Problem1.py

# Problem 1 - Markov Absorbing Chain

import numpy as np
from numpy.linalg import inv


def GetAverageMatrix(mTable):
    bTable = mTable[:4, :4]
    iden = np.identity(4)
    sub = iden - bTable
    res = inv(sub)
    return res

def GetGraduationChance(mTable):
    testTable = np.matmul(mTable, mTable)
    for i in range(1000):
        testTable = np.matmul(testTable, mTable)
    start = np.array([1, 0, 0, 0, 0, 0])
    grad = np.matmul(start, testTable)
    return grad[4]

def GenerateStudent(mTable, aTable, bTable):
    ogQuit = 0.15
    i = 0.01
    while i < 0.16:
        row = int(i*100)
        aTable[row, 0] = i
        bTable[row, 0] = i
        mTable[0, 5] = i
        mTable[0, 0] = 0.1 + ogQuit - i
        aTable[row, 1] = GetGraduationChance(mTable)
        res = GetAverageMatrix(mTable)
        bTable[row, 1] = np.sum(res[0]) + 1

        mTable[0, 0] = 0.1
        mTable[0, 1] = 0.75 + ogQuit - i
        aTable[row, 2] = GetGraduationChance(mTable)
        res = GetAverageMatrix(mTable)
        bTable[row, 2] = np.sum(res[0]) + 1

        half = (ogQuit - i)/2
        mTable[0, 0] = 0.1 + half
        mTable[0, 1] = 0.75 + half
        aTable[row, 3] = GetGraduationChance(mTable)
        res = GetAverageMatrix(mTable)
        bTable[row, 3] = np.sum(res[0]) + 1

        i += 0.01
    return


def main():
    print()
    print("CSE 3504 Project 2 - Problem 1:")
    print()
    mTable = np.array([[0.1, 0.75, 0, 0, 0, 0.15], \
            [0, 0.1, 0.8, 0, 0, 0.1], \
            [0, 0, 0.15, 0.75, 0, 0.1], \
            [0, 0, 0, 0.1, 0.8, 0.1], \
            [0, 0, 0, 0, 1, 0], \
            [0, 0, 0, 0, 0, 1]])
    print("Problem 1: Part b")
    print()
    sol = GetAverageMatrix(mTable)
    print(sol) 
    print()
    print("With average execution time (years to graduate), we get: ")
    print(np.sum(sol[0])+1) # the +1 is for graduation (since example online shows s5 as a 1 because absorb state)
    print()
    print()
    print("Problem 1: Part c") # Probability of graduation - This is definitely wrong?
    print()
    print("Graduation chance, I think: ") # AYYYYY I think this is it. Although 58% seems low... lets put it to the test!
    print(GetGraduationChance(mTable))
    print()

    # okay so for now forget the P(graduate) cause thats clearly wrong
    aTable = np.zeros((16,4))
    aTable[0] = [0, 1, 2, 3]
    bTable = np.zeros((16,4))
    bTable[0] = [0, 1, 2, 3]
    GenerateStudent(mTable, aTable, bTable)
    print("Quit Value, Stay Fresh, Become Soph, Middleman")
    print(aTable)
    print(bTable)


if __name__ == '__main__':
    main()