Golden_section_search

def golden_search(bracket, t, y, max_steps=100, tolerance=1e-4):
     """Find the maximum of the series of data using golden search algorithm 
    
    :Input:
     - *bracket* (list) - a bracket in which the maximum lies
     - *y* (list) - set of y values
     - *t* (list) - set of t values
     - *max_step* (int) - maximum number of steps allowed
     - *tolerance* (float) - Stopping tolerance for iteration
     
    :Output:
    If the iteration was successful the return values are:
     - *t_star* (float) - where the maximum occurs.
     
    """

    phi = (numpy.sqrt(5.0) - 1.0) / 2.0
    x= [bracket[0],None,None,bracket[1]]
    x[1] = x[3] - phi * (x[3] - x[0])
    x[2] = x[0] + phi * (x[3] - x[0])

    for n in xrange(1, max_steps + 1):
        f_1 = linear_eval(t,y,x[1])
        f_2 = linear_eval(t,y,x[2])

        if f_1 > f_2:
            x[3] = x[2]
            x[2] = x[1]
            x[1] = x[3] - phi * (x[3] - x[0])
        else:
            x[0] = x[1]
            x[1] = x[2]
            x[2] = x[0] + phi * (x[3] - x[0])
        
        if numpy.abs(x[3] - x[0]) < tolerance:
            break   
    t_star=(x[3] + x[0]) / 2.0
    return t_star