*
* $Id: mnderi.F,v 1.2 1996/03/15 18:02:43 james Exp $
*
* $Log: mnderi.F,v $
* Revision 1.2  1996/03/15 18:02:43  james
*     Modified Files:
* mnderi.F eliminate possible division by zero
* mnexcm.F suppress print on STOP when print flag=-1
*          set FVAL3 to flag if FCN already called with IFLAG=3
* mninit.F set version 96.03
* mnlims.F remove arguments, not needed
* mnmigr.F VLEN -> LENV in debug print statement
* mnparm.F move call to MNRSET to after NPAR redefined, to zero all
* mnpsdf.F eliminate possible division by zero
* mnscan.F suppress printout when print flag =-1
* mnset.F  remove arguments in call to MNLIMS
* mnsimp.F fix CSTATU so status is PROGRESS only if new minimum
* mnvert.F eliminate possible division by zero
*
* Revision 1.1.1.1  1996/03/07 14:31:29  mclareni
* Minuit
*
*
#include "minuit/pilot.h"
      SUBROUTINE MNDERI(FCN,FUTIL)
#include "minuit/d506dp.inc"
CC        Calculates the first derivatives of FCN (GRD),
CC        either by finite differences or by transforming the user-
CC        supplied derivatives to internal coordinates,
CC        according to whether ISW(3) is zero or one.
CC
#include "minuit/d506cm.inc"
      EXTERNAL FCN,FUTIL
      LOGICAL LDEBUG
      CHARACTER CBF1*22
      NPARX = NPAR
      LDEBUG = (IDBG(2) .GE. 1)
      IF (AMIN .EQ. UNDEFI)  CALL MNAMIN(FCN,FUTIL)
      IF (ISW(3) .EQ. 1)  GO TO 100
      IF (LDEBUG) THEN
C                       make sure starting at the right place
        CALL MNINEX(X)
        NPARX = NPAR
        CALL FCN(NPARX,GIN,FS1,U,4,FUTIL)
        NFCN = NFCN + 1
        IF (FS1 .NE. AMIN) THEN
           DF = AMIN - FS1
           WRITE (CBF1(1:12),'(G12.3)') DF
           CALL MNWARN('D','MNDERI',
     +         'function value differs from AMIN by '//CBF1(1:12) )
           AMIN = FS1
        ENDIF
          WRITE
     +   (ISYSWR,'(/''  FIRST DERIVATIVE DEBUG PRINTOUT.  MNDERI''/
     +   '' PAR    DERIV     STEP      MINSTEP   OPTSTEP '',
     +   '' D1-D2    2ND DRV'')')
      ENDIF
      DFMIN = 8. * EPSMA2*(ABS(AMIN)+UP)
      VRYSML = 8.* EPSMAC**2
      IF (ISTRAT .LE. 0) THEN
         NCYC = 2
         TLRSTP = 0.5
         TLRGRD = 0.1
      ELSE IF (ISTRAT .EQ. 1) THEN
         NCYC = 3
         TLRSTP = 0.3
         TLRGRD = 0.05
      ELSE
         NCYC = 5
         TLRSTP = 0.1
         TLRGRD = 0.02
      ENDIF
C                                loop over variable parameters
      DO 60  I=1,NPAR
      EPSPRI = EPSMA2 + ABS(GRD(I)*EPSMA2)
C         two-point derivatives always assumed necessary
C         maximum number of cycles over step size depends on strategy
      XTF = X(I)
      STEPB4 = 0.
C                               loop as little as possible here!
      DO 45 ICYC= 1, NCYC
C                 ........ theoretically best step
      OPTSTP = SQRT(DFMIN/(ABS(G2(I))+EPSPRI))
C                     step cannot decrease by more than a factor of ten
      STEP = MAX(OPTSTP, ABS(0.1*GSTEP(I)))
C                 but if parameter has limits, max step size = 0.5
      IF (GSTEP(I).LT.ZERO .AND. STEP.GT.0.5)  STEP=0.5
C                 and not more than ten times the previous step
      STPMAX = 10.*ABS(GSTEP(I))
      IF (STEP .GT. STPMAX)  STEP = STPMAX
C                 minimum step size allowed by machine precision
      STPMIN = MAX(VRYSML, 8.*ABS(EPSMA2*X(I)))
      IF (STEP .LT. STPMIN)  STEP = STPMIN
C                 end of iterations if step change less than factor 2
      IF (ABS((STEP-STEPB4)/STEP) .LT. TLRSTP)  GO TO 50
C         take step positive
      GSTEP(I) = SIGN(STEP, GSTEP(I))
      STEPB4 = STEP
      X(I) = XTF + STEP
      CALL MNINEX(X)
      CALL FCN(NPARX,GIN,FS1,U,4,FUTIL)
      NFCN=NFCN+1
C         take step negative
      X(I) = XTF - STEP
      CALL MNINEX(X)
      CALL FCN(NPARX,GIN,FS2,U,4,FUTIL)
      NFCN=NFCN+1
      GRBFOR = GRD(I)
      GRD(I) = (FS1-FS2)/(2.0*STEP)
      G2(I) = (FS1+FS2-2.0*AMIN)/(STEP**2)
      X(I) = XTF
      IF (LDEBUG) THEN
         D1D2 = (FS1+FS2-2.0*AMIN)/STEP
         WRITE (ISYSWR,41) I,GRD(I),STEP,STPMIN,OPTSTP,D1D2,G2(I)
   41    FORMAT (I4,2G11.3,5G10.2)
      ENDIF
C         see if another iteration is necessary
      IF (ABS(GRBFOR-GRD(I))/(ABS(GRD(I))+DFMIN/STEP) .LT. TLRGRD)
     +        GO TO 50
   45 CONTINUE
C                           end of ICYC loop. too many iterations
      IF (NCYC .EQ. 1)  GO TO 50
         WRITE (CBF1,'(2E11.3)')  GRD(I),GRBFOR
         CALL MNWARN('D','MNDERI',
     +         'First derivative not converged. '//CBF1)
   50 CONTINUE
C
   60 CONTINUE
      CALL MNINEX(X)
      RETURN
C                                        .  derivatives calc by fcn
  100 DO 150 IINT= 1, NPAR
      IEXT = NEXOFI(IINT)
      IF (NVARL(IEXT) .GT. 1)  GO TO 120
      GRD(IINT) = GIN(IEXT)
      GO TO 150
  120 DD = (BLIM(IEXT)-ALIM(IEXT))*0.5 *COS(X(IINT))
      GRD(IINT) = GIN(IEXT)*DD
  150 CONTINUE
  200 RETURN
      END