ComputeAlpha_a

   Compute the alpha_i_n-element for the given action and belief.

   Define the alpha-elements to be used in the backup (The \alpha_n^i
   elements).
   Particularly, this function defines those elements as described at the
   end of section 6.2 of the paper (see the last equation before 
   Section 7).

   This function is only applied to POMDPs with discrete actions sets.
   Recall that continuous action sets are always discretized before
   entering the backup (See Table 2 in page 21). Thus, in practice the
   input 'P' is a DS_CO_DA_POMDP.

   Note that in this case the Alpha_j_a_o elements can not be pre-computed
   and that this parameter is given for compatibility with similar
   functions for other types of POMDP.

0001 function Element_a=ComputeAlpha_a(P,V,b,a,Alphas_j_a_o)
0002 %   Compute the alpha_i_n-element for the given action and belief.
0003 %
0004 %   Define the alpha-elements to be used in the backup (The \alpha_n^i
0005 %   elements).
0006 %   Particularly, this function defines those elements as described at the
0007 %   end of section 6.2 of the paper (see the last equation before
0008 %   Section 7).
0009 %
0010 %   This function is only applied to POMDPs with discrete actions sets.
0011 %   Recall that continuous action sets are always discretized before
0012 %   entering the backup (See Table 2 in page 21). Thus, in practice the
0013 %   input 'P' is a DS_CO_DA_POMDP.
0014 %
0015 %   Note that in this case the Alpha_j_a_o elements can not be pre-computed
0016 %   and that this parameter is given for compatibility with similar
0017 %   functions for other types of POMDP.
0018 
0019   P1=DiscretizeObsModel(P,V,b,a); % This returns a CS_DO_DA_POMDP
0020   nj=size(V);
0021   gamma=get(P,'gamma');
0022   Element_a=ComputeAlpha_j_a_o(P1,V,1,a,1);
0023   for j=2:nj
0024     Element_a=Element_a+ComputeAlpha_j_a_o(P1,V,j,a,j);
0025   end  
0026   Element_a=GetRewardModelFixedA(P,a)+gamma*Element_a;
0027 
0028