#Math UBC / Numerical Differentiation

import numpy as np
import matplotlib.pyplot as plt
#%matplotlib online

def derivative(f, a, method, h):
    """
    Compute the difference formula for f'(a) with step h.

     Parameters
    ----------
    f : function
        Vectorized function of one variable
    a : number
        Compute derivative at x = a
    method : string
        Difference formula: 'forward', 'backward' or 'central'
    h : number
        Step size in difference formula

    Returns
    -------
    float
        Difference formula:
            central: f(a+h) - f(a-h))/2h
            forward: f(a+h) - f(a))/h
            backward: f(a) - f(a-h))/h
    """
    if method == 'central':
        return (f(a+h) - f(a-h))/2*h
    elif method == 'forward':
        return (f(a+h) - f(a))/h
    elif method == 'backward':
        return (f(a) - f(a-h))/h
    else:
        raise ValueError("Method must be 'central', 'forward' or 'backward'.")

answer1 = derivative(np.exp,0,method ='central', h = 0.001)
print("Central", answer1)
answer2 = derivative(np.exp,0,method ='forward', h = 0.001)
print("Forward", answer2)
answer3 = derivative(np.exp,0,method ='backward', h = 0.001)
print("Backward", answer3)