updated markov for general case (incomplete)

markov/markov_test.py

@@ -29,18 +29,26 @@ transitionMatrix = np.array([[0.6, 0.1, 0.3],
 
 # Starting state
 startingState = 'w'
-initial_dist = np.array([0.3, 0.3, 0.4])
+initial_dist = np.array([0, 1, 0])
+# initial_dist = None
 
 # Steps to run
-stepTime = 2
+stepTime = 100
 # End state you want to find probabilites of
 endState = 'W'
 
-# Get P_steps
-p_steps = False
+""" Find the transition matrix for the given number of steps
+This finds the probabilities of going from step i to step j
+in N number of steps, where N is your step size
+E.g 10 steps would give P_10 which is prob of going from step i
+to step j in exactly 10 steps """
+transition_matrix_step = True
 
-# Get Stationary Dist
-stat_dist = False
+""" Get Stationary distribution of the Markov Chain
+This tells you what % of time you spend in each state if you
+simulated the Markov Chain for a high number of steps
+THIS NEEDS THE INTIIAL DISTRIBUTION SETTING """
+stat_dist = True
 
 
 # A class that implements the Markov chain to forecast the state/mood:
@@ -73,20 +81,22 @@ class markov(object):
         return np.random.seed(num)
 
     @staticmethod
-    def p_steps(transitionMatrix, initial_dist, steps):
+    def transition_matrix_step(transitionMatrix, steps):
         for _ in itertools.repeat(None, steps):
-            initial_dist = transitionMatrix.T.dot(initial_dist)
-        return initial_dist
+            step_mat = np.matmul(transitionMatrix, transitionMatrix)
+        return step_mat
 
     @staticmethod
     def stationary_dist(transitionMatrix, initial_dist, steps):
-        for _ in itertools.repeat(None, steps):
-            initial_dist = transitionMatrix.T.dot(initial_dist)
-        return initial_dist
+        w, v = np.linalg.eig(transitionMatrix.T)
+        j_stationary = np.argmin(abs(w - 1.0))
+        p_stationary = v[:, j_stationary].real
+        p_stationary /= p_stationary.sum()
+        return p_stationary
 
     @functools.lru_cache(maxsize=128)
     def forecast(self):
-        print(f'Start state: {self.currentState}')
+        print(f'Start state: {self.currentState}\n')
         # Shall store the sequence of states taken
         self.stateList = [self.currentState]
         i = 0
@@ -142,13 +152,20 @@ class markov(object):
                     self.currentState = "w"
                     self.stateList.append("w")
             i += 1
-        print(f'Possible states: {self.stateList}')
+        print(f'Path Markov Chain took in this iteration: {self.stateList}')
         print(f'End state after {self.steps} steps: {self.currentState}')
-        print(f'Probability of all the possible sequence of states:'
-              f' {self.prob}\n')
+        print(f'Probability of this specific path:'
+              f' {self.prob:.4f} or {self.prob:.2%}\n')
         return self.stateList
 
 
+def checker(item, name):
+    try:
+        item is not None
+    except Exception:
+        raise Exception(f'{name} is not set - set it and try again.')
+
+
 def main(*args, **kwargs):
     global startingState
     try:
@@ -190,18 +207,21 @@ def main(*args, **kwargs):
                                      stepTime).forecast())
     for list in list_state:
         if(list[-1] == f'{endState!s}'):
-            print(True, list)
+            print(f'SUCCESS - path ended in the requested state {endState!s}'
+                  f':', list)
             count += 1
         else:
-            print(False, list)
+            print(f'FAILURE - path did not end in the requested state'
+                  f' {endState!s}:', list)
     if setSim is False:
         simNum = 1
     print(f'\nThe probability of starting in {startingState} and finishing'
-          f' in {endState} after {stepTime} steps is {(count / simNum):.2%}')
-    if p_steps:
-        print(f'P_{stepTime} is '
-              f'{markov.p_steps(transitionMatrix, initial_dist, stepTime)}')
+          f' in {endState} after {stepTime} steps is {(count / simNum):.2%}\n')
+    if transition_matrix_step:
+        print(f'P_{stepTime} is: \n'
+              f'{markov.transition_matrix_step(transitionMatrix, stepTime)}\n')
     if stat_dist:
+        checker(initial_dist, 'initial distribution')
         print(f'Stat dist is {markov.stationary_dist(transitionMatrix,initial_dist, stepTime)}')