/** DST COMBINATION C CODE **/
/**
	by Gavin Powell, 3D Vision and Geometry, Dept Compter Science, Cardiff University
	g.r.powell@cs.cf.ac.uk
**/
/***

This is a macintosh codewarrior project.
It will work fine on other systems. It has compiled with strict ANSI etc...
For non codewarrior users all your code is in src and headers.

****/

/** SETUP **/
/*
	In "defs.h"
	NO_SINGLETONS -> How many singletons there are in Omega.
	STORE1 -> This just defines the position within our data structure. Add or take away as necessary. Must agree with NO_SINGLETONS
	NOTE:- print_frame() in  "print.c" uses these defs so check it out and alter as necessary if you alter these! 
	
	N -> the number of sets to combine. (how many pieces of evidence)

*/

/**

printc.c - print_frame
This can be used to print any frame. So you can output values of frames before combining etc.


file_io.c - get_sample
Reads in data from file in this order....

for Omega = {a, b, c}
{0} (empty set)
{a}
{b}
{a, b}
{c}
{a, c}
{b, c}
{a, b, c}

this order is created in frame_discernment
**/

/***

MEMORY - The "Shypothesis **samples" is not freed. Everything else should be ok, but I have not tested on a large data set
so there may well be some leaks, please inform me if you find any.

**/


/** General DST Stuff **/
/*
a hypothesis is defined....
type[x][y][z].
where x, y, z can be 0,1
and say
x = Store1
y = Store2
z = Store3
so type[0][1][1] would be a hypothesis for Store2 and Store3.
x, y, and z are 'named' as singletons. So the more possible matches the more singletons
they are also the original set, and we assign bpn's etc to all of the subsets of this power ste.

The two frames are combined to calculate the bpa/bpn of the third 'fused' frame. Then the belief and plausability are calc'd.

If we know nothing about any of the subsets probabilities then we can assign 1 to [1][1][1].

Defn's
BPN m(A) := Evidence supporting that hypothesis. DOES NOT have any relevance on sub-sets.
Belief Bel(A) := Belief in that hypothesis, from the evidence supporting that hypothesis and all subsets of it.
Plausability Pl = 1-Bel(`A) := Bel(`A) is the total evidence not supporting A. Remember {x} supports {x, y} and vice versa. 
                  Shows how much evidence DOESN'T disrepute A.
                  
The length of Bel(A)->Pl(A) Is the belief interval and show ingnorance. The longer it is the more ignorant we are i.e. 
High plausability says that there is little evidnce against our hypothesis and a low belief says we have no evidence for, or know little about.
Hence we are ignorant of evidnence supporting this hypothesis.
==========
BPA is the function saying that all (sum)BPN's = 1 and empty set =0;
BPN is each m(A). It is how much belief we assign to that set given a piece of evidence (i.e the results from our ATR).
==========
The bel is adding the total belief's in A and any that A implies (i.e. subsets).
This is done using the Belief function or Bel(A).
When A is a singleton it become a Bayesian belief!
Since the belief functions != 1  then Bel(A) + Bel(`A) != 1 so Pl = 1-Bel(`A) is how much we 'fail to doubt' A.
The Belief function finds the TOTAL belief in that hypothesis as opposed to m(A) which is the sigular belief in that hypothesis, irrespective of supporting hypothesise.

When we have a singleton, Bayesian probability, Bel = Pl.

******/