minimize.py

#!/usr/bin/env python
import argparse
from numpy.random import random, choice, randint
from numpy import zeros, copyto
import matplotlib.pyplot as plt
plt.ion()


def main():
    args = arguments()
    m = generate_matrix(args.N)
    s = generate_spin_vector(args.N)
    results = list()
    current = H(m,s)
    for i in range(args.steps):
        candidate_s = flip_spins(s)
        result = H(m,candidate_s )
        if current - result > args.T:
            s = candidate_s 
            results.append(result)
            current = result
        else:
            results.append(current)
    make_plot(results)
    
    
def flip_spins(s):
    candidate = zeros(len(s))
    copyto(candidate,s)
    random_index = randint(0,len(s))
    candidate[random_index] *= -1
    return candidate
    
def arguments():
    parser = argparse.ArgumentParser()
    parser.add_argument("N",help="number of guests at the party",type=int)
    parser.add_argument("T",help="""Temperature - threshold in change of H which
                        has to be exceeded in order for proposed change in
                        vector S to be accepted""",type=float)
    parser.add_argument("steps",help="number of iterations of the algorithm",type=int)
    return parser.parse_args()

def generate_matrix(N):
    m = zeros((N,N))
    for i in range(N):
        for j in range(N):
            m[i,j] = random() * choice([-1,1])
    return m


def generate_spin_vector(N):
    s = zeros(N)
    for i in range(N):
        s[i] = choice([-1,1])
    return s
    

def H(m,s):
    value = 0
    N = len(m)
    for i in range(N):
        for j in range(N):
            if not i == j:
                value += -1*( m[i,j]*s[i]*s[j])
    return value
    

def make_plot(results):
    plt.figure()
    plt.plot(range(len(results)),results,label="H")
    plt.xlabel("step")
    plt.ylabel("Frustration")
    plt.legend()
    plt.savefig("Frustration at the party.png")


if __name__ == '__main__':
    main()