// matrix_example.cpp
// This module demonstrates how to use the matrix11 class to transform a 2-D coordinate
// 
#include <time.h>                    
#include "matrix.h"  
#include <iomanip>


using namespace std;
using namespace math;
//using namespace math;


int main ()
{
	const float RAD=3.14159/180.0;	// degrees to radians conversion factor

	math::matrix<float> a(3,3);	// a 3x3 matrix of floats
	a.Unit();				// sets the a matrix to be a unit matrix; ie: 1's on the diagonal

	// setup the matrix elements to represent a transformation including 30 degrees of rotation
	// and a translation of 10, -15
	a(0,0) = cos(30*RAD);		
	a(1,0) = sin(30*RAD);
	a(0,1) = -sin(30*RAD);
	a(1,1) = cos(30*RAD);

	a(0,2) = 10.0;				// =px
	a(1,2) = -15.0;				// =py
	
	// echo the matrix to the console
	std::cout << std::endl;
	std::cout << std::setprecision(4) << std::setw(12) << "a" << std::endl<< a << std::endl;
	std::cout << std::endl;

	matrix<float> v2(3,1);		// a 3x1 column homogeneous vector representing the coordinate v2=15,20
	v2(0,0) = 15.0;
	v2(1,0) = 20.0;
	v2(2,0) = 1.0;
	
	matrix<float> v1(3,1);		// another 3x1 column vector - used to represent v1
	v1 = a*v2;					// operator* is overloaded to allow easy matrix multiplication
	// At this point, v1 is the transformed coordinate v2

	std::cout << std::endl;
	std::cout << std::setprecision(4) << "v2" << std::endl<< v2 << std::endl;
	std::cout << std::endl;
	std::cout << std::setprecision(4) << "v1" << std::endl<< v1 << std::endl;

	matrix<float> b(3,3);	// another matrix to represent the inverse of a
	b = !a;					// operator! is overloaded; !a returns the inverse of a

	std::cout << std::setprecision(4) << std::setw(12) << "a" << std::endl<< a << std::endl;
	std::cout << std::endl;
	std::cout << std::setprecision(4) << std::setw(12) << "b" << std::endl<< b << std::endl;
	std::cout << std::endl;

	v2 = b*v1;				// the result should be what we started out with for v2
	// v2 should have the same values at it did originally (except for roundoff); the diggity!

	std::cout << std::endl;
	std::cout << std::setprecision(4) << "v2" << std::endl<< v2 << std::endl;
	std::cout << std::endl;
	std::cout << std::setprecision(4) << "v1" << std::endl<< v1 << std::endl;
}