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*DECK AIKINT
FUNCTION AIKINT(Z,X,Y,N,EPS)
C----
C REVISION HISTORY
C - CREATED 80-AUG, BY E.G. LONG
C - CHECK THAT X-VALUES ARE MONOTONICALLY INCREASING,
C - REVISED FROM AELIB 1985 OCT 16 BY P CARLSON
C - CHANGED TO RELATIVE EPS AUGUST 1986 JV DONNELLY
C - IMPLEMENTED IN DRAGON AUGUST 1993 (G. MARLEAU)
C ABNORMAL TERMINATION
C 1. PARAMETER CHECKS FAIL-
C A. X NOT MONOTONICALLY INCREASING
C 2. REQUESTED ACCURACY NOT OBTAINED
C PARAMETERS
C Z : INTERPOLATION POINT
C X : INTERPOLATION POINT TABLULATION
C Y : TABULATED FUNCTION AT POINTS X
C N : NUMBER OF TABULATED POINTS
C EPS : TABULATION ERROR PERMITTED
C----
SAVE ICALLB,ICALLA
PARAMETER (IOUT=6)
LOGICAL RELOK,ABSOK
REAL X(N),Y(N),W(10),F(10)
DATA ICALLB,ICALLA /0,0/
C----
C CHECK FOR MONOTONICALLY INCREASING TABLE
C----
IL=0
MC=0
IF(N.GE.2) THEN
DO 120 I = 2, N
IF (X(I) .LE. X(I-1)) THEN
WRITE(IOUT,2000)
CALL XABORT('AIKINT: ILLEGAL FORMAT TABLE')
ENDIF
120 CONTINUE
ENDIF
C----
C HANDLE INTEROPOLATION WITH N<=2
C----
IF(N.LE.2) THEN
IF(N.LE.0) AIKINT=0.0
IF(N.EQ.1) AIKINT=Y(1)
IF(N.EQ.2) AIKINT=((Z-X(2))*Y(1)-(Z-X(1))*Y(2))
> /(X(1) - X(2))
C----
C RETURN FROM AIKINT
C----
RETURN
ENDIF
C----
C INTERPOLATION FOR N>2
C CHECK IF Z=X(1)
C----
IX=1
IF(X(1).NE.Z) GO TO 20
C----
C Z IS AT ONE OF X(I)
C----
21 CONTINUE
AIKINT=Y(IX)
C----
C RETURN FROM AIKINT
C----
RETURN
C
C-----------------------------------------------------------
20 CONTINUE
IF(X(IX).GT.Z) THEN
C----
C EXTRAPOLATION BEFORE TABLE BEGINS
C----
IF(ICALLB.EQ.0) WRITE(IOUT,2001)
ICALLB=ICALLB+1
IU = 1
JA = 1
K = 2
NA=MIN0(N,10)
DO 40 I=1,NA
W(I) = X(I)
F(I) = Y(I)
40 CONTINUE
GO TO 600
ELSE
C----
C CHECK IF Z=X(N)
C----
IX=N
IF(X(IX).EQ.Z) GO TO 21
IF(X(IX).LT.Z) THEN
C----
C EXTRAPOLATION BEYOND END OF TABLE
C----
IF(ICALLA.EQ.0) WRITE(IOUT,2002)
C ICALLA=ICALLA+1
C IL=N
C JA=2
C K=2
C NA=MIN0(N,10)
C DO 41 I=1,NA
C J = N - I + 1
C W(I) = X(J)
C F(I) = Y(J)
C 41 CONTINUE
C GO TO 600
AIKINT=Y(N)
RETURN
ENDIF
ENDIF
C----
C Z IS WITHIN X(I), FIND WHERE Z LIES IN THE TABLE
C----
IL = 1
IU = N
JA = 3
A = N
M = INT(ALOG(FLOAT(N))/0.693147) + 2
DO 11 I = 1, M
IR = IU - IL
IF( IR .EQ. 1 ) GO TO 30
IX = IL + IR/2
IF( X(IX) .EQ. Z ) GO TO 21
IF( X(IX) .GT. Z ) THEN
IU = IX
ELSE
IL = IX
ENDIF
11 CONTINUE
IU = N
IL = N - 1
30 CONTINUE
K=0
MC=3
C----
C FINDING NEAREST ARGUMENTS TO Z
C IF POSSIBLE, THE ARGUMENTS ARE CHOSEN IN PAIRS, SO THAT THEY ARE
C ON THE SAME SIDE OF Z. THE FIRST LINEAR CROSS MEANS IS
C CALCULATED USING THE CLOSEST PAIR. SUBSEQUENT LINEAR CROSS
C MEANS ARE CALCULATED USING FIRST THE CLOSEST ARGUMENT TO Z OF
C THE NEXT PAIR AND THEN THE OTHER ARGUMENT
C OTHERWISE THE ARGUMENTS ARE CHOSEN IN ORDER OF CLOSENESS.
C----
NA=MIN0(N,10)
601 IF( K .EQ. NA ) GO TO 501
I450=1
I400=1
IF( IU .EQ. (N+1) ) THEN
I450=0
I400=0
ELSE IF( IL .EQ. 0) THEN
I450=0
ELSE IF(MC-2 .EQ. -1) THEN
I450=0
I400=0
ELSE IF(MC-2 .EQ. 0) THEN
I450=0
ENDIF
* I450
IF( I450 .EQ. 1) THEN
MC=0
D1=ABS(X(IU)-Z)
D2=ABS(X(IL)-Z)
IF( D1 .GT. D2 ) THEN
I400=0
ENDIF
ENDIF
* I400
IF( I400 .EQ. 1) THEN
MC = MC + 1
K = K + 1
F(K) = Y(IU)
W(K) = X(IU)
IU = IU + 1
ELSE
MC = MC + 2
K = K + 1
F(K) = Y(IL)
W(K) = X(IL)
IL = IL - 1
ENDIF
IF(K .LT. 2) GO TO 601
C----
C EVALUATION OF POSSIBLE ANSWERS
C----
600 CONTINUE
KA = K - 1
DO 200 I= 1, KA
F(K) = ( ( Z - W(K) )*F(I) -
> ( Z - W(I) )*F(K) )/( W(I) - W(K) )
200 CONTINUE
C----
C TEST FOR CONVERGENCE OF INTERPOLATION
C----
IF( F(KA) .EQ. 0.0 ) THEN
IF( ABS(F(K)) .LT. EPS ) THEN
AIKINT = F(K)
RETURN
ENDIF
ELSE
IF( ABS( 1. - F(K)/F(KA) ) .LT. EPS) THEN
AIKINT = F(K)
RETURN
ENDIF
ENDIF
C----
C NOT CONVERGED YET, TRY NEXT ORDER IF POSSIBLE
C----
IF( JA .GT. 2 ) GO TO 601
IF( K .EQ. NA ) GO TO 501
K = K + 1
GO TO 600
C----
C REQUESTED ACCURACY WAS NOT OBTAINED
C REVERT TO LEAST DIVERGENT INTERPOLATION
C BASED ON RELATVE AND ABSOLUTE CONVERGENCE
C----
501 CONTINUE
KR = 1
CONR = 100.
KA = 1
CONA = 100.*ABS(F(1))
ABSOK = .TRUE.
RELOK = .TRUE.
DO 10 I = 2, NA
IF( F(I-1) .NE. 0.0 ) THEN
CON = ABS( 1.0 - F(I)/F(I-1) )
ELSE
CON = 1.0
ENDIF
IF( RELOK .AND. CON .LT. CONR ) THEN
KR = I
CONR = CON
ELSE
RELOK = .FALSE.
ENDIF
CON = ABS( F(I) - F(I-1) )
IF( ABSOK .AND. CON .LT. CONA ) THEN
KA = I
CONA = CON
ELSE
ABSOK = .FALSE.
ENDIF
10 CONTINUE
IF( KR .GT. KA ) THEN
KK = KR
CONMIN = CONR
ELSE
KK = KA
CONMIN = CONA
IF( F(KK) .NE. 0.0 ) CONMIN = CONMIN/F(KK)
ENDIF
AIKINT = F(KK)
RETURN
C----
C FORMAT
C----
2000 FORMAT(' --- ERROR IN AIKINT: X-VALUES ARE',
> ' NOT MONOTONICALLY INCREASING ---')
2001 FORMAT(' --- WARNING FROM AIKINT: EXTRAPOLATION',
> ' BEFORE TABLE BEGINS AT LEAST ONCE ---')
2002 FORMAT(' --- WARNING FROM AIKINT: EXTRAPOLATION',
> ' BEYOND END OF TABLE AT LEAST ONCE ---')
END
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