pyerrors.roots

 0import numpy as np
 1import scipy.optimize
 2from autograd import jacobian
 3from .obs import derived_observable
 4
 5
 6def find_root(d, func, guess=1.0, **kwargs):
 7    r'''Finds the root of the function func(x, d) where d is an `Obs`.
 8
 9    Parameters
10    -----------------
11    d : Obs
12        Obs passed to the function.
13    func : object
14        Function to be minimized. Any numpy functions have to use the autograd.numpy wrapper.
15        Example:
16        ```python
17        import autograd.numpy as anp
18        def root_func(x, d):
19            return anp.exp(-x ** 2) - d
20        ```
21    guess : float
22        Initial guess for the minimization.
23
24    Returns
25    -------
26    Obs
27        `Obs` valued root of the function.
28    '''
29    root = scipy.optimize.fsolve(func, guess, d.value)
30
31    # Error propagation as detailed in arXiv:1809.01289
32    dx = jacobian(func)(root[0], d.value)
33    try:
34        da = jacobian(lambda u, v: func(v, u))(d.value, root[0])
35    except TypeError:
36        raise Exception("It is required to use autograd.numpy instead of numpy within root functions, see the documentation for details.") from None
37    deriv = - da / dx
38
39    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])
40    return res

 7def find_root(d, func, guess=1.0, **kwargs):
 8    r'''Finds the root of the function func(x, d) where d is an `Obs`.
 9
10    Parameters
11    -----------------
12    d : Obs
13        Obs passed to the function.
14    func : object
15        Function to be minimized. Any numpy functions have to use the autograd.numpy wrapper.
16        Example:
17        ```python
18        import autograd.numpy as anp
19        def root_func(x, d):
20            return anp.exp(-x ** 2) - d
21        ```
22    guess : float
23        Initial guess for the minimization.
24
25    Returns
26    -------
27    Obs
28        `Obs` valued root of the function.
29    '''
30    root = scipy.optimize.fsolve(func, guess, d.value)
31
32    # Error propagation as detailed in arXiv:1809.01289
33    dx = jacobian(func)(root[0], d.value)
34    try:
35        da = jacobian(lambda u, v: func(v, u))(d.value, root[0])
36    except TypeError:
37        raise Exception("It is required to use autograd.numpy instead of numpy within root functions, see the documentation for details.") from None
38    deriv = - da / dx
39
40    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])
41    return res