OpenLibm/slatec/spinit.f

*DECK SPINIT
      SUBROUTINE SPINIT (MRELAS, NVARS, COSTS, BL, BU, IND, PRIMAL,
     +   INFO, AMAT, CSC, COSTSC, COLNRM, XLAMDA, ANORM, RHS, RHSNRM,
     +   IBASIS, IBB, IMAT, LOPT)
C***BEGIN PROLOGUE  SPINIT
C***SUBSIDIARY
C***PURPOSE  Subsidiary to SPLP
C***LIBRARY   SLATEC
C***TYPE      SINGLE PRECISION (SPINIT-S, DPINIT-D)
C***AUTHOR  (UNKNOWN)
C***DESCRIPTION
C
C     THE EDITING REQUIRED TO CONVERT THIS SUBROUTINE FROM SINGLE TO
C     DOUBLE PRECISION INVOLVES THE FOLLOWING CHARACTER STRING CHANGES.
C
C     USE AN EDITING COMMAND (CHANGE) /STRING-1/(TO)STRING-2/.
C     /REAL (12 BLANKS)/DOUBLE PRECISION/,/SCOPY/DCOPY/
C     REVISED 810519-0900
C     REVISED YYMMDD-HHMM
C
C     INITIALIZATION SUBROUTINE FOR SPLP(*) PACKAGE.
C
C***SEE ALSO  SPLP
C***ROUTINES CALLED  PNNZRS, SASUM, SCOPY
C***REVISION HISTORY  (YYMMDD)
C   811215  DATE WRITTEN
C   890531  Changed all specific intrinsics to generic.  (WRB)
C   890605  Removed unreferenced labels.  (WRB)
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   900328  Added TYPE section.  (WRB)
C***END PROLOGUE  SPINIT
      REAL             AIJ,AMAT(*),ANORM,BL(*),BU(*),CMAX,
     * COLNRM(*),COSTS(*),COSTSC,CSC(*),CSUM,ONE,PRIMAL(*),
     * RHS(*),RHSNRM,SCALR,TESTSC,XLAMDA,ZERO
      INTEGER IBASIS(*),IBB(*),IMAT(*),IND(*)
      LOGICAL CONTIN,USRBAS,COLSCP,CSTSCP,MINPRB,LOPT(8)
C
C***FIRST EXECUTABLE STATEMENT  SPINIT
      ZERO=0.
      ONE=1.
      CONTIN=LOPT(1)
      USRBAS=LOPT(2)
      COLSCP=LOPT(5)
      CSTSCP=LOPT(6)
      MINPRB=LOPT(7)
C
C     SCALE DATA. NORMALIZE BOUNDS. FORM COLUMN CHECK SUMS.
      GO TO 30001
C
C     INITIALIZE ACTIVE BASIS MATRIX.
20002 CONTINUE
      GO TO 30002
20003 RETURN
C
C     PROCEDURE (SCALE DATA. NORMALIZE BOUNDS. FORM COLUMN CHECK SUMS)
C
C     DO COLUMN SCALING IF NOT PROVIDED BY THE USER.
30001 IF (.NOT.(.NOT. COLSCP)) GO TO 20004
      J=1
      N20007=NVARS
      GO TO 20008
20007 J=J+1
20008 IF ((N20007-J).LT.0) GO TO 20009
      CMAX=ZERO
      I=0
20011 CALL PNNZRS(I,AIJ,IPLACE,AMAT,IMAT,J)
      IF (.NOT.(I.EQ.0)) GO TO 20013
      GO TO 20012
20013 CONTINUE
      CMAX=MAX(CMAX,ABS(AIJ))
      GO TO 20011
20012 IF (.NOT.(CMAX.EQ.ZERO)) GO TO 20016
      CSC(J)=ONE
      GO TO 20017
20016 CSC(J)=ONE/CMAX
20017 CONTINUE
      GO TO 20007
20009 CONTINUE
C
C     FORM CHECK SUMS OF COLUMNS. COMPUTE MATRIX NORM OF SCALED MATRIX.
20004 ANORM = ZERO
      J=1
      N20019=NVARS
      GO TO 20020
20019 J=J+1
20020 IF ((N20019-J).LT.0) GO TO 20021
      PRIMAL(J)=ZERO
      CSUM = ZERO
      I=0
20023 CALL PNNZRS(I,AIJ,IPLACE,AMAT,IMAT,J)
      IF (.NOT.(I.LE.0)) GO TO 20025
      GO TO 20024
20025 CONTINUE
      PRIMAL(J)=PRIMAL(J)+AIJ
      CSUM = CSUM+ABS(AIJ)
      GO TO 20023
20024 IF (IND(J).EQ.2) CSC(J)=-CSC(J)
      PRIMAL(J)=PRIMAL(J)*CSC(J)
      COLNRM(J)=ABS(CSC(J)*CSUM)
      ANORM = MAX(ANORM,COLNRM(J))
      GO TO 20019
C
C     IF THE USER HAS NOT PROVIDED COST VECTOR SCALING THEN SCALE IT
C     USING THE MAX. NORM OF THE TRANSFORMED COST VECTOR, IF NONZERO.
20021 TESTSC=ZERO
      J=1
      N20028=NVARS
      GO TO 20029
20028 J=J+1
20029 IF ((N20028-J).LT.0) GO TO 20030
      TESTSC=MAX(TESTSC,ABS(CSC(J)*COSTS(J)))
      GO TO 20028
20030 IF (.NOT.(.NOT.CSTSCP)) GO TO 20032
      IF (.NOT.(TESTSC.GT.ZERO)) GO TO 20035
      COSTSC=ONE/TESTSC
      GO TO 20036
20035 COSTSC=ONE
20036 CONTINUE
      CONTINUE
20032 XLAMDA=(COSTSC+COSTSC)*TESTSC
      IF (XLAMDA.EQ.ZERO) XLAMDA=ONE
C
C     IF MAXIMIZATION PROBLEM, THEN CHANGE SIGN OF COSTSC AND LAMDA
C     =WEIGHT FOR PENALTY-FEASIBILITY METHOD.
      IF (.NOT.(.NOT.MINPRB)) GO TO 20038
      COSTSC=-COSTSC
20038 GO TO 20002
C:CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C     PROCEDURE (INITIALIZE RHS(*),IBASIS(*), AND IBB(*))
C
C     INITIALLY SET RIGHT-HAND SIDE VECTOR TO ZERO.
30002 CALL SCOPY(MRELAS,ZERO,0,RHS,1)
C
C     TRANSLATE RHS ACCORDING TO CLASSIFICATION OF INDEPENDENT VARIABLES
      J=1
      N20041=NVARS
      GO TO 20042
20041 J=J+1
20042 IF ((N20041-J).LT.0) GO TO 20043
      IF (.NOT.(IND(J).EQ.1)) GO TO 20045
      SCALR=-BL(J)
      GO TO 20046
20045 IF (.NOT.(IND(J).EQ.2)) GO TO 10001
      SCALR=-BU(J)
      GO TO 20046
10001 IF (.NOT.(IND(J).EQ.3)) GO TO 10002
      SCALR=-BL(J)
      GO TO 20046
10002 IF (.NOT.(IND(J).EQ.4)) GO TO 10003
      SCALR=ZERO
10003 CONTINUE
20046 CONTINUE
      IF (.NOT.(SCALR.NE.ZERO)) GO TO 20048
      I=0
20051 CALL PNNZRS(I,AIJ,IPLACE,AMAT,IMAT,J)
      IF (.NOT.(I.LE.0)) GO TO 20053
      GO TO 20052
20053 CONTINUE
      RHS(I)=SCALR*AIJ+RHS(I)
      GO TO 20051
20052 CONTINUE
20048 CONTINUE
      GO TO 20041
C
C     TRANSLATE RHS ACCORDING TO CLASSIFICATION OF DEPENDENT VARIABLES.
20043 I=NVARS+1
      N20056=NVARS+MRELAS
      GO TO 20057
20056 I=I+1
20057 IF ((N20056-I).LT.0) GO TO 20058
      IF (.NOT.(IND(I).EQ.1)) GO TO 20060
      SCALR=BL(I)
      GO TO 20061
20060 IF (.NOT.(IND(I).EQ.2)) GO TO 10004
      SCALR=BU(I)
      GO TO 20061
10004 IF (.NOT.(IND(I).EQ.3)) GO TO 10005
      SCALR=BL(I)
      GO TO 20061
10005 IF (.NOT.(IND(I).EQ.4)) GO TO 10006
      SCALR=ZERO
10006 CONTINUE
20061 CONTINUE
      RHS(I-NVARS)=RHS(I-NVARS)+SCALR
      GO TO 20056
20058 RHSNRM=SASUM(MRELAS,RHS,1)
C
C     IF THIS IS NOT A CONTINUATION OR THE USER HAS NOT PROVIDED THE
C     INITIAL BASIS, THEN THE INITIAL BASIS IS COMPRISED OF THE
C     DEPENDENT VARIABLES.
      IF (.NOT.(.NOT.(CONTIN .OR. USRBAS))) GO TO 20063
      J=1
      N20066=MRELAS
      GO TO 20067
20066 J=J+1
20067 IF ((N20066-J).LT.0) GO TO 20068
      IBASIS(J)=NVARS+J
      GO TO 20066
20068 CONTINUE
C
C     DEFINE THE ARRAY IBB(*)
20063 J=1
      N20070=NVARS+MRELAS
      GO TO 20071
20070 J=J+1
20071 IF ((N20070-J).LT.0) GO TO 20072
      IBB(J)=1
      GO TO 20070
20072 J=1
      N20074=MRELAS
      GO TO 20075
20074 J=J+1
20075 IF ((N20074-J).LT.0) GO TO 20076
      IBB(IBASIS(J))=-1
      GO TO 20074
C
C     DEFINE THE REST OF IBASIS(*)
20076 IP=MRELAS
      J=1
      N20078=NVARS+MRELAS
      GO TO 20079
20078 J=J+1
20079 IF ((N20078-J).LT.0) GO TO 20080
      IF (.NOT.(IBB(J).GT.0)) GO TO 20082
      IP=IP+1
      IBASIS(IP)=J
20082 GO TO 20078
20080 GO TO 20003
      END