import numpy as np
import matplotlib.pyplot as plt
import random
from tabulate import tabulate
import matplotlib.mlab as mlab

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(matrix2))
    baseprob = []
    baseprob2 = []
    baseprob3 = []
    baseprob4 = []

    for i in range(1,s): #changed to do a range 1-s instead of 1000

 #must use the loop variable here, not s (s is always the same)
        matrix_n = np.linalg.matrix_power(matrix2, i)
        baseprob.append(matrix_n.item(0))
        baseprob2.append(matrix_n.item(1))
        baseprob3.append(matrix_n.item(2))

    baseprob = np.array(baseprob)
    baseprob2 = np.array(baseprob2)
    baseprob3 = np.array(baseprob3)
    baseprob4 = np.array(baseprob4)

    # Here I tried to make a histogram using the plt.hist() command, but the normed=True doesn't work like I assumed it would.
    '''
   plt.hist(baseprob, bins=20, normed=True)
   plt.show()
   '''

    #Here I tried to make a histogram using the method from the second link in my post.
    # The code runs, but then the graph that is outputted isn't doesn't have the relative frequency on the y axis.
    '''
    n, bins, patches = plt.hist(baseprob, bins=30,normed=True,facecolor = "green",)
    y = mlab.normpdf(bins,mu,sigma)
    plt.plot(bins,y,'b-')
    plt.title('Main Plot Title',fontsize=25,horizontalalignment='right')
    plt.ylabel('Count',fontsize=20)
    plt.yticks(fontsize=15)
    plt.xlabel('X Axis Label',fontsize=20)
    plt.xticks(fontsize=15)
    plt.show()
    '''
    # Here I tried to make a histogram using the method seen in the Stackoverflow question I mentioned.
    # The figure that pops out looks correct in terms of the axes, but no actual data is posted. Instead the error below is shown in the console.
    # AttributeError: 'list' object has no attribute 'size'


    fig = plt.figure()
    ax = fig.add_subplot(111)
    ax.hist(baseprob, weights=np.zeros_like(baseprob)+1./ baseprob.size)
    n, bins, patches = ax.hist(baseprob, bins=100, normed=1, cumulative=0)
    ax.set_xlabel('Bins', size=20)
    ax.set_ylabel('Frequency', size=20)
    ax.legend
    plt.show()


    print("The final probability matrix.")
    print(tabulate(matrix_n))
    matrixTranspose = zip(*matrix_n)
    evectors = np.linalg.eig(matrixTranspose)[1][:,0]
    print("The steady state vector is:")
    print(evectors)






MarkovChain(5, 1000)


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


 runfile('C:/Users/Raleigh/Documents/Python Scripts/MarkovChainSO.py', wdir='C:/Users/Raleigh/Documents/Python Scripts')
The intial probability matrix.


Traceback (most recent call last):

  File "<ipython-input-52-15a2bf632b19>", line 1, in <module>
    runfile('C:/Users/Raleigh/Documents/Python Scripts/MarkovChainSO.py', wdir='C:/Users/Raleigh/Documents/Python Scripts')

  File "C:\Users\Raleigh\Anaconda3\lib\site-packages\spyderlib\widgets\externalshell\sitecustomize.py", line 682, in runfile
    execfile(filename, namespace)

  File "C:\Users\Raleigh\Anaconda3\lib\site-packages\spyderlib\widgets\externalshell\sitecustomize.py", line 85, in execfile
    exec(compile(open(filename, 'rb').read(), filename, 'exec'), namespace)

  File "C:/Users/Raleigh/Documents/Python Scripts/MarkovChainSO.py", line 97, in <module>
    MarkovChain(5, 1000)

  File "C:/Users/Raleigh/Documents/Python Scripts/MarkovChainSO.py", line 41, in MarkovChain
    matrix_n = np.linalg.matrix_power(matrix2, i)

  File "C:\Users\Raleigh\Anaconda3\lib\site-packages\numpy\matrixlib\defmatrix.py", line 171, in matrix_power
    raise ValueError("input must be a square array")

ValueError: input must be a square array