pyerrors.roots
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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], [d], man_grad=[deriv]) res._value = root[0] return res
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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], [d], man_grad=[deriv]) res._value = root[0] return res
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.