markov/markov.py

@@ -27,14 +27,18 @@ transitionMatrix = np.array([[0.6, 0.1, 0.3],
                              [0.1, 0.7, 0.2],
                              [0.2, 0.2, 0.6]])
 
-# Starting state
+# Starting state - Given as a list of probabilities of starting
-# startingState = 'L'
+# in each state. To always start at the same state set one of them
+# to 1 and the rest to 0. These must add to 1!
 initial_dist = np.array([1, 0, 0])
-# initial_dist = None
 
-# Steps to run
+# Steps to run - How many steps or jumps we want the markov chain to make
-stepTime = 5
+stepTime = 1
-# End state you want to find probabilites of
+# End state you want to find probabilites of - we can estimate the stationary
+# distribution by running this many times for many steps.
+# E.g to find the stat distribution for L run the simulation 10,000 times
+# for 1000 jumps. This should be very close to the actual value which
+# we can find below.
 endState = 'L'
 
 """ Find the transition matrix for the given number of steps
@@ -82,9 +86,12 @@ class markov(object):
 
     @staticmethod
     def transition_matrix_step(transitionMatrix, steps):
-        for _ in itertools.repeat(None, steps):
+        try:
+            for _ in itertools.repeat(None, steps - 1):
                 step_mat = np.matmul(transitionMatrix, transitionMatrix)
             return step_mat
+        except UnboundLocalError:
+            return transitionMatrix
 
     @staticmethod
     def stationary_dist(transitionMatrix, initial_dist, steps):
@@ -116,46 +123,46 @@ class markov(object):
                     self.currentState = self.states[1]
                     self.stateList.append(self.states[1])
                 else:
-                    self.prob == self.transitionMatrix[0][2]
+                    self.prob = self.transitionMatrix[0][2]
                     self.currentState = self.states[2]
                     self.stateList.append(self.states[2])
-            elif self.currentState == "w":
+            elif self.currentState == self.states[1]:
                 self.change = np.random.choice(self.transitionName[1],
                                                replace=True,
                                                p=transitionMatrix[1])
-                if self.change == "ww":
+                if self.change == self.transitionName[1][0]:
-                    self.prob = self.prob * 0.15
+                    self.prob = self.prob * self.transitionMatrix[1][0]
-                    self.stateList.append("w")
+                    self.currentState = self.states[0]
+                    self.stateList.append(self.states[0])
+                elif self.change == self.transitionName[1][1]:
+                    self.prob = self.prob * self.transitionMatrix[1][1]
+                    self.stateList.append(self.states[1])
                     pass
-                elif self.change == "wL":
-                    self.prob = self.prob * 0.8
-                    self.currentState = "L"
-                    self.stateList.append("L")
                 else:
-                    self.prob = self.prob * 0.05
+                    self.prob = self.prob * self.transitionMatrix[1][2]
-                    self.currentState = "W"
+                    self.currentState = self.states[2]
-                    self.stateList.append("W")
+                    self.stateList.append(self.states[2])
-            elif self.currentState == "W":
+            elif self.currentState == self.states[2]:
                 self.change = np.random.choice(self.transitionName[2],
                                                replace=True,
                                                p=transitionMatrix[2])
-                if self.change == "WW":
+                if self.change == self.transitionName[2][0]:
-                    self.prob = self.prob * 0.05
+                    self.prob = self.prob * self.transitionMatrix[2][0]
-                    self.stateList.append("W")
+                    self.currentState = self.states[0]
-                    pass
+                    self.stateList.append(self.states[0])
-                elif self.change == "WL":
+                elif self.change == self.transitionName[2][1]:
-                    self.prob = self.prob * 0.8
+                    self.prob = self.prob * self.transitionMatrix[2][1]
-                    self.currentState = "L"
+                    self.currentState = self.states[1]
-                    self.stateList.append("L")
+                    self.stateList.append(self.states[1])
                 else:
-                    self.prob = self.prob * 0.15
+                    self.prob = self.prob * self.transitionMatrix[2][2]
-                    self.currentState = "w"
+                    self.stateList.append(self.states[2])
-                    self.stateList.append("w")
+                    pass
             i += 1
         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 this specific path:'
+        print(f'Probability of taking these exact steps in this order is:'
-              f' {self.prob:.4f} or {self.prob:.2%}\n')
+              f' {self.prob:.2f} or {self.prob:.2%}\n')
         return self.stateList
 
 
@@ -215,8 +222,11 @@ def main(*args, **kwargs):
                   f' {endState!s}:', list)
     if setSim is False:
         simNum = 1
-    print(f'\nThe probability of starting in {startingState} and finishing'
+    print(f'\nTherefore the estimated probability of starting in'
-          f' in {endState} after {stepTime} steps is {(count / simNum):.2%}\n')
+          f' {startingState} and finishing in {endState} after '
+          f'{stepTime} steps is '
+          f'{(count / simNum):.2%}.\n'
+          f'This is calculated by number of success/total steps\n')
     if transition_matrix_step:
         print(f'P_{stepTime} is: \n'
               f'{markov.transition_matrix_step(transitionMatrix, stepTime)}\n')