#include <string>
#include <iostream>
#include <iomanip>

#include "TRandom3.h"

#include "JLang/JException.hh"

#include "JMath/JMatrix3S.hh"
#include "JMath/JMathTestkit.hh"

#include "Jeep/JParser.hh"
#include "Jeep/JMessage.hh"


/**
 * \file
 *
 * Example program to test inversion of symmetric matrix.
 * \author mdejong
 */
int main(int argc, char**argv)
{
  using namespace std;
  using namespace JPP;

  double precision;
  int    debug;

  try {

    JParser<> zap("Example program to test inversion and eigenvalue decomposition of 3D symmetric matrix.");

    zap['e'] = make_field(precision)      = 1.0e-6;
    zap['d'] = make_field(debug)          = 3;

    zap(argc, argv);
  }
  catch(const exception &error) {
    FATAL(error.what() << endl);
  }


  gRandom->SetSeed(0);


  JMatrix3S A = getRandom<JMatrix3S>();

  DEBUG("Matrix A" << endl);
  DEBUG(A << endl);

  NOTICE("Determinant A " << A.getDeterminant() << endl);

  try {

    JMatrix3S B(A);
    
    B.invert();

    DEBUG("Matrix A^-1" << endl);
    DEBUG(B << endl);

    NOTICE("Determinant A^-1 = " << B.getDeterminant() << endl);

    JMatrix3D C(A * B);

    DEBUG("Matrix A x A^-1" << endl);
    DEBUG(C << endl);

    NOTICE("Determinant (A x A^-1)           = " << C.getDeterminant()                      << endl);
    NOTICE("Determinant A x Determinant A^-1 = " << A.getDeterminant() * B.getDeterminant() << endl);
    NOTICE("A x A^-1 = I ? "                     << C.isIdentity(precision)                 << endl);
      
    if (!C.isIdentity(precision)) {
      ERROR("Matrix A x A^-1 /= I" << endl);
    }      

    JMatrix3D D = C - JMatrix3D::getIdentity();

    DEBUG("Matrix D = C - I" << endl);
    DEBUG(D << endl);

    DEBUG("Eigenvalues v of matrix A" << endl);

    JMatrix3S::eigen_values v = A.getEigenValues();

    for (JMatrix3S::eigen_values::const_iterator i = v.cbegin(); i != v.cend(); ++i) {
      DEBUG(SCIENTIFIC(12,3) << *i);
    }

    DEBUG(endl);

    ASSERT(fabs(v[0]) > fabs(v[1]));
    ASSERT(fabs(v[1]) > fabs(v[2]));

    ASSERT(JMatrix3S(A).sub(v[0] * JMatrix3D::getIdentity()).getDeterminant() < precision);
    ASSERT(JMatrix3S(A).sub(v[1] * JMatrix3D::getIdentity()).getDeterminant() < precision);
    ASSERT(JMatrix3S(A).sub(v[2] * JMatrix3D::getIdentity()).getDeterminant() < precision);

    ASSERT(C.isIdentity(precision));
  }
  catch (const JException& error) {
    FATAL(error << endl);
  }

  return 0;
}