pyerrors/pyerrors/roots.py
2022-03-02 15:49:29 +00:00

41 lines
1.3 KiB
Python

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)
try:
da = jacobian(lambda u, v: func(v, u))(d.value, root[0])
except TypeError:
raise Exception("It is required to use autograd.numpy instead of numpy within root functions, see the documentation for details.") from None
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