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*DECK LIBLAG
SUBROUTINE LIBLAG(NEF,XE,GE,XI,GS)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Lagrange interpolation in a table of points using the APOLLO2 recipe.
*
*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
*
*Parameters: input
* NEF number of points.
* XE x-values.
* GE f(x)-values.
* XI interpolating x-value.
*
*Parameters: output
* GS interpolated value f(XI).
*
*-----------------------------------------------------------------------
*
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER NEF
REAL XE(NEF),GE(NEF),XI,GS
*----
* LOCAL VARIABLES
*----
PARAMETER(NINT=3)
REAL WEIGHT(NINT)
*----
* CONSTANT FUNCTION DEFINED BY A SINGLE POINT
*----
IF(NEF.EQ.1) THEN
GS=GE(1)
RETURN
ENDIF
*
IORD=MIN(NINT,NEF)
*----
* LOCATE FIRST POINT TO THE RIGHT OF XI (PT IXP)
*----
DO 30 IXP=1,NEF
IF(ABS(XE(IXP)-XI).LE.1.0E-5*ABS(XI)) THEN
GS=GE(IXP)
RETURN
ELSE IF(XE(IXP).GT.XI) THEN
IMIN=IXP-(IORD+1)/2
IMAX=IMIN+IORD-1
GO TO 40
ENDIF
30 CONTINUE
*----
* XI IS TO THE RIGHT OF EVERY POINT XE
*----
IMAX=NEF
IMIN=NEF-IORD+1
GO TO 70
*
40 IF(IMIN.LT.1) THEN
IMIN=1
IMAX=IORD
ELSE IF(IMAX.GT.NEF) THEN
IMIN=NEF-IORD+1
IMAX=NEF
ENDIF
*
70 I0=IMIN-1
DO 90 I=IMIN,IMAX
PP=1.0
DO 80 J=IMIN,IMAX
IF(I.NE.J) PP=PP*((XI-XE(J))/(XE(I)-XE(J)))
80 CONTINUE
WEIGHT(I+1-IMIN)=PP
90 CONTINUE
*
GS=0.0
DO 110 I=1,IORD
GS=GS+WEIGHT(I)*GE(I+I0)
110 CONTINUE
DO 120 I=1,IORD
I1=I+I0
IF(XE(I1).GT.XI) THEN
IF(I1-1.GT.0) THEN
YMIN=MIN(GE(I1-1),GE(I1))
YMAX=MAX(GE(I1-1),GE(I1))
IF((GS.GT.YMAX).OR.(GS.LT.YMIN)) THEN
GS=GE(I1-1)+(GE(I1)-GE(I1-1))*
1 (XI-XE(I1-1))/(XE(I1)-XE(I1-1))
ENDIF
ELSE
GS=GE(1)+(GE(2)-GE(1))*(XI-XE(1))/(XE(2)-XE(1))
IF(GS.LE.0.) GS=GE(1)
ENDIF
RETURN
ENDIF
120 CONTINUE
RETURN
END
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