import random
import math
import numpy
import scipy
import scipy.linalg
import scipy.sparse.linalg
import numpy.linalg
import numpy
from tabulate import tabulate


precision = 100000000000

def MarkovChain(n,s) :
    """

    """
    matrix = []
    for l in range(n) :
        lineLst = []
        sum = 0
        crtPrec = precision
        for i in range(n-1) :
            val = random.randrange(crtPrec)
            sum += val
            lineLst.append(float(val)/precision)
            crtPrec -= val
        lineLst.append(float(precision - sum)/precision)
        matrix2 = matrix.append(lineLst)
    print("The intial probability matrix.")
    print(tabulate(matrix))
    matrix_n = numpy.linalg.matrix_power(matrix, s)
    print("The final probability matrix.")
    print(tabulate(matrix_n))
    matrixTranspose = zip(*matrix_n)

    def evecs(matrixTranspose):
         evectors = numpy.linalg.eig(matrixTranspose)[1][:,0]
         return evectors


    if any(x<0 for x in evectors) == False:
        print(evectors)


MarkovChain(3, 10000000000)

------------------------------------------------------------------------------------------------------------------------

runfile('/home/raleigh/Downloads/Python-3.4.3/MarkovChain.py', wdir='/home/raleigh/Downloads/Python-3.4.3/ipython-3.2.0')
Reloaded modules: tabulate
The intial probability matrix.
--------  ---------  --------
0.523984  0.324034   0.151982
0.359689  0.0638557  0.576455
0.107243  0.304804   0.587953
--------  ---------  --------
The final probability matrix.
--------  --------  --------
0.292137  0.250149  0.457714
0.292137  0.250149  0.457714
0.292137  0.250149  0.457714
--------  --------  --------
Traceback (most recent call last):

  File "<ipython-input-174-9b2fc1fd0b8f>", line 1, in <module>
    runfile('/home/raleigh/Downloads/Python-3.4.3/MarkovChain.py', wdir='/home/raleigh/Downloads/Python-3.4.3/ipython-3.2.0')

  File "/usr/local/lib/python2.7/dist-packages/spyderlib/widgets/externalshell/sitecustomize.py", line 685, in runfile
    execfile(filename, namespace)

  File "/usr/local/lib/python2.7/dist-packages/spyderlib/widgets/externalshell/sitecustomize.py", line 78, in execfile
    builtins.execfile(filename, *where)

  File "/home/raleigh/Downloads/Python-3.4.3/MarkovChain.py", line 52, in <module>
    MarkovChain(3, 10000000000)

  File "/home/raleigh/Downloads/Python-3.4.3/MarkovChain.py", line 48, in MarkovChain
    if any(x<0 for x in evectors) == False:

NameError: global name 'evectors' is not defined