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*DECK PLLEMK
SUBROUTINE PLLEMK(N,M,EPS,IMPR,P,IROW,ICOL,IERR)
*
*-----------------------------------------------------------------------
*
*Purpose:
* This subroutine solve the parametric linear complementary problem.
* PLLEMK = Linear Programming LEMKe
*
*Copyright:
* Copyright (C) 2002 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 and T. Falcon
*
*Parameters: input
* N number of control variables.
* M number of constraints.
* EPS tolerence used for pivoting.
* IMPR print flag.
* P coefficient matrix.
* IROW permutation vector for row elements.
* ICOL permutation vector for column elements.
*
*Parameters: ouput
* P coefficient matrix.
* IROW permutation vector for row elements.
* ICOL permutation vector for column elements.
* IERR return code (=0: normal completion).
*
*-----------------------------------------------------------------------
*
IMPLICIT NONE
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER M,N,IERR,IMPR,IROW(N),ICOL(N+1)
DOUBLE PRECISION EPS,P(N,M)
*----
* LOCAL VARIABLES
*----
DOUBLE PRECISION WWW,S
INTEGER MNOP,NP1,IC,L,I,J,K,JJ,J1,LGAR
DOUBLE PRECISION, ALLOCATABLE, DIMENSION(:) :: PLJ
*----
* SCRATCH STORAGE ALLOCATION
*----
ALLOCATE(PLJ(M))
*
MNOP = N + M
NP1 = N + 1
IC = 0
*
S = 0.0D0
L = 0
*
DO I=1,N
P(I,NP1) = 1.0D0
IF(P(I,M).GE.0.0D0) CYCLE
WWW = P(I,M)
IF(WWW.LE.S) THEN
L = I
S = WWW
ENDIF
ENDDO
*
IF(L.EQ.0) GO TO 30
LGAR = L
*
K = NP1
*
10 IC = IC + 1
IF(IC.GT.MNOP) THEN
IERR = 1
GOTO 40
ENDIF
*
IF(IMPR.GE.5) WRITE (6,1000) L,K
IF(IMPR.GE.6) THEN
DO J=1,M,12
JJ = MIN0(J+11,M)
WRITE (6,3000) (J1,J1=J,JJ)
DO I=1,N
WRITE (6,4000) I,(P(I,J1),J1=J,JJ)
ENDDO
IF(JJ.NE.M) WRITE (6,5000)
ENDDO
ENDIF
*
CALL PLPIVT(N,M,L,K,P,IROW,ICOL)
*
IF(ICOL(K).EQ.-NP1) GOTO 30
DO J=1,NP1
IF(J.EQ.K) CYCLE
IF(IABS(ICOL(K)).EQ.IABS(ICOL(J))) THEN
K = J
GOTO 20
ENDIF
ENDDO
*
IERR = 2
GOTO 40
*
20 DO I=1,N
IF(P(I,K)/P(I,M).LT.-EPS) THEN
PLJ(I) = -P(I,M)/P(I,K)
ELSE
PLJ(I) = 1.0D50
ENDIF
ENDDO
*
S = PLJ(LGAR)
L = LGAR
*
IF(IMPR.GE.7) THEN
WRITE (6,*) 'K=',K
WRITE (6,6000) L,(PLJ(I),I=1,N)
ENDIF
*
DO I=1,N
WWW = PLJ(I)
IF((ABS(WWW-S).GT.ABS(S)*EPS).AND.(WWW.LT.S)) THEN
S = WWW
L = I
ENDIF
ENDDO
*
IF(S.EQ.1.0D50) THEN
IERR = 3
GOTO 40
ENDIF
*
GOTO 10
30 IERR = 0
*
40 IF(IMPR.GE.6) THEN
WRITE (6,2000) IC
DO J=1,M,12
JJ = MIN0(J+11,M)
WRITE (6,3000) (J1,J1=J,JJ)
DO I=1,N
WRITE (6,4000) I,(P(I,J1),J1=J,JJ)
ENDDO
IF(JJ.NE.M) WRITE (6,5000)
ENDDO
ENDIF
*----
* SCRATCH STORAGE DEALLOCATION
*----
DEALLOCATE(PLJ)
RETURN
*
1000 FORMAT (//,10X,'+ + + + + MATRIX P(N,N+3) :',5X,'PIVOT = (',
> I4,' ,',I4,' )'/)
2000 FORMAT (//,10X,'NUMBER OF PIVOTS =',I5,
> //,10X,'+ + + + + FINAL MATRIX P(N,N+3) :'/)
3000 FORMAT (5X,12I12)
4000 FORMAT (1X,I4,1P,10E12.4/(5X,1P,10E12.4))
5000 FORMAT (//)
6000 FORMAT (//,10X,'LGAR =',I4/(1X,1P,8E12.4))
END
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