"""
A script to compare different root-finding algorithms.

This version of the script is buggy and does not execute. It is your task
to find an fix these bugs.

The output of the script sould look like:

    Benching 1D root-finder optimizers from scipy.optimize:
                brenth:   604678 total function calls
                brentq:   594454 total function calls
                ridder:   778394 total function calls
                bisect:  2148380 total function calls
"""
from itertools import product

import numpy as np
from scipy import optimize

FUNCTIONS = (np.tan,  # Dilating map
             np.tanh, # Contracting map
             lambda x: x**3 + 1e-4*x, # Almost null gradient at the root
             lambda x: x+np.sin(2*x), # Non monotonous function
             lambda x: 1.1*x+np.sin(4*x), # Fonction with several local maxima
            )

OPTIMIZERS = (optimize.brenth, optimize.brentq, optimize.ridder,
              optimize.bisect)


def apply_optimizer(optimizer, func, a, b):
    """ Return the number of function calls given an root-finding optimizer, 
        a function and upper and lower bounds.
    """
    return optimizer(func, a, b, full_output=True)[1].function_calls,


def bench_optimizer(optimizer, param_grid):
    """ Find roots for all the functions, and upper and lower bounds
        given and return the total number of function calls.
    """
    return sum(apply_optimizer(optimizer, func, a, b)
               for func, a, b in param_grid)


def compare_optimizers(optimizers):
    """ Compare all the optimizers given on a grid of a few different
        functions all admitting a signle root in zero and a upper and
        lower bounds.
    """
    random_a = -1.3 + np.random.random(size=100)
    random_b =   .3 + np.random.random(size=100)
    param_grid = product(FUNCTIONS, random_a, random_b)
    print("Benching 1D root-finder optimizers from scipy.optimize:")
    for optimizer in OPTIMIZERS:
        print('% 20s: % 8i total function calls' % (
                    optimizer.__name__, 
                    bench_optimizer(optimizer, param_grid)
                ))


if __name__ == '__main__':
    compare_optimizers(OPTIMIZERS)