//-------------------------------------------------------------------
//	markov.cpp
//
//	This program shows the transition matrix and a sequence of
//	the state vectors for a Markov Chain with prescribed data.
//
//		to compile:  $ g++ markov.cpp -o markov
//		to execute:  $ ./markov
//
//	programmer: ALLAN CRUSE
//	written on: 01 MAR 2011
//-------------------------------------------------------------------

#include <stdio.h>		// for printf() 
#include <string.h>		// for memcpy()

#define	N_STATES	2	// number of states 
#define N_STEPS		13	// number of steps

typedef double Vector[ N_STATES ];
typedef double Matrix[ N_STATES ][ N_STATES ];

Vector initial = { .50, .50 };
Matrix transition = { .8, .2, .3, .7 };

int main( int argc, char **argv )
{
	// display the transition matrix
	printf( "\n The Markov Chain Transition Matrix: " );
	for (int i = 0; i < N_STATES; i++)
		{
		printf( "\n         " );
		for (int j = 0; j < N_STATES; j++)
			printf( " %1.4f ", transition[ i ][ j ] );
		}
	printf( "\n\n" );

	// display the sequence of state vectors
	Vector	current;
	memcpy( current, initial, sizeof( current ) );
	for (int step = 0; step < N_STEPS; step++)
		{
		// display the current state vector
		printf( " State Vector %-4d ", step );
		for (int j = 0; j < N_STATES; j++)
			printf( " %1.4f ", current[ j ] );
		printf( "\n\n" );
		// compute the next state vector
		Vector	product;
		for (int j = 0; j < N_STATES; j++)
			{
			double	sum = 0.0;
			for (int k = 0; k < N_STATES; k++)
				sum += current[ k ] * transition[ k ][ j ];
			product[ j ] = sum;
			}
		memcpy( current, product, sizeof( current ) );
		}
}