working on forward/backward procedure

markov.py

@@ -21,7 +21,7 @@ class MarkovModel:
 
     def __init__(self, states: list, observations: list = list(), state_transitions: list = list()):
         self.observations = observations
-        self.state_transitions = state_transitions
+        self.state_transitions = state_transitions # use state number not state index, is padded by entry and exit probs
 
         self.states = states # number of states
         # self.timesteps = list()
@@ -29,11 +29,75 @@ class MarkovModel:
         self.forward = np.zeros((len(states), len(observations)))
         self.backward = np.zeros((len(states), len(observations)))
 
+    def get_other_state_index(self, state_in):
+        """For when state changes, get other index for retrieving state transitions (FOR 0 INDEXING)"""
+        if state_in == 0:
+            return 1
+        elif state_in == 1:
+            return 0
+        else:
+            print(f"invalid state index provided, ({state_in})")
+
+    def get_other_state_number(self, state_in):
+        """For when state changes, get other number for retrieving state transitions (FOR 1 INDEXING)"""
+        return self.get_other_state_index(state_in - 1) + 1
+    
     def populate_forward(self):
         for t, observation in enumerate(self.observations): # iterate through observations (time)
-            for state_number, state in enumerate(self.states):
+            for state_index, state in enumerate(self.states):
+
+                state_number = state_index + 1 # for easier reading (arrays 0-indexed, numbers start at 1)
 
                 if t == 0: # calcualte initial
-                    self.forward[state_number, t] = self.state_transitions[0, state_number + 1] * gaussian(observation, state.mean, state.std_dev)
+                    self.forward[state_index, t] = self.state_transitions[0, state_number] * gaussian(observation, state.mean, state.std_dev)
                 else:
-                    self.forward[state_number, t] = gaussian(observation, state.mean, state.std_dev)
+                    # each state for each time has two paths leading to
+
+                    other_index = self.get_other_state_index(state_index)
+                    other_number = other_index + 1 # for 1 indexing
+                    
+                    #                      previous value             prob of changing from previous state to current
+                    this_to_this = self.forward[state_index, t - 1] * self.state_transitions[state_number, state_number]
+                    other_to_this = self.forward[other_index, t - 1] * self.state_transitions[other_number, state_number]
+
+                    self.forward[state_index, t] = (this_to_this + other_to_this) * gaussian(observation, state.mean, state.std_dev)
+
+    @property
+    def p_observations_forward(self):
+
+        sum = 0
+        for state_index, final_likelihood in enumerate(self.forward[:, -1]):            
+            sum += final_likelihood * self.state_transitions[state_index + 1, -1] # get exit prob from state transitions
+
+        return sum
+
+    #TODO finish
+    def populate_backward(self):
+
+        # initialise from exit probabilities
+        self.backward[:, -1] = self.state_transitions[1:len(self.states) + 1, -1]
+
+        for t, observation in list(enumerate(self.observations[1:]))[::-1]: # iterate backwards through observations (time)
+            print(t, observation)
+            for state_index, state in enumerate(self.states):
+
+                state_number = state_index + 1 # for easier reading (arrays 0-indexed, numbers start at 1)
+
+                other_index = self.get_other_state_index(state_index)
+                other_number = other_index + 1 # for 1 indexing
+                
+                #                      previous value             prob of changing from previous state to current
+                this_to_this = self.backward[state_index, t + 1] * self.state_transitions[state_number, state_number]
+                other_to_this = self.backward[other_index, t + 1] * self.state_transitions[other_number, state_number]
+
+                self.backward[state_index, t] = (this_to_this + other_to_this) * gaussian(observation, state.mean, state.std_dev)
+
+    #TODO finish
+    @property
+    def p_observations_backward(self):
+
+        sum = 0
+        for state_index, initial_likelihood in enumerate(self.backward[:, 0]):            
+            sum += self.state_transitions[0, state_index + 1] * gaussian(self.observations[0], self.states[state_index].mean, self.states[state_index].std_dev) * initial_likelihood
+
+        return sum

report/report.lyx

@@ -136,7 +136,7 @@ Andy Pack
 \begin_layout Standard
 \align center
 \begin_inset Graphics
-	filename ../../../matlab/lpss/report/surrey.png
+	filename surrey.png
 	lyxscale 15
 	width 40col%
 
@@ -323,6 +323,17 @@ lstparams "language=Python,breaklines=true,frame=tb,otherkeywords={self},emph={S
 \end_inset
 
 
+\end_layout
+
+\begin_layout Standard
+\begin_inset CommandInset include
+LatexCommand lstinputlisting
+filename "../markov.py"
+lstparams "language=Python,breaklines=true,frame=tb,otherkeywords={self},emph={State},emphstyle={\\ttb\\color{darkred}},basicstyle={\\ttfamily},commentstyle={\\color{commentgreen}\\itshape},keywordstyle={\\color{darkblue}},emphstyle={\\color{red}},stringstyle={\\color{red}},caption={Markov model object defining forward and backward procedure},label={markov-listing}"
+
+\end_inset
+
+
 \end_layout
 
 \end_body