bisect_example.py

import numpy as np
from numba import jit

def root_func(x):
    return x**4 - 2*x**2 - x - 3

def compile_specialized_bisect(f):
    """
    Returns a compiled bisection implementation for ``f``.
    """

    def python_bisect(a, b, tol, mxiter):
        """
        Beautiful Docstring ...

        Parameters
        ----------
        a : scalar(int)
            An initial guess
        b : scalar(int)
            An initial guess
        tol : scalar(float)
            The convergence tolerance
        mxiter : scalar(int)
            Max number of iterations to allow

        Note: f(a) should be less than 0 and f(b) should be greater than 0.
              I removed the checks to simplify code.

        """
        its = 0
        fa = jit_root_func(a)
        fb = jit_root_func(b)

        c = (a+b)/2.
        fc = jit_root_func(c)

        while abs(fc)>tol and its<mxiter:

            its = its + 1

            if fa*fc < 0:
                b = c
                fb = fc

            else:
                a = c
                fa = fc

            c = (a+b)/2.
            fc = jit_root_func(c)

        return c

    # Have to give explicit type signature for root function to be able
    # to call this function from another nopython function
    jit_root_func = jit('float64(float64)', nopython=True)(root_func)
    return jit(nopython=True)(python_bisect)

jit_bisect_root_func = compile_specialized_bisect(root_func)

print jit_bisect_root_func(-.5, 50., 1e-8, 500)