Self-descriptive number

__author__ = 'shagas'

import numpy as np

# Get cost of the solution
def cost(y):

    # Turn into a list so that we can use the 'count()' function
    x = list(y)

    # Error sum
    err = np.zeros((len(x)))
    for i in range(len(x)):
        err[i] = 0.5*(x[i] - x.count(i))**2 # J_i = 0.5*( x_i - z_i )^2

    return sum(err)

# Get vector of partial derivatives of the cost function
def getGrad(y):

    # Turn into a list so that we can use the 'count()' function
    x = list(y)

    z = np.zeros((len(x)))
    grad = np.zeros((len(x)))

    for i in range(len(x)):
        z[i] = x.count(i)
        grad[i] = (x[i] - z[i])  # dJ/dx_i = ( x_i - z_i )

    return grad


# Initialize the solution to either random or all zeros or custom
sol = np.zeros((10))
#sol = np.random.rand(10)*10
#sol = np.array([0,2,0,4,5,2,1,0,4,2])

# Parameters
iters = 800
alpha = 0.01

# Optimize
for i in range(iters):

    # Error of solution
    err = cost(np.round(sol))

    # Update
    sol -= alpha*getGrad(np.round(sol))*err

    # Print out current solution every so often
    if i % (iters/30) == 0:
        print 'Solution: ' + str(np.round(sol)) + ' cost: ' + str(err)