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

    Grid physics library, www.github.com/paboyle/Grid 

    Source file: ./lib/algorithms/iterative/ImplicitlyRestartedLanczos.h

    Copyright (C) 2015

Author: Peter Boyle <paboyle@ph.ed.ac.uk>
Author: paboyle <paboyle@ph.ed.ac.uk>
Author: Chulwoo Jung <chulwoo@bnl.gov>

    This program is free software; you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation; either version 2 of the License, or
    (at your option) any later version.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License along
    with this program; if not, write to the Free Software Foundation, Inc.,
    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.

    See the full license in the file "LICENSE" in the top level distribution directory
    *************************************************************************************/
    /*  END LEGAL */
#ifndef GRID_LANC_H
#define GRID_LANC_H

#include <string.h> //memset

#ifdef USE_LAPACK
#ifdef USE_MKL
#include<mkl_lapack.h>
#else
void LAPACK_dstegr(char *jobz, char *range, int *n, double *d, double *e,
                   double *vl, double *vu, int *il, int *iu, double *abstol,
                   int *m, double *w, double *z, int *ldz, int *isuppz,
                   double *work, int *lwork, int *iwork, int *liwork,
                   int *info);
//#include <lapacke/lapacke.h>
#endif
#endif

#include <Grid/algorithms/densematrix/DenseMatrix.h>
#include <Grid/algorithms/iterative/EigenSort.h>

// eliminate temorary vector in calc()
#define MEM_SAVE

namespace Grid {

struct Bisection {

#if 0
static void get_eig2(int row_num,std::vector<RealD> &ALPHA,std::vector<RealD> &BETA, std::vector<RealD> & eig)
{
  int i,j;
  std::vector<RealD> evec1(row_num+3);
  std::vector<RealD> evec2(row_num+3);
  RealD eps2;
  ALPHA[1]=0.;
  BETHA[1]=0.;
  for(i=0;i<row_num-1;i++) {
    ALPHA[i+1] = A[i*(row_num+1)].real();
    BETHA[i+2] = A[i*(row_num+1)+1].real();
  }
  ALPHA[row_num] = A[(row_num-1)*(row_num+1)].real();
  bisec(ALPHA,BETHA,row_num,1,row_num,1e-10,1e-10,evec1,eps2);
  bisec(ALPHA,BETHA,row_num,1,row_num,1e-16,1e-16,evec2,eps2);

  // Do we really need to sort here?
  int begin=1;
  int end = row_num;
  int swapped=1;
  while(swapped) {
    swapped=0;
    for(i=begin;i<end;i++){
      if(mag(evec2[i])>mag(evec2[i+1]))	{
	swap(evec2+i,evec2+i+1);
	swapped=1;
      }
    }
    end--;
    for(i=end-1;i>=begin;i--){
      if(mag(evec2[i])>mag(evec2[i+1]))	{
	swap(evec2+i,evec2+i+1);
	swapped=1;
      }
    }
    begin++;
  }

  for(i=0;i<row_num;i++){
    for(j=0;j<row_num;j++) {
      if(i==j) H[i*row_num+j]=evec2[i+1];
      else H[i*row_num+j]=0.;
    }
  }
}
#endif

static void bisec(std::vector<RealD> &c,   
		  std::vector<RealD> &b,
		  int n,
		  int m1,
		  int m2,
		  RealD eps1,
		  RealD relfeh,
		  std::vector<RealD> &x,
		  RealD &eps2)
{
  std::vector<RealD> wu(n+2);

  RealD h,q,x1,xu,x0,xmin,xmax; 
  int i,a,k;

  b[1]=0.0;
  xmin=c[n]-fabs(b[n]);
  xmax=c[n]+fabs(b[n]);
  for(i=1;i<n;i++){
    h=fabs(b[i])+fabs(b[i+1]);
    if(c[i]+h>xmax) xmax= c[i]+h;
    if(c[i]-h<xmin) xmin= c[i]-h;
  }
  xmax *=2.;

  eps2=relfeh*((xmin+xmax)>0.0 ? xmax : -xmin);
  if(eps1<=0.0) eps1=eps2;
  eps2=0.5*eps1+7.0*(eps2);
  x0=xmax;
  for(i=m1;i<=m2;i++){
    x[i]=xmax;
    wu[i]=xmin;
  }

  for(k=m2;k>=m1;k--){
    xu=xmin;
    i=k;
    do{
      if(xu<wu[i]){
	xu=wu[i];
	i=m1-1;
      }
      i--;
    }while(i>=m1);
    if(x0>x[k]) x0=x[k];
    while((x0-xu)>2*relfeh*(fabs(xu)+fabs(x0))+eps1){
      x1=(xu+x0)/2;

      a=0;
      q=1.0;
      for(i=1;i<=n;i++){
	q=c[i]-x1-((q!=0.0)? b[i]*b[i]/q:fabs(b[i])/relfeh);
	if(q<0) a++;
      }
//  	printf("x1=%0.14e a=%d\n",x1,a);
      if(a<k){
	if(a<m1){
	  xu=x1;
	  wu[m1]=x1;
	}else {
	  xu=x1;
	  wu[a+1]=x1;
	  if(x[a]>x1) x[a]=x1;
	}
      }else x0=x1;
    }
    printf("x0=%0.14e xu=%0.14e k=%d\n",x0,xu,k);
    x[k]=(x0+xu)/2;
  }
}
};

/////////////////////////////////////////////////////////////
// Implicitly restarted lanczos
/////////////////////////////////////////////////////////////


template<class Field> 
    class SimpleLanczos {

    const RealD small = 1.0e-16;
public:       
    int lock;
    int get;
    int Niter;
    int converged;

    int Nstop;   // Number of evecs checked for convergence
    int Nk;      // Number of converged sought
    int Np;      // Np -- Number of spare vecs in kryloc space
    int Nm;      // Nm -- total number of vectors


    RealD OrthoTime;

    RealD eresid;

    SortEigen<Field> _sort;

    LinearOperatorBase<Field> &_Linop;

    OperatorFunction<Field>   &_poly;

    /////////////////////////
    // Constructor
    /////////////////////////
    void init(void){};
    void Abort(int ff, DenseVector<RealD> &evals,  DenseVector<DenseVector<RealD> > &evecs);

    SimpleLanczos(
				LinearOperatorBase<Field> &Linop, // op
			       OperatorFunction<Field> & poly,   // polynmial
			       int _Nstop, // sought vecs
			       int _Nk, // sought vecs
			       int _Nm, // spare vecs
			       RealD _eresid, // resid in lmdue deficit 
			       int _Niter) : // Max iterations
      _Linop(Linop),
      _poly(poly),
      Nstop(_Nstop),
      Nk(_Nk),
      Nm(_Nm),
      eresid(_eresid),
      Niter(_Niter)
    { 
      Np = Nm-Nk; assert(Np>0);
    };

    /////////////////////////
    // Sanity checked this routine (step) against Saad.
    /////////////////////////
    void RitzMatrix(DenseVector<Field>& evec,int k){

      if(1) return;

      GridBase *grid = evec[0]._grid;
      Field w(grid);
      std::cout<<GridLogMessage << "RitzMatrix "<<std::endl;
      for(int i=0;i<k;i++){
	_poly(_Linop,evec[i],w);
	std::cout<<GridLogMessage << "["<<i<<"] ";
	for(int j=0;j<k;j++){
	  ComplexD in = innerProduct(evec[j],w);
	  if ( fabs((double)i-j)>1 ) { 
	    if (abs(in) >1.0e-9 )  { 
	      std::cout<<GridLogMessage<<"oops"<<std::endl;
	      abort();
	    } else 
	      std::cout<<GridLogMessage << " 0 ";
	  } else { 
	    std::cout<<GridLogMessage << " "<<in<<" ";
	  }
	}
	std::cout<<GridLogMessage << std::endl;
      }
    }

    void step(DenseVector<RealD>& lmd,
	    DenseVector<RealD>& lme, 
	    Field& last,
	    Field& current, 
	  	Field & next,
		uint64_t k)
    {
	  if (lmd.size()<=k) lmd.resize(k+Nm);
	  if (lme.size()<=k) lme.resize(k+Nm);
      
	
      _poly(_Linop,current,next );   // 3. wk:=Avk−βkv_{k−1}
      if(k>0){
		next -= lme[k-1] * last;
      }    
//	std::cout<<GridLogMessage << "<last|next>" << innerProduct(last,next) <<std::endl;

      ComplexD zalph = innerProduct(current,next); // 4. αk:=(wk,vk)
      RealD     alph = real(zalph);

      next = next - alph * current ;// 5. wk:=wk−αkvk
//	std::cout<<GridLogMessage << "<current|next>" << innerProduct(current,next) <<std::endl;

      RealD beta = normalise(next); // 6. βk+1 := ∥wk∥2. If βk+1 = 0 then Stop
                                 // 7. vk+1 := wk/βk+1
//	 norm=beta;

	int interval = Nm/100+1;
	if ((k%interval)==0) 
	std::cout<<GridLogMessage << k << " : alpha = " << zalph << " beta "<<beta<<std::endl;
      const RealD tiny = 1.0e-20;
      if ( beta < tiny ) { 
	std::cout<<GridLogMessage << " beta is tiny "<<beta<<std::endl;
     }
      lmd[k] = alph;
      lme[k]  = beta;

    }

    void qr_decomp(DenseVector<RealD>& lmd,
		   DenseVector<RealD>& lme,
		   int Nk,
		   int Nm,
		   DenseVector<RealD>& Qt,
		   RealD Dsh, 
		   int kmin,
		   int kmax)
    {
      int k = kmin-1;
      RealD x;

      RealD Fden = 1.0/hypot(lmd[k]-Dsh,lme[k]);
      RealD c = ( lmd[k] -Dsh) *Fden;
      RealD s = -lme[k] *Fden;
      
      RealD tmpa1 = lmd[k];
      RealD tmpa2 = lmd[k+1];
      RealD tmpb  = lme[k];

      lmd[k]   = c*c*tmpa1 +s*s*tmpa2 -2.0*c*s*tmpb;
      lmd[k+1] = s*s*tmpa1 +c*c*tmpa2 +2.0*c*s*tmpb;
      lme[k]   = c*s*(tmpa1-tmpa2) +(c*c-s*s)*tmpb;
      x        =-s*lme[k+1];
      lme[k+1] = c*lme[k+1];
      
      for(int i=0; i<Nk; ++i){
	RealD Qtmp1 = Qt[i+Nm*k  ];
	RealD Qtmp2 = Qt[i+Nm*(k+1)];
	Qt[i+Nm*k    ] = c*Qtmp1 - s*Qtmp2;
	Qt[i+Nm*(k+1)] = s*Qtmp1 + c*Qtmp2; 
      }

      // Givens transformations
      for(int k = kmin; k < kmax-1; ++k){

	RealD Fden = 1.0/hypot(x,lme[k-1]);
	RealD c = lme[k-1]*Fden;
	RealD s = - x*Fden;
	
	RealD tmpa1 = lmd[k];
	RealD tmpa2 = lmd[k+1];
	RealD tmpb  = lme[k];

	lmd[k]   = c*c*tmpa1 +s*s*tmpa2 -2.0*c*s*tmpb;
	lmd[k+1] = s*s*tmpa1 +c*c*tmpa2 +2.0*c*s*tmpb;
	lme[k]   = c*s*(tmpa1-tmpa2) +(c*c-s*s)*tmpb;
	lme[k-1] = c*lme[k-1] -s*x;

	if(k != kmax-2){
	  x = -s*lme[k+1];
	  lme[k+1] = c*lme[k+1];
	}

	for(int i=0; i<Nk; ++i){
	  RealD Qtmp1 = Qt[i+Nm*k    ];
	  RealD Qtmp2 = Qt[i+Nm*(k+1)];
	  Qt[i+Nm*k    ] = c*Qtmp1 -s*Qtmp2;
	  Qt[i+Nm*(k+1)] = s*Qtmp1 +c*Qtmp2;
	}
      }
    }

#ifdef USE_LAPACK
#ifdef USE_MKL
#define LAPACK_INT MKL_INT
#else
#define LAPACK_INT long long
#endif
    void diagonalize_lapack(DenseVector<RealD>& lmd,
		     DenseVector<RealD>& lme, 
		     int N1, // all
		     int N2, // get
		     GridBase *grid) {
  const int size = Nm;
  LAPACK_INT NN = N1;
  double evals_tmp[NN];
  double DD[NN];
  double EE[NN];
  for (int i = 0; i< NN; i++)
    for (int j = i - 1; j <= i + 1; j++)
      if ( j < NN && j >= 0 ) {
        if (i==j) DD[i] = lmd[i];
        if (i==j) evals_tmp[i] = lmd[i];
        if (j==(i-1)) EE[j] = lme[j];
      }
  LAPACK_INT evals_found;
  LAPACK_INT lwork = ( (18*NN) > (1+4*NN+NN*NN)? (18*NN):(1+4*NN+NN*NN)) ;
  LAPACK_INT liwork =  3+NN*10 ;
  LAPACK_INT iwork[liwork];
  double work[lwork];
  LAPACK_INT isuppz[2*NN];
  char jobz = 'N'; // calculate evals only
  char range = 'I'; // calculate il-th to iu-th evals
  //    char range = 'A'; // calculate all evals
  char uplo = 'U'; // refer to upper half of original matrix
  char compz = 'I'; // Compute eigenvectors of tridiagonal matrix
  int ifail[NN];
  LAPACK_INT info;
//  int total = QMP_get_number_of_nodes();
//  int node = QMP_get_node_number();
//  GridBase *grid = evec[0]._grid;
  int total = grid->_Nprocessors;
  int node = grid->_processor;
  int interval = (NN/total)+1;
  double vl = 0.0, vu = 0.0;
  LAPACK_INT il = interval*node+1 , iu = interval*(node+1);
  if (iu > NN)  iu=NN;
  double tol = 0.0;
    if (1) {
      memset(evals_tmp,0,sizeof(double)*NN);
      if ( il <= NN){
        printf("total=%d node=%d il=%d iu=%d\n",total,node,il,iu);
#ifdef USE_MKL
        dstegr(&jobz, &range, &NN,
#else
        LAPACK_dstegr(&jobz, &range, &NN,
#endif
            (double*)DD, (double*)EE,
            &vl, &vu, &il, &iu, // these four are ignored if second parameteris 'A'
            &tol, // tolerance
            &evals_found, evals_tmp, (double*)NULL, &NN,
            isuppz,
            work, &lwork, iwork, &liwork,
            &info);
        for (int i = iu-1; i>= il-1; i--){
          printf("node=%d evals_found=%d evals_tmp[%d] = %g\n",node,evals_found, i - (il-1),evals_tmp[i - (il-1)]);
          evals_tmp[i] = evals_tmp[i - (il-1)];
          if (il>1) evals_tmp[i-(il-1)]=0.;
        }
      }
      {
         grid->GlobalSumVector(evals_tmp,NN);
      }
    } 
// cheating a bit. It is better to sort instead of just reversing it, but the document of the routine says evals are sorted in increasing order. qr gives evals in decreasing order.
}
#undef LAPACK_INT 
#endif


    void diagonalize(DenseVector<RealD>& lmd,
		     DenseVector<RealD>& lme, 
		     int N2,
		     int N1,
		     GridBase *grid)
    {

#ifdef USE_LAPACK
    const int check_lapack=0; // just use lapack if 0, check against lapack if 1

    if(!check_lapack)
	return diagonalize_lapack(lmd,lme,N2,N1,grid);

//	diagonalize_lapack(lmd2,lme2,Nm2,Nm,Qt,grid);
#endif
    }

#if 1
    static RealD normalise(Field& v) 
    {
      RealD nn = norm2(v);
      nn = sqrt(nn);
      v = v * (1.0/nn);
      return nn;
    }

    void orthogonalize(Field& w,
		       DenseVector<Field>& evec,
		       int k)
    {
      double t0=-usecond()/1e6;
      typedef typename Field::scalar_type MyComplex;
      MyComplex ip;

      if ( 0 ) {
	for(int j=0; j<k; ++j){
	  normalise(evec[j]);
	  for(int i=0;i<j;i++){
	    ip = innerProduct(evec[i],evec[j]); // are the evecs normalised? ; this assumes so.
	    evec[j] = evec[j] - ip *evec[i];
	  }
	}
      }

      for(int j=0; j<k; ++j){
	ip = innerProduct(evec[j],w); // are the evecs normalised? ; this assumes so.
	w = w - ip * evec[j];
      }
      normalise(w);
      t0+=usecond()/1e6;
      OrthoTime +=t0;
    }

    void setUnit_Qt(int Nm, DenseVector<RealD> &Qt) {
      for(int i=0; i<Qt.size(); ++i) Qt[i] = 0.0;
      for(int k=0; k<Nm; ++k) Qt[k + k*Nm] = 1.0;
    }


    void calc(
		DenseVector<RealD>& eval,
	      const Field& src,
	      int& Nconv)
      {

	GridBase *grid = src._grid;
//	assert(grid == src._grid);

	std::cout<<GridLogMessage << " -- Nk = " << Nk << " Np = "<< Np << std::endl;
	std::cout<<GridLogMessage << " -- Nm = " << Nm << std::endl;
	std::cout<<GridLogMessage << " -- size of eval   = " << eval.size() << std::endl;
	
//	assert(c.size() && Nm == eval.size());
	
	DenseVector<RealD> lme(Nm);  
	DenseVector<RealD> lmd(Nm);  

	
	Field current(grid);
	Field last(grid);
	Field next(grid);
  
	Nconv = 0;

	RealD beta_k;
  
	// Set initial vector
	// (uniform vector) Why not src??
	//	evec[0] = 1.0;
	current = src;
	std:: cout<<GridLogMessage <<"norm2(src)= " << norm2(src)<<std::endl;
	normalise(current);
	std:: cout<<GridLogMessage <<"norm2(evec[0])= " << norm2(current) <<std::endl;
	
	// Initial Nk steps
	OrthoTime=0.;
	double t0=usecond()/1e6;
	RealD norm; // sqrt norm of last vector

	uint64_t iter=0;

while(1){
	std::vector <RealD> lme2(Nm);
	std::vector <RealD> lmd2(Nm);
	for(uint64_t k=0; k<Nm ; ++k,iter++){
		step(lmd,lme,last,current,next,iter);
		last=current;
		current=next;
	}
	double t1=usecond()/1e6;
	std::cout<<GridLogMessage <<"IRL::Initial steps: "<<t1-t0<< "seconds"<<std::endl; t0=t1;
	std::cout<<GridLogMessage <<"IRL::Initial steps:OrthoTime "<<OrthoTime<< "seconds"<<std::endl;

	  // getting eigenvalues
	lmd2.resize(iter+2);
	lme2.resize(iter+2);
	for(uint64_t k=0; k<iter; ++k){
		lmd2[k+1] = lmd[k];
		lme2[k+2] = lme[k];
	}
	t1=usecond()/1e6;
	std::cout<<GridLogMessage <<"IRL:: copy: "<<t1-t0<< "seconds"<<std::endl; t0=t1;
{
  int total = grid->_Nprocessors;
  int node = grid->_processor;
  int interval = (Nstop/total)+1;
  int iu = (iter+1) - (interval*node+1);
  int il = (iter+1) - (interval*(node+1));
  RealD eps2;
	  Bisection::bisec(lmd2,lme2,iter,il,iu,1e-16,1e-10, eval,eps2);
//	  diagonalize(eval2,lme2,iter,Nk,grid);
	for(int i=il;i<=iu;i++)
	printf("eval[%d]=%0.14e\n",i,eval[i]);
	t1=usecond()/1e6;
	std::cout<<GridLogMessage <<"IRL:: diagonalize: "<<t1-t0<< "seconds"<<std::endl; t0=t1;
}

	for(uint64_t k=0; k<Nk; ++k){
//	    eval[k] = eval2[k];
    }
}

	}






/**
   There is some matrix Q such that for any vector y
   Q.e_1 = y and Q is unitary.
**/
  template<class T>
  static T orthQ(DenseMatrix<T> &Q, DenseVector<T> y){
    int N = y.size();	//Matrix Size
    Fill(Q,0.0);
    T tau;
    for(int i=0;i<N;i++){
      Q[i][0]=y[i];
    }
    T sig = conj(y[0])*y[0];
    T tau0 = fabs(sqrt(sig));
    
    for(int j=1;j<N;j++){
      sig += conj(y[j])*y[j]; 
      tau = abs(sqrt(sig) ); 	

      if(abs(tau0) > 0.0){
	
	T gam = conj( (y[j]/tau)/tau0 );
	for(int k=0;k<=j-1;k++){  
	  Q[k][j]=-gam*y[k];
	}
	Q[j][j]=tau0/tau;
      } else {
	Q[j-1][j]=1.0;
      }
      tau0 = tau;
    }
    return tau;
  }

/**
	There is some matrix Q such that for any vector y
	Q.e_k = y and Q is unitary.
**/
  template< class T>
  static T orthU(DenseMatrix<T> &Q, DenseVector<T> y){
    T tau = orthQ(Q,y);
    SL(Q);
    return tau;
  }


/**
	Wind up with a matrix with the first con rows untouched

say con = 2
	Q is such that Qdag H Q has {x, x, val, 0, 0, 0, 0, ...} as 1st colum
	and the matrix is upper hessenberg
	and with f and Q appropriately modidied with Q is the arnoldi factorization

**/

template<class T>
static void Lock(DenseMatrix<T> &H, 	///Hess mtx	
		 DenseMatrix<T> &Q, 	///Lock Transform
		 T val, 		///value to be locked
		 int con, 	///number already locked
		 RealD small,
		 int dfg,
		 bool herm)
{	
  //ForceTridiagonal(H);

  int M = H.dim;
  DenseVector<T> vec; Resize(vec,M-con);

  DenseMatrix<T> AH; Resize(AH,M-con,M-con);
  AH = GetSubMtx(H,con, M, con, M);

  DenseMatrix<T> QQ; Resize(QQ,M-con,M-con);

  Unity(Q);   Unity(QQ);
  
  DenseVector<T> evals; Resize(evals,M-con);
  DenseMatrix<T> evecs; Resize(evecs,M-con,M-con);

  Wilkinson<T>(AH, evals, evecs, small);

  int k=0;
  RealD cold = abs( val - evals[k]); 
  for(int i=1;i<M-con;i++){
    RealD cnew = abs( val - evals[i]);
    if( cnew < cold ){k = i; cold = cnew;}
  }
  vec = evecs[k];

  ComplexD tau;
  orthQ(QQ,vec);
  //orthQM(QQ,AH,vec);

  AH = Hermitian(QQ)*AH;
  AH = AH*QQ;

  for(int i=con;i<M;i++){
    for(int j=con;j<M;j++){
      Q[i][j]=QQ[i-con][j-con];
      H[i][j]=AH[i-con][j-con];
    }
  }

  for(int j = M-1; j>con+2; j--){

    DenseMatrix<T> U; Resize(U,j-1-con,j-1-con);
    DenseVector<T> z; Resize(z,j-1-con); 
    T nm = norm(z); 
    for(int k = con+0;k<j-1;k++){
      z[k-con] = conj( H(j,k+1) );
    }
    normalise(z);

    RealD tmp = 0;
    for(int i=0;i<z.size()-1;i++){tmp = tmp + abs(z[i]);}

    if(tmp < small/( (RealD)z.size()-1.0) ){ continue;}	

    tau = orthU(U,z);

    DenseMatrix<T> Hb; Resize(Hb,j-1-con,M);	
	
    for(int a = 0;a<M;a++){
      for(int b = 0;b<j-1-con;b++){
	T sum = 0;
	for(int c = 0;c<j-1-con;c++){
	  sum += H[a][con+1+c]*U[c][b];
	}//sum += H(a,con+1+c)*U(c,b);}
	Hb[b][a] = sum;
      }
    }
	
    for(int k=con+1;k<j;k++){
      for(int l=0;l<M;l++){
	H[l][k] = Hb[k-1-con][l];
      }
    }//H(Hb[k-1-con][l] , l,k);}}

    DenseMatrix<T> Qb; Resize(Qb,M,M);	
	
    for(int a = 0;a<M;a++){
      for(int b = 0;b<j-1-con;b++){
	T sum = 0;
	for(int c = 0;c<j-1-con;c++){
	  sum += Q[a][con+1+c]*U[c][b];
	}//sum += Q(a,con+1+c)*U(c,b);}
	Qb[b][a] = sum;
      }
    }
	
    for(int k=con+1;k<j;k++){
      for(int l=0;l<M;l++){
	Q[l][k] = Qb[k-1-con][l];
      }
    }//Q(Qb[k-1-con][l] , l,k);}}

    DenseMatrix<T> Hc; Resize(Hc,M,M);	
	
    for(int a = 0;a<j-1-con;a++){
      for(int b = 0;b<M;b++){
	T sum = 0;
	for(int c = 0;c<j-1-con;c++){
	  sum += conj( U[c][a] )*H[con+1+c][b];
	}//sum += conj( U(c,a) )*H(con+1+c,b);}
	Hc[b][a] = sum;
      }
    }

    for(int k=0;k<M;k++){
      for(int l=con+1;l<j;l++){
	H[l][k] = Hc[k][l-1-con];
      }
    }//H(Hc[k][l-1-con] , l,k);}}

  }
}
#endif


 };

}
#endif