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				@@ -31,11 +31,16 @@ Author: paboyle <paboyle@ph.ed.ac.uk>
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				#include <string.h> //memset
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				#ifdef USE_LAPACK
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				#ifdef USE_MKL
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				#include<mkl_lapack.h>
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				#else
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				void LAPACK_dstegr(char *jobz, char *range, int *n, double *d, double *e,
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				                   double *vl, double *vu, int *il, int *iu, double *abstol,
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				                   int *m, double *w, double *z, int *ldz, int *isuppz,
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				                   double *work, int *lwork, int *iwork, int *liwork,
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				                   int *info);
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				//#include <lapacke/lapacke.h>
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				#endif
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				#endif
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				#include "DenseMatrix.h"
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				#include "EigenSort.h"
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				@@ -62,12 +67,13 @@ public:
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				    int Np;      // Np -- Number of spare vecs in kryloc space
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				    int Nm;      // Nm -- total number of vectors
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				    RealD OrthoTime;
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				    RealD eresid;
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				    SortEigen<Field> _sort;
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				//    GridCartesian &_fgrid;
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				    LinearOperatorBase<Field> &_Linop;
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				    OperatorFunction<Field>   &_poly;
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				@@ -124,23 +130,23 @@ public:
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				      GridBase *grid = evec[0]._grid;
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				      Field w(grid);
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				      std::cout << "RitzMatrix "<<std::endl;
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				      std::cout<<GridLogMessage << "RitzMatrix "<<std::endl;
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				      for(int i=0;i<k;i++){
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					_poly(_Linop,evec[i],w);
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					std::cout << "["<<i<<"] ";
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					std::cout<<GridLogMessage << "["<<i<<"] ";
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					for(int j=0;j<k;j++){
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					  ComplexD in = innerProduct(evec[j],w);
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					  if ( fabs((double)i-j)>1 ) { 
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					    if (abs(in) >1.0e-9 )  { 
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					      std::cout<<"oops"<<std::endl;
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					      std::cout<<GridLogMessage<<"oops"<<std::endl;
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					      abort();
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					    } else 
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					      std::cout << " 0 ";
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					      std::cout<<GridLogMessage << " 0 ";
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					  } else { 
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					    std::cout << " "<<in<<" ";
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					    std::cout<<GridLogMessage << " "<<in<<" ";
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					  }
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					}
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					std::cout << std::endl;
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					std::cout<<GridLogMessage << std::endl;
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				      }
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				    }
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				@@ -174,10 +180,10 @@ public:
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				      RealD beta = normalise(w); // 6. βk+1 := ∥wk∥2. If βk+1 = 0 then Stop
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				                                 // 7. vk+1 := wk/βk+1
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				//	std::cout << "alpha = " << zalph << " beta "<<beta<<std::endl;
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					std::cout<<GridLogMessage << "alpha = " << zalph << " beta "<<beta<<std::endl;
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				      const RealD tiny = 1.0e-20;
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				      if ( beta < tiny ) { 
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					std::cout << " beta is tiny "<<beta<<std::endl;
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					std::cout<<GridLogMessage << " beta is tiny "<<beta<<std::endl;
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				     }
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				      lmd[k] = alph;
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				      lme[k]  = beta;
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				@@ -253,6 +259,7 @@ public:
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				    }
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				#ifdef USE_LAPACK
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				#define LAPACK_INT long long
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				    void diagonalize_lapack(DenseVector<RealD>& lmd,
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						     DenseVector<RealD>& lme, 
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						     int N1,
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				@@ -262,7 +269,7 @@ public:
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				  const int size = Nm;
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				//  tevals.resize(size);
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				//  tevecs.resize(size);
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				  int NN = N1;
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				  LAPACK_INT NN = N1;
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				  double evals_tmp[NN];
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				  double evec_tmp[NN][NN];
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				  memset(evec_tmp[0],0,sizeof(double)*NN*NN);
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				@@ -276,19 +283,19 @@ public:
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				        if (i==j) evals_tmp[i] = lmd[i];
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				        if (j==(i-1)) EE[j] = lme[j];
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				      }
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				  int evals_found;
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				  int lwork = ( (18*NN) > (1+4*NN+NN*NN)? (18*NN):(1+4*NN+NN*NN)) ;
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				  int liwork =  3+NN*10 ;
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				  int iwork[liwork];
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				  LAPACK_INT evals_found;
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				  LAPACK_INT lwork = ( (18*NN) > (1+4*NN+NN*NN)? (18*NN):(1+4*NN+NN*NN)) ;
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				  LAPACK_INT liwork =  3+NN*10 ;
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				  LAPACK_INT iwork[liwork];
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				  double work[lwork];
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				  int isuppz[2*NN];
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				  LAPACK_INT isuppz[2*NN];
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				  char jobz = 'V'; // calculate evals & evecs
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				  char range = 'I'; // calculate all evals
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				  //    char range = 'A'; // calculate all evals
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				  char uplo = 'U'; // refer to upper half of original matrix
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				  char compz = 'I'; // Compute eigenvectors of tridiagonal matrix
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				  int ifail[NN];
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				  int info;
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				  long long info;
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				//  int total = QMP_get_number_of_nodes();
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				//  int node = QMP_get_node_number();
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				//  GridBase *grid = evec[0]._grid;
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				@@ -296,14 +303,18 @@ public:
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				  int node = grid->_processor;
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				  int interval = (NN/total)+1;
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				  double vl = 0.0, vu = 0.0;
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				  int il = interval*node+1 , iu = interval*(node+1);
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				  LAPACK_INT il = interval*node+1 , iu = interval*(node+1);
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				  if (iu > NN)  iu=NN;
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				  double tol = 0.0;
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				    if (1) {
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				      memset(evals_tmp,0,sizeof(double)*NN);
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				      if ( il <= NN){
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				        printf("total=%d node=%d il=%d iu=%d\n",total,node,il,iu);
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				#ifdef USE_MKL
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				        dstegr(&jobz, &range, &NN,
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				#else
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				        LAPACK_dstegr(&jobz, &range, &NN,
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				#endif
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				            (double*)DD, (double*)EE,
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				            &vl, &vu, &il, &iu, // these four are ignored if second parameteris 'A'
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				            &tol, // tolerance
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				@@ -335,6 +346,7 @@ public:
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				      lmd [NN-1-i]=evals_tmp[i];
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				  }
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				}
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				#undef LAPACK_INT 
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				#endif
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				@@ -365,12 +377,14 @@ public:
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				//	diagonalize_lapack(lmd2,lme2,Nm2,Nm,Qt,grid);
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				#endif
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				      int Niter = 100*N1;
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				      int Niter = 10000*N1;
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				      int kmin = 1;
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				      int kmax = N2;
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				      // (this should be more sophisticated)
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				      for(int iter=0; iter<Niter; ++iter){
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				      for(int iter=0; ; ++iter){
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				      if ( (iter+1)%(100*N1)==0) 
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				      std::cout<<GridLogMessage << "[QL method] Not converged - iteration "<<iter+1<<"\n";
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					// determination of 2x2 leading submatrix
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					RealD dsub = lmd[kmax-1]-lmd[kmax-2];
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				@@ -399,11 +413,11 @@ public:
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				        _sort.push(lmd3,N2);
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				        _sort.push(lmd2,N2);
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				         for(int k=0; k<N2; ++k){
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					    if (fabs(lmd2[k] - lmd3[k]) >SMALL)  std::cout <<"lmd(qr) lmd(lapack) "<< k << ": " << lmd2[k] <<" "<< lmd3[k] <<std::endl;
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				//	    if (fabs(lme2[k] - lme[k]) >SMALL)  std::cout <<"lme(qr)-lme(lapack) "<< k << ": " << lme2[k] - lme[k] <<std::endl;
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					    if (fabs(lmd2[k] - lmd3[k]) >SMALL)  std::cout<<GridLogMessage <<"lmd(qr) lmd(lapack) "<< k << ": " << lmd2[k] <<" "<< lmd3[k] <<std::endl;
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				//	    if (fabs(lme2[k] - lme[k]) >SMALL)  std::cout<<GridLogMessage <<"lme(qr)-lme(lapack) "<< k << ": " << lme2[k] - lme[k] <<std::endl;
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					  }
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				         for(int k=0; k<N1*N1; ++k){
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				//	    if (fabs(Qt2[k] - Qt[k]) >SMALL)  std::cout <<"Qt(qr)-Qt(lapack) "<< k << ": " << Qt2[k] - Qt[k] <<std::endl;
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				//	    if (fabs(Qt2[k] - Qt[k]) >SMALL)  std::cout<<GridLogMessage <<"Qt(qr)-Qt(lapack) "<< k << ": " << Qt2[k] - Qt[k] <<std::endl;
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					}
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				    }
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				#endif
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				@@ -418,7 +432,7 @@ public:
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					  }
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				 | 
			
			 | 
			 | 
			
					}
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				      }
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				      std::cout << "[QL method] Error - Too many iteration: "<<Niter<<"\n";
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				      std::cout<<GridLogMessage << "[QL method] Error - Too many iteration: "<<Niter<<"\n";
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				      abort();
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				    }
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				
 | 
			
		
		
	
	
		
			
				
					
					| 
						
					 | 
				
			
			 | 
			 | 
			
				@@ -435,6 +449,7 @@ public:
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
						       DenseVector<Field>& evec,
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
						       int k)
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				    {
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				      double t0=-usecond()/1e6;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				      typedef typename Field::scalar_type MyComplex;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				      MyComplex ip;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				
 | 
			
		
		
	
	
		
			
				
					
					| 
						
					 | 
				
			
			 | 
			 | 
			
				@@ -453,6 +468,8 @@ public:
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					w = w - ip * evec[j];
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				      }
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				      normalise(w);
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				      t0+=usecond()/1e6;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				      OrthoTime +=t0;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				    }
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				    void setUnit_Qt(int Nm, DenseVector<RealD> &Qt) {
 | 
			
		
		
	
	
		
			
				
					
					| 
						
					 | 
				
			
			 | 
			 | 
			
				@@ -486,10 +503,10 @@ until convergence
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					GridBase *grid = evec[0]._grid;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					assert(grid == src._grid);
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					std::cout << " -- Nk = " << Nk << " Np = "<< Np << std::endl;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					std::cout << " -- Nm = " << Nm << std::endl;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					std::cout << " -- size of eval   = " << eval.size() << std::endl;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					std::cout << " -- size of evec  = " << evec.size() << std::endl;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					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;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					std::cout<<GridLogMessage << " -- size of evec  = " << evec.size() << std::endl;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					assert(Nm == evec.size() && Nm == eval.size());
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					
 | 
			
		
		
	
	
		
			
				
					
					| 
						
					 | 
				
			
			 | 
			 | 
			
				@@ -500,6 +517,7 @@ until convergence
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					DenseVector<int>   Iconv(Nm);
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					DenseVector<Field>  B(Nm,grid); // waste of space replicating
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				//	DenseVector<Field>  Btemp(Nm,grid); // waste of space replicating
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					Field f(grid);
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					Field v(grid);
 | 
			
		
		
	
	
		
			
				
					
					| 
						
					 | 
				
			
			 | 
			 | 
			
				@@ -515,35 +533,48 @@ until convergence
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					// (uniform vector) Why not src??
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					//	evec[0] = 1.0;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					evec[0] = src;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					std:: cout <<"norm2(src)= " << norm2(src)<<std::endl;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					std:: cout<<GridLogMessage <<"norm2(src)= " << norm2(src)<<std::endl;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				// << src._grid  << std::endl;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					normalise(evec[0]);
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					std:: cout <<"norm2(evec[0])= " << norm2(evec[0]) <<std::endl;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					std:: cout<<GridLogMessage <<"norm2(evec[0])= " << norm2(evec[0]) <<std::endl;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				// << evec[0]._grid << std::endl;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					// Initial Nk steps
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					OrthoTime=0.;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					double t0=usecond()/1e6;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					for(int k=0; k<Nk; ++k) step(eval,lme,evec,f,Nm,k);
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				//	std:: cout <<"norm2(evec[1])= " << norm2(evec[1]) << std::endl;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				//	std:: cout <<"norm2(evec[2])= " << norm2(evec[2]) << std::endl;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					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;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				//	std:: cout<<GridLogMessage <<"norm2(evec[1])= " << norm2(evec[1]) << std::endl;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				//	std:: cout<<GridLogMessage <<"norm2(evec[2])= " << norm2(evec[2]) << std::endl;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					RitzMatrix(evec,Nk);
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					t1=usecond()/1e6;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					std::cout<<GridLogMessage <<"IRL::RitzMatrix: "<<t1-t0<< "seconds"<<std::endl; t0=t1;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					for(int k=0; k<Nk; ++k){
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				//	std:: cout <<"eval " << k << " " <<eval[k] << std::endl;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				//	std:: cout <<"lme " << k << " " << lme[k] << std::endl;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				//	std:: cout<<GridLogMessage <<"eval " << k << " " <<eval[k] << std::endl;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				//	std:: cout<<GridLogMessage <<"lme " << k << " " << lme[k] << std::endl;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					}
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					// Restarting loop begins
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					for(int iter = 0; iter<Niter; ++iter){
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  std::cout<<"\n Restart iteration = "<< iter << std::endl;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  std::cout<<GridLogMessage<<"\n Restart iteration = "<< iter << std::endl;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  // 
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  // Rudy does a sort first which looks very different. Getting fed up with sorting out the algo defs.
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  // We loop over 
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  //
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					OrthoTime=0.;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  for(int k=Nk; k<Nm; ++k) step(eval,lme,evec,f,Nm,k);
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					t1=usecond()/1e6;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					std::cout<<GridLogMessage <<"IRL:: "<<Np <<" steps: "<<t1-t0<< "seconds"<<std::endl; t0=t1;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					std::cout<<GridLogMessage <<"IRL::Initial steps:OrthoTime "<<OrthoTime<< "seconds"<<std::endl;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  f *= lme[Nm-1];
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  RitzMatrix(evec,k2);
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					t1=usecond()/1e6;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					std::cout<<GridLogMessage <<"IRL:: RitzMatrix: "<<t1-t0<< "seconds"<<std::endl; t0=t1;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  // getting eigenvalues
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  for(int k=0; k<Nm; ++k){
 | 
			
		
		
	
	
		
			
				
					
					| 
						
					 | 
				
			
			 | 
			 | 
			
				@@ -552,18 +583,27 @@ until convergence
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  }
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  setUnit_Qt(Nm,Qt);
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  diagonalize(eval2,lme2,Nm,Nm,Qt,grid);
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					t1=usecond()/1e6;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					std::cout<<GridLogMessage <<"IRL:: diagonalize: "<<t1-t0<< "seconds"<<std::endl; t0=t1;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  // sorting
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  _sort.push(eval2,Nm);
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					t1=usecond()/1e6;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					std::cout<<GridLogMessage <<"IRL:: eval sorting: "<<t1-t0<< "seconds"<<std::endl; t0=t1;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  // Implicitly shifted QR transformations
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  setUnit_Qt(Nm,Qt);
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  for(int ip=0; ip<k2; ++ip){
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					std::cout<<GridLogMessage << "eval "<< ip << " "<< eval2[ip] << std::endl;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					}
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  for(int ip=k2; ip<Nm; ++ip){ 
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					std::cout << "qr_decomp "<< ip << " "<< eval2[ip] << std::endl;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					std::cout<<GridLogMessage << "qr_decomp "<< ip << " "<< eval2[ip] << std::endl;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					    qr_decomp(eval,lme,Nm,Nm,Qt,eval2[ip],k1,Nm);
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
						
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					}
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				    
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					t1=usecond()/1e6;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					std::cout<<GridLogMessage <<"IRL::qr_decomp: "<<t1-t0<< "seconds"<<std::endl; t0=t1;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				if (0) {  
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  for(int i=0; i<(Nk+1); ++i) B[i] = 0.0;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  for(int j=k1-1; j<k2+1; ++j){
 | 
			
		
		
	
	
		
			
				
					
					| 
						
					 | 
				
			
			 | 
			 | 
			
				@@ -572,14 +612,38 @@ until convergence
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					      B[j] += Qt[k+Nm*j] * evec[k];
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					    }
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  }
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  for(int j=k1-1; j<k2+1; ++j) evec[j] = B[j];
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					t1=usecond()/1e6;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					std::cout<<GridLogMessage <<"IRL::QR Rotate: "<<t1-t0<< "seconds"<<std::endl; t0=t1;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				}
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				if (1) {
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					for(int i=0; i<(Nk+1); ++i) {
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
						B[i] = 0.0;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  	B[i].checkerboard = evec[0].checkerboard;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					}
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					int j_block = 24; int k_block=24;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				PARALLEL_FOR_LOOP
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					for(int ss=0;ss < grid->oSites();ss++){
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					for(int jj=k1-1; jj<k2+1; jj += j_block)
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					for(int kk=0; kk<Nm; kk += k_block)
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					for(int j=jj; (j<(k2+1)) && j<(jj+j_block); ++j){
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					for(int k=kk; (k<Nm) && k<(kk+k_block) ; ++k){
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					    B[j]._odata[ss] +=Qt[k+Nm*j] * evec[k]._odata[ss]; 
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					}
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					}
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					}
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					t1=usecond()/1e6;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					std::cout<<GridLogMessage <<"IRL::QR rotation: "<<t1-t0<< "seconds"<<std::endl; t0=t1;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				}
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					for(int j=k1-1; j<k2+1; ++j) evec[j] = B[j];
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  // Compressed vector f and beta(k2)
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  f *= Qt[Nm-1+Nm*(k2-1)];
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  f += lme[k2-1] * evec[k2];
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  beta_k = norm2(f);
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  beta_k = sqrt(beta_k);
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  std::cout<<" beta(k) = "<<beta_k<<std::endl;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  std::cout<<GridLogMessage<<" beta(k) = "<<beta_k<<std::endl;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
				
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  RealD betar = 1.0/beta_k;
 | 
			
		
		
	
		
			
				 | 
				 | 
			
			 | 
			 | 
			
					  evec[k2] = betar * f;
 | 
			
		
		
	
	
		
			
				
					
					| 
						
					 | 
				
			
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				@@ -592,7 +656,10 @@ until convergence
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					  }
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					  setUnit_Qt(Nm,Qt);
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					  diagonalize(eval2,lme2,Nk,Nm,Qt,grid);
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					t1=usecond()/1e6;
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					std::cout<<GridLogMessage <<"IRL::diagonalize: "<<t1-t0<< "seconds"<<std::endl; t0=t1;
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				if (0) {
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					  for(int k = 0; k<Nk; ++k) B[k]=0.0;
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					  for(int j = 0; j<Nk; ++j){
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				@@ -600,12 +667,34 @@ until convergence
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					    B[j].checkerboard = evec[k].checkerboard;
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					      B[j] += Qt[k+j*Nm] * evec[k];
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					    }
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				//	    std::cout << "norm(B["<<j<<"])="<<norm2(B[j])<<std::endl;
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					    std::cout<<GridLogMessage << "norm(B["<<j<<"])="<<norm2(B[j])<<std::endl;
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					  }
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				//	_sort.push(eval2,B,Nk);
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					t1=usecond()/1e6;
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					std::cout<<GridLogMessage <<"IRL::Convergence rotation: "<<t1-t0<< "seconds"<<std::endl; t0=t1;
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				}
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				if (1) {
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					for(int i=0; i<(Nk+1); ++i) {
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						B[i] = 0.0;
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					  	B[i].checkerboard = evec[0].checkerboard;
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					}
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					int j_block = 24; int k_block=24;
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				PARALLEL_FOR_LOOP
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					for(int ss=0;ss < grid->oSites();ss++){
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					for(int jj=0; jj<Nk; jj += j_block)
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					for(int kk=0; kk<Nk; kk += k_block)
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					for(int j=jj; (j<Nk) && j<(jj+j_block); ++j){
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					for(int k=kk; (k<Nk) && k<(kk+k_block) ; ++k){
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					    B[j]._odata[ss] +=Qt[k+Nm*j] * evec[k]._odata[ss]; 
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					}
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					}
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					}
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					t1=usecond()/1e6;
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					std::cout<<GridLogMessage <<"IRL::convergence rotation : "<<t1-t0<< "seconds"<<std::endl; t0=t1;
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				}
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					  Nconv = 0;
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					  //	  std::cout << std::setiosflags(std::ios_base::scientific);
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					  //	  std::cout<<GridLogMessage << std::setiosflags(std::ios_base::scientific);
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					  for(int i=0; i<Nk; ++i){
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				//	    _poly(_Linop,B[i],v);
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				@@ -613,14 +702,16 @@ until convergence
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					    RealD vnum = real(innerProduct(B[i],v)); // HermOp.
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					    RealD vden = norm2(B[i]);
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					    RealD vv0 = norm2(v);
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					    eval2[i] = vnum/vden;
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					    v -= eval2[i]*B[i];
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					    RealD vv = norm2(v);
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					    std::cout.precision(13);
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					    std::cout << "[" << std::setw(3)<< std::setiosflags(std::ios_base::right) <<i<<"] ";
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					    std::cout << "eval = "<<std::setw(25)<< std::setiosflags(std::ios_base::left)<< eval2[i];
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					    std::cout <<" |H B[i] - eval[i]B[i]|^2 "<< std::setw(25)<< std::setiosflags(std::ios_base::right)<< vv<< std::endl;
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					    std::cout<<GridLogMessage << "[" << std::setw(3)<< std::setiosflags(std::ios_base::right) <<i<<"] ";
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					    std::cout<<"eval = "<<std::setw(25)<< std::setiosflags(std::ios_base::left)<< eval2[i];
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					    std::cout<<"|H B[i] - eval[i]B[i]|^2 "<< std::setw(25)<< std::setiosflags(std::ios_base::right)<< vv;
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					    std::cout<<" "<< vnum/(sqrt(vden)*sqrt(vv0)) << std::endl;
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					// change the criteria as evals are supposed to be sorted, all evals smaller(larger) than Nstop should have converged
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					    if((vv<eresid*eresid) && (i == Nconv) ){
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				@@ -629,17 +720,19 @@ until convergence
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					    }
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					  }  // i-loop end
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					  //	  std::cout << std::resetiosflags(std::ios_base::scientific);
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					  //	  std::cout<<GridLogMessage << std::resetiosflags(std::ios_base::scientific);
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					t1=usecond()/1e6;
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					std::cout<<GridLogMessage <<"IRL::convergence testing: "<<t1-t0<< "seconds"<<std::endl; t0=t1;
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					  std::cout<<" #modes converged: "<<Nconv<<std::endl;
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					  std::cout<<GridLogMessage<<" #modes converged: "<<Nconv<<std::endl;
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					  if( Nconv>=Nstop ){
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					    goto converged;
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					  }
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					} // end of iter loop
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					std::cout<<"\n NOT converged.\n";
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					std::cout<<GridLogMessage<<"\n NOT converged.\n";
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					abort();
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				      converged:
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				@@ -652,10 +745,10 @@ until convergence
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				       }
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				      _sort.push(eval,evec,Nconv);
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				      std::cout << "\n Converged\n Summary :\n";
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				      std::cout << " -- Iterations  = "<< Nconv  << "\n";
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				      std::cout << " -- beta(k)     = "<< beta_k << "\n";
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				      std::cout << " -- Nconv       = "<< Nconv  << "\n";
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				      std::cout<<GridLogMessage << "\n Converged\n Summary :\n";
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				      std::cout<<GridLogMessage << " -- Iterations  = "<< Nconv  << "\n";
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				      std::cout<<GridLogMessage << " -- beta(k)     = "<< beta_k << "\n";
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				      std::cout<<GridLogMessage << " -- Nconv       = "<< Nconv  << "\n";
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				     }
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				    /////////////////////////////////////////////////
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				@@ -678,25 +771,25 @@ until convergence
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					}
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				      }
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				      std::cout<<"Lanczos_Factor start/end " <<start <<"/"<<end<<std::endl;
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				      std::cout<<GridLogMessage<<"Lanczos_Factor start/end " <<start <<"/"<<end<<std::endl;
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				      // Starting from scratch, bq[0] contains a random vector and |bq[0]| = 1
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				      int first;
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				      if(start == 0){
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					std::cout << "start == 0\n"; //TESTING
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					std::cout<<GridLogMessage << "start == 0\n"; //TESTING
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					_poly(_Linop,bq[0],bf);
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					alpha = real(innerProduct(bq[0],bf));//alpha =  bq[0]^dag A bq[0]
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					std::cout << "alpha = " << alpha << std::endl;
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					std::cout<<GridLogMessage << "alpha = " << alpha << std::endl;
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					bf = bf - alpha * bq[0];  //bf =  A bq[0] - alpha bq[0]
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					H[0][0]=alpha;
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					std::cout << "Set H(0,0) to " << H[0][0] << std::endl;
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					std::cout<<GridLogMessage << "Set H(0,0) to " << H[0][0] << std::endl;
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					first = 1;
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				@@ -716,19 +809,19 @@ until convergence
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					beta = 0;sqbt = 0;
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					std::cout << "cont is true so setting beta to zero\n";
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					std::cout<<GridLogMessage << "cont is true so setting beta to zero\n";
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				      }	else {
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					beta = norm2(bf);
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					sqbt = sqrt(beta);
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					std::cout << "beta = " << beta << std::endl;
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					std::cout<<GridLogMessage << "beta = " << beta << std::endl;
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				      }
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				      for(int j=first;j<end;j++){
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					std::cout << "Factor j " << j <<std::endl;
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					std::cout<<GridLogMessage << "Factor j " << j <<std::endl;
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					if(cont){ // switches to factoring; understand start!=0 and initial bf value is right.
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					  bq[j] = bf; cont = false;
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				@@ -751,7 +844,7 @@ until convergence
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					beta = fnorm;
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					sqbt = sqrt(beta);
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					std::cout << "alpha = " << alpha << " fnorm = " << fnorm << '\n';
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					std::cout<<GridLogMessage << "alpha = " << alpha << " fnorm = " << fnorm << '\n';
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					///Iterative refinement of orthogonality V = [ bq[0]  bq[1]  ...  bq[M] ]
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					int re = 0;
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				@@ -786,8 +879,8 @@ until convergence
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					  bck = sqrt( nmbex );
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					  re++;
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					}
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					std::cout << "Iteratively refined orthogonality, changes alpha\n";
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					if(re > 1) std::cout << "orthagonality refined " << re << " times" <<std::endl;
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				 | 
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					std::cout<<GridLogMessage << "Iteratively refined orthogonality, changes alpha\n";
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					if(re > 1) std::cout<<GridLogMessage << "orthagonality refined " << re << " times" <<std::endl;
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					H[j][j]=alpha;
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				 | 
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				      }
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				@@ -802,11 +895,13 @@ until convergence
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				    void ImplicitRestart(int TM, DenseVector<RealD> &evals,  DenseVector<DenseVector<RealD> > &evecs, DenseVector<Field> &bq, Field &bf, int cont)
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				    {
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				      std::cout << "ImplicitRestart begin. Eigensort starting\n";
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				      std::cout<<GridLogMessage << "ImplicitRestart begin. Eigensort starting\n";
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				      DenseMatrix<RealD> H; Resize(H,Nm,Nm);
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				#ifndef USE_LAPACK
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				      EigenSort(evals, evecs);
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				#endif
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				      ///Assign shifts
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				      int K=Nk;
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				@@ -829,15 +924,15 @@ until convergence
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				      /// Shifted H defines a new K step Arnoldi factorization
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				      RealD  beta = H[ff][ff-1]; 
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				      RealD  sig  = Q[TM - 1][ff - 1];
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				      std::cout << "beta = " << beta << " sig = " << real(sig) <<std::endl;
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				      std::cout<<GridLogMessage << "beta = " << beta << " sig = " << real(sig) <<std::endl;
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				      std::cout << "TM = " << TM << " ";
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				      std::cout << norm2(bq[0]) << " -- before" <<std::endl;
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				      std::cout<<GridLogMessage << "TM = " << TM << " ";
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				      std::cout<<GridLogMessage << norm2(bq[0]) << " -- before" <<std::endl;
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				      /// q -> q Q
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				      times_real(bq, Q, TM);
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				      std::cout << norm2(bq[0]) << " -- after " << ff <<std::endl;
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				      std::cout<<GridLogMessage << norm2(bq[0]) << " -- after " << ff <<std::endl;
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				      bf =  beta* bq[ff] + sig* bf;
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				      /// Do the rest of the factorization
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				@@ -861,7 +956,7 @@ until convergence
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				      int ff = Lanczos_Factor(0, M, cont, bq,bf,H); // 0--M to begin with
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				      if(ff < M) {
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					std::cout << "Krylov: aborting ff "<<ff <<" "<<M<<std::endl;
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					std::cout<<GridLogMessage << "Krylov: aborting ff "<<ff <<" "<<M<<std::endl;
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					abort(); // Why would this happen?
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				      }
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				@@ -870,7 +965,7 @@ until convergence
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				      for(int it = 0; it < Niter && (converged < Nk); ++it) {
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					std::cout << "Krylov: Iteration --> " << it << std::endl;
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					std::cout<<GridLogMessage << "Krylov: Iteration --> " << it << std::endl;
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					int lock_num = lock ? converged : 0;
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					DenseVector<RealD> tevals(M - lock_num );
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					DenseMatrix<RealD> tevecs; Resize(tevecs,M - lock_num,M - lock_num);
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				@@ -886,7 +981,7 @@ until convergence
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				      Wilkinson<RealD>(H, evals, evecs, small); 
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				      //      Check();
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				      std::cout << "Done  "<<std::endl;
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				      std::cout<<GridLogMessage << "Done  "<<std::endl;
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				    }
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				@@ -951,7 +1046,7 @@ until convergence
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						  DenseVector<RealD> &tevals, DenseVector<DenseVector<RealD> > &tevecs, 
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						  int lock, int converged)
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				    {
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				      std::cout << "Converged " << converged << " so far." << std::endl;
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				      std::cout<<GridLogMessage << "Converged " << converged << " so far." << std::endl;
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				      int lock_num = lock ? converged : 0;
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				      int M = Nm;
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				@@ -966,7 +1061,9 @@ until convergence
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				      RealD small=1.0e-16;
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				      Wilkinson<RealD>(AH, tevals, tevecs, small);
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				#ifndef USE_LAPACK
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				      EigenSort(tevals, tevecs);
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				#endif
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				      RealD resid_nrm=  norm2(bf);
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				@@ -977,7 +1074,7 @@ until convergence
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					RealD diff = 0;
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					diff = abs( tevecs[i][Nm - 1 - lock_num] ) * resid_nrm;
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					std::cout << "residual estimate " << SS-1-i << " " << diff << " of (" << tevals[i] << ")" << std::endl;
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					std::cout<<GridLogMessage << "residual estimate " << SS-1-i << " " << diff << " of (" << tevals[i] << ")" << std::endl;
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					if(diff < converged) {
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				@@ -993,13 +1090,13 @@ until convergence
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					    lock_num++;
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					  }
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					  converged++;
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					  std::cout << " converged on eval " << converged << " of " << Nk << std::endl;
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					  std::cout<<GridLogMessage << " converged on eval " << converged << " of " << Nk << std::endl;
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					} else {
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					  break;
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					}
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				      }
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				#endif
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				      std::cout << "Got " << converged << " so far " <<std::endl;	
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				      std::cout<<GridLogMessage << "Got " << converged << " so far " <<std::endl;	
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				    }
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				    ///Check
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				@@ -1008,7 +1105,9 @@ until convergence
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				      DenseVector<RealD> goodval(this->get);
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				#ifndef USE_LAPACK
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				      EigenSort(evals,evecs);
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				#endif
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				      int NM = Nm;
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				@@ -1080,10 +1179,10 @@ say con = 2
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				**/
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				template<class T>
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				static void Lock(DenseMatrix<T> &H, 	// Hess mtx	
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						 DenseMatrix<T> &Q, 	// Lock Transform
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						 T val, 		// value to be locked
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						 int con, 	// number already locked
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				static void Lock(DenseMatrix<T> &H, 	///Hess mtx	
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						 DenseMatrix<T> &Q, 	///Lock Transform
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						 T val, 		///value to be locked
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						 int con, 	///number already locked
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						 RealD small,
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						 int dfg,
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						 bool herm)
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