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41 lines
1.3 KiB
Python
41 lines
1.3 KiB
Python
import numpy as np
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import scipy.optimize
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from autograd import jacobian
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from .obs import derived_observable
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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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-----------------
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d : Obs
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Obs passed to the function.
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func : object
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Function to be minimized. Any numpy functions have to use the autograd.numpy wrapper.
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Example:
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```python
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import autograd.numpy as anp
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def root_func(x, d):
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return anp.exp(-x ** 2) - d
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```
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guess : float
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Initial guess for the minimization.
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Returns
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-------
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Obs
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`Obs` valued root of the function.
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'''
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root = scipy.optimize.fsolve(func, guess, d.value)
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# Error propagation as detailed in arXiv:1809.01289
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dx = jacobian(func)(root[0], d.value)
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try:
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da = jacobian(lambda u, v: func(v, u))(d.value, root[0])
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except TypeError:
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raise Exception("It is required to use autograd.numpy instead of numpy within root functions, see the documentation for details.") from None
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deriv = - da / dx
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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])
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return res
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