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#include "cctk.h"
c ========================================================================
SUBROUTINE ADMmass_integrand3D(origin,Dx,Dy,Dz,x,y,z,gxx,gxy,gxz,
& gyy,gyz,gzz,ADMmass_int,Psi,Psi_power)
c ------------------------------------------------------------------------
c
c Estimates the ADM mass at a given radius using Equation (7) from
c O Murchadha and York, Phys Rev D, 10, 1974 page 2345
c
c ------------------------------------------------------------------------
IMPLICIT NONE
c Input variables
INTEGER,INTENT(IN) ::
& Psi_power
CCTK_REAL,INTENT(IN) ::
& Dx,Dy,Dz,origin(3)
CCTK_REAL,DIMENSION(:),INTENT(IN) ::
& x,y,z
CCTK_REAL,DIMENSION(:,:,:),INTENT(IN) ::
& gxx,gxy,gxz,gyy,gyz,gzz,Psi
c Output variables
CCTK_REAL,DIMENSION(:,:,:),INTENT(OUT) ::
& ADMmass_int
c Local variables, here only
INTEGER ::
& i,j,k,ip
CCTK_REAL,PARAMETER ::
& half = 0.5D0
CCTK_REAL ::
& rad,ux,uy,uz,det,dxx,dxy,dxz,dyy,dyz,dzz,uxx,uxy,uxz,uyy,
& uyz,uzz,term1,term2,term3,dxx_y,dxx_z,dxy_x,dxy_y,dxy_z,
& dyy_x,dxz_x,dxz_y,dxz_z,dyz_x,dzz_x,dyy_z,dyz_y,dyz_z,dzz_y,
& Pi,idet,p,pip,pim,pjp,pjm,pkp,pkm
c ------------------------------------------------------------------------
Pi = ACOS(-1D0)
c Because other codes evolve Psi**4
SELECT CASE (Psi_power)
CASE (1)
ip = 4
CASE (4)
ip = 1
CASE DEFAULT
WRITE(*,*) "This value of Psi_power is not supported"
END SELECT
DO k = 2, SIZE(z)-1
DO j = 2, SIZE(y)-1
DO i = 2, SIZE(x)-1
rad = SQRT((x(i)-origin(1))**2
& +(y(j)-origin(2))**2
& +(z(k)-origin(3))**2)
IF (rad.NE.0) THEN
ux = (x(i)-origin(1))/rad
uy = (y(j)-origin(2))/rad
uz = (z(k)-origin(3))/rad
c Abbreviations for metric coefficients
c -------------------------------------
p = psi(i,j,k)**ip
dxx = p*gxx(i,j,k); dxy = p*gxy(i,j,k)
dxz = p*gxz(i,j,k); dyy = p*gyy(i,j,k)
dyz = p*gyz(i,j,k); dzz = p*gzz(i,j,k)
c Determinant of 3-metric
c -----------------------
det = (dxx*dyy*dzz + 2.0D0*dxy*dxz*dyz
& - (dxx*dyz**2 + dyy*dxz**2 + dzz*dxy**2))
idet = 1.0/det
c Inverse 3-metric
c ----------------
uxx = idet*(dyy*dzz - dyz**2)
uyy = idet*(dxx*dzz - dxz**2)
uzz = idet*(dxx*dyy - dxy**2)
uxy = idet*(dxz*dyz - dzz*dxy)
uxz = idet*(dxy*dyz - dyy*dxz)
uyz = idet*(dxy*dxz - dxx*dyz)
c Derivatives of the 3-metric
c ---------------------------
pip = psi(i+1,j,k)**ip
pim = psi(i-1,j,k)**ip
pjp = psi(i,j+1,k)**ip
pjm = psi(i,j-1,k)**ip
pkp = psi(i,j,k+1)**ip
pkm = psi(i,j,k-1)**ip
dxx_y = half/Dy*(pjp*gxx(i,j+1,k)-pjm*gxx(i,j-1,k))
dxx_z = half/Dz*(pkp*gxx(i,j,k+1)-pkm*gxx(i,j,k-1))
dxy_x = half/Dx*(pip*gxy(i+1,j,k)-pim*gxy(i-1,j,k))
dxy_y = half/Dy*(pjp*gxy(i,j+1,k)-pjm*gxy(i,j-1,k))
dxy_z = half/Dz*(pkp*gxy(i,j,k+1)-pkm*gxy(i,j,k-1))
dyy_x = half/Dx*(pip*gyy(i+1,j,k)-pim*gyy(i-1,j,k))
dyy_z = half/Dz*(pkp*gyy(i,j,k+1)-pkm*gyy(i,j,k-1))
dxz_x = half/Dx*(pip*gxz(i+1,j,k)-pim*gxz(i-1,j,k))
dxz_y = half/Dy*(pjp*gxz(i,j+1,k)-pjm*gxz(i,j-1,k))
dxz_z = half/Dz*(pkp*gxz(i,j,k+1)-pkm*gxz(i,j,k-1))
dyz_x = half/Dx*(pip*gyz(i+1,j,k)-pim*gyz(i-1,j,k))
dyz_y = half/Dy*(pjp*gyz(i,j+1,k)-pjm*gyz(i,j-1,k))
dyz_z = half/Dz*(pkp*gyz(i,j,k+1)-pkm*gyz(i,j,k-1))
dzz_x = half/Dx*(pip*gzz(i+1,j,k)-pim*gzz(i-1,j,k))
dzz_y = half/Dy*(pjp*gzz(i,j+1,k)-pjm*gzz(i,j-1,k))
term1 = uxy*(dxx_y-dxy_x)+uxz*(dxx_z-dxz_x)
& +uyy*(dxy_y-dyy_x)+uyz*(dxy_z-dyz_x)
& +uyz*(dxz_y-dyz_x)+uzz*(dxz_z-dzz_x)
term2 = uyz*(dyy_z-dyz_y)+uxy*(dyy_x-dxy_y)
& +uzz*(dyz_z-dzz_y)+uxz*(dyz_x-dxz_y)
& +uxz*(dxy_z-dxz_y)+uxx*(dxy_x-dxx_y)
term3 = uxz*(dzz_x-dxz_z)+uyz*(dzz_y-dyz_z)
& +uxx*(dxz_x-dxx_z)+uxy*(dxz_y-dxy_z)
& +uxy*(dyz_x-dxy_z)+uyy*(dyz_y-dyy_z)
ADMmass_int(i,j,k) = 1.0D0/16.0D0/Pi*(ux*term1+
& uy*term2+uz*term3)*SQRT(det)*rad**2
ELSE
ADMmass_int(i,j,k) = 0.0D0
ENDIF
ENDDO
ENDDO
ENDDO
c This is needed when the grid is an octant, but it does not hurt
c if it is not
DO k = 2, size(z)-1
DO j = 2, size(y)-1
ADMmass_int(1,j,k) = ADMmass_int(2,j,k)
ENDDO
ENDDO
DO k = 2, size(z)-1
DO i = 1, size(x)-1
ADMmass_int(i,1,k) = ADMmass_int(i,2,k)
ENDDO
ENDDO
DO j = 1, size(y)-1
DO i = 1, size(x)-1
ADMmass_int(i,j,1) = ADMmass_int(i,j,2)
ENDDO
ENDDO
END SUBROUTINE ADMmass_integrand3D
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