C PRISIX    SOURCE    CHAT      05/01/13    02:27:44     5004           
      SUBROUTINE PRISIX(ICM,XE,XEC,XX,SHPC,SGA,QSI,IG)
      IMPLICIT INTEGER(I-N)
      IMPLICIT REAL*8 (A-H,O-Z)
      DIMENSION A(3,6),AJ(3,3),X(3),XE(3,*),XEC(3,2),XX(3,2),
     & BJ(3,3),F(3),SHPC(6,20,*),SGA(3,5,5),QSI(3,2),DT(3),SIB(3)
      DATA EPSI/1.D-7/
C  IG: NUMERO DU POINT DE GAUSS
      DO 10 I=1,3
      A(I,1)= XE(I,1)+XE(I,4)-2.D0*XX(I,IG)
      A(I,2)=-XE(I,1)+XE(I,2)-XE(I,4)+XE(I,5)
      A(I,3)=-XE(I,1)+XE(I,3)-XE(I,4)+XE(I,6)
      A(I,4)=-XE(I,1)+XE(I,4)
      A(I,5)= XE(I,1)-XE(I,2)-XE(I,4)+XE(I,5)
  10  A(I,6)= XE(I,1)-XE(I,3)-XE(I,4)+XE(I,6)
C --- Initialisation
      DO 15 I=1,3
  15  X(I)=0.0
C
      ITER=0
      ICRI=0
 100  CONTINUE
C --- LES DERIVEES DES FONCTIONS DE TRANSFORMATION
      DO 20 I=1,3
      AJ(I,1)=A(I,2)+A(I,5)*X(3)
      AJ(I,2)=A(I,3)+A(I,6)*X(3)
  20  AJ(I,3)=A(I,4)+A(I,5)*X(1)+A(I,6)*X(2)
C --- Calcul de l'inverse de la matrice AJ et son determinant :BJ=inverse(AJ)
      CALL INVERT(AJ,BJ,DET,ICRI)
      X13=X(1)*X(3)
      X23=X(2)*X(3)
      DO 40 I=1,3
  40  F(I)=A(I,1)+A(I,2)*X(1)+A(I,3)*X(2)+A(I,4)*X(3)+A(I,5)*X13
     &    +A(I,6)*X23
      DD=SQRT(F(1)*F(1)+F(2)*F(2)+F(3)*F(3))
      IF(DD.GT.EPSI) THEN
      ITER=ITER+1
      DO 50 I=1,3
  50  X(I)=X(I)-BJ(I,1)*F(1)-BJ(I,2)*F(2)-BJ(I,3)*F(3)
      GOTO 100
      END IF
      DO 60 I=1,3
  60  QSI(I,IG)=X(I)
      DLAMD=1.D0-X(1)-X(2)
      AA=0.5D0-0.5D0*X(3)
      BB=0.5D0+0.5D0*X(3)
C --- Calcul des fonctions d'interpolation et leur derivees
C --- Fonctions d'interpolation Ni
      SHPC(1,1,IG)=DLAMD*AA
      SHPC(1,2,IG)= X(1)*AA
      SHPC(1,3,IG)= X(2)*AA
      SHPC(1,4,IG)=DLAMD*BB
      SHPC(1,5,IG)= X(1)*BB
      SHPC(1,6,IG)= X(2)*BB
      IF(ICM.NE.0) THEN
C --- Derivee de Ni par rapport a QSI
      SHPC(2,1,IG)=-AA
      SHPC(2,2,IG)= AA
      SHPC(2,3,IG)=0.D0
      SHPC(2,4,IG)=-BB
      SHPC(2,5,IG)= BB
      SHPC(2,6,IG)=0.D0
C --- Derivee de Ni par rapport a ETA
      SHPC(3,1,IG)=-AA
      SHPC(3,2,IG)=0.D0
      SHPC(3,3,IG)= AA
      SHPC(3,4,IG)=-BB
      SHPC(3,5,IG)=0.D0
      SHPC(3,6,IG)= BB
C --- Derivee de Ni par rapport a DZE
      SHPC(4,1,IG)=-0.5D0*DLAMD
      SHPC(4,2,IG)=-0.5D0*X(1)
      SHPC(4,3,IG)=-0.5D0*X(2)
      SHPC(4,4,IG)= 0.5D0*DLAMD
      SHPC(4,5,IG)= 0.5D0*X(1)
      SHPC(4,6,IG)= 0.5D0*X(2)
      END IF
      CALL PROSGA(ICM,XE,XEC,XX,X,SHPC,SGA,QSI,IG,6)
      END