C MARCH 3, 2001; MARCH 24, 2005
C FUNCTION DECLARATIONS FOR THE COST FUNCTION OF A GENERALIZED
C NETWORK FLOW PROBLEM.  THE FUNCTIONS C(I,F), DC(I,F), DCINV(I,F)
C GIVE THE FUNCTION VALUE, DERIVATIVE VALUE, DERIVATIVE INVERSE VALUE
C FOR A LINEAR COST FUNCTION OR AN
C          PIPE COST FUNCTION  WITH  EXPONENT S=.5
C FOR ARC I WITH FLOW F.  [REF. G. KEADY'S 1991 PAPER.]
C THE FUNCTION PARAMETERS A(I), CDAT(I,1) ARE SPECIFIED IN THE
C ASCII FILE   NL013.DAT
C A(I) IS THE LINEAR COST COEFFICIENT.  CDAT(I,1) IS THE ALPHA
C COEFFICIENT.  CDAT(I,1)=0.0 INDICATES A LINEAR COST ARC.

      FUNCTION C(I,F)
      IMPLICIT NONE
      INTEGER*4 MAXARCS,MAXNDAT,I
      PARAMETER (MAXARCS=20000, MAXNDAT=5)
      REAL*8 A(MAXARCS),CDAT(MAXARCS,MAXNDAT),F,C
      COMMON /LCOS/A
      COMMON /QCO1/CDAT

      IF (CDAT(I,1).EQ.0.0) THEN
        C=A(I)*F
      ELSE
         C=F**3/(3*CDAT(I,1)**2)
      END IF
      RETURN
      END
      
      FUNCTION DC(I,F)
      IMPLICIT NONE
      INTEGER*4 MAXARCS,MAXNDAT,I
      PARAMETER (MAXARCS=20000, MAXNDAT=5)
      REAL*8 A(MAXARCS),CDAT(MAXARCS,MAXNDAT),F,DC
      COMMON /LCOS/A
      COMMON /QCO1/CDAT
  
      IF (CDAT(I,1).EQ.0.0) THEN
        DC=A(I)
      ELSE

C IGNORE CASE OF NEGATIVE F
        DC=F**2/CDAT(I,1)**2
      END IF
      RETURN
      END
      
      FUNCTION DCINV(I,T)
      IMPLICIT NONE
      INTEGER*4 MAXARCS,MAXNDAT,I
      PARAMETER (MAXARCS=20000, MAXNDAT=5)
      REAL*8 A(MAXARCS),CDAT(MAXARCS,MAXNDAT),T,DCINV
      COMMON /LCOS/A
      COMMON /QCO1/CDAT
      
      IF (T.GE.0.0) THEN
        DCINV=CDAT(I,1)*DSQRT(T)
      ELSE
        DCINV=-CDAT(I,1)*DSQRT(-T)
      END IF
      RETURN
      END