Calculates coefficients for an equation to redistribute a random distribution between 0 and 1.

redistribution_solver.py

# -*- coding: utf-8 -*-
"""
Created on Mon Jun 26 21:05:22 2017

@author: Xorgon
"""

import numpy as np
import scipy.optimize as opt
import matplotlib.pyplot as plt
import warnings

def func(x, a, b, c, d):
    return - np.log(a/(x+b) - 1)/c + d   
    
def calculate(f, y75=0.58, p0=[1.025, 0.0125, 9.19, 0.5], 
              eqn_string="- Math.log(%f/(x+%f) - 1)/%f + %f"):
    """
    Calculates coefficients for an equation to redistribute a random
    distribution between 0 and 1.
    
    Defaults are all set to be usable for the example function 'func' provided.
    
    Arguments:
    f -- a function with parameters (x, a, b, c, d) where x is the independant 
         variable and a, b, c, and d are coefficients to be determined. This
         should map from x in range 0 to 1, to y in range 0 to 1.
         
    Keyword arguments:
    y75 -- The value of the function for an x value of 0.75.
    p0 -- The initial guess at parameters, this can be quite sensitive so
          attempting to approximate this using a graphing calculator may be
          necessary, e.g. desmos.com/calculator. 
    eqn_string -- A string of the equation with formatting characters to be
                  replaced by a, b, c, and d (in that order).
                  
    Returns:
    a, b, c, d -- Coefficients for the equation.
    """
    
    xdata = [0.0, 0.5, 0.75, 1.0]
    ydata = [0.001, 0.5, y75, 0.999]    
    
    
    warnings.filterwarnings("ignore") # Remove annoying messages.    
    result = opt.curve_fit(f, xdata, ydata, p0=p0, maxfev=int(1e4))
    warnings.filterwarnings("default") # Warnings might be needed elsewhere.

    a, b, c, d = result[0]
    print("a = %f, b = %f, c = %f, d = %f" % (a, b, c, d))
    
    xs = []
    ys = []
    for i in range(0, 998):
        xs.append((i + 1)/1000)
        ys.append(func((i+1)/1000, a, b, c, d))

    plt.plot(xs, ys)
    plt.xlabel("Random between 0 and 1", fontsize=10)
    plt.ylabel("Redistributed random between 0 and 1", fontsize=10)    
    
    print("Copy-pastable formula for Java:")
    print(eqn_string % (a, b, c, d))    
    
    return a, b, c, d
    
calculate(func)