// Validity test for 6x6 similarity transforms
#include <iostream>
#include "CovMatrices/Similarity6.h"

using namespace CovMatrices;
using namespace std;

CovMatrix6 C(6., 
	5.5, 5.4, 
	4.5, 4.4, 4.3, 
	3., 3.1, 3.2, 3.3, 
	2., 2.1, 2.2, 2.2, 2.4, 
	1., 1.1, 1.2, 1.3, 1.4, 1.5);
Vector6 V, vv[6], vv2[6];
CovMatrix6 C2;

int main()
{
  cout << C;
  cout << C.determinant() << std::endl;
  C.diagonalize(V,vv);
  // NOTE: diagonalize produces an array of eigenvectors
  // When used as a matrix, the array is the TRANSPOSE of the
  // similarity matrix needed to diagonalize the original matrix
  cout<<V<<std::endl;
  cout << "*** " << V[0]*V[1]*V[2]*V[3]*V[4]*V[5] << " ***" << std::endl;
  // The following similarity transformations should produce
  // (approximate) diagonal matrices with the eigenvectors as
  // the diagonal elements.
  cout << "*** Trying similarityPAPt ***\n";
  similarityPAPt(C,vv,C2);
  cout << C2 << std::endl;
  for (int i = 0; i < 6; ++i)
  {
    for (int j = 0; j < 6; ++j)
    {
      vv2[i][j] = vv[j][i];
    }
  }
  cout << "*** Trying similarityPtAP ***\n";
  similarityPtAP(C,vv2,C2);
  cout << C2 << std::endl;
  return 0;
}