check_weight1.py

#here we generate a Ham and simulate the weight to see if they are negative 
from numpy import array, bmat, zeros , dot , diag , eye, ones , sort , prod 
from numpy.random import rand 
from scipy.linalg import det , expm, eig , logm 

import numpy as np 
np.set_printoptions(suppress=True, precision=2, linewidth=100)


def build_Ham(n):
    B = (rand(n/2, n/2)-0.5)*4.
    Ham = bmat([[zeros((n/2,n/2),float), B], [B.transpose(), zeros((n/2,n/2),float)]])

    return Ham 

Ns = 6 #size of the A matrix 
N = 4  #number of the A matrices 
for itry in range(1):

    tmp = expm(build_Ham(Ns))
    for i in range(N):
        tmp = dot( expm(build_Ham(Ns)) , tmp)

    res = eye(Ns) + tmp
    print "det(1+e^{A}...e^{A}): ", det(res) #>=0 according to the conjecture 

    M = logm(tmp)
    print "M = log(e^{A}...e^{A}):\n",  M

    w, v = eig(M)
    print "eig(M): ", w