Include copy of ALF in Solution directory.

Tutorial/Solutions/Exercise_1/ALF/Analysis/Makefile

+.PHONY : all tidy clean
+BINS= cov_scal.out cov_tau.out cov_tau_ph.out Max_SAC.out   cov_eq.out
+OBJS= cov_scal.o   cov_tau.o   cov_tau_ph.o   Max_SAC.o   cov_eq.o
+OBJS1 = Predefined_Latt_mod.o 
+MODS=predefined_lattices.mod
+
+all: $(OBJS1) $(BINS) 
+
+cov_tau_ph.F90 : cov_tau.F90
+	cpp -w -P -DPartHole cov_tau.F90 -o cov_tau_ph.F90
+
+%.o: %.F90
+	$(ALF_FC) -c $*.F90 $(ALF_FLAGS_ANA) 
+
+%.out: %.F90
+	$(ALF_FC) -c $(ALF_FLAGS_ANA) $<
+	$(ALF_FC) -o $@ $*.o $(OBJS1) $(ALF_LIB)
+
+tidy:
+	rm -f $(OBJS) $(OBJS1) $(MODS) cov_tau_ph.F90
+
+clean: tidy
+	rm -f $(BINS)

Tutorial/Solutions/Exercise_1/ALF/Analysis/Max_SAC.F90

+!  Copyright (C) 2016-2019 The ALF project
+!
+!     The ALF project 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 3 of the License, or
+!     (at your option) any later version.
+!
+!     The ALF project 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 Foobar.  If not, see http://www.gnu.org/licenses/.
+!
+!     Under Section 7 of GPL version 3 we require you to fulfill the following additional terms:
+!
+!     - It is our hope that this program makes a contribution to the scientific community. Being
+!       part of that community we feel that it is reasonable to require you to give an attribution
+!       back to the original authors if you have benefitted from this program.
+!       Guidelines for a proper citation can be found on the project's homepage
+!       http://alf.physik.uni-wuerzburg.de .
+!
+!     - We require the preservation of the above copyright notice and this license in all original files.
+!
+!     - We prohibit the misrepresentation of the origin of the original source files. To obtain
+!       the original source files please visit the homepage http://alf.physik.uni-wuerzburg.de .
+!
+!     - If you make substantial changes to the program we require you to either consider contributing
+!       to the ALF project or to mark your material in a reasonable way as different from the original version.
+     Program MaxEnt_Wrapper
+
+!--------------------------------------------------------------------
+!> @author
+!> ALF-project
+!
+!> @brief
+!> General wrapper for maxent.  Handles particle, partile-hole, particle-particle,
+!> channels as well as zero temperature.  See documentation for details.
+!>
+!
+!--------------------------------------------------------------------
+       Use MaxEnt_stoch_mod
+
+       Implicit  None
+       !Implicit Real (Kind=Kind(0.d0)) (A-G,O-Z)
+       !Implicit Integer (H-N)
+
+       Interface
+          Subroutine  Rescale ( XCOV, XQMC,XTAU, Ntau_st, Ntau_en, Tolerance,  Ntau)
+            Implicit none
+            Real (Kind=Kind(0.d0)), INTENT(INOUT),allocatable ::  XCOV(:,:), XQMC(:), XTAU(:)
+            Real (Kind=Kind(0.d0)), INTENT (IN) :: Tolerance
+            Integer,  INTENT(IN)    ::  Ntau_st, Ntau_en
+            Integer,  INTENT(INOUT) ::  Ntau
+          end Subroutine Rescale
+       end Interface
+
+       Real (Kind=Kind(0.d0)), Dimension(:)  , allocatable :: XQMC, XQMC_st, XTAU, Xtau_st, &
+            &                                                 Alpha_tot, om_bf, alp_bf, xom, A
+       Real (Kind=Kind(0.d0)), Dimension(:,:), allocatable :: XCOV, XCOV_st
+       Real (Kind=Kind(0.d0))                              :: X_moments(2), Xerr_moments(2)
+       Real (Kind=Kind(0.d0)), External                    :: XKER_ph, Back_trans_ph, XKER_pp, Back_trans_pp, &
+            &                                                 XKER_p, Back_trans_p, XKER_T0, Back_trans_T0
+       Character (Len=64)                                  :: command, File1, File2
+       Complex (Kind=Kind(0.d0))                           :: Z
+
+
+       Integer                :: Ngamma, Ndis,  NBins, NSweeps, Nwarm, N_alpha, N_cov
+       Integer                :: N_skip, N_rebin, Norb
+       Real (Kind=Kind(0.d0)) :: OM_st, OM_en,  alpha_st, R, Tolerance
+       Logical                :: Checkpoint
+       Character (Len=2)      :: Channel
+
+       Integer                :: nt, nt1, io_error, n,nw, nwp, ntau, N_alpha_1, i,  nbin_qmc
+       Integer                :: ntau_st, ntau_en, ntau_new, Ntau_old
+       Real (Kind=Kind(0.d0)) :: dtau, pi, xmom1, x,x1,x2, tau, omp, om, Beta,err, delta, Dom
+       Real (Kind=Kind(0.d0)) :: Zero
+
+       NAMELIST /VAR_Max_Stoch/ Ngamma, Ndis,  NBins, NSweeps, Nwarm, N_alpha, &
+            &                   OM_st, OM_en,  alpha_st, R,  Checkpoint, Channel, Tolerance
+
+       NAMELIST /VAR_errors/    N_skip, N_rebin, N_cov
+
+       open(unit=30,file='parameters',status='old',action='read', iostat=io_error)
+       if (io_error.eq.0) then
+          READ(30,NML=VAR_errors)
+          READ(30,NML=VAR_Max_Stoch)
+       else
+          write(error_unit,*) 'No file parameters '
+          error stop 1
+       endif
+       close(30)
+
+       Open(unit=50,File='Info_MaxEnt',Status="unknown")
+       write(50,*) 'Channel      :: ', Channel
+       If (Channel == "ph" )  then
+          Write(50,*)  'Om_start is set to zero. PH channel corresponds to symmetric data '
+          Om_st = 0.d0
+       endif
+       Write(50, "('Covariance         :: ',I2)")  N_cov
+       Write(50, "('Checkpoint         :: ',L )")  Checkpoint
+       Write(50, "('Om_st, Om_en       :: ',2x,F12.6,2x,F12.6)") Om_st, Om_en
+       Write(50, "('Delta Om           :: ',2x,F12.6)")  (Om_en - Om_st)/real(Ndis,kind(0.d0))
+       Write(50, "('Bins, Sweeps, Warm :: ',2x,I4,2x,I4,2x,I4)") NBins, NSweeps, Nwarm
+       If (N_alpha <= 10 ) then
+          Write(error_unit,*) 'Not enough temperatures: N_alpha has to be bigger than 10'
+          error stop 1
+       Endif
+       Write(50, "('N_Alpha, Alpha_st,R:: ',2x,I4,F12.6,2x,F12.6)") N_alpha, alpha_st, R
+
+
+       open (unit=10,File="g_dat", status="unknown")
+       read(10,*)  ntau, nbin_qmc, Beta, Norb
+       Allocate ( XCOV(NTAU,NTAU), XQMC(NTAU),XTAU(NTAU) )
+       XCOV  = 0.d0
+       Do nt = 1,NTAU
+          read(10,*)  xtau(nt), xqmc(nt), err
+          xcov(nt,nt) = err*err
+       Enddo
+       if (N_cov.eq.1) then
+          do nt = 1,ntau
+             do nt1 = 1,ntau
+                read(10,*) xcov(nt,nt1)
+             enddo
+          enddo
+       endif
+       close(10)
+       dtau = Xtau(2) - Xtau(1)
+
+       Zero = 1.D-10
+       pi = acos(-1.d0)
+       Ntau_st = 1
+       Ntau_en = Ntau
+       Select Case (Channel)
+       Case ("PH")
+          xmom1 = pi * xqmc(1)
+       Case ("PP")
+          xmom1 = 2.d0* pi * xqmc(1)
+       Case ("P")
+          xmom1 =  pi * real(norb,Kind(0.d0))
+          !  Remove the tau = beta point from the data since it is  correlated
+          !  due to the sum rule with  the tau=0 data point. Also if the tau = 0
+          !  data point has no fluctations (due to particle-hole symmetry for instance)
+          !  it will be removed.
+          Ntau_en = Ntau - 1
+          Ntau_st = 1
+          if ( xcov(1,1) < zero )  ntau_st = 2
+       Case ("T0")
+          xmom1 =  pi*xqmc(1)
+          Ntau_st = 1
+          if ( xcov(1,1) < zero )  ntau_st = 2
+       Case default
+          Write(error_unit,*) "Channel not yet implemented"
+          error stop 1
+       end Select
+       Ntau_old = Ntau
+       Call Rescale ( XCOV, XQMC,XTAU, Ntau_st, Ntau_en, Tolerance, NTAU)
+       Write(50,"('Data has been rescaled from Ntau  ',  I4,' to ', I4)")  NTAU_old, Ntau
+       If ( Ntau <= 4 ) then
+          write(error_unit,*) 'Not enough data!'
+          error stop 1
+       Endif
+       If (  nbin_qmc > 2*Ntau .and. N_cov == 0  )   Write(50,*) 'Consider using the covariance. You seem to have enough bins'
+       If (  nbin_qmc < 2*Ntau .and. N_cov == 1  )   Write(50,*) 'You do not seem to have enough bins for a reliable estimate of the covariance '
+
+
+       ! Store
+       Allocate ( XCOV_st(NTAU,NTAU), XQMC_st(NTAU),XTAU_st(NTAU) )
+       XCOV_st = XCOV
+       XQMC_st = XQMC
+       XTAU_st = XTAU
+
+
+       Allocate (Alpha_tot(N_alpha) )
+       do nt = 1,N_alpha
+          alpha_tot(nt) = alpha_st*(R**(nt-1))
+       enddo
+       write(50,"('First Moment, Beta  ',2x,F12.6,2x,F12.6)")  Xmom1, Beta
+
+       Select Case (Channel)
+       Case ("PH")
+          If (N_cov == 1 ) then
+             Call MaxEnt_stoch(XQMC, Xtau, Xcov, Xmom1, XKER_ph, Back_Trans_ph, Beta, &
+                  &            Alpha_tot, Ngamma, OM_ST, OM_EN, Ndis, Nsweeps, NBins, NWarm, N_Cov)
+          else
+             Call MaxEnt_stoch(XQMC, Xtau, Xcov, Xmom1, XKER_ph, Back_Trans_ph, Beta, &
+                  &            Alpha_tot, Ngamma, OM_ST, OM_EN, Ndis, Nsweeps, NBins, NWarm)
+          endif
+          ! Beware: Xqmc and cov are modified in the MaxEnt_stoch call.
+       Case ("PP")
+          If (N_cov == 1 ) then
+             Call MaxEnt_stoch(XQMC, Xtau, Xcov, Xmom1, XKER_pp, Back_Trans_pp, Beta, &
+                  &            Alpha_tot, Ngamma, OM_ST, OM_EN, Ndis, Nsweeps, NBins, NWarm, N_Cov)
+          else
+             Call MaxEnt_stoch(XQMC, Xtau, Xcov, Xmom1, XKER_pp, Back_Trans_pp, Beta, &
+                  &            Alpha_tot, Ngamma, OM_ST, OM_EN, Ndis, Nsweeps, NBins, NWarm)
+          endif
+          ! Beware: Xqmc and cov are modified in the MaxEnt_stoch call.
+       Case ("P")
+          If (N_cov == 1 ) then
+             Call MaxEnt_stoch(XQMC, Xtau, Xcov, Xmom1, XKER_p, Back_Trans_p, Beta, &
+                  &            Alpha_tot, Ngamma, OM_ST, OM_EN, Ndis, Nsweeps, NBins, NWarm, N_Cov)
+          else
+             Call MaxEnt_stoch(XQMC, Xtau, Xcov, Xmom1, XKER_p, Back_Trans_p, Beta, &
+                  &            Alpha_tot, Ngamma, OM_ST, OM_EN, Ndis, Nsweeps, NBins, NWarm)
+          endif
+          ! Beware: Xqmc and cov are modified in the MaxEnt_stoch call.
+       Case ("T0")
+          If (N_cov == 1 ) then
+             Call MaxEnt_stoch(XQMC, Xtau, Xcov, Xmom1, XKER_T0, Back_Trans_T0, Beta, &
+                  &            Alpha_tot, Ngamma, OM_ST, OM_EN, Ndis, Nsweeps, NBins, NWarm, N_Cov)
+          else
+             Call MaxEnt_stoch(XQMC, Xtau, Xcov, Xmom1, XKER_T0, Back_Trans_T0, Beta, &
+                  &            Alpha_tot, Ngamma, OM_ST, OM_EN, Ndis, Nsweeps, NBins, NWarm)
+          endif
+          ! Beware: Xqmc and cov are modified in the MaxEnt_stoch call.
+       Case default
+          Write(error_unit,*) "Channel not yet implemented"
+          error stop 1
+       end Select
+
+       If ( .not.  Checkpoint ) then
+          Command = "rm dump*"
+          Call System (Command)
+          Command = "ls"
+          Call System (Command)
+       endif
+       Open (Unit=10,File="energies",status="unknown")
+
+       Do n = 1,N_alpha
+          Read(10,*) X,X1,X2
+       enddo
+       Write(50,"('Chisq at lowest temperature: 1/T, Chi^2, Error',2x,F12.6,2x,F12.6,2x,F12.6)") X,X1,X2
+       close(50)
+
+
+
+       Open (Unit = 10,File="Best_fit", Status ="unknown")
+       Allocate (om_bf(Ngamma), alp_bf(Ngamma) )
+       DO i = 1, Ngamma
+          read(10,*)  om_bf(i), alp_bf(i)
+       Enddo
+       close(10)
+
+       Open (Unit = 11,File="Data_out", Status ="unknown")
+       do nt = 1,Ntau
+          X = 0.d0
+          tau = xtau_st(nt)
+          Select Case (Channel)
+          Case ("PH")
+             do i = 1,Ngamma
+                X = X + alp_bf(i)*Xker_ph(tau,om_bf(i), beta)
+             enddo
+          Case ("PP")
+             do i = 1,Ngamma
+                X = X + alp_bf(i)*Xker_pp(tau,om_bf(i), beta)
+             enddo
+          Case ("P")
+             do i = 1,Ngamma
+                X = X + alp_bf(i)*Xker_p(tau,om_bf(i), beta)
+             enddo
+          Case ("T0")
+             do i = 1,Ngamma
+                X = X + alp_bf(i)*Xker_T0(tau,om_bf(i), beta)
+             enddo
+          Case default
+             Write(error_unit,*) "Channel not yet implemented"
+             error stop 1
+          end Select
+          Write(11,"(F14.7,2x,F14.7,2x,F14.7,2x,F14.7)")  xtau_st(nt), xqmc_st(nt),  sqrt(xcov_st(nt,nt)), xmom1*X
+       enddo
+       close(11)
+
+       N_alpha_1 = N_alpha - 10
+       File1 ="Aom_ps"
+       file2 =File_i(File1,N_alpha_1)
+       Open(Unit=66,File=file2,status="unknown")
+       Allocate (xom(Ndis), A(Ndis))
+       do nw = 1,Ndis
+          read(66,*) xom(nw), A(nw), x, x1, x2
+       enddo
+       close(66)
+       Dom = xom(2) - xom(1)
+
+       ! Compute the real frequency Green function.
+       delta = Dom
+       Open (Unit=43,File="Green", Status="unknown", action="write")
+       pi = acos(-1.d0)
+       do nw = 1,Ndis
+          Z = cmplx(0.d0,0.d0,Kind(0.d0))
+          om = xom(nw)
+          do nwp = 1,Ndis
+             omp = xom(nwp)
+             Z = Z + A(nwp)/cmplx( om -  omp, delta, kind(0.d0))
+          enddo
+          Z = Z * dom
+          write(43,"('X'2x,F14.7,2x,F16.8,2x,F16.8)" ) xom(nw), dble(Z), -Aimag(Z)/pi
+       enddo
+       close(43)
+
+
+     end Program MaxEnt_Wrapper
+
+
+
+     Real (Kind=Kind(0.d0)) function XKER_ph(tau,om, beta)
+
+       Implicit None
+       real (Kind=Kind(0.d0)) :: tau, om, pi, beta
+
+       pi = 3.1415927
+
+       XKER_ph = (exp(-tau*om) + exp(-( beta - tau )*om ) )/( pi*(1.d0 + exp( - beta * om ) ) )
+
+     end function XKER_ph
+
+     Real (Kind=Kind(0.d0)) function XKER_pp(tau,om, beta)
+
+       Implicit None
+       real (Kind=Kind(0.d0)) :: tau, om, pi, beta
+
+       pi = 3.1415927
+
+       XKER_pp = exp(-tau*om) / ( pi*(1.d0 + exp( - beta * om ) ) )
+
+     end function XKER_pp
+
+     Real (Kind=Kind(0.d0)) function XKER_p(tau,om, beta)
+
+       Implicit None
+       real (Kind=Kind(0.d0)) :: tau, om, pi, beta
+
+       pi = 3.1415927
+
+       XKER_p  = exp(-tau*om) / ( pi*(1.d0 + exp( - beta * om ) ) )
+
+     end function XKER_p
+
+     Real (Kind=Kind(0.d0)) function XKER_T0(tau,om, beta)
+
+       Implicit None
+       real (Kind=Kind(0.d0)) :: tau, om, pi, beta
+
+       pi = 3.1415927
+
+       XKER_T0  = exp(-tau*om) / pi
+
+     end function XKER_T0
+
+
+     Real (Kind=Kind(0.d0)) function Back_trans_ph(Aom, om, beta)
+
+       Implicit None
+       real (Kind=Kind(0.d0)) ::  Aom, om, beta
+
+       Back_trans_ph = Aom/(1.d0 + exp(-beta*om) )
+       ! This gives S(q,om) = chi(q,om)/(1 - e^(-beta om))
+
+     end function BACK_TRANS_PH
+
+     Real (Kind=Kind(0.d0)) function Back_trans_pp(Aom, om, beta)
+
+       Implicit None
+       real (Kind=Kind(0.d0)) ::  Aom, om, beta
+       real (Kind=Kind(0.d0)) :: Zero
+
+       Zero = 1.D-8
+
+       if ( abs(om) < zero ) then
+          Back_trans_pp = beta * Aom/2.d0
+       else
+          Back_trans_pp = Aom * (1.d0 - exp(-beta*om) ) / (om *( 1.d0 + exp(-beta*om) ) )
+       endif
+       ! This gives  = chi(q,om)/omega
+
+     end function BACK_TRANS_PP
+
+     Real (Kind=Kind(0.d0)) function Back_trans_p(Aom, om, beta)
+
+       Implicit None
+       real (Kind=Kind(0.d0)) ::  Aom, om, beta
+
+       Back_trans_p =  Aom
+
+     end function BACK_TRANS_P
+
+     Real (Kind=Kind(0.d0)) function Back_trans_T0(Aom, om, beta)
+
+       Implicit None
+       real (Kind=Kind(0.d0)) ::  Aom, om, beta
+
+       Back_trans_T0 =  Aom
+
+     end function BACK_TRANS_T0
+
+
+     Subroutine  Rescale ( XCOV, XQMC,XTAU, Ntau_st, Ntau_en, Tolerance,  Ntau)
+
+       Implicit none
+
+       Real (Kind=Kind(0.d0)), INTENT(INOUT), allocatable ::  XCOV(:,:), XQMC(:), XTAU(:)
+       Real (Kind=Kind(0.d0)), INTENT (IN) :: Tolerance
+
+       Integer,  INTENT(IN)    ::  Ntau_st, Ntau_en
+       Integer,  INTENT(INOUT) ::  Ntau
+
+       !Local
+       Integer :: Ntau_new, nt, nt1
+       Integer, allocatable :: List(:)
+       Real (Kind=Kind(0.d0)), dimension(:,:), allocatable  ::  XCOV_st
+       Real (Kind=Kind(0.d0)), dimension(:)  , allocatable  ::  XQMC_st, XTAU_st
+
+
+
+       ! Count the number of elements
+       ntau_new = 0
+       Do nt = ntau_st,ntau_en
+          if ( sqrt(xcov(nt,nt))/xqmc(nt) < Tolerance .and. xqmc(nt) > 0.d0  ) then
+             ntau_new  = ntau_new + 1
+          endif
+       Enddo
+       Allocate ( XCOV_st(NTAU_new,NTAU_new), XQMC_st(NTAU_new),XTAU_st(NTAU_new), List(NTAU_new) )
+       ntau_new = 0
+       Do nt = ntau_st,ntau_en
+          if ( sqrt(xcov(nt,nt))/xqmc(nt) < Tolerance .and. xqmc(nt) > 0.d0 ) then
+             ntau_new  = ntau_new + 1
+             List(ntau_new) = nt
+          endif
+       Enddo
+       do nt = 1,ntau_new
+          XQMC_st(nt) = XQMC( List(nt) )
+          XTAU_st(nt) = XTAU( List(nt) )
+       enddo
+       do nt = 1,ntau_new
+          do nt1 = 1,ntau_new
+             Xcov_st(nt,nt1) = Xcov(List(nt), List(nt1) )
+          enddo
+       enddo
+       NTAU = NTAU_New
+       Deallocate (XCOV, XQMC,XTAU )
+       allocate   (XCOV(NTAU,NTAU), XQMC(NTAU),XTAU(NTAU) )
+       XCOV = XCOV_st
+       XQMC = XQMC_st
+       XTAU = XTAU_st
+       Deallocate (XCOV_st, XQMC_st,XTAU_st, List )
+
+
+
+
+       end Subroutine Rescale

Tutorial/Solutions/Exercise_1/ALF/Analysis/Old_Stuff/jackv5.F90

+      Program enerJ
+
+        
+        Use ERRORS
+        Implicit none
+
+        REAL    (Kind=Kind(0.d0)), DIMENSION(:,:), ALLOCATABLE :: OBS
+        REAL    (Kind=Kind(0.d0)), DIMENSION(:),   ALLOCATABLE :: EN, SIGN
+        REAL    (Kind=Kind(0.d0)) :: XM, XERR
+
+        Complex (Kind=Kind(0.d0)) Z1,Z2,Z3,Z4,Z5
+        Integer :: NST, NS, NS1, NS2, NSTEP, NC, NP, NOBS, Nbins, NP_EFF, ISEED, I, IOBS
+        Integer :: N, NBIN
+
+        ! Count the number of bins
+        Open (Unit=10, File="ener", status="unknown") 
+        !Open (Unit=12, File="ener_hist", status="unknown") 
+        nbins = 0
+        do
+            read(10,*,End=10)  Z1, Z2, Z3, Z4, Z5
+            nbins = nbins + 1
+         enddo
+10       continue
+         Write(6,*) "# of bins: ", Nbins
+         Close(10) 
+         !Close(12)
+         
+         NP = NBINS
+         NOBS = 5
+         
+         ALLOCATE(OBS(NP,NOBS))
+         !	Error on energy
+
+         !Open (Unit=25, File="statdat1", status="unknown") 
+         !read(25,*) NST, NS1, NS2, NSTEP
+         !Close(25)
+         NST = 1; NS1 = 1; NS2 = 2; NSTEP = 1
+         !If ( L == 15 ) NST = 10
+         !If ( L == 12 ) NST = 8 
+         !If ( L == 9  ) NST = 3 
+         !If ( L == 6  ) NST = 2 
+         !If ( L == 3  ) NST = 2 
+         OPEN (UNIT=20, FILE='ener', STATUS='old')
+         NC = 0
+         DO N = 1,NP
+            IF (N.GE.NST) THEN
+               NC = NC + 1
+               READ(20,*) Z1,Z2,Z3, Z4, Z5
+               OBS(NC,1) = dble(Z1) 
+               OBS(NC,2) = dble(Z2) 
+               OBS(NC,3) = dble(Z3)
+               OBS(NC,4) = dble(Z4) 
+               OBS(NC,5) = dble(Z5)
+            ELSE
+               READ(20,*) Z1,Z2,Z3, Z4, Z5
+            ENDIF
+         ENDDO
+         CLOSE(20)
+2100     FORMAT(I6,2X,F16.8)
+         
+         OPEN (UNIT=21, FILE='enerJ', STATUS='unknown')
+         WRITE(21,*) 'Effective number of bins, and bins: ', NC, NP
+         NP_EFF = NC
+         ALLOCATE (EN(NP_EFF), SIGN(NP_EFF))
+         DO IOBS = 1,NOBS
+            WRITE(21,*)
+            DO I = 1,NP_EFF
+               EN  (I) = OBS(I,IOBS)
+               SIGN(I) = OBS(I,NOBS)
+            ENDDO
+            IF (IOBS.EQ.1) WRITE(21,*) ' rho           '
+            IF (IOBS.EQ.2) WRITE(21,*) ' kin           '
+            IF (