An implementation of the Euler method for approximating function returns

euler.py

# Tom A. Thorogood - 2013 - github.com/tomthorogood
#
# This software is free to use, modify, and distribute as you wish. It is intended for educational purposes only, and is 
# provided without a guarantee of functionality or warranty of any sort. Usage is solely at your own risk.
#
# The Euler provides a method to estimate the value of a function (f) given an input value (x).
#
# The class requires the following:
# 1) An equation with two variables (x and y)
# 2) A known x, and known y value
# 3) An x value for which a y value is desired
# 4) A degree of precision (smaller values are more precise)
#
#
# The class is stateful, and can be interacted with and examined stepwise:
#
# e.step()
# e.x         # returns the last used x value
# e.y         # returns the last estimated y value
# e.f_prime   # returns the last estimated value of the derivative of f(x) at value x
# e.num_steps # returns the number of steps elapsed
#
# ===================================================
# BASIC USAGE:
# 
# from euler import Euler
# 
# def diff(x,y): return (2*x) + (3*y**2)
# e = Euler(
#     differential = diff,
#     known_x = -3,
#     known_y = 1,
#     goal = -1,
#     h = 0.25
# )
#
# e.run()
# [returns -.862823900]
# ====================================================
#
# You do not need to pass in the sign of 'h'. The class will determine the sign of h based on known_x and goal.
# If you do pass in the sign of h, only the absolute value will be stored, so it also will not hurt anything.
#
# You can use a combination of step-wise and automatic processing:
#
# e.step() #advance the calculation one step
# e.step() #advance the calculation one step
# e.run()  #complete the calculation through to the end

class Euler(object):
    def __init__(self, differential, known_x, known_y, goal, h = 1): 
        self.differential = differential
        self.goal = float(goal)
        self.h = float(abs(h))
        self.x = float(known_x)
        self.y = float(known_y)
        self.slope = self.differential(self.x, self.y)
        self.direction = self.step_increase
        self.num_steps = 0 

        if self.goal < self.x:
            self.h = -self.h
            self.direction = self.step_decrease
     
    
    def step(self):
        self.num_steps += 1
        self.f_prime = self.differential(self.x,self.y)
        self.y = self.y + (self.h * self.f_prime)
        self.x = self.x + self.h

    def step_increase(self):
        while self.x < self.goal:
            self.step()

    def step_decrease(self):
        while self.h > self.goal:
            self.step()

    def run(self):
        self.direction()
        return self.y