Nadam.py

# This code implements the Nadam optimization algorithm based on the cost function provided by the user.


import sys
import numpy as np
import scipy as sc
from sympy import *


def nadam(cost_function, f):
    x = Symbol('x')
    print("f(x) = ", cost_function)
    f_dash = diff(cost_function, x)
    print("df(x)/dx = ", f_dash)
    initialApproximation = float(input("\n---> Enter initial approximation: "))
    x0 = initialApproximation
    errorTolerance = float(input("---> Enter error tolerance: "))
    learningRate = float(input("---> Enter learning rate: "))
    print("\n---------------------------------------------------------------")
    print(" *** Starting Nadam")
    print("        --->  x0 = ", initialApproximation)
    print("        --->  f(x0) = ", f(initialApproximation))
 
    #---------------------------------------------------------------------------------------------------------------------------------
    iterationCount = 0
    xk = x0
    x_prev = 0.0
    m0 = 0.0
    mk = 0.0
    v0 = 0.0
    vk = 0.0
    b1 = 0.9
    b2 = 0.999
    epsilon = 10 ** -8
    while True:
        iterationCount += 1
        x_prev = x0
        x0 = xk
        m0 = mk
        v0 = vk
        fk_dash = lambdify(x, f_dash, "numpy")(xk)
        gt = fk_dash
        mk = b1 * m0 + (1 - b1) * gt
        vk = b2 * v0 + (1 - b2) * (gt ** 2)
        mc_k = mk / (1 - b1 ** iterationCount)
        vc_k = vk / (1 - b2 ** iterationCount)
        xk = xk - (learningRate / (vc_k ** 0.5 + epsilon)) * (b1 * mc_k + (1 - b1) * gt / (1 - b1 ** iterationCount))
        if abs(N(xk - x0)) < float(errorTolerance) or abs(N(xk - x_prev)) < 0.1 * float(errorTolerance):
            break
    #---------------------------------------------------------------------------------------------------------------------------------

    print(" *** Number of Iterations = ", iterationCount)
    print("        --->  Minima is at = ", xk)
    print("        --->  Minimum value of Cost Function = ", f(xk))
    print("---------------------------------------------------------------\n")



# Code execution section

def main():
  x = Symbol('x')
  cost_function = input("---> Enter cost function f(x): ").strip()
  c_f = sympify(cost_function)
  f = lambdify(x, c_f, "numpy")
  nadam(c_f, f)

if __name__ == "__main__":
    main()