Initial commit from Polytechnique Montreal

1 files changed, 172 insertions, 0 deletions

diff --git a/Utilib/src/ALTERP.f b/Utilib/src/ALTERP.f
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+*DECK ALTERP
+      SUBROUTINE ALTERP(LCUBIC,N,X,VAL,LDERIV,TERP)
+*
+*-----------------------------------------------------------------------
+*
+*Purpose:
+* determination of the TERP interpolation/derivation components using
+* the order 4 Ceschino method with cubic Hermite polynomials.
+*
+*Copyright:
+* Copyright (C) 2006 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
+* LCUBIC  =.TRUE.: cubic Ceschino interpolation; =.FALSE: linear
+*         Lagrange interpolation.
+* N       number of points.
+* X       abscissas
+* VAL     abscissa of the interpolated point.
+* LDERIV  set to .true. to compute the first derivative with respect
+*         to X. Set to .false. to interpolate.
+*
+*Parameters: output
+* TERP    interpolation/derivation components.
+*
+*-----------------------------------------------------------------------
+*
+*----
+*  SUBROUTINE ARGUMENTS
+*----
+      INTEGER N
+      LOGICAL LCUBIC,LDERIV
+      REAL X(N),VAL,TERP(N)
+*---
+* LOCAL VARIABLES
+*---
+      CHARACTER HSMG*131
+      REAL, ALLOCATABLE, DIMENSION(:,:) :: WK
+*
+      I0=0
+      IF(N.LE.1) CALL XABORT('ALTERP: INVALID NUMBER OF POINTS.')
+      IF(N.EQ.2) GO TO 110
+      DO 10 I=1,N
+      TERP(I)=0.0
+   10 CONTINUE
+*----
+*  INTERVAL IDENTIFICATION.
+*----
+      DO 20 I=1,N-1
+      IF((VAL.GE.X(I)).AND.(VAL.LE.X(I+1))) THEN
+         I0=I
+         GO TO 30
+      ENDIF
+   20 CONTINUE
+      WRITE(HSMG,'(35HALTERP: UNABLE TO INTERPOLATE (VAL=,1P,E11.4,
+     1 8H LIMITS=,E11.4,2H, ,E11.4,2H).)') VAL,X(1),X(N)
+      CALL XABORT(HSMG)
+   30 DX=X(I0+1)-X(I0)
+*----
+*  LINEAR LAGRANGE POLYNOMIAL.
+*----
+      IF(.NOT.LCUBIC) THEN
+        IF(LDERIV) THEN
+           TERP(I0)=-1.0/DX
+           TERP(I0+1)=1.0/DX
+        ELSE
+           TERP(I0)=(X(I0+1)-VAL)/DX
+           TERP(I0+1)=1.0-TERP(I0)
+        ENDIF
+        RETURN
+      ENDIF
+*----
+*  CESCHINO CUBIC POLYNOMIAL.
+*----
+      ALLOCATE(WK(3,N))
+      DO 35 I=1,N
+      WK(3,I)=0.0
+   35 CONTINUE
+      U=(VAL-0.5*(X(I0)+X(I0+1)))/DX
+      IF(LDERIV) THEN
+         H1=(-6.0*(0.5-U)+6.0*(0.5-U)**2)/DX
+         H2=(-2.0*(0.5-U)+3.0*(0.5-U)**2)/DX
+         H3=(6.0*(0.5+U)-6.0*(0.5+U)**2)/DX
+         H4=(-2.0*(0.5+U)+3.0*(0.5+U)**2)/DX
+         TEST=0.0
+      ELSE
+         H1=3.0*(0.5-U)**2-2.0*(0.5-U)**3
+         H2=(0.5-U)**2-(0.5-U)**3
+         H3=3.0*(0.5+U)**2-2.0*(0.5+U)**3
+         H4=-(0.5+U)**2+(0.5+U)**3
+         TEST=1.0
+      ENDIF
+      TERP(I0)=H1
+      TERP(I0+1)=H3
+      WK(3,I0)=H2*DX
+      WK(3,I0+1)=H4*DX
+*----
+*  COMPUTE THE COEFFICIENT MATRIX.
+*----
+      HP=1.0/(X(2)-X(1))
+      WK(1,1)=HP
+      WK(2,1)=HP
+      DO 40 I=2,N-1
+      HM=HP
+      HP=1.0/(X(I+1)-X(I))
+      WK(1,I)=2.0*(HM+HP)
+      WK(2,I)=HP
+   40 CONTINUE
+      WK(1,N)=HP
+      WK(2,N)=HP
+*----
+*  FORWARD ELIMINATION.
+*----
+      PMX=WK(1,1)
+      WK(3,1)=WK(3,1)/PMX
+      DO 50 I=2,N
+      GAR=WK(2,I-1)
+      WK(2,I-1)=WK(2,I-1)/PMX
+      PMX=WK(1,I)-GAR*WK(2,I-1)
+      WK(3,I)=(WK(3,I)-GAR*WK(3,I-1))/PMX
+   50 CONTINUE
+*----
+*  BACK SUBSTITUTION.
+*----
+      DO 60 I=N-1,1,-1
+      WK(3,I)=WK(3,I)-WK(2,I)*WK(3,I+1)
+   60 CONTINUE
+*----
+*  COMPUTE THE INTERPOLATION FACTORS.
+*----
+      DO 100 J=1,N
+      IMIN=MAX(2,J-1)
+      IMAX=MIN(N-1,J+1)
+      DO 70 I=1,N
+      WK(1,I)=0.0
+   70 CONTINUE
+      WK(1,J)=1.0
+      HP=1.0/(X(IMIN)-X(IMIN-1))
+      YLAST=WK(1,IMIN-1)
+      WK(1,IMIN-1)=2.0*HP*HP*(WK(1,IMIN)-WK(1,IMIN-1))
+      DO 80 I=IMIN,IMAX
+      HM=HP
+      HP=1.0/(X(I+1)-X(I))
+      PMX=3.0*(HM*HM*(WK(1,I)-YLAST)+HP*HP*(WK(1,I+1)-WK(1,I)))
+      YLAST=WK(1,I)
+      WK(1,I)=PMX
+   80 CONTINUE
+      WK(1,IMAX+1)=2.0*HP*HP*(WK(1,IMAX+1)-YLAST)
+      DO 90 I=IMIN-1,IMAX+1
+      TERP(J)=TERP(J)+WK(1,I)*WK(3,I)
+   90 CONTINUE
+      IF(ABS(TERP(J)).LE.1.0E-7) TERP(J)=0.0
+      TEST=TEST-TERP(J)
+  100 CONTINUE
+      IF(ABS(TEST).GT.1.0E-5) CALL XABORT('ALTERP: WRONG TERP FACTORS.')
+      DEALLOCATE(WK)
+      RETURN
+*
+  110 IF(LDERIV) THEN
+         TERP(1)=-1.0/(X(2)-X(1))
+         TERP(2)=1.0/(X(2)-X(1))
+      ELSE
+         TERP(1)=(X(2)-VAL)/(X(2)-X(1))
+         TERP(2)=1.0-TERP(1)
+      ENDIF
+      RETURN
+      END