//-----------------------------------------------------------------
//	orthog.cpp	(Gram-Schmidt Orthogonalization Algorithm)	
//	
//	This program implements the Gram-Schmidt orthogonalization
//	process applied to the row-vectors in a matrix of rational 
//	numbers which are typed in by the user.	
//	
//		compile using:  $ g++ orthog.cpp -o orthog	
//	
//	programmer: ALLAN CRUSE	
//	written on: 28 APR 2011
//	revised on: 29 APR 2011 -- to fix prompt and verify basis
//-----------------------------------------------------------------

#include "vmatrix.h"

int input_components( void )
{
	int	m;
	cout << "\nHow many vector-components? ";
	cin >> m;
	cout << endl;
	return	m;
}

int input_dimensions( void )
{
	int	n;
	cout << "\nHow many basis-vectors? ";
	cin >> n;
	cout << endl;
	return	n;
}


int main( void )
{
	system( "clear " );
	int	n = input_dimensions();
	int	m = input_components();

	FractionMatrix	a(n,m);
	cin >> a;
	cout << "\nThe matrix of row-vectors appears below:\n" << a;
	cout << endl;
	getchar();

	// Here's we copy from a[] to b[]
	FractionMatrix	b(n,m);
	for (int r = 0; r < n; r++)
	for (int k = 0; k < m; k++)
		{
		Fraction	f;
		f = a.obtain( r, k );
		b.assign( r, k, f );
		}

	// confirm linear independence of matrix row-vectors
	Fraction	det = 1;
	while ( !a.row_reduced( det ) );
	if ( det == 0 )
		{
		cout << "\nReduced row-echelon form: " << endl << a << endl;
		cout << "determinant = " << det << endl;
		cout << "Quitting: row-vectors are not independent" << endl;
		cout << endl;
		exit(1);
		}
	getchar();

	// main loop to orthogonalize the rows in b[]
	for (int k = 0; k < n; k++)
		{
		for (int r = 0; r < k; r++)
			{
			Fraction	dot_rk = 0;
			Fraction	dot_rr = 0;
			for (int j = 0; j < m; j++)
				{
				dot_rk += b.obtain( r, j ) * b.obtain( k, j );
				dot_rr += b.obtain( r, j ) * b.obtain( r, j );
				}
			Fraction	x = dot_rk / dot_rr;
			b.combine_rows( x, r, k );
			}

		cout << "\nApplying step " << k+1;
		cout << " of Gram-Schmidt algorithm:" << endl;
		cout << b << endl;
		getchar();
		}
}