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|
C INTLINMEQ.F - Gateway function for solving Sylvester and Lyapunov matrix
C equations using SLICOT routines SB04MD, SB04ND, SB04PD,
C SB04QD, SB04RD, SB03MD, and SB03OD.
C
C Copyright INRIA 2001
C Scilab syntax
C [X(,sep)] = linmeq(task,A(,B),C,flag,trans(,schur))
C
C task = 1 : [X] = linmeq(1,A,B,C,flag,trans,schur)
C task = 2 : [X,sep] = linmeq(2,A,C,flag,trans)
C [X] = linmeq(2,A,C,flag,trans)
C task = 3 : [X] = linmeq(3,A,C,flag,trans)
C
C Purpose:
C To solve the Sylvester and Lyapunov linear matrix equations
C
C task = 1:
C
C op(A)*X + X*op(B) = C, (1a)
C
C op(A)*X*op(B) + X = C, (1b)
C
C task = 2:
C
C op(A)'*X + X*op(A) = C, (2a)
C
C op(A)'*X*op(A) - X = C, (2b)
C
C task = 3:
C
C op(A)'*(op(X)'*op(X)) + (op(X)'*op(X))*op(A) =
C - op(C)'*op(C), (3a)
C
C op(A)'*(op(X)'*op(X))*op(A) - op(X)'*op(X) =
C - op(C)'*op(C), (3b)
C
C where op(M) = M, if trans = 0, and op(M) = M', if trans = 1.
C
C Input parameters:
C task - integer option to determine the equation type:
C = 1 : solve the Sylvester equation (1a) or (1b);
C = 2 : solve the Lyapunov equation (2a) or (2b);
C = 3 : solve for the Cholesky factor op(X) the Lyapunov
C equation (3a) or (3b).
C A - real coefficient N-by-N matrix.
C When task = 3, matrix A must be stable.
C B - another real coefficient M-by-M matrix for
C equations (1a) or (1b).
C C - right hand side matrix.
C task = 1 : C is N-by-M;
C task = 2 : C is N-by-N symmetric;
C task = 3 : op(C) is P-by-N.
C flag - (optional) integer vector of length 3 or 2 containing
C options.
C task = 1 : flag has length 3
C flag(1) = 0 : solve the continuous-time equation (1a);
C otherwise, solve the discrete-time
C equation (1b).
C flag(2) = 1 : A is (quasi) upper triangular;
C 2 : A is upper Hessenberg;
C otherwise, A is in general form.
C flag(3) = 1 : B is (quasi) upper triangular;
C 2 : B is upper Hessenberg;
C otherwise, B is in general form.
C task = 2 : flag has length 2
C flag(1) = 0 : solve continuous-time equation (2a);
C otherwise, solve discrete-time
C equation (2b).
C flag(2) = 1 : A is (quasi) upper triangular;
C otherwise, A is in general form.
C task = 3 : flag has length 2
C flag(1) = 0 : solve continuous-time equation (3a);
C otherwise, solve discrete-time
C equation (3b).
C flag(2) = 1 : A is (quasi) upper triangular;
C otherwise, A is in general form.
C Default: flag(1) = 0, flag(2) = 0 (, flag(3) = 0).
C trans - (optional) integer specifying a transposition option.
C trans = 0 : solve the equations (1) - (3) with op(M) = M.
C trans = 1 : solve the equations (1) - (3) with op(M) = M'.
C trans = 2 : solve the equations (1) with op(A) = A',
C op(B) = B.
C trans = 3 : solve the equations (1) with op(A) = A,
C op(B) = B'.
C Default: trans = 0.
C schur - (optional) integer specifying whether the Hessenberg-Schur
C or Schur method should be used.
C Available for task = 1.
C schur = 1 : Hessenberg-Schur method (one matrix is reduced
C to Schur form).
C schur = 2 : Schur method (two matrices are reduced to Schur
C form).
C Default: schur = 1.
C
C Output parameters:
C X - solution of the equation (or its Cholesky factor for (3)).
C sep - (optional) estimator of Sep(op(A),-op(A)') for (2.a) or
C Sepd(A,A') for (2.b).
C
C Comments:
C 1. For equation (1a) or (1b), when schur = 1, the Hessenberg-Schur
C method is used, reducing one matrix to Hessenberg form and the
C other one to a real Schur form.
C Otherwise, both matrices are reduced to real Schur forms.
C If one or both matrices are already reduced to Schur/Hessenberg
C forms, this could be specified by flag(2) and flag(3).
C For general matrices, the Hessenberg-Schur method could be
C significantly more efficient than the Schur method.
C 2. For equation (3a) or (3b), the computed matrix X is the Cholesky
C factor of the solution, i.e., the real solution is op(X)'*op(X),
C where X is an N-by-N upper triangular matrix.
C
C References:
C This interface is based on the SLICOT routines:
C SB04PD, SB04MD, SB04QD, DTRSYL, SB04PY, SB04ND, SB04RD, SB03MD, SB03OD
C
C
C Revisions:
C Adapted from the Slicot Matlab Mexfile by S. Steer Oct 2001
C
C **********************************************************************
C
C
SUBROUTINE intlinmeq (fname)
include '../stack.h'
character*(*) fname
C .. Parameters ..
double precision ONE ,ZERO
parameter (ONE =1.0D0,ZERO =0.0D0)
C .. Scalar parameters used by SLICOT subroutines ..
character DICO ,FACT ,FACTA ,FACTB ,JOB ,SCHU ,TRANA ,TRANB ,ULA ,
$ ULB
integer INFO ,ISGN ,LDA ,LDB ,LDC ,LDU ,LDV ,NDWORK ,M ,N ,P
double precision FERR ,SCALE ,SEP ,TOL
integer lA, lB, lC, lDWORK, lU, lV, lWR, lWI
C
C .. Local variables and constant dimension arrays ..
logical PERTRB
integer FLAG (3),IB ,IP ,J ,LDW1 ,LDW2 ,NIWORK ,MC ,MXMN ,
$ NC ,NM ,NSCHUR ,TASK ,TRANS
double precision TEMP
C
C .. External functions ..
logical lsame, createvar, checkrhs, checklhs, getrhsvar
logical getscalar, getrmat, iscomplex
external lsame , createvar, checkrhs, checklhs, getrhsvar
external getscalar, getrmat
C
C .. External subroutines ..
external dlacpy ,dlaset ,dswap ,dtrsyl ,sb03md ,sb03od ,sb04md ,
$ sb04nd ,sb04pd ,sb04py ,sb04qd ,sb04rd
C
C ..Intrinsic functions..
intrinsic max ,min
C Check for proper number of arguments.
C
if(.not.checkrhs(fname,3,7)) return
if(.not.checklhs(fname,1,2)) return
C
C Check dimensions of input parameters and read/set scalar parameters.
C
C task
if(.not.getrhsvar(1,'i', Mt, Nt, ilTASK)) return
if(Mt*Nt.ne.1) then
err=1
call error(204)
return
endif
TASK=istk(ilTASK)
if (TASK.LT.1 .OR.TASK.GT.3 )THEN
buf='TASK HAS 1, 2, OR 3 THE ONLY ADMISSIBLE VALUES'
call error(1003)
return
endif
C
if (TASK.EQ.1 )THEN
if (RHS.LT.4 )THEN
buf='TASK=1: LINMEQ REQUIRES AT LEAST 4 INPUT ARGUMENTS'
call error(1003)
return
endif
IP =6
else
IP =5
endif
C
C trans
C
TRANS =0
if (RHS.GE.IP )THEN
if(.not.getrhsvar(IP,'i', Mt, Nt, ilTRANS)) return
if(Mt*Nt.gt.1) then
err=1
call error(204)
return
endif
if(Mt*Nt.eq.1) TRANS=istk(ilTRANS)
endif
if (TASK.EQ.1 .AND.(TRANS.LT.0 .OR.TRANS.GT.3 ))THEN
buf='TRANS HAS 0, 1, 2, OR 3 THE ONLY ADMISSIBLE VALUES'
call error(1003)
return
elseif (TASK.NE.1 .AND.(TRANS.LT.0 .OR.TRANS.GT.1 ))THEN
buf='TRANS HAS 0, OR 1 THE ONLY ADMISSIBLE VALUES'
call error(1003)
return
endif
C
C schur
C
if (TASK.EQ.1 )THEN
NSCHUR =1
if (RHS.EQ.IP +1) THEN
if(.not.getrhsvar(IP+1,'i', Mt, Nt, ilSCHUR)) return
if(Mt*Nt.gt.1) then
err=1
call error(204)
return
endif
if(Mt*Nt.eq.1) NSCHUR=istk(ilSCHUR)
if (NSCHUR.LT.1 .OR.NSCHUR.GT.2 )THEN
buf='SCHUR HAS 1, OR 2 THE ONLY ADMISSIBLE VALUES'
call error(1003)
return
endif
endif
endif
C
C A(NxN), (B(MxM),) C(NxM), or C(NxN), or op(C)(PxN)
C
if(.not.getrhsvar(2,'d', MA, NA, lA)) return
if(iscomplex(2)) then
err=2
call error(52)
return
endif
if(MA.NE.NA) then
err=2
call error(20)
return
endif
N=MA
if (TASK.EQ.1) THEN
if(.not.getrhsvar(3,'d', MB, NB, lB)) return
if(iscomplex(3)) then
err=3
call error(52)
return
endif
if(MB.NE.NB) then
err=3
call error(20)
return
endif
M=Mb
if(.not.getrhsvar(4,'d', MC, NC, lC)) return
if(iscomplex(4)) then
err=4
call error(52)
return
endif
if(MC.NE.N) then
err=4
call error(89)
return
endif
M=NC
lhsvar(1)=4
else
if(.not.getrhsvar(3,'d', MC, NC, lC)) return
if(iscomplex(3)) then
err=3
call error(52)
return
endif
c if (TASK.EQ.3 )THEN
if (TRANS.EQ.0 )THEN
P = MC
if(NC.ne.N) then
err=3
call error(89)
return
endif
else
if(MC.ne.N) then
err=3
call error(89)
return
endif
P = NC
c endif
endif
lhsvar(1)=3
endif
C
if(TASK.eq.1) then
IP=5
else
IP=4
endif
FLAG (1)=0
FLAG (2)=0
FLAG (3)=0
if (RHS.GE.IP )THEN
C
C flag
C
if(.not.getrhsvar(IP,'i', Mt, Nt, ilFLAG)) return
if (TASK.EQ.1 )THEN
if (MT*NT.GT.3) then
buf='FLAG MUST BE A VECTOR WITH AT MOST 3 ELEMENTS'
call error(1003)
return
endif
else
if (MT*NT.GT.2 ) THEN
buf='FLAG MUST BE A VECTOR WITH AT MOST 2 ELEMENTS'
call error(1003)
return
endif
endif
DO I=1,MT*NT
FLAG(I)=istk(ilFLAG-1+i)
enddo
endif
C
C Determine the lenghts of working arrays.
C Use a larger value for NDWORK for enabling calls of block algorithms
C in DGEES, and possibly in DGEHRD, DGEQRF, DGERQF, SB04PD.
C
LDA =MAX (1,N )
if (TASK.EQ.1 )THEN
LDB =MAX (1,M )
if (NSCHUR.EQ.2 )THEN
if (FLAG (2).EQ.1)THEN
LDW1 =0
LDW2 =0
else
LDW1 =1+2*N
LDW2 =3*N
endif
IB =0
if (FLAG (3).NE.1)THEN
IB =2*M
if (FLAG (2).EQ.1)IB =IB +1
LDW2 =MAX (LDW2 ,IB +3*M )
endif
LDW2 =MAX (LDW2 ,IB +2*N )
NDWORK =MAX (1,LDW1 +LDW2 )
else
if (FLAG (2)*FLAG (3).EQ.1)THEN
NIWORK =0
if (FLAG (1).NE.0)THEN
NDWORK =2*N
else
NDWORK =0
endif
elseif (FLAG (2)*FLAG (3).EQ.2)THEN
MXMN =MAX (M ,N )
NIWORK =2*MXMN
NDWORK =2*MXMN *(4+2*MXMN )
else
NIWORK =4*N
NDWORK =MAX (1,5*M ,N +M )
if (FLAG (1).EQ.0)THEN
NDWORK =MAX (NDWORK ,2*N *N +8*N )
else
NDWORK =MAX (NDWORK ,2*N *N +9*N )
endif
endif
endif
NM =M
C
elseif (TASK.EQ.2 )THEN
NDWORK =MAX (1,N *N ,3*N )
if (LHS.EQ.2 )THEN
NDWORK =MAX (NDWORK ,2*N *N )
if (FLAG (1).NE.0)NDWORK =MAX (NDWORK ,2*(N *N +N ))
endif
NM =N
endif
if (TASK.NE.3 )THEN
LDC =LDA
else
if (TRANS.EQ.0 )THEN
LDC =MAX (1,N ,P )
else
LDC =LDA
endif
MXMN =MIN (P ,N )
NDWORK =MAX (1,4*N +MXMN )
NM =N
endif
C
C Allocate variable dimension local arrays.
C
if (TASK.EQ.1 )THEN
if(.NOT.CREATEVAR(NBVARS+1,'d',NDWORK,1,lDWORK)) RETURN
if (NSCHUR.EQ.2 )THEN
if (FLAG (2).EQ.1)THEN
FACTA ='S'
LDU =1
if(.NOT.CREATEVAR(NBVARS+1,'d',LDU,1,lU)) RETURN
else
FACTA ='N'
LDU =LDA
if(.NOT.CREATEVAR(NBVARS+1,'d',LDU,N,lU)) RETURN
endif
if (FLAG (3).EQ.1)THEN
FACTB ='S'
LDV =1
if(.NOT.CREATEVAR(NBVARS+1,'d',LDV,1,lV)) RETURN
else
FACTB ='N'
LDV =LDB
if(.NOT.CREATEVAR(NBVARS+1,'d',LDV,M,lV)) RETURN
endif
else
SCHU ='N'
if(.NOT.CREATEVAR(NBVARS+1,'i',NIWORK,1,lIWORK)) RETURN
if (FLAG (2).EQ.1)THEN
if (FLAG (3).EQ.1)THEN
SCHU ='S'
elseif (FLAG (3).EQ.2)THEN
SCHU ='A'
endif
elseif (FLAG (2).EQ.2.AND. FLAG (3).EQ.1)THEN
SCHU ='B'
endif
C
if (LSAME (SCHU ,'N'))THEN
LDU =LDB
if(.NOT.CREATEVAR(NBVARS+1,'d',LDU,M,lU)) RETURN
endif
endif
C
elseif (TASK.EQ.2 )THEN
LDU =LDA
if(.NOT.CREATEVAR(NBVARS+1,'d',LDU,N,lU)) RETURN
if(.NOT.CREATEVAR(NBVARS+1,'d',NDWORK,1,lDWORK)) RETURN
if(.NOT.CREATEVAR(NBVARS+1,'d',N,1,lWI)) RETURN
if(.NOT.CREATEVAR(NBVARS+1,'d',N,1,lWR)) RETURN
if (LHS.EQ.1 )THEN
if(.NOT.CREATEVAR(NBVARS+1,'i',1,1,lIWORK)) RETURN
else
if(.NOT.CREATEVAR(NBVARS+1,'i',N*N,1,lIWORK)) RETURN
endif
else
LDU =LDA
if(.NOT.CREATEVAR(NBVARS+1,'d',LDU,N,lU)) RETURN
if(.NOT.CREATEVAR(NBVARS+1,'d',NDWORK,1,lDWORK)) RETURN
if(.NOT.CREATEVAR(NBVARS+1,'d',N,1,lWI)) RETURN
if(.NOT.CREATEVAR(NBVARS+1,'d',N,1,lWR)) RETURN
endif
C
C Do the actual computations.
C
if (TASK.EQ.1 )THEN
C
if (NSCHUR.EQ.2 )THEN
if (TRANS.EQ.0 )THEN
TRANA ='N'
TRANB ='N'
elseif (TRANS.EQ.1 )THEN
TRANA ='T'
TRANB ='T'
elseif (TRANS.EQ.2 )THEN
TRANA ='T'
TRANB ='N'
elseif (TRANS.EQ.3 )THEN
TRANA ='N'
TRANB ='T'
endif
if (FLAG (1).NE.0)THEN
DICO ='D'
else
DICO ='C'
endif
ISGN =1
call SB04PD (DICO ,FACTA ,FACTB ,TRANA ,TRANB ,ISGN ,N ,M ,
$ stk(lA), LDA ,stk(lU),LDU ,stk(lB),LDB ,stk(lV),LDV ,
$ stk(lC), LDC ,SCALE ,stk(lDWORK),NDWORK ,INFO )
else
if (TRANS.EQ.0 )THEN
if (LSAME (SCHU ,'S'))THEN
TRANA ='N'
TRANB ='N'
else
ULA ='U'
ULB ='U'
endif
elseif (TRANS.EQ.1 )THEN
if (LSAME (SCHU ,'S'))THEN
TRANA ='T'
TRANB ='T'
else
ULA ='L'
ULB ='L'
DO 10J =2,N
call DSWAP (J -1,stk(lA+1-1 +(J-1)*LDA),1,stk(lA+J-
$ 1 +(1-1)*LDA),LDA )
10 CONTINUE
DO 20J =2,M
call DSWAP (J -1,stk(lB+1-1 +(J-1)*LDB),1,stk(lB+J-
$ 1 +(1-1)*LDB),LDB )
20 CONTINUE
endif
elseif (TRANS.EQ.2 )THEN
if (LSAME (SCHU ,'S'))THEN
TRANA ='T'
TRANB ='N'
else
ULA ='L'
ULB ='U'
DO 30J =2,N
call DSWAP (J -1,stk(lA+1-1 +(J-1)*LDA),1,stk(lA+J-
$ 1 +(1-1)*LDA),LDA )
30 CONTINUE
endif
elseif (TRANS.EQ.3 )THEN
if (LSAME (SCHU ,'S'))THEN
TRANA ='N'
TRANB ='T'
else
ULA ='U'
ULB ='L'
DO 40J =2,M
call DSWAP (J -1,stk(lB+1-1 +(J-1)*LDB),1,stk(lB+J-
$ 1 +(1-1)*LDB),LDB )
40 CONTINUE
endif
endif
C
if (LSAME (SCHU ,'N'))THEN
C
SCALE =ONE
if (FLAG (1).EQ.0)THEN
call SB04MD (N ,M ,stk(lA),LDA ,stk(lB),LDB ,stk(lC),
$ LDC ,stk(lU),LDU ,istk(lIWORK),stk(lDWORK),NDWORK ,
$ INFO )
else
call SB04QD (N ,M ,stk(lA),LDA ,stk(lB),LDB ,stk(lC),
$ LDC ,stk(lU),LDU ,istk(lIWORK),stk(lDWORK),NDWORK ,
$ INFO )
endif
C
elseif (LSAME (SCHU ,'S'))THEN
C
if (FLAG (1).EQ.0)THEN
call DTRSYL (TRANA ,TRANB ,1,N ,M ,stk(lA),LDA ,
$ stk(lB), LDB ,stk(lC),LDC ,SCALE ,INFO )
else
call SB04PY (TRANA ,TRANB ,1,N ,M ,stk(lA),LDA ,
$ stk(lB), LDB ,stk(lC),LDC ,SCALE ,stk(lDWORK),INFO)
endif
else
SCALE =ONE
TOL =ZERO
C
C Default tolerance (epsilon_machine) is used.
C
if (FLAG (1).EQ.0)THEN
call SB04ND (SCHU ,ULA ,ULB ,N ,M ,stk(lA),LDA ,
$ stk(lB), LDB ,stk(lC),LDC ,TOL ,istk(lIWORK),
$ stk(lDWORK), NDWORK ,INFO )
else
call SB04RD (SCHU ,ULA ,ULB ,N ,M ,stk(lA),LDA ,
$ stk(lB), LDB ,stk(lC),LDC ,TOL ,istk(lIWORK),
$ stk(lDWORK), NDWORK ,INFO )
endif
C
endif
endif
C
else
C
if (FLAG (1).EQ.0)THEN
DICO ='C'
else
DICO ='D'
endif
if (FLAG (2).NE.1)THEN
FACT ='N'
else
FACT ='F'
call DLASET ('FULL',N ,N ,ZERO ,ONE ,stk(lU),LDU )
endif
C
if (TRANS.EQ.0 )THEN
TRANA ='N'
else
TRANA ='T'
endif
C
if (TASK.EQ.2 )THEN
if (LHS.EQ.2 )THEN
JOB ='B'
else
JOB ='X'
endif
C
call SB03MD (DICO ,JOB ,FACT ,TRANA ,N ,stk(lA), LDA ,
$ stk(lU), LDU ,stk(lC),LDC ,SCALE ,SEP ,FERR, stk(lWR),
$ stk(lWI), istk(lIWORK), stk(lDWORK), NDWORK ,INFO )
C
else
C
call SB03OD (DICO ,FACT ,TRANA ,N ,P ,stk(lA),LDA ,stk(lU),
$ LDU ,stk(lC),LDC ,SCALE ,stk(lWR),stk(lWI),stk(lDWORK),
$ NDWORK ,INFO )
C
endif
endif
C
C form output
C
PERTRB =(TASK.EQ.1 .AND.(INFO.EQ.N +M +1.OR. (FLAG (2)*FLAG (3)
$ .EQ.1.AND. INFO.EQ.1 ))).OR.
$ (TASK.EQ.2 .AND.INFO.EQ.N +1).OR.(TASK.EQ.3 .AND.INFO.EQ.1 )
if (INFO.EQ.0 .OR.PERTRB )THEN
if (LHS.GE.1 )THEN
if (TASK.EQ.3 )THEN
if (TRANS.EQ.0 .AND.P.GT.N )call DLACPY ('UPPER',N ,N ,
$ stk(lC),LDC ,stk(lC),LDA )
if (N.GT.1 )call DLASET ('LOWER',N -1,N -1,ZERO ,ZERO ,
$ stk(lC+2-1 +(1-1)*LDC),LDA )
endif
endif
C
if (TASK.EQ.2 )THEN
if (LHS.GE.2 )THEN
if (N.EQ.ZERO ) SEP =ZERO
if(.NOT.CREATEVAR(NBVARS+1,'d',1,1,lSEP)) RETURN
stk(lSEP)=SEP
LHSVAR(2)=NBVARS
endif
endif
endif
C
C Error and warning handling.
C
if (INFO.GT.0 )THEN
if (TASK.EQ.1 )THEN
if (NSCHUR.EQ.2 )THEN
c . messages from SB04PD
if(INFO.le.M+N) then
c . Failure when computing eigenvalues
call error(24)
elseif(INFO.gt.M+N) then
c . Equation is singular
call error(19)
endif
return
else
if (LSAME (SCHU ,'N')) THEN
c . messages from SB04MD or SB04QD
if(INFO.le.M) then
c . Failure when computing eigenvalues
call error(24)
elseif(INFO.gt.M) then
c . Equation is singular
call error(19)
endif
else
c . Equation is singular
call error(19)
endif
return
endif
elseif (TASK.EQ.2 )THEN
if(INFO.le.N) then
c . Failure when computing eigenvalues
call error(24)
elseif(INFO.gt.N) then
c . Equation is singular
call error(19)
endif
return
elseif (TASK.EQ.3 )THEN
if (INFO.eq.1) then
c . Equation is singular
call error(19)
elseif (INFO.eq.2.or.INFO.eq.3) then
err=1
if(lsame(DICO,'C')) then
c . Matrix is not stable (cont)
call error(269)
else
call error(270)
endif
elseif (INFO.eq.4.or.INFO.eq.5) then
c . not a schur form
call error(270)
elseif (INFO.eq.6) then
c . Failure when computing eigenvalues
call error(24)
endif
return
endif
elseif(INFO.LT.0) then
c . message displayed by slicot or lapack
buf=' '
call error(999)
endif
C
if ((INFO.EQ.0 .OR.PERTRB ).AND.SCALE.NE.ONE )THEN
if (TASK.LE.2 )THEN
TEMP =SCALE
else
TEMP =SCALE **2
endif
WRITE (buf ,'
$ ( '' WARNING: THE RIGHT HAND SIDES WERE '',''SCALED BY'',
$ D13.6, '' TO AVOID OVERFLOW. '' )')TEMP
endif
C
if (INFO.NE.0 .AND..NOT.PERTRB )THEN
call error(1004)
elseif (SCALE.NE.ONE )THEN
call msgs(1000,0)
endif
if (PERTRB )THEN
WRITE (buf ,'
$ ( '' WARNING: THE EQUATION IS (ALMOST) '',
$ ''SINGULAR; PERTURBED VALUES HAVE BEEN USED. '' )')
call msgs(1000,0)
endif
C
RETURN
C *** Last line of LINMEQ ***
end
logical function iscomplex(pos)
include '../stack.h'
integer pos
c
integer iadr,sadr
c
iadr(l)=l+l-1
sadr(l)=(l/2)+1
c
il=iadr(lstk(pos + top - rhs))
if (istk(il).lt.0) il=iadr(istk(il+2))
if (istk(il+3).eq.1) then
iscomplex=.true.
else
iscomplex=.false.
endif
return
end
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