SUBROUTINE CHRM2(Y,G,i)
C
C     EVALUATES ELEMENTS OF THE CHRISTOFFEL MATRIX
C
      DIMENSION a(21),Y(6),G(3,3)
      COMMON/GAM/G11,G12,G13,G22,G23,G33
      COMMON /APROX1/ e(21,10)
C
      do 1 j=1,21
      a(j)=e(j,i)
    1 continue
      P1=Y(4)
      P2=Y(5)
      P3=Y(6)
      P11=P1*P1
      P12=P1*P2
      P13=P1*P3
      P22=P2*P2
      P23=P2*P3
      P33=P3*P3
      G11=A(1)*P11+A(21)*P22+A(19)*P33+
     1    2.*(A(6)*P12+A(5)*P13+A(20)*P23)
      G22=A(21)*P11+A(7)*P22+A(16)*P33+
     1    2.*(A(11)*P12+A(18)*P13+A(9)*P23)
      G33=A(19)*P11+A(16)*P22+A(12)*P33+
     1    2.*(A(17)*P12+A(14)*P13+A(13)*P23)
      G12=A(6)*P11+A(11)*P22+A(17)*P33+
     1    (A(21)+A(2))*P12+(A(20)+A(4))*P13+(A(10)+A(18))*P23
      G13=A(5)*P11+A(18)*P22+A(14)*P33+
     1    (A(20)+A(4))*P12+(A(19)+A(3))*P13+(A(17)+A(15))*P23
      G23=A(20)*P11+A(9)*P22+A(13)*P33+
     1    (A(10)+A(18))*P12+(A(17)+A(15))*P13+(A(16)+A(8))*P23
      G(1,1)=G11
      G(1,2)=G12
      G(1,3)=G13
      G(2,1)=G12
      G(2,2)=G22
      G(2,3)=G23
      G(3,1)=G13
      G(3,2)=G23
      G(3,3)=G33
      RETURN
      END
      SUBROUTINE PCHRM(Y,G,L,i)
C
C     EVALUATES FIRST DERIVATIVES OF ELEMENTS OF CHRISTOFFEL MATRIX
C     WITH RESPECT TO THE L-TH COMPONENT OF THE SLOWNESS VECTOR
C
      DIMENSION a(21),Y(6),G(3,3)
      COMMON /APROX1/ e(21,10)
C
      do 1 j=1,21
      a(j)=e(j,i)
    1 continue
      P1=Y(4)
      P2=Y(5)
      P3=Y(6)
      IF(L.EQ.1)THEN
        G(1,1)=2.*(A(1)*P1+A(6)*P2+A(5)*P3)
        G(2,2)=2.*(A(21)*P1+A(11)*P2+A(18)*P3)
        G(3,3)=2.*(A(19)*P1+A(17)*P2+A(14)*P3)
        AUX=2.*A(6)*P1+(A(21)+A(2))*P2+(A(20)+A(4))*P3
        G(1,2)=AUX
        G(2,1)=AUX
        AUX=2.*A(5)*P1+(A(20)+A(4))*P2+(A(19)+A(3))*P3
        G(1,3)=AUX
        G(3,1)=AUX
        AUX=2.*A(20)*P1+(A(10)+A(18))*P2+(A(17)+A(15))*P3
        G(2,3)=AUX
        G(3,2)=AUX
      END IF
      IF(L.EQ.2)THEN
        G(1,1)=2.*(A(6)*P1+A(21)*P2+A(20)*P3)
        G(2,2)=2.*(A(11)*P1+A(7)*P2+A(9)*P3)
        G(3,3)=2.*(A(17)*P1+A(16)*P2+A(13)*P3)
        AUX=2.*A(11)*P2+(A(21)+A(2))*P1+(A(10)+A(18))*P3
        G(1,2)=AUX
        G(2,1)=AUX
        AUX=2.*A(18)*P2+(A(20)+A(4))*P1+(A(17)+A(15))*P3
        G(1,3)=AUX
        G(3,1)=AUX
        AUX=2.*A(9)*P2+(A(10)+A(18))*P1+(A(16)+A(8))*P3
        G(2,3)=AUX
        G(3,2)=AUX
      END IF
      IF(L.EQ.3)THEN
        G(1,1)=2.*(A(5)*P1+A(20)*P2+A(19)*P3)
        G(2,2)=2.*(A(18)*P1+A(9)*P2+A(16)*P3)
        G(3,3)=2.*(A(14)*P1+A(13)*P2+A(12)*P3)
        AUX=2.*A(17)*P3+(A(20)+A(4))*P1+(A(10)+A(18))*P2
        G(1,2)=AUX
        G(2,1)=AUX
        AUX=2.*A(14)*P3+(A(19)+A(3))*P1+(A(17)+A(15))*P2
        G(1,3)=AUX
        G(3,1)=AUX
        AUX=2.*A(13)*P3+(A(17)+A(15))*P1+(A(16)+A(8))*P2
        G(2,3)=AUX
        G(3,2)=AUX
      END IF
      RETURN
      END
      SUBROUTINE PPCHRM(G,L,M,i)
C
C     EVALUATES SECOND DERIVATIVES OF ELEMENTS OF CHRISTOFFEL MATRIX
C     WITH RESPECT TO THE L-TH AND M-TH COMPONENTS OF THE SLOWNESS
C     VECTOR
C
      DIMENSION a(21),G(3,3)
      COMMON /APROX1/ e(21,10)
C
      do 1 j=1,21
      a(j)=e(j,i)
    1 continue
      IF(L.EQ.1.AND.M.EQ.1)THEN
        G(1,1)=2.*A(1)
        G(2,2)=2.*A(21)
        G(3,3)=2.*A(19)
        AUX=2.*A(6)
        G(1,2)=AUX
        G(2,1)=AUX
        AUX=2.*A(5)
        G(1,3)=AUX
        G(3,1)=AUX
        AUX=2.*A(20)
        G(2,3)=AUX
        G(3,2)=AUX
      END IF
      IF(L.EQ.2.AND.M.EQ.2)THEN
        G(1,1)=2.*A(21)
        G(2,2)=2.*A(7)
        G(3,3)=2.*A(16)
        AUX=2.*A(11)
        G(1,2)=AUX
        G(2,1)=AUX
        AUX=2.*A(18)
        G(1,3)=AUX
        G(3,1)=AUX
        AUX=2.*A(9)
        G(2,3)=AUX
        G(3,2)=AUX
      END IF
      IF(L.EQ.3.AND.M.EQ.3)THEN
        G(1,1)=2.*A(19)
        G(2,2)=2.*A(16)
        G(3,3)=2.*A(12)
        AUX=2.*A(17)
        G(1,2)=AUX
        G(2,1)=AUX
        AUX=2.*A(14)
        G(1,3)=AUX
        G(3,1)=AUX
        AUX=2.*A(13)
        G(2,3)=AUX
        G(3,2)=AUX
      END IF
      IF((L.EQ.1.AND.M.EQ.2).OR.(L.EQ.2.AND.M.EQ.1))THEN
        G(1,1)=2.*A(6)
        G(2,2)=2.*A(11)
        G(3,3)=2.*A(17)
        AUX=A(21)+A(2)
        G(1,2)=AUX
        G(2,1)=AUX
        AUX=A(20)+A(4)
        G(1,3)=AUX
        G(3,1)=AUX
        AUX=A(10)+A(18)
        G(2,3)=AUX
        G(3,2)=AUX
      END IF
      IF((L.EQ.1.AND.M.EQ.3).OR.(L.EQ.3.AND.M.EQ.1))THEN
        G(1,1)=2.*A(5)
        G(2,2)=2.*A(18)
        G(3,3)=2.*A(14)
        AUX=A(20)+A(4)
        G(1,2)=AUX
        G(2,1)=AUX
        AUX=A(19)+A(3)
        G(1,3)=AUX
        G(3,1)=AUX
        AUX=A(17)+A(15)
        G(2,3)=AUX
        G(3,2)=AUX
      END IF
      IF((L.EQ.2.AND.M.EQ.3).OR.(L.EQ.3.AND.M.EQ.2))THEN
        G(1,1)=2.*A(20)
        G(2,2)=2.*A(9)
        G(3,3)=2.*A(13)
        AUX=A(10)+A(18)
        G(1,2)=AUX
        G(2,1)=AUX
        AUX=A(17)+A(15)
        G(1,3)=AUX
        G(3,1)=AUX
        AUX=A(16)+A(8)
        G(2,3)=AUX
        G(3,2)=AUX
      END IF
      RETURN
      END