!-------------------------------------- LICENCE BEGIN ------------------------------------
!Environment Canada - Atmospheric Science and Technology License/Disclaimer,
!                     version 3; Last Modified: May 7, 2008.
!This is free but copyrighted software; you can use/redistribute/modify it under the terms
!of the Environment Canada - Atmospheric Science and Technology License/Disclaimer
!version 3 or (at your option) any later version that should be found at:
!http://collaboration.cmc.ec.gc.ca/science/rpn.comm/license.html
!
!This software is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY;
!without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
!See the above mentioned License/Disclaimer for more details.
!You should have received a copy of the License/Disclaimer along with this software;
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!CANADA, H9P 1J3; or send e-mail to service.rpn@ec.gc.ca
!-------------------------------------- LICENCE END --------------------------------------
!

      SUBROUTINE MATAPATST(S,ALPHA,N,VMA,VMB,VMC,VMD,VME,VMF) 
* 
****************************************************************
*     CALCULE LES ELEMENTS DE LA MATRICE TRIDIAGONALE ASSOCIEE A LA 
*     SOLUTION PAR UN ALGORITHME DU 4EME ORDRE DE L'EQUATION
*     T*S**ALPHA=D(P)/DS OU T ET P SONT DEUX FONCTIONS ECHANTILLONNEES
*     AUX N NIVEAUX SIGMA. LES MATRICES GENEREES ICI SERONT UTILISEES 
*     PAR LES SUBR. VTAP ET VPAT. L'ALGORITHME EST DU A J. COTE.
*     NOTE: ON CALCULE IMMEDIATEMENT DANS LE COMMON MAPAT 
*           LES COEFFICIENTS GENERES PAR LA REDUCTION GAUSSIENNE
*           LORS DU CALCUL DE T.
*     A(I),B(I),C(I): DIAG. INF., PRINC., ET SUP. DE LA MAT.
*     ALPHA         : EXPOSANT DE SIGMA.
*     N             : NOMBRE DE NIVEAUX SIGMA DU MODELE.
*     ADAPTE AU MODELE SEF PAR MICHEL BELAND, AVRIL 1984. 
*     RECODAGE PAR HAL RITCHIE, JANVIER 1993.
*     MODIFIER PAR S. LAROCHE POUR L'ANALYSE REGIONALE DECEMBRE 1996.
******************************************************************* 
* 
* 
      integer   N
      REAL*8      VMA(N), VMB(N), VMC(N)
      REAL*8      VMD(N), VME(N), VMF(N)
      REAL*8      S(N),Q(3), ALPHA
C
C
      DO 20 K=1,N 
      X0=S(K) 
      IF (K.EQ.1) THEN
        XM=S(1)
        XP=S(2)
        AA=S(3)-X0
        BB=S(2)-X0
      ELSEIF (K.EQ.N) THEN
        XM=S(N-1)
        XP=S(N)
        AA=S(N-1)-X0
        BB=S(N-2)-X0
      ELSE
        XM=S(K-1)
        XP=S(K+1)
        AA=XM-X0
        BB=XP-X0
      ENDIF
      DO 10 L=1,3
      EX=ALPHA+FLOAT(L) 
        IF(EX.NE.0.) Q(L)=(XP**EX-XM**EX)/EX
        IF(EX.EQ.0.) Q(L)=ALOG(XP/XM) 
   10 CONTINUE
      Q(3)=Q(3)-X0*(2.0*Q(2)-X0*Q(1)) 
      Q(2)=Q(2)-X0*Q(1) 
      CC=AA**2
      DD=BB**2
      DET=AA*DD-BB*CC 
      VMA(K)=(DD*Q(2)-BB*Q(3))/(2.0*DET)
      VMC(K)=(AA*Q(3)-CC*Q(2))/(2.0*DET)
      VMB(K)=Q(1)/2.0-VMA(K)-VMC(K) 
   20 CONTINUE
* 
*     COEFFICIENTS DE L'OPERATEUR INVERSE 
* 
      DO 30 K=1,N 
      VMD(K)=VMA(K) 
      VME(K)=VMB(K) 
      VMF(K)=VMC(K) 
   30 CONTINUE
* 
      VMD(1)=VMD(1)/VMF(2)
      VME(1)=VME(1)-VMD(1)*VMD(2) 
      VMF(1)=VMF(1)-VMD(1)*VME(2) 
      VMF(N)=VMF(N)/VMD(N-1)
      VMD(N)=VMD(N)-VMF(N)*VME(N-1) 
      VME(N)=VME(N)-VMF(N)*VMF(N-1) 
* 
      VME(1)=1.0/VME(1) 
      DO 31 K=2,N 
      KM=K-1
      VMF(KM)=VMF(KM)*VME(KM) 
   31 VME(K)=1.0/(VME(K)-VMD(K)*VMF(KM))
* 
*
      RETURN
      END