pyerrors/pyerrors/roots.py

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import scipy.optimize
from autograd import jacobian
from .obs import derived_observable, pseudo_Obs
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def find_root(d, func, guess=1.0, **kwargs):
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r'''Finds the root of the function func(x, d) where d is an `Obs`.
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Parameters
-----------------
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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.
'''
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root = scipy.optimize.fsolve(func, guess, d.value)
# Error propagation as detailed in arXiv:1809.01289
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dx = jacobian(func)(root[0], d.value)
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da = jacobian(lambda u, v: func(v, u))(d.value, root[0])
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deriv = - da / dx
return derived_observable(lambda x, **kwargs: x[0], [pseudo_Obs(root, 0.0, d.names[0], d.shape[d.names[0]]), d], man_grad=[0, deriv])