/**********************************************************

This software is part of J.-S. Caux's ABACUS library.

Copyright (c).

-----------------------------------------------------------

File:  LiebLin_Gaudin_lnnorm.cc

Purpose:  calculates the Gaudin norm of a vector of arbitrary
          complex rapidities 

***********************************************************/

#include "JSC.h"

using namespace std;
using namespace JSC;

namespace JSC {

  DP LiebLin_Twisted_lnnorm (Vect<complex<DP> >& lambdaoc, double cxL)
  {
    // Calculates the lnnorm of an eigenstate of the twisted transfer matrix
    // so Gaudin can be used.

    int N = lambdaoc.size();

    SQMat<complex<DP> > Gaudin(N);

    complex<DP> sum_Kernel = 0.0;

    for (int j = 0; j < N; ++j) 
      for (int k = 0; k < N; ++k) {
	if (j == k) {
	  sum_Kernel = 0.0;
	  for (int kp = 0; kp < N; ++kp) if (j != kp) sum_Kernel += 2.0/((lambdaoc[j] - lambdaoc[kp]) * (lambdaoc[j] - lambdaoc[kp]) + 1.0);
	  Gaudin[j][k] = cxL + sum_Kernel;
	}
	else Gaudin[j][k] = - 2.0/((lambdaoc[j] - lambdaoc[k]) * (lambdaoc[j] - lambdaoc[k]) + 1.0);
      }

    DP lnnorm = real(lndet_LU_CX_dstry(Gaudin));

    // Add the pieces outside of Gaudin determinant
    for (int j = 0; j < N - 1; ++j) for (int k = j+1; k < N; ++k) lnnorm += log(1.0 + 1.0/norm(lambdaoc[j] - lambdaoc[k]));

    return(lnnorm);
  }

} // namespace JSC