307 lines
19 KiB
Fortran
307 lines
19 KiB
Fortran
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! for ADM variables
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subroutine adm_ricci_gamma(ex, X, Y, Z, &
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dxx , gxy , gxz , dyy , gyz , dzz,&
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Gamxxx,Gamxxy,Gamxxz,Gamxyy,Gamxyz,Gamxzz,&
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Gamyxx,Gamyxy,Gamyxz,Gamyyy,Gamyyz,Gamyzz,&
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Gamzxx,Gamzxy,Gamzxz,Gamzyy,Gamzyz,Gamzzz,&
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Rxx,Rxy,Rxz,Ryy,Ryz,Rzz,&
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Symmetry)
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implicit none
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!~~~~~~> Input parameters:
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integer,intent(in ):: ex(1:3), Symmetry
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real*8, intent(in ):: X(1:ex(1)),Y(1:ex(2)),Z(1:ex(3))
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real*8, dimension(ex(1),ex(2),ex(3)),intent(in ) :: dxx,gxy,gxz,dyy,gyz,dzz
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! when out, physical second kind of connection
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real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: Gamxxx, Gamxxy, Gamxxz
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real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: Gamxyy, Gamxyz, Gamxzz
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real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: Gamyxx, Gamyxy, Gamyxz
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real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: Gamyyy, Gamyyz, Gamyzz
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real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: Gamzxx, Gamzxy, Gamzxz
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real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: Gamzyy, Gamzyz, Gamzzz
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! when out, physical Ricci tensor
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real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: Rxx,Rxy,Rxz,Ryy,Ryz,Rzz
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!~~~~~~> Other variables:
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real*8, dimension(ex(1),ex(2),ex(3)) :: gxx,gyy,gzz
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real*8, dimension(ex(1),ex(2),ex(3)) :: gxxx,gxyx,gxzx,gyyx,gyzx,gzzx
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real*8, dimension(ex(1),ex(2),ex(3)) :: gxxy,gxyy,gxzy,gyyy,gyzy,gzzy
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real*8, dimension(ex(1),ex(2),ex(3)) :: gxxz,gxyz,gxzz,gyyz,gyzz,gzzz
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real*8, dimension(ex(1),ex(2),ex(3)) :: ass_Gamxxx,ass_Gamxxy,ass_Gamxxz
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real*8, dimension(ex(1),ex(2),ex(3)) :: ass_Gamxyy,ass_Gamxyz,ass_Gamxzz
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real*8, dimension(ex(1),ex(2),ex(3)) :: ass_Gamyxx,ass_Gamyxy,ass_Gamyxz
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real*8, dimension(ex(1),ex(2),ex(3)) :: ass_Gamyyy,ass_Gamyyz,ass_Gamyzz
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real*8, dimension(ex(1),ex(2),ex(3)) :: ass_Gamzxx,ass_Gamzxy,ass_Gamzxz
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real*8, dimension(ex(1),ex(2),ex(3)) :: ass_Gamzyy,ass_Gamzyz,ass_Gamzzz
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real*8, dimension(ex(1),ex(2),ex(3)) :: gupxx,gupxy,gupxz
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real*8, dimension(ex(1),ex(2),ex(3)) :: gupyy,gupyz,gupzz
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real*8, dimension(ex(1),ex(2),ex(3)) :: gxxxx,gxxxy,gxxxz,gxxyy,gxxyz,gxxzz
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real*8, dimension(ex(1),ex(2),ex(3)) :: gxyxx,gxyxy,gxyxz,gxyyy,gxyyz,gxyzz
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real*8, dimension(ex(1),ex(2),ex(3)) :: gxzxx,gxzxy,gxzxz,gxzyy,gxzyz,gxzzz
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real*8, dimension(ex(1),ex(2),ex(3)) :: gyyxx,gyyxy,gyyxz,gyyyy,gyyyz,gyyzz
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real*8, dimension(ex(1),ex(2),ex(3)) :: gyzxx,gyzxy,gyzxz,gyzyy,gyzyz,gyzzz
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real*8, dimension(ex(1),ex(2),ex(3)) :: gzzxx,gzzxy,gzzxz,gzzyy,gzzyz,gzzzz
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real*8, dimension(ex(1),ex(2),ex(3)) :: Rxyxy, Rxyxz, Rxyyz, Rxzxz, Rxzyz, Ryzyz
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real*8, parameter :: ONE = 1.D0, TWO = 2.D0, FOUR = 4.D0
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real*8, parameter :: HALF = 0.5D0, F2o3 = 2.d0/3.d0, F3o2 = 1.5d0
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real*8, parameter :: SYM = 1.D0, ANTI= - 1.D0
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gxx = dxx + ONE
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gyy = dyy + ONE
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gzz = dzz + ONE
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call fderivs(ex,dxx,gxxx,gxxy,gxxz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0)
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call fderivs(ex,gxy,gxyx,gxyy,gxyz,X,Y,Z,ANTI,ANTI,SYM ,Symmetry,0)
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call fderivs(ex,gxz,gxzx,gxzy,gxzz,X,Y,Z,ANTI,SYM ,ANTI,Symmetry,0)
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call fderivs(ex,dyy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0)
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call fderivs(ex,gyz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,0)
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call fderivs(ex,dzz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0)
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call kind1_connection(ex, &
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gxxx,gxyx,gxzx,gyyx,gyzx,gzzx, &
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gxxy,gxyy,gxzy,gyyy,gyzy,gzzy, &
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gxxz,gxyz,gxzz,gyyz,gyzz,gzzz, &
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ass_Gamxxx, ass_Gamxxy, ass_Gamxxz, ass_Gamxyy, ass_Gamxyz, ass_Gamxzz, &
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ass_Gamyxx, ass_Gamyxy, ass_Gamyxz, ass_Gamyyy, ass_Gamyyz, ass_Gamyzz, &
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ass_Gamzxx, ass_Gamzxy, ass_Gamzxz, ass_Gamzyy, ass_Gamzyz, ass_Gamzzz)
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! invert metric
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gupzz = gxx * gyy * gzz + gxy * gyz * gxz + gxz * gxy * gyz - &
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gxz * gyy * gxz - gxy * gxy * gzz - gxx * gyz * gyz
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gupxx = ( gyy * gzz - gyz * gyz ) / gupzz
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gupxy = - ( gxy * gzz - gyz * gxz ) / gupzz
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gupxz = ( gxy * gyz - gyy * gxz ) / gupzz
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gupyy = ( gxx * gzz - gxz * gxz ) / gupzz
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gupyz = - ( gxx * gyz - gxy * gxz ) / gupzz
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gupzz = ( gxx * gyy - gxy * gxy ) / gupzz
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call kind2_connection(ex, &
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gupxx,gupxy,gupxz,gupyy,gupyz,gupzz, &
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ass_Gamxxx, ass_Gamxxy, ass_Gamxxz, ass_Gamxyy, ass_Gamxyz, ass_Gamxzz, &
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ass_Gamyxx, ass_Gamyxy, ass_Gamyxz, ass_Gamyyy, ass_Gamyyz, ass_Gamyzz, &
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ass_Gamzxx, ass_Gamzxy, ass_Gamzxz, ass_Gamzyy, ass_Gamzyz, ass_Gamzzz, &
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Gamxxx, Gamxxy, Gamxxz, Gamxyy, Gamxyz, Gamxzz, &
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Gamyxx, Gamyxy, Gamyxz, Gamyyy, Gamyyz, Gamyzz, &
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Gamzxx, Gamzxy, Gamzxz, Gamzyy, Gamzyz, Gamzzz)
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call fdderivs(ex,dxx,gxxxx,gxxxy,gxxxz,gxxyy,gxxyz,gxxzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0)
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call fdderivs(ex,gxy,gxyxx,gxyxy,gxyxz,gxyyy,gxyyz,gxyzz,X,Y,Z,ANTI,ANTI,SYM ,Symmetry,0)
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call fdderivs(ex,gxz,gxzxx,gxzxy,gxzxz,gxzyy,gxzyz,gxzzz,X,Y,Z,ANTI,SYM ,ANTI,Symmetry,0)
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call fdderivs(ex,dyy,gyyxx,gyyxy,gyyxz,gyyyy,gyyyz,gyyzz,X,Y,Z,SYM, SYM ,SYM ,Symmetry,0)
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call fdderivs(ex,gyz,gyzxx,gyzxy,gyzxz,gyzyy,gyzyz,gyzzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,0)
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call fdderivs(ex,dzz,gzzxx,gzzxy,gzzxz,gzzyy,gzzyz,gzzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0)
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call adm_riemann(ex, &
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gxxxx,gxxxy,gxxxz,gxxyy,gxxyz,gxxzz, &
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gxyxx,gxyxy,gxyxz,gxyyy,gxyyz,gxyzz, &
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gxzxx,gxzxy,gxzxz,gxzyy,gxzyz,gxzzz, &
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gyyxx,gyyxy,gyyxz,gyyyy,gyyyz,gyyzz, &
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gyzxx,gyzxy,gyzxz,gyzyy,gyzyz,gyzzz, &
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gzzxx,gzzxy,gzzxz,gzzyy,gzzyz,gzzzz, &
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Gamxxx, Gamxxy, Gamxxz, Gamxyy, Gamxyz, Gamxzz, &
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Gamyxx, Gamyxy, Gamyxz, Gamyyy, Gamyyz, Gamyzz, &
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Gamzxx, Gamzxy, Gamzxz, Gamzyy, Gamzyz, Gamzzz, &
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ass_Gamxxx,ass_Gamxxy,ass_Gamxxz, ass_Gamxyy,ass_Gamxyz,ass_Gamxzz, &
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ass_Gamyxx,ass_Gamyxy,ass_Gamyxz, ass_Gamyyy,ass_Gamyyz,ass_Gamyzz, &
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ass_Gamzxx,ass_Gamzxy,ass_Gamzxz, ass_Gamzyy,ass_Gamzyz,ass_Gamzzz, &
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Rxyxy, Rxyxz, Rxyyz, Rxzxz, Rxzyz, Ryzyz)
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call adm_ricci(ex, &
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gupxx , gupxy , gupxz , gupyy , gupyz , gupzz , &
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Rxyxy, Rxyxz, Rxyyz, Rxzxz, Rxzyz, Ryzyz, &
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Rxx , Rxy , Rxz , Ryy , Ryz , Rzz)
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return
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end subroutine adm_ricci_gamma
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!----------------------------------------------------------------------------
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subroutine adm_ricci_gamma_ss(ex,crho,sigma,R,X, Y, Z, &
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drhodx, drhody, drhodz, &
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dsigmadx,dsigmady,dsigmadz, &
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dRdx,dRdy,dRdz, &
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drhodxx,drhodxy,drhodxz,drhodyy,drhodyz,drhodzz, &
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dsigmadxx,dsigmadxy,dsigmadxz,dsigmadyy,dsigmadyz,dsigmadzz, &
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dRdxx,dRdxy,dRdxz,dRdyy,dRdyz,dRdzz, &
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dxx , gxy , gxz , dyy , gyz , dzz,&
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Gamxxx,Gamxxy,Gamxxz,Gamxyy,Gamxyz,Gamxzz,&
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Gamyxx,Gamyxy,Gamyxz,Gamyyy,Gamyyz,Gamyzz,&
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Gamzxx,Gamzxy,Gamzxz,Gamzyy,Gamzyz,Gamzzz,&
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Rxx,Rxy,Rxz,Ryy,Ryz,Rzz,&
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Symmetry,Lev,sst)
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implicit none
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!~~~~~~> Input parameters:
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integer,intent(in ):: ex(1:3), Symmetry,Lev,sst
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double precision,intent(in),dimension(ex(1))::crho
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double precision,intent(in),dimension(ex(2))::sigma
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double precision,intent(in),dimension(ex(3))::R
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real*8, intent(in ),dimension(ex(1),ex(2),ex(3)):: X,Y,Z
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double precision,intent(in),dimension(ex(1),ex(2),ex(3))::drhodx, drhody, drhodz
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double precision,intent(in),dimension(ex(1),ex(2),ex(3))::dsigmadx,dsigmady,dsigmadz
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double precision,intent(in),dimension(ex(1),ex(2),ex(3))::dRdx,dRdy,dRdz
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double precision,intent(in),dimension(ex(1),ex(2),ex(3))::drhodxx,drhodxy,drhodxz,drhodyy,drhodyz,drhodzz
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double precision,intent(in),dimension(ex(1),ex(2),ex(3))::dsigmadxx,dsigmadxy,dsigmadxz,dsigmadyy,dsigmadyz,dsigmadzz
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double precision,intent(in),dimension(ex(1),ex(2),ex(3))::dRdxx,dRdxy,dRdxz,dRdyy,dRdyz,dRdzz
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real*8, dimension(ex(1),ex(2),ex(3)),intent(in ) :: dxx,gxy,gxz,dyy,gyz,dzz
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! when out, physical second kind of connection
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real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: Gamxxx, Gamxxy, Gamxxz
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real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: Gamxyy, Gamxyz, Gamxzz
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real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: Gamyxx, Gamyxy, Gamyxz
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real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: Gamyyy, Gamyyz, Gamyzz
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real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: Gamzxx, Gamzxy, Gamzxz
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real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: Gamzyy, Gamzyz, Gamzzz
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! when out, physical Ricci tensor
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real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: Rxx,Rxy,Rxz,Ryy,Ryz,Rzz
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!~~~~~~> Other variables:
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real*8, dimension(ex(1),ex(2),ex(3)) :: gxx,gyy,gzz
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real*8, dimension(ex(1),ex(2),ex(3)) :: gxxx,gxyx,gxzx,gyyx,gyzx,gzzx
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real*8, dimension(ex(1),ex(2),ex(3)) :: gxxy,gxyy,gxzy,gyyy,gyzy,gzzy
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real*8, dimension(ex(1),ex(2),ex(3)) :: gxxz,gxyz,gxzz,gyyz,gyzz,gzzz
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real*8, dimension(ex(1),ex(2),ex(3)) :: ass_Gamxxx,ass_Gamxxy,ass_Gamxxz
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real*8, dimension(ex(1),ex(2),ex(3)) :: ass_Gamxyy,ass_Gamxyz,ass_Gamxzz
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real*8, dimension(ex(1),ex(2),ex(3)) :: ass_Gamyxx,ass_Gamyxy,ass_Gamyxz
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real*8, dimension(ex(1),ex(2),ex(3)) :: ass_Gamyyy,ass_Gamyyz,ass_Gamyzz
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real*8, dimension(ex(1),ex(2),ex(3)) :: ass_Gamzxx,ass_Gamzxy,ass_Gamzxz
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real*8, dimension(ex(1),ex(2),ex(3)) :: ass_Gamzyy,ass_Gamzyz,ass_Gamzzz
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real*8, dimension(ex(1),ex(2),ex(3)) :: gupxx,gupxy,gupxz
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real*8, dimension(ex(1),ex(2),ex(3)) :: gupyy,gupyz,gupzz
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real*8, dimension(ex(1),ex(2),ex(3)) :: gxxxx,gxxxy,gxxxz,gxxyy,gxxyz,gxxzz
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real*8, dimension(ex(1),ex(2),ex(3)) :: gxyxx,gxyxy,gxyxz,gxyyy,gxyyz,gxyzz
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real*8, dimension(ex(1),ex(2),ex(3)) :: gxzxx,gxzxy,gxzxz,gxzyy,gxzyz,gxzzz
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real*8, dimension(ex(1),ex(2),ex(3)) :: gyyxx,gyyxy,gyyxz,gyyyy,gyyyz,gyyzz
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real*8, dimension(ex(1),ex(2),ex(3)) :: gyzxx,gyzxy,gyzxz,gyzyy,gyzyz,gyzzz
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real*8, dimension(ex(1),ex(2),ex(3)) :: gzzxx,gzzxy,gzzxz,gzzyy,gzzyz,gzzzz
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real*8, dimension(ex(1),ex(2),ex(3)) :: Rxyxy, Rxyxz, Rxyyz, Rxzxz, Rxzyz, Ryzyz
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real*8, parameter :: ONE = 1.D0, TWO = 2.D0, FOUR = 4.D0
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real*8, parameter :: HALF = 0.5D0, F2o3 = 2.d0/3.d0, F3o2 = 1.5d0
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real*8, parameter :: SYM = 1.D0, ANTI= - 1.D0
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gxx = dxx + ONE
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gyy = dyy + ONE
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gzz = dzz + ONE
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call fderivs_shc(ex,dxx,gxxx,gxxy,gxxz,crho,sigma,R, SYM, SYM,SYM,Symmetry,Lev,sst, &
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drhodx, drhody, drhodz, &
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dsigmadx,dsigmady,dsigmadz, &
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dRdx,dRdy,dRdz)
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call fderivs_shc(ex,gxy,gxyx,gxyy,gxyz,crho,sigma,R,ANTI,ANTI,SYM,Symmetry,Lev,sst, &
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drhodx, drhody, drhodz, &
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dsigmadx,dsigmady,dsigmadz, &
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dRdx,dRdy,dRdz)
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call fderivs_shc(ex,gxz,gxzx,gxzy,gxzz,crho,sigma,R,ANTI,SYM ,ANTI,Symmetry,Lev,sst, &
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drhodx, drhody, drhodz, &
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dsigmadx,dsigmady,dsigmadz, &
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dRdx,dRdy,dRdz)
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call fderivs_shc(ex,dyy,gyyx,gyyy,gyyz,crho,sigma,R, SYM, SYM,SYM,Symmetry,Lev,sst, &
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drhodx, drhody, drhodz, &
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dsigmadx,dsigmady,dsigmadz, &
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dRdx,dRdy,dRdz)
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call fderivs_shc(ex,gyz,gyzx,gyzy,gyzz,crho,sigma,R,SYM ,ANTI,ANTI,Symmetry,Lev,sst, &
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drhodx, drhody, drhodz, &
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dsigmadx,dsigmady,dsigmadz, &
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dRdx,dRdy,dRdz)
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call fderivs_shc(ex,dzz,gzzx,gzzy,gzzz,crho,sigma,R, SYM, SYM,SYM,Symmetry,Lev,sst, &
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drhodx, drhody, drhodz, &
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dsigmadx,dsigmady,dsigmadz, &
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dRdx,dRdy,dRdz)
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call kind1_connection(ex, &
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gxxx,gxyx,gxzx,gyyx,gyzx,gzzx, &
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gxxy,gxyy,gxzy,gyyy,gyzy,gzzy, &
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gxxz,gxyz,gxzz,gyyz,gyzz,gzzz, &
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ass_Gamxxx, ass_Gamxxy, ass_Gamxxz, ass_Gamxyy, ass_Gamxyz, ass_Gamxzz, &
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ass_Gamyxx, ass_Gamyxy, ass_Gamyxz, ass_Gamyyy, ass_Gamyyz, ass_Gamyzz, &
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ass_Gamzxx, ass_Gamzxy, ass_Gamzxz, ass_Gamzyy, ass_Gamzyz, ass_Gamzzz)
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! invert metric
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gupzz = gxx * gyy * gzz + gxy * gyz * gxz + gxz * gxy * gyz - &
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gxz * gyy * gxz - gxy * gxy * gzz - gxx * gyz * gyz
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gupxx = ( gyy * gzz - gyz * gyz ) / gupzz
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gupxy = - ( gxy * gzz - gyz * gxz ) / gupzz
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gupxz = ( gxy * gyz - gyy * gxz ) / gupzz
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gupyy = ( gxx * gzz - gxz * gxz ) / gupzz
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gupyz = - ( gxx * gyz - gxy * gxz ) / gupzz
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gupzz = ( gxx * gyy - gxy * gxy ) / gupzz
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call kind2_connection(ex, &
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gupxx,gupxy,gupxz,gupyy,gupyz,gupzz, &
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ass_Gamxxx, ass_Gamxxy, ass_Gamxxz, ass_Gamxyy, ass_Gamxyz, ass_Gamxzz, &
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ass_Gamyxx, ass_Gamyxy, ass_Gamyxz, ass_Gamyyy, ass_Gamyyz, ass_Gamyzz, &
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ass_Gamzxx, ass_Gamzxy, ass_Gamzxz, ass_Gamzyy, ass_Gamzyz, ass_Gamzzz, &
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Gamxxx, Gamxxy, Gamxxz, Gamxyy, Gamxyz, Gamxzz, &
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Gamyxx, Gamyxy, Gamyxz, Gamyyy, Gamyyz, Gamyzz, &
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Gamzxx, Gamzxy, Gamzxz, Gamzyy, Gamzyz, Gamzzz)
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call fdderivs_shc(ex,dxx,gxxxx,gxxxy,gxxxz,gxxyy,gxxyz,gxxzz,crho,sigma,R, SYM, SYM,SYM ,Symmetry,Lev,sst, &
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drhodx, drhody, drhodz, &
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dsigmadx,dsigmady,dsigmadz, &
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dRdx,dRdy,dRdz, &
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drhodxx,drhodxy,drhodxz,drhodyy,drhodyz,drhodzz, &
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dsigmadxx,dsigmadxy,dsigmadxz,dsigmadyy,dsigmadyz,dsigmadzz, &
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dRdxx,dRdxy,dRdxz,dRdyy,dRdyz,dRdzz)
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call fdderivs_shc(ex,dyy,gyyxx,gyyxy,gyyxz,gyyyy,gyyyz,gyyzz,crho,sigma,R, SYM, SYM,SYM ,Symmetry,Lev,sst, &
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drhodx, drhody, drhodz, &
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dsigmadx,dsigmady,dsigmadz, &
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dRdx,dRdy,dRdz, &
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drhodxx,drhodxy,drhodxz,drhodyy,drhodyz,drhodzz, &
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dsigmadxx,dsigmadxy,dsigmadxz,dsigmadyy,dsigmadyz,dsigmadzz, &
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dRdxx,dRdxy,dRdxz,dRdyy,dRdyz,dRdzz)
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call fdderivs_shc(ex,dzz,gzzxx,gzzxy,gzzxz,gzzyy,gzzyz,gzzzz,crho,sigma,R, SYM, SYM,SYM ,Symmetry,Lev,sst, &
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drhodx, drhody, drhodz, &
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dsigmadx,dsigmady,dsigmadz, &
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dRdx,dRdy,dRdz, &
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drhodxx,drhodxy,drhodxz,drhodyy,drhodyz,drhodzz, &
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dsigmadxx,dsigmadxy,dsigmadxz,dsigmadyy,dsigmadyz,dsigmadzz, &
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dRdxx,dRdxy,dRdxz,dRdyy,dRdyz,dRdzz)
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call fdderivs_shc(ex,gxy,gxyxx,gxyxy,gxyxz,gxyyy,gxyyz,gxyzz,crho,sigma,R,ANTI,ANTI,SYM ,Symmetry,Lev,sst, &
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drhodx, drhody, drhodz, &
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dsigmadx,dsigmady,dsigmadz, &
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dRdx,dRdy,dRdz, &
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drhodxx,drhodxy,drhodxz,drhodyy,drhodyz,drhodzz, &
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dsigmadxx,dsigmadxy,dsigmadxz,dsigmadyy,dsigmadyz,dsigmadzz, &
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dRdxx,dRdxy,dRdxz,dRdyy,dRdyz,dRdzz)
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call fdderivs_shc(ex,gxz,gxzxx,gxzxy,gxzxz,gxzyy,gxzyz,gxzzz,crho,sigma,R,ANTI,SYM ,ANTI,Symmetry,Lev,sst, &
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drhodx, drhody, drhodz, &
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dsigmadx,dsigmady,dsigmadz, &
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dRdx,dRdy,dRdz, &
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drhodxx,drhodxy,drhodxz,drhodyy,drhodyz,drhodzz, &
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dsigmadxx,dsigmadxy,dsigmadxz,dsigmadyy,dsigmadyz,dsigmadzz, &
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dRdxx,dRdxy,dRdxz,dRdyy,dRdyz,dRdzz)
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call fdderivs_shc(ex,gyz,gyzxx,gyzxy,gyzxz,gyzyy,gyzyz,gyzzz,crho,sigma,R,SYM ,ANTI,ANTI,Symmetry,Lev,sst, &
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drhodx, drhody, drhodz, &
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dsigmadx,dsigmady,dsigmadz, &
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dRdx,dRdy,dRdz, &
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drhodxx,drhodxy,drhodxz,drhodyy,drhodyz,drhodzz, &
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dsigmadxx,dsigmadxy,dsigmadxz,dsigmadyy,dsigmadyz,dsigmadzz, &
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dRdxx,dRdxy,dRdxz,dRdyy,dRdyz,dRdzz)
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call adm_riemann(ex, &
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gxxxx,gxxxy,gxxxz,gxxyy,gxxyz,gxxzz, &
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gxyxx,gxyxy,gxyxz,gxyyy,gxyyz,gxyzz, &
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gxzxx,gxzxy,gxzxz,gxzyy,gxzyz,gxzzz, &
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gyyxx,gyyxy,gyyxz,gyyyy,gyyyz,gyyzz, &
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gyzxx,gyzxy,gyzxz,gyzyy,gyzyz,gyzzz, &
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gzzxx,gzzxy,gzzxz,gzzyy,gzzyz,gzzzz, &
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Gamxxx, Gamxxy, Gamxxz, Gamxyy, Gamxyz, Gamxzz, &
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Gamyxx, Gamyxy, Gamyxz, Gamyyy, Gamyyz, Gamyzz, &
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Gamzxx, Gamzxy, Gamzxz, Gamzyy, Gamzyz, Gamzzz, &
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ass_Gamxxx,ass_Gamxxy,ass_Gamxxz, ass_Gamxyy,ass_Gamxyz,ass_Gamxzz, &
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ass_Gamyxx,ass_Gamyxy,ass_Gamyxz, ass_Gamyyy,ass_Gamyyz,ass_Gamyzz, &
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ass_Gamzxx,ass_Gamzxy,ass_Gamzxz, ass_Gamzyy,ass_Gamzyz,ass_Gamzzz, &
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Rxyxy, Rxyxz, Rxyyz, Rxzxz, Rxzyz, Ryzyz)
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call adm_ricci(ex, &
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gupxx , gupxy , gupxz , gupyy , gupyz , gupzz , &
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Rxyxy, Rxyxz, Rxyyz, Rxzxz, Rxzyz, Ryzyz, &
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Rxx , Rxy , Rxz , Ryy , Ryz , Rzz)
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return
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end subroutine adm_ricci_gamma_ss
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