, root[0]) deriv = - da / dx res = derived_observable(lambda x, **kwargs: (x[0] + np.finfo(np.float64).eps) / (d.value + np.finfo(np.float64).eps) * root[0], [d], man_grad=[deriv]) return res