//File name  : exMat2d.cc
//Description: an example of 2*2 matrix usage
//Modification: 23/7/98



#include <iostream.h>
#include "amma/Matrix2d.hh"
#include "amma/VecMat2d.hh"
#include "amma/StdMath.hh"
#include "amma/StdStrm.hh"

int main()
{

     //Generate two rotation matrices
  double angle1 = 30./180. *3.14159265;
  double angle2 = 45./180. *3.14159265;

  Matrix2d2C rot1 (::Cos(angle1), -::Sin(angle1),
		   ::Sin(angle1),  ::Cos(angle1));
  
  Matrix2d2C rot2 (::Cos(angle2), -::Sin(angle2),
		   ::Sin(angle2),  ::Cos(angle2));

  //Generate a matrix.
  Matrix2d2C m1(-3, 0, 0, 5) ;

  //Transposition of a matrix
  Matrix2d2C rot1T=rot1.T();

  //Multiplication of matrices
  Matrix2d2C m2(rot1 * m1* rot1.T());
  Matrix2d2C m3(rot2 * m1* rot1.T());

  //Calculate eigenvalues
  Matrix2d2C eV(m2.EigenValues());

  //Represent eigenvalues and its eigenvectors
  VecMat2dC  eVV(m2.EigenSystem());

  //Define three matrices as the output matrice of SVD 
  Matrix2d2C u2, s2, v2;
  Matrix2d2C u3, s3, v3;

  //Calculate two matrices m1 and m2's SVD
  m2.SVD(u2,s2,v2);
  m3.SVD(u3,s3,v3);


  cout    <<"rot1: " <<rot1 <<'\n'
           <<"rot2: " <<rot2 <<'\n'
	   <<"rot1T: " <<rot1T <<'\n'
	   <<"m1: " <<m1 <<'\n'
           <<"m2: " <<m2 <<'\n'
	   <<"m3: " <<m3 <<'\n'
           <<"eV: " <<eV <<'\n'
	   <<"eVV: " <<eVV <<'\n'
	   <<"u2: " <<u2 <<'\n'
	   <<"s2: " <<s2 <<'\n'
	   <<"v2: " <<v2 <<'\n'
	   <<"u3: " <<u3 <<'\n'
	   <<"s3: " <<s3 <<'\n'
	  <<"v3: " <<v3 <<'\n' << endl;

  //Check the results
  Matrix2d2C ceVV = eVV.Matrix();
  Matrix2d2C cm2e = ceVV.T()* m2 *ceVV;
  Matrix2d2C cm2s = u2.T()* m2 *v2;
  Matrix2d2C cm3s = u3.T()* m3 *v3;

  cout    <<"checking\n "
          <<"cm2e: "<< cm2e  <<'\n'          
          <<"cm2s: "<< cm2s << '\n'
          <<"cm3s: "<< cm3s << '\n';
return 0;

}