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*DECK GRAD
      SUBROUTINE GRAD(NENTRY,HENTRY,IENTRY,JENTRY,KENTRY)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Compute gradients of system characteristics.
*
*Copyright:
* Copyright (C) 2012 Ecole Polytechnique de Montreal
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version
*
*Author(s): 
* A. Hebert
*
*Parameters: input
* NENTRY  number of data structures transfered to this module.
* HENTRY  name of the data structures.
* IENTRY  data structure type where:
*         IENTRY=1 for LCM memory object;
*         IENTRY=2 for XSM file;
*         IENTRY=3 for sequential binary file;
*         IENTRY=4 for sequential ASCII file.
* JENTRY  access permission for the data structure where:
*         JENTRY=0 for a data structure in creation mode;
*         JENTRY=1 for a data structure in modifications mode;
*         JENTRY=2 for a data structure in read-only mode.
* KENTRY  data structure pointer.
*
*Comments:
* The calling specifications are:
* OPTIM := GRAD: [ OPTIM ] DFLUX GPT :: (grad\_data) ;
* where
*   OPTIM : name of the \emph{optimize} object (L\_OPTIMIZE signature) 
*     containing the optimization informations. Object OPTIM must appear on the 
*     RHS to be able to updated the previous values.
*   DFLUX : name of the \emph{flux} object (L\_FLUX signature) containing a set
*     of solutions of fixed-source eigenvalue problems.
*   GPT   : name of the \emph{gpt} object (L\_GPT signature) containing a set 
*     of direct or adjoint sources.
*   (grad\_data) : structure containing the data to the module GRAD:.
*
*-----------------------------------------------------------------------
*
      USE GANLIB
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
*----
*  SUBROUTINE ARGUMENTS
*----
      INTEGER      NENTRY,IENTRY(NENTRY),JENTRY(NENTRY)
      TYPE(C_PTR)  KENTRY(NENTRY)
      CHARACTER    HENTRY(NENTRY)*12
*----
*  LOCAL VARIABLES
*----
      PARAMETER (NSTATE=40)
      TYPE(C_PTR) IPFLX,IPGPT,IPGRAD
      CHARACTER HSIGN*12,TEXT4*4,TEXT12*12,TEXT16*16
      INTEGER ISTATE(NSTATE)
      REAL FLOTT
      DOUBLE PRECISION DFLOTT,SR,EPS1,EPS2,EPS3,EPS4
      DOUBLE PRECISION OPTPRR(NSTATE)
*----
*  ALLOCATABLE ARRAYS
*----
      INTEGER, ALLOCATABLE, DIMENSION(:) :: IREL
      DOUBLE PRECISION, ALLOCATABLE, DIMENSION(:) :: VARV,CSTV,RHS,
     1 DERIV,DERIV0
*----
*  PARAMETER VALIDATION.
*----
      IF((IENTRY(1).NE.1).AND.(IENTRY(1).NE.2)) CALL XABORT('GRAD: LCM'
     1 //' OBJECT EXPECTED AT LHS.')
      IF(JENTRY(1).EQ.2) CALL XABORT('GRAD: OPTIMIZE ENTRY IN CREATE O'
     1 //'R MODIFICATION MODE EXPECTED.')
      DO I=2,NENTRY
         TEXT12=HENTRY(I)
         IF((JENTRY(I).NE.2).OR.((IENTRY(I).NE.1).AND.(IENTRY(I).NE.2)))
     1   CALL XABORT('GRAD: LCM OBJECT IN READ-ONLY MODE EXPECTED AT R'
     2   //'HS ('//TEXT12//').')
      ENDDO
      IPGRAD=KENTRY(1)
      IPFLX=C_NULL_PTR
      IPGPT=C_NULL_PTR
*----
*  RECOVER THE ACTUAL FLUX SOLUTION AND CORRESPONDING TRACKING.
*----
      NVAR0=0
      NCST0=0
      ITYPE=0
      IF(NENTRY.EQ.3) THEN
        CALL LCMGTC(KENTRY(2),'SIGNATURE',12,HSIGN)
        IF(HSIGN.NE.'L_FLUX') THEN
           TEXT12=HENTRY(2)
           CALL XABORT('GRAD: SIGNATURE OF '//TEXT12//' IS '//HSIGN//
     1     '. L_FLUX EXPECTED.')
        ENDIF
        IPFLX=KENTRY(2)
        CALL LCMGET(IPFLX,'STATE-VECTOR',ISTATE)
        ITYPE=ISTATE(3)
        NGPT=ISTATE(5)
        IF(NGPT.EQ.0)  CALL XABORT('GRAD: MISSING FIXED-SOURCE EIGENVA'
     1  //'LUE SOLUTION')
        IPGPT=KENTRY(3)
        CALL LCMGTC(IPGPT,'SIGNATURE',12,HSIGN)
        IF(HSIGN.NE.'L_SOURCE') THEN
           TEXT12=HENTRY(3)
           CALL XABORT('GRAD: SIGNATURE OF '//TEXT12//' IS '//HSIGN//
     1     '. L_SOURCE EXPECTED.')
        ENDIF
        CALL LCMGET(IPGPT,'STATE-VECTOR',ISTATE)
        ND=ISTATE(3)
        NA=ISTATE(4)
*----
*  COMPUTE THE NUMBER OF CONSTRAINTS AND OF CONTROL VARIABLES
*----
        IF(ITYPE.EQ.100) THEN
          NVAR0=NGPT
          NCST0=NA-1
        ELSE IF(ITYPE.EQ.1000) THEN
          NVAR0=ND
          NCST0=NGPT-1
        ELSE
          CALL XABORT('GRAD: INVALID FLUX OBJECT')
        ENDIF
      ENDIF
*----
*  READ INPUT PARAMETERS
*----
      IPRINT=1
      IOPT=1
      ICONV=0
      IEXT=0
      IEDSTP=2
      IHESS=0
      ISEARC=0
      IMETH=2
      ISTEP=0
      JCONV=0
      SR=1.0D0
      EPS1=0.1D0
      EPS2=1.0D-4
      EPS3=1.0D-4
      EPS4=1.0D-4
      IF(JENTRY(1).EQ.0) THEN
        HSIGN='L_OPTIMIZE'
        CALL LCMPTC(IPGRAD,'SIGNATURE',12,HSIGN)
      ELSE IF (JENTRY(1).EQ.1) THEN
        CALL LCMGTC(IPGRAD,'SIGNATURE',12,HSIGN)
        IF(HSIGN.NE.'L_OPTIMIZE') THEN
           TEXT12=HENTRY(3)
           CALL XABORT('GRAD: SIGNATURE OF '//TEXT12//' IS '//HSIGN//
     1     '. L_OPTIMIZE EXPECTED.')
        ENDIF
        CALL LCMGET(IPGRAD,'STATE-VECTOR',ISTATE)
        NVAR=ISTATE(1)
        NCST=ISTATE(2)
        IOPT=ISTATE(3)
        ICONV=ISTATE(4)
        IEXT=ISTATE(5)
        IEDSTP=ISTATE(6)
        IHESS=ISTATE(7)
        ISEARC=ISTATE(8)
        IMETH=ISTATE(9)
        MAXEXT=ISTATE(12)
        NSTART=ISTATE(13)
        CALL LCMGET(IPGRAD,'OPT-PARAM-R',OPTPRR)
        SR=OPTPRR(1)
        EPS1=OPTPRR(2)
        EPS2=OPTPRR(3)
        EPS3=OPTPRR(4)
        EPS4=OPTPRR(5)
      ENDIF
   10 CALL REDGET(INDIC,NITMA,FLOTT,TEXT12,DFLOTT)
      IF(INDIC.EQ.10) GO TO 20
      IF(INDIC.NE.3) CALL XABORT('GRAD: CHARACTER DATA EXPECTED.')
      IF(TEXT12(:4).EQ.'EDIT') THEN
        CALL REDGET(INDIC,IPRINT,FLOTT,TEXT12,DFLOTT)
        IF(INDIC.NE.1) CALL XABORT('GRAD: INTEGER DATA EXPECTED FOR IP'
     1  //'RINT.')
      ELSE IF(TEXT12(:8).EQ.'MINIMIZE') THEN
        IOPT=1
      ELSE IF(TEXT12(:8).EQ.'MAXIMIZE') THEN
        IOPT=-1
      ELSE IF(TEXT12.EQ.'OUT-STEP-LIM') THEN
        CALL REDGET(INDIC,NITMA,FLOTT,TEXT12,DFLOTT)
        IF(INDIC.NE.2) CALL XABORT('GRAD: REAL DATA EXPECTED(1)')
        SR=FLOTT
      ELSE IF((TEXT12(:9).EQ.'VAR-VALUE').OR.
     1        (TEXT12(:10).EQ.'VAR-WEIGHT')) THEN
        ALLOCATE(VARV(NVAR))
        DO IVAR=1,NVAR
          CALL REDGET(INDIC,NITMA,FLOTT,TEXT4,DFLOTT)
          IF(INDIC.NE.2) CALL XABORT('GRAD: REAL DATA EXPECTED(2)')
          VARV(IVAR)=FLOTT
        ENDDO
        CALL LCMPUT(IPGRAD,TEXT12,NVAR,4,VARV)
        DEALLOCATE(VARV)
      ELSE IF((TEXT12(:11).EQ.'VAR-VAL-MIN').OR.
     1        (TEXT12(:11).EQ.'VAR-VAL-MAX')) THEN
        ALLOCATE(VARV(NVAR))
        CALL REDGET(INDIC,NITMA,FLOTT,TEXT4,DFLOTT)
        IF(INDIC.EQ.2) THEN
          VARV=FLOTT
          DO IVAR=2,NVAR
            CALL REDGET(INDIC,NITMA,FLOTT,TEXT4,DFLOTT)
            IF(INDIC.NE.2) CALL XABORT('GRAD: REAL DATA EXPECTED(3)')
            VARV(IVAR)=FLOTT
          ENDDO
        ELSE IF((INDIC.EQ.3).AND.(TEXT4.EQ.'ALL')) THEN
          CALL REDGET(INDIC,NITMA,FLOTT,TEXT4,DFLOTT)
          IF(INDIC.NE.2) CALL XABORT('GRAD: REAL DATA EXPECTED(4)')
          DO IVAR=1,NVAR
            VARV(IVAR)=FLOTT
          ENDDO
        ELSE
          CALL XABORT('GRAD: REAL DATA OR ALL KEYWORD EXPECTED')
        ENDIF
        CALL LCMPUT(IPGRAD,TEXT12,NVAR,4,VARV)
        DEALLOCATE(VARV)
      ELSE IF(TEXT12.EQ.'FOBJ-CST-VAL') THEN
        ALLOCATE(CSTV(NCST+1))
        DO ICST=1,NCST+1
          CALL REDGET(INDIC,NITMA,FLOTT,TEXT4,DFLOTT)
          IF(INDIC.NE.2) CALL XABORT('GRAD: REAL DATA EXPECTED(5)')
          CSTV(ICST)=FLOTT
        ENDDO
        CALL LCMPUT(IPGRAD,'FOBJ-CST-VAL',NCST+1,4,CSTV)
        OBJNEW=CSTV(1)
        DEALLOCATE(CSTV)
      ELSE IF(TEXT12(:8).EQ.'CST-TYPE') THEN
        IF(NCST.EQ.0) CALL XABORT('GRAD: CST-TYPE KEYWORD FORBIDDEN')
        ALLOCATE(IREL(NCST))
        DO ICST=1,NCST
          CALL REDGET(INDIC,NITMA,FLOTT,TEXT4,DFLOTT)
          IF(INDIC.NE.1) THEN
            CALL XABORT('GRAD: INTEGER DATA EXPECTED')
          ELSE IF((NITMA.LT.-1).OR.(NITMA.GT.1)) THEN
            CALL XABORT('GRAD: -1, 0 or 1 EXPECTED')
          ENDIF
          IREL(ICST)=NITMA
        ENDDO
        CALL LCMPUT(IPGRAD,'CST-TYPE',NCST,1,IREL)
        DEALLOCATE(IREL)
      ELSE IF(TEXT12(:7).EQ.'CST-OBJ') THEN
        IF(NCST.EQ.0) CALL XABORT('GRAD: CST-OBJ KEYWORD FORBIDDEN')
        CALL REDGET(INDIC,NITMA,FLOTT,TEXT4,DFLOTT)
        IF(INDIC.EQ.2) THEN
          ALLOCATE(RHS(NCST))
          RHS(1)=FLOTT
          DO ICST=2,NCST
            CALL REDGET(INDIC,NITMA,FLOTT,TEXT4,DFLOTT)
            IF(INDIC.NE.2) CALL XABORT('GRAD: REAL DATA EXPECTED(6)')
            RHS(ICST)=FLOTT
          ENDDO
          CALL LCMPUT(IPGRAD,'CST-OBJ',NCST,4,RHS)
          DEALLOCATE(RHS)
        ELSE
          CALL XABORT('GRAD: REAL DATA OR KEEP KEYWORD EXPECTED')
        ENDIF
      ELSE IF(TEXT12(:10).EQ.'CST-WEIGHT') THEN
        IF(NCST.EQ.0) CALL XABORT('GRAD: CST-WEIGHT KEYWORD FORBIDDEN')
        ALLOCATE(RHS(NCST))
        DO ICST=1,NCST
          CALL REDGET(INDIC,NITMA,FLOTT,TEXT4,DFLOTT)
          IF(INDIC.NE.2) CALL XABORT('GRAD: REAL DATA EXPECTED(7)')
          RHS(ICST)=FLOTT
        ENDDO
        CALL LCMPUT(IPGRAD,'CST-WEIGHT',NCST,4,RHS)
        DEALLOCATE(RHS)
      ELSE IF(TEXT12(:1).EQ.';') THEN
        GO TO 20
      ELSE 
        CALL XABORT('GRAD: '//TEXT12//' IS AN INVALID KEYWORD')
      ENDIF
      GO TO 10
*----
*  CALCULATION OF THE NEW GRADIENT
*----
   20 IF(IPRINT.GT.0) THEN
        IF(ITYPE.EQ.100) THEN
          WRITE(6,'(/25H GRAD: EXPLICIT APPROACH.)')
        ELSE IF(ITYPE.EQ.1000) THEN
          WRITE(6,'(/25H GRAD: IMPLICIT APPROACH.)')
        ENDIF
      ENDIF
      ALLOCATE(DERIV(NVAR*(NCST+1)))
      DERIV(:NVAR*(NCST+1))=0.0D0
      IF(C_ASSOCIATED(IPFLX).AND.C_ASSOCIATED(IPGPT)) THEN
        IF(NVAR0.NE.NVAR) CALL XABORT('GRAD: INCONSISTENT NVAR.')
        IF(NCST0.GT.NCST) CALL XABORT('GRAD: INCONSISTENT NCST.')
*       ------------------------------------------
        CALL GRA001(IPFLX,IPGPT,NVAR0,NCST0,DERIV)
*       ------------------------------------------
      ENDIF
      CALL LCMLEN(IPGRAD,'GRADIENT-DIR',LENGTH,ITYLCM)
      IF(LENGTH.EQ.NVAR*(NCST+1)) THEN
        ALLOCATE(DERIV0(NVAR*(NCST+1)))
        CALL LCMGET(IPGRAD,'GRADIENT-DIR',DERIV0)
        DO I=1,NVAR*(NCST+1)
          DERIV(I)=DERIV(I)+DERIV0(I)
        ENDDO
        DEALLOCATE(DERIV0)
      ENDIF
      CALL LCMPUT(IPGRAD,'GRADIENT',NVAR*(NCST+1),4,DERIV)
      DEALLOCATE(DERIV)
*----
*  PRINT INFORMATION
*----
      IF(IPRINT.GT.0) THEN
        WRITE(6,'(/31H GRAD: INFORMATION AT ITERATION,I5)') IEXT+1
        CALL LCMLEN(IPGRAD,'VAR-VALUE',ILONG,ITYLCM)
        IF(ILONG.GT.0) THEN 
          ALLOCATE(VARV(NVAR))
          CALL LCMGET(IPGRAD,'VAR-VALUE',VARV)
          WRITE(6,100) 'CONTROL VARIABLES:',(VARV(IVAR),IVAR=1,NVAR)
          DEALLOCATE(VARV)
        ENDIF
        IF(IPRINT.GT.1) THEN
          ALLOCATE(DERIV(NVAR*(NCST+1)))
          CALL LCMGET(IPGRAD,'GRADIENT',DERIV)
          WRITE(6,'(/29H GRADIENTS-------------------)')
          WRITE(6,100) 'OBJECTIVE FUNCTION:',(DERIV(IVAR),IVAR=1,NVAR)
          IF(IPRINT.GT.2) THEN
            DO 60 ICST=1,NCST
            WRITE(TEXT16,'(10HCONSTRAINT,I4,1H:)') ICST
            WRITE(6,100) TEXT16,(DERIV(ICST*NVAR+IVAR),IVAR=1,NVAR)
   60       CONTINUE
          ENDIF
          DEALLOCATE(DERIV)
        ENDIF
      ENDIF
*----
*  SAVE THE STATE VECTORS
*----
      ISTATE(1)=NVAR
      ISTATE(2)=NCST
      ISTATE(3)=IOPT
      ISTATE(4)=ICONV
      ISTATE(5)=IEXT
      ISTATE(6)=IEDSTP
      ISTATE(7)=IHESS
      ISTATE(8)=ISEARC
      ISTATE(9)=IMETH
      ISTATE(10)=ISTEP
      ISTATE(11)=JCONV
      ISTATE(14)=0
      IF(IPRINT.GT.0) WRITE(6,110) (ISTATE(I),I=1,9)
      CALL LCMPUT(IPGRAD,'STATE-VECTOR',NSTATE,1,ISTATE)
      OPTPRR(:NSTATE)=0.0D0
      OPTPRR(1)=SR
      OPTPRR(2)=EPS1
      OPTPRR(3)=EPS2
      OPTPRR(4)=EPS3
      OPTPRR(5)=EPS4
      IF(IPRINT.GT.0) WRITE(6,120) (OPTPRR(I),I=1,5)
      CALL LCMPUT(IPGRAD,'OPT-PARAM-R',NSTATE,4,OPTPRR)
      IF(IPRINT.GT.2) CALL LCMLIB(IPGRAD)
      RETURN
*
  100 FORMAT(1X,A28,1P,8E12.4/(29X,8E12.4))
  110 FORMAT(/8H OPTIONS/8H -------/
     1 7H NVAR  ,I8,32H   (NUMBER OF CONTROL VARIABLES)/
     2 7H NCST  ,I8,26H   (NUMBER OF CONSTRAINTS)/
     3 7H IOPT  ,I8,37H   (=1/-1: MINIMIZATION/MAXIMIZATION)/
     4 7H ICONV ,I8,43H   (=0/1: EXTERNAL NOT CONVERGED/CONVERGED)/
     5 7H IEXT  ,I8,32H   (INDEX OF EXTERNAL ITERATION)/
     6 7H IEDSTP,I8,43H   (=1/2: HALF REDUCTION/PARABOLIC FORMULA)/
     7 7H IHESS ,I8,29H   (=0/1/2: STEEPEST/CG/BFGS)/
     8 7H ISEARC,I8,35H   (=0/1/2: NO SEARCH/OPTEX/NEWTON)/
     9 7H IMETH ,I8,42H   (=1/2/3: SIMPLEX-LEMKE/LEMKE-LEMKE/MAP))
  120 FORMAT(/
     1 12H REAL PARAM:,1P/12H -----------/
     2 7H SR    ,D12.4,39H   (RADIUS OF THE QUADRATIC CONSTRAINT)/
     3 7H EPS1  ,D12.4,13H   (NOT USED)/
     4 7H EPS2  ,D12.4,31H   (EXTERNAL CONVERGENCE LIMIT)/
     5 7H EPS3  ,D12.4,31H   (INTERNAL CONVERGENCE LIMIT)/
     6 7H EPS4  ,D12.4,43H   (QUADRATIC CONSTRAINT CONVERGENCE LIMIT))
      END