!  tune3.f95: matrix algebra with modified vector tuning  

      Program  tune3   
      PARAMETER (ldim = 2050)   
      Implicit Double Precision (a-h,o-z)   
      Dimension ham(ldim,ldim),coef(ldim),sigma(ldim),diag(ldim)   
!   
!       set up Hamiltonian and starting vector   
      Do  i = 1,ldim   
         Do  j = 1,ldim   
             If( Abs(j-i) > 10) Then   
                ham(j,i) = 0.0   
             Else   
                ham(j,i) = 0.3**Abs(j-i)   
             EndIf   
         End Do
      End Do
!   
!       start iterating towards the solution   
      Do i = 1,ldim   
         ham(i,i) = i   
         coef(i) = 0.0   
         diag(i) = ham(i,i)
      End Do   
      coef(1) = 1.0   
      err = 1.0   
      iter = 0   
 20   If(iter<15 .and. err>1.0e-6) Then   
          iter = iter+1   
!     compute energy, norm of current approximation,\&  normalize   
! 
      ener = 0.0   
      ovlp = 0.0   
      Do    i = 1,ldim   
         ovlp = ovlp+coef(i)*coef(i)   
         t = 0.0   
         Do    j = 1,ldim   
            t = t + coef(j)*ham(j,i)   
         End Do   
         sigma(i) = t   
         ener = ener + coef(i)*t   
      End Do   
      ener = ener/ovlp   
      fact  = 1.0/Sqrt(ovlp)   
      coef(1)  =  fact*coef(1)   
      err  =  0.0   
      Do    i = 2,ldim   
          t         =   fact*coef(i)   
          u         =   fact*sigma(i) - ener*t   
          step      =   u/(ener - diag(i))   
          coef(i)   =   t + step   
          err       =   err + step*step   
      End Do   
      err = Sqrt(err)   
      Write(*,'(1x,i2,7f10.5)') iter,ener,err,coef(1)   
      GoTo 20    
      EndIf   
      Stop   
      End Program  tune3