# probDBN.py - Dynamic belief networks
# AIFCA Python3 code Version 0.9.5 Documentation at http://aipython.org
# Download the zip file and read aipython.pdf for documentation

# Artificial Intelligence: Foundations of Computational Agents http://artint.info
# Copyright David L Poole and Alan K Mackworth 2017-2022.
# This work is licensed under a Creative Commons
# Attribution-NonCommercial-ShareAlike 4.0 International License.
# See: http://creativecommons.org/licenses/by-nc-sa/4.0/deed.en

from probVariables import Variable
from probGraphicalModels import GraphicalModel, BeliefNetwork
from probFactors import Prob, Factor, CPD
from probVE import VE
from display import Displayable
from utilities import dict_union

class DBNvariable(Variable):
    """A random variable that incorporates the stage (time)

    A variable can have both a name and an index. The index defaults to 1.
    """
    def __init__(self,name,domain=[False,True],index=1):
        Variable.__init__(self,f"{name}_{index}",domain)
        self.basename = name
        self.domain = domain
        self.index = index
        self.previous = None
        
    def __lt__(self,other):
        if self.name != other.name:
            return self.name<other.name
        else:
            return self.index<other.index

    def __gt__(self,other):
        return other<self

def variable_pair(name,domain=[False,True]):
    """returns a variable and its predecessor. This is used to define 2-stage DBNs

    If the name is X, it returns the pair of variables X_prev,X_now"""
    var_now = DBNvariable(name,domain,index='now')
    var_prev = DBNvariable(name,domain,index='prev')
    var_now.previous = var_prev
    return var_prev, var_now

class FactorRename(Factor):
    def __init__(self,fac,renaming):
        """A  renamed factor.
        fac is a factor
        renaming is a dictionary of the form {new:old} where old and new var variables, 
           where the variables in fac appear exactly once in  the renaming
        """
        Factor.__init__(self,[n for (n,o) in renaming.items() if o in fac.variables])
        self.orig_fac = fac
        self.renaming = renaming

    def get_value(self,assignment):
        return self.orig_fac.get_value({self.renaming[var]:val
                                        for (var,val) in assignment.items()
                                        if var in self.variables})

class CPDrename(FactorRename, CPD):
    def __init__(self, cpd, renaming):
        renaming_inverse = {old:new for (new,old) in renaming.items()}
        CPD.__init__(self,renaming_inverse[cpd.child],[renaming_inverse[p] for p in cpd.parents])
        self.orig_fac = cpd
        self.renaming = renaming
        
class DBN(Displayable):
    """The class of stationary Dynamic Belief networks.
    * name is the DBN name
    * vars_now is a list of current variables (each must have
    previous variable).
    * transition_factors is a list of factors for P(X|parents) where X
    is a current variable and parents is a list of current or previous variables.
    * init_factors is a list of factors for P(X|parents) where X is a
    current variable and parents can only include current variables
    The graph of transition factors + init factors must be acyclic.
    
    """
    def __init__(self, title, vars_now, transition_factors=None, init_factors=None):
        self.title = title
        self.vars_now = vars_now
        self.vars_prev = [v.previous for v in vars_now]
        self.transition_factors = transition_factors
        self.init_factors = init_factors
        self.var_index = {}       # var_index[v] is the index of variable v
        for i,v in enumerate(vars_now):
            self.var_index[v]=i

A0,A1 = variable_pair("A", domain=[False,True])
B0,B1 = variable_pair("B", domain=[False,True])
C0,C1 = variable_pair("C", domain=[False,True])

# dynamics
pc = Prob(C1,[B1,C0],[[[0.03,0.97],[0.38,0.62]],[[0.23,0.77],[0.78,0.22]]])
pb = Prob(B1,[A0,A1],[[[0.5,0.5],[0.77,0.23]],[[0.4,0.6],[0.83,0.17]]])
pa = Prob(A1,[A0,B0],[[[0.1,0.9],[0.65,0.35]],[[0.3,0.7],[0.8,0.2]]])

# initial distribution
pa0 = Prob(A1,[],[0.9,0.1])
pb0 = Prob(B1,[A1],[[0.3,0.7],[0.8,0.2]])
pc0 = Prob(C1,[],[0.2,0.8])

dbn1 = DBN("Simple DBN",[A1,B1,C1],[pa,pb,pc],[pa0,pb0,pc0])

from probHMM import closeMic, farMic, midMic, sm, mmc, sc, mcm, mcc

Pos_0,Pos_1 = variable_pair("Position",domain=[0,1,2,3])
Mic1_0,Mic1_1 = variable_pair("Mic1")
Mic2_0,Mic2_1 = variable_pair("Mic2")
Mic3_0,Mic3_1 = variable_pair("Mic3")

# conditional probabilities - see hmm for the values of sm,mmc, etc
ppos = Prob(Pos_1, [Pos_0], 
            [[sm, mmc, mmc, mmc],  #was in middle
             [mcm, sc, mcc, mcc],  #was in corner 1
             [mcm, mcc, sc, mcc],  #was in corner 2
             [mcm, mcc, mcc, sc]]) #was in corner 3
pm1 = Prob(Mic1_1, [Pos_1], [[1-midMic, midMic], [1-closeMic, closeMic], 
                            [1-farMic, farMic], [1-farMic, farMic]])
pm2 = Prob(Mic2_1, [Pos_1], [[1-midMic, midMic], [1-farMic, farMic], 
                            [1-closeMic, closeMic], [1-farMic, farMic]])
pm3 = Prob(Mic3_1, [Pos_1], [[1-midMic, midMic], [1-farMic, farMic], 
                            [1-farMic, farMic], [1-closeMic, closeMic]])
ipos = Prob(Pos_1,[], [0.25, 0.25, 0.25, 0.25])
dbn_an =DBN("Animal DBN",[Pos_1,Mic1_1,Mic2_1,Mic3_1], 
            [ppos, pm1, pm2, pm3],
            [ipos, pm1, pm2, pm3])
            
class BNfromDBN(BeliefNetwork):
    """Belief Network unrolled from a dynamic belief network
    """

    def __init__(self,dbn,horizon):
        """dbn is the dynamic belief network being unrolled
        horizon>0 is the number of steps (so there will be horizon+1 variables for each DBN variable.
        """
        self.name2var = {var.basename: [DBNvariable(var.basename,var.domain,index) for index in range(horizon+1)]
                         for var in dbn.vars_now}
        self.display(1,f"name2var={self.name2var}")
        variables = {v for vs in self.name2var.values() for v in vs}
        self.display(1,f"variables={variables}")
        bnfactors = {CPDrename(fac,{self.name2var[var.basename][0]:var
                                         for var in fac.variables})
                      for fac in dbn.init_factors}
        bnfactors |= {CPDrename(fac,dict_union({self.name2var[var.basename][i]:var
                                         for var in fac.variables if var.index=='prev'}
                                   , {self.name2var[var.basename][i+1]:var
                                         for var in fac.variables if var.index=='now'}))
                      for fac in dbn.transition_factors
                          for i in range(horizon)}
        self.display(1,f"bnfactors={bnfactors}")
        BeliefNetwork.__init__(self,  dbn.title, variables, bnfactors)

# Try
#from probRC import ProbRC
#bn = BNfromDBN(dbn1,2)   # construct belief network
#drc = ProbRC(bn)               # initialize recursive conditioning
#B2 = bn.name2var['B'][2]
#drc.query(B2)  #P(B2)
#drc.query(bn.name2var['B'][1],{bn.name2var['B'][0]:True,bn.name2var['C'][1]:False}) #P(B1|B0,C1)
class DBNVEfilter(VE):
    def __init__(self,dbn):
        self.dbn = dbn
        self.current_factors = dbn.init_factors
        self.current_obs = {}

    def observe(self, obs):
        """updates the current observations with obs.
        obs is a variable:value dictionary where variable is a current
        variable.
        """
        assert all(self.current_obs[var]==obs[var] for var in obs 
                   if var in self.current_obs),"inconsistent current observations"
        self.current_obs.update(obs)  # note 'update' is a dict method

    def query(self,var):
        """returns the posterior probability of current variable var"""
        return VE(GraphicalModel(self.dbn.title,self.dbn.vars_now,self.current_factors)).query(var,self.current_obs)

    def advance(self):
        """advance to the next time"""
        prev_factors = [self.make_previous(fac) for fac in self.current_factors]
        prev_obs = {var.previous:val for var,val in self.current_obs.items()}
        two_stage_factors = prev_factors + self.dbn.transition_factors
        self.current_factors = self.elim_vars(two_stage_factors,self.dbn.vars_prev,prev_obs)
        self.current_obs = {}

    def make_previous(self,fac):
         """Creates new factor from fac where the current variables in fac
         are renamed to previous variables.
         """
         return FactorRename(fac, {var.previous:var for var in fac.variables})

    def elim_vars(self,factors, vars, obs):
        for var in vars:
            if var in obs:
                factors = [self.project_observations(fac,obs) for fac in factors]
            else:
                factors = self.eliminate_var(factors, var)
        return factors

#df = DBNVEfilter(dbn1)
#df.observe({B1:True}); df.advance(); df.observe({C1:False})
#df.query(B1)   #P(B1|B0,C1)
#df.advance(); df.query(B1)
#dfa = DBNVEfilter(dbn_an)
# dfa.observe({Mic1_1:0, Mic2_1:1, Mic3_1:1})
# dfa.advance()
# dfa.observe({Mic1_1:1, Mic2_1:0, Mic3_1:1})
# dfa.query(Pos_1)