// Validity test for 5x5 similarity transforms
#include <iostream>
#include "CovMatrices/Similarity5.h"

using namespace CovMatrices;
using namespace std;

CovMatrix5 C(5., 4., 4.1, 3., 3.1, 3.2, 2., 2.1, 2.2, 2.3, 1., 1.1, 1.2, 1.3, 1.4);
Vector5 V, vv[5], vv2[5];
CovMatrix5 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] << " ***" << 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 < 5; ++i)
  {
    for (int j = 0; j < 5; ++j)
    {
      vv2[i][j] = vv[j][i];
    }
  }
  cout << "*** Trying similarityPtAP ***\n";
  similarityPtAP(C,vv2,C2);
  cout << C2 << std::endl;
  return 0;
}