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SUBROUTINE HUNT(XX,N,X,JLO)
C .. Scalar Arguments ..
DOUBLE PRECISION X
INTEGER JLO,N
C ..
C .. Array Arguments ..
DOUBLE PRECISION XX(N)
C ..
C .. Local Scalars ..
INTEGER INC,JHI,JM
LOGICAL ASCND
C ..
ASCND = XX(N) .GT. XX(1)
IF (JLO.LE.0 .OR. JLO.GT.N) THEN
JLO = 0
JHI = N + 1
GO TO 3
END IF
INC = 1
IF (X.GE.XX(JLO) .EQV. ASCND) THEN
1 JHI = JLO + INC
IF (JHI.GT.N) THEN
JHI = N + 1
ELSE IF (X.GE.XX(JHI) .EQV. ASCND) THEN
JLO = JHI
INC = INC + INC
GO TO 1
END IF
ELSE
JHI = JLO
2 JLO = JHI - INC
IF (JLO.LT.1) THEN
JLO = 0
ELSE IF (X.LT.XX(JLO) .EQV. ASCND) THEN
JHI = JLO
INC = INC + INC
GO TO 2
END IF
END IF
3 IF (JHI-JLO.EQ.1) RETURN
JM = (JHI+JLO)/2
IF (X.GT.XX(JM) .EQV. ASCND) THEN
JLO = JM
ELSE
JHI = JM
END IF
GO TO 3
END
SUBROUTINE LOCATE(XX,N,X,J)
C
C .. Scalar Arguments ..
DOUBLE PRECISION X
INTEGER J,N
C ..
C .. Array Arguments ..
DOUBLE PRECISION XX(N)
C ..
C .. Local Scalars ..
INTEGER JL,JM,JU
C ..
JL = 0
JU = N + 1
10 IF (JU-JL.GT.1) THEN
JM = (JU+JL)/2
IF ((XX(N).GT.XX(1)) .EQV. (X.GT.XX(JM))) THEN
JL = JM
ELSE
JU = JM
END IF
GO TO 10
END IF
J = JL
RETURN
END
SUBROUTINE ODEINT(YSTART,NVAR,X1,X2,EPS,H1,HMIN,NOK,NBAD,DERIVS,
+ RKQC)
C
include 'ode_path.h'
C ..
C .. Parameters ..
INTEGER MAXSTP
PARAMETER (MAXSTP=10000)
DOUBLE PRECISION TWO
PARAMETER (TWO=2.0D0)
DOUBLE PRECISION ZERO
PARAMETER (ZERO=0.0D0)
DOUBLE PRECISION TINY
PARAMETER (TINY=1.D-30)
C ..
C .. Scalar Arguments ..
DOUBLE PRECISION EPS,H1,HMIN,X1,X2
INTEGER NBAD,NOK,NVAR
C ..
C .. Array Arguments ..
DOUBLE PRECISION YSTART(NVAR)
C ..
C .. Subroutine Arguments ..
EXTERNAL DERIVS,RKQC
C ..
C .. Local Scalars ..
DOUBLE PRECISION H,HDID,HNEXT,X,XSAV
INTEGER I,NSTP
C ..
C .. Local Arrays ..
DOUBLE PRECISION DYDX(NMAX),Y(NMAX),YSCAL(NMAX)
C ..
C .. Intrinsic Functions ..
INTRINSIC ABS,SIGN
C ..
X = X1
H = SIGN(H1,X2-X1)
NOK = 0
NBAD = 0
KOUNT = 0
DO 11 I = 1,NVAR
Y(I) = YSTART(I)
11 CONTINUE
XSAV = X - DXSAV*TWO
DO 16 NSTP = 1,MAXSTP
CALL DERIVS(X,Y,DYDX)
DO 12 I = 1,NVAR
YSCAL(I) = ABS(Y(I)) + ABS(H*DYDX(I)) + TINY
12 CONTINUE
IF (KMAX.GT.0) THEN
IF (ABS(X-XSAV).GT.ABS(DXSAV)) THEN
IF (KOUNT.LT.KMAX-1) THEN
KOUNT = KOUNT + 1
XP(KOUNT) = X
DO 13 I = 1,NVAR
YP(I,KOUNT) = Y(I)
13 CONTINUE
XSAV = X
END IF
END IF
END IF
IF ((X+H-X2)* (X+H-X1).GT.ZERO) H = X2 - X
CALL RKQC(Y,DYDX,NVAR,X,H,EPS,YSCAL,HDID,HNEXT,DERIVS)
IF (HDID.EQ.H) THEN
NOK = NOK + 1
ELSE
NBAD = NBAD + 1
END IF
IF ((X-X2)* (X2-X1).GE.ZERO) THEN
DO 14 I = 1,NVAR
YSTART(I) = Y(I)
14 CONTINUE
IF (KMAX.NE.0) THEN
KOUNT = KOUNT + 1
XP(KOUNT) = X
DO 15 I = 1,NVAR
YP(I,KOUNT) = Y(I)
15 CONTINUE
END IF
RETURN
END IF
IF (ABS(HNEXT).LT.HMIN) THEN
WRITE (*,FMT=*) 'ODEINT - Stepsize smaller than minimum.'
RETURN
END IF
H = HNEXT
16 CONTINUE
WRITE (*,FMT=*) 'ODEINT - Too many steps.'
RETURN
END
SUBROUTINE POLINT(XA,YA,N,X,Y,DY)
C
C .. Parameters ..
INTEGER NMAX
PARAMETER (NMAX=10)
C ..
C .. Scalar Arguments ..
DOUBLE PRECISION DY,X,Y
INTEGER N
C ..
C .. Array Arguments ..
DOUBLE PRECISION XA(N),YA(N)
C ..
C .. Local Scalars ..
DOUBLE PRECISION DEN,DIF,DIFT,HO,HP,W
INTEGER I,M,NS
C ..
C .. Local Arrays ..
DOUBLE PRECISION C(NMAX),D(NMAX)
C ..
C .. Intrinsic Functions ..
INTRINSIC ABS
C ..
NS = 1
DIF = ABS(X-XA(1))
DO 11 I = 1,N
DIFT = ABS(X-XA(I))
IF (DIFT.LT.DIF) THEN
NS = I
DIF = DIFT
END IF
C(I) = YA(I)
D(I) = YA(I)
11 CONTINUE
Y = YA(NS)
NS = NS - 1
DO 13 M = 1,N - 1
DO 12 I = 1,N - M
HO = XA(I) - X
HP = XA(I+M) - X
W = C(I+1) - D(I)
DEN = HO - HP
IF (DEN.EQ.0.D0) THEN
WRITE (*,FMT=*) 'POLINT - DEN=0.0'
RETURN
END IF
DEN = W/DEN
D(I) = HP*DEN
C(I) = HO*DEN
12 CONTINUE
IF (2*NS.LT.N-M) THEN
DY = C(NS+1)
ELSE
DY = D(NS)
NS = NS - 1
END IF
Y = Y + DY
13 CONTINUE
RETURN
END
SUBROUTINE RKQC(Y,DYDX,N,X,HTRY,EPS,YSCAL,HDID,HNEXT,DERIVS)
C
C .. Parameters ..
INTEGER NMAX
PARAMETER (NMAX=10)
DOUBLE PRECISION FCOR
PARAMETER (FCOR=.0666666667D0)
DOUBLE PRECISION ONE
PARAMETER (ONE=1.D0)
DOUBLE PRECISION SAFETY
PARAMETER (SAFETY=0.9D0)
DOUBLE PRECISION ERRCON
PARAMETER (ERRCON=6.D-4)
C ..
C .. Scalar Arguments ..
DOUBLE PRECISION EPS,HDID,HNEXT,HTRY,X
INTEGER N
C ..
C .. Array Arguments ..
DOUBLE PRECISION DYDX(N),Y(N),YSCAL(N)
C ..
C .. Subroutine Arguments ..
EXTERNAL DERIVS
C ..
C .. Local Scalars ..
DOUBLE PRECISION ERRMAX,H,HH,PGROW,PSHRNK,XSAV
INTEGER I
C ..
C .. Local Arrays ..
DOUBLE PRECISION DYSAV(NMAX),YSAV(NMAX),YTEMP(NMAX)
C ..
C .. External Subroutines ..
EXTERNAL RK4
C ..
C .. Intrinsic Functions ..
INTRINSIC ABS,MAX
C ..
PGROW = -0.20D0
PSHRNK = -0.25D0
XSAV = X
DO 11 I = 1,N
YSAV(I) = Y(I)
DYSAV(I) = DYDX(I)
11 CONTINUE
H = HTRY
1 HH = 0.5D0*H
CALL RK4(YSAV,DYSAV,N,XSAV,HH,YTEMP,DERIVS)
X = XSAV + HH
CALL DERIVS(X,YTEMP,DYDX)
CALL RK4(YTEMP,DYDX,N,X,HH,Y,DERIVS)
X = XSAV + H
IF (X.EQ.XSAV) THEN
WRITE (*,FMT=*) 'Stepsize not significant in RKQC.'
RETURN
END IF
CALL RK4(YSAV,DYSAV,N,XSAV,H,YTEMP,DERIVS)
ERRMAX = 0.D0
DO 12 I = 1,N
YTEMP(I) = Y(I) - YTEMP(I)
ERRMAX = MAX(ERRMAX,ABS(YTEMP(I)/YSCAL(I)))
12 CONTINUE
ERRMAX = ERRMAX/EPS
IF (ERRMAX.GT.ONE) THEN
H = SAFETY*H* (ERRMAX**PSHRNK)
GO TO 1
ELSE
HDID = H
IF (ERRMAX.GT.ERRCON) THEN
HNEXT = SAFETY*H* (ERRMAX**PGROW)
ELSE
HNEXT = 4.D0*H
END IF
END IF
DO 13 I = 1,N
Y(I) = Y(I) + YTEMP(I)*FCOR
13 CONTINUE
RETURN
END
SUBROUTINE RK4(Y,DYDX,N,X,H,YOUT,DERIVS)
C
C
C .. Parameters ..
INTEGER NMAX
PARAMETER (NMAX=10)
C ..
C .. Scalar Arguments ..
DOUBLE PRECISION H,X
INTEGER N
C ..
C .. Array Arguments ..
DOUBLE PRECISION DYDX(N),Y(N),YOUT(N)
C ..
C .. Subroutine Arguments ..
EXTERNAL DERIVS
C ..
C .. Local Scalars ..
DOUBLE PRECISION H6,HH,XH
INTEGER I
C ..
C .. Local Arrays ..
DOUBLE PRECISION DYM(NMAX),DYT(NMAX),YT(NMAX)
C ..
HH = H*0.5D0
H6 = H/6.D0
XH = X + HH
DO 11 I = 1,N
YT(I) = Y(I) + HH*DYDX(I)
11 CONTINUE
CALL DERIVS(XH,YT,DYT)
DO 12 I = 1,N
YT(I) = Y(I) + HH*DYT(I)
12 CONTINUE
CALL DERIVS(XH,YT,DYM)
DO 13 I = 1,N
YT(I) = Y(I) + H*DYM(I)
DYM(I) = DYT(I) + DYM(I)
13 CONTINUE
CALL DERIVS(X+H,YT,DYT)
DO 14 I = 1,N
YOUT(I) = Y(I) + H6* (DYDX(I)+DYT(I)+2.D0*DYM(I))
14 CONTINUE
RETURN
END
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