diff options
| author | eschnett <eschnett@4f5cb9a8-4dd8-4c2d-9bbd-173fa4467843> | 2010-03-29 10:45:17 +0000 |
|---|---|---|
| committer | eschnett <eschnett@4f5cb9a8-4dd8-4c2d-9bbd-173fa4467843> | 2010-03-29 10:45:17 +0000 |
| commit | f33a18fee7267ff212baec75795ecb13670643e8 (patch) | |
| tree | 26461682ee96a7bd5f8da6879432d88fe49e2124 /src | |
| parent | d7ddbe354ebe7072ff6687124e5f620d56a16b28 (diff) | |
Make self-updating work again after moving the "m" directory into the
thorn.
Add README.
Re-generate thorn.
git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinAnalysis/WeylScal4/trunk@51 4f5cb9a8-4dd8-4c2d-9bbd-173fa4467843
Diffstat (limited to 'src')
| -rw-r--r-- | src/Differencing.h | 84 | ||||
| -rw-r--r-- | src/psis_calc_2nd.c | 1979 | ||||
| -rw-r--r-- | src/psis_calc_4th.c | 1979 |
3 files changed, 2062 insertions, 1980 deletions
diff --git a/src/Differencing.h b/src/Differencing.h index 220d0d5..60c4baf 100644 --- a/src/Differencing.h +++ b/src/Differencing.h @@ -1,42 +1,42 @@ -#define PDstandard2nd1(u,i,j,k) (p1o2dx*(-(u)[CCTK_GFINDEX3D(cctkGH,(int)(-1 + i),(int)(j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(j),(int)(k))])) -#define PDstandard2nd2(u,i,j,k) (p1o2dy*(-(u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(-1 + j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(1 + j),(int)(k))])) -#define PDstandard2nd3(u,i,j,k) (p1o2dz*(-(u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(-1 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(1 + k))])) -#define PDstandard2nd11(u,i,j,k) (p1odx2*((u)[CCTK_GFINDEX3D(cctkGH,(int)(-1 + i),(int)(j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(j),(int)(k))] - 2*(u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(k))])) -#define PDstandard2nd22(u,i,j,k) (p1ody2*((u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(-1 + j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(1 + j),(int)(k))] - 2*(u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(k))])) -#define PDstandard2nd33(u,i,j,k) (p1odz2*((u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(-1 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(1 + k))] - 2*(u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(k))])) -#define PDstandard2nd12(u,i,j,k) (p1o4dxdy*((u)[CCTK_GFINDEX3D(cctkGH,(int)(-1 + i),(int)(-1 + j),(int)(k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(-1 + i),(int)(1 + j),(int)(k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(-1 + j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(1 + j),(int)(k))])) -#define PDstandard2nd13(u,i,j,k) (p1o4dxdz*((u)[CCTK_GFINDEX3D(cctkGH,(int)(-1 + i),(int)(j),(int)(-1 + k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(-1 + i),(int)(j),(int)(1 + k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(j),(int)(-1 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(j),(int)(1 + k))])) -#define PDstandard2nd21(u,i,j,k) (p1o4dxdy*((u)[CCTK_GFINDEX3D(cctkGH,(int)(-1 + i),(int)(-1 + j),(int)(k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(-1 + i),(int)(1 + j),(int)(k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(-1 + j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(1 + j),(int)(k))])) -#define PDstandard2nd23(u,i,j,k) (p1o4dydz*((u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(-1 + j),(int)(-1 + k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(-1 + j),(int)(1 + k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(1 + j),(int)(-1 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(1 + j),(int)(1 + k))])) -#define PDstandard2nd31(u,i,j,k) (p1o4dxdz*((u)[CCTK_GFINDEX3D(cctkGH,(int)(-1 + i),(int)(j),(int)(-1 + k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(-1 + i),(int)(j),(int)(1 + k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(j),(int)(-1 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(j),(int)(1 + k))])) -#define PDstandard2nd32(u,i,j,k) (p1o4dydz*((u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(-1 + j),(int)(-1 + k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(-1 + j),(int)(1 + k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(1 + j),(int)(-1 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(1 + j),(int)(1 + k))])) -#define PDstandard4th1(u,i,j,k) (p1o12dx*(-8*(u)[CCTK_GFINDEX3D(cctkGH,(int)(-1 + i),(int)(j),(int)(k))] + 8*(u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(-2 + i),(int)(j),(int)(k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(2 + i),(int)(j),(int)(k))])) -#define PDstandard4th2(u,i,j,k) (p1o12dy*(-8*(u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(-1 + j),(int)(k))] + 8*(u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(1 + j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(-2 + j),(int)(k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(2 + j),(int)(k))])) -#define PDstandard4th3(u,i,j,k) (p1o12dz*(-8*(u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(-1 + k))] + 8*(u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(1 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(-2 + k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(2 + k))])) -#define PDstandard4th11(u,i,j,k) (pm1o12dx2*(-16*((u)[CCTK_GFINDEX3D(cctkGH,(int)(-1 + i),(int)(j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(j),(int)(k))]) + (u)[CCTK_GFINDEX3D(cctkGH,(int)(-2 + i),(int)(j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(2 + i),(int)(j),(int)(k))] + 30*(u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(k))])) -#define PDstandard4th22(u,i,j,k) (pm1o12dy2*(-16*((u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(-1 + j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(1 + j),(int)(k))]) + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(-2 + j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(2 + j),(int)(k))] + 30*(u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(k))])) -#define PDstandard4th33(u,i,j,k) (pm1o12dz2*(-16*((u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(-1 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(1 + k))]) + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(-2 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(2 + k))] + 30*(u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(k))])) -#define PDstandard4th12(u,i,j,k) (p1o144dxdy*(-64*((u)[CCTK_GFINDEX3D(cctkGH,(int)(-1 + i),(int)(1 + j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(-1 + j),(int)(k))]) + 64*((u)[CCTK_GFINDEX3D(cctkGH,(int)(-1 + i),(int)(-1 + j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(1 + j),(int)(k))]) + 8*((u)[CCTK_GFINDEX3D(cctkGH,(int)(-1 + i),(int)(2 + j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(-2 + j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(-2 + i),(int)(1 + j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(2 + i),(int)(-1 + j),(int)(k))]) - 8*((u)[CCTK_GFINDEX3D(cctkGH,(int)(-1 + i),(int)(-2 + j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(2 + j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(-2 + i),(int)(-1 + j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(2 + i),(int)(1 + j),(int)(k))]) + (u)[CCTK_GFINDEX3D(cctkGH,(int)(-2 + i),(int)(-2 + j),(int)(k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(-2 + i),(int)(2 + j),(int)(k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(2 + i),(int)(-2 + j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(2 + i),(int)(2 + j),(int)(k))])) -#define PDstandard4th13(u,i,j,k) (p1o144dxdz*(-64*((u)[CCTK_GFINDEX3D(cctkGH,(int)(-1 + i),(int)(j),(int)(1 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(j),(int)(-1 + k))]) + 64*((u)[CCTK_GFINDEX3D(cctkGH,(int)(-1 + i),(int)(j),(int)(-1 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(j),(int)(1 + k))]) + 8*((u)[CCTK_GFINDEX3D(cctkGH,(int)(-1 + i),(int)(j),(int)(2 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(j),(int)(-2 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(-2 + i),(int)(j),(int)(1 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(2 + i),(int)(j),(int)(-1 + k))]) - 8*((u)[CCTK_GFINDEX3D(cctkGH,(int)(-1 + i),(int)(j),(int)(-2 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(j),(int)(2 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(-2 + i),(int)(j),(int)(-1 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(2 + i),(int)(j),(int)(1 + k))]) + (u)[CCTK_GFINDEX3D(cctkGH,(int)(-2 + i),(int)(j),(int)(-2 + k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(-2 + i),(int)(j),(int)(2 + k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(2 + i),(int)(j),(int)(-2 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(2 + i),(int)(j),(int)(2 + k))])) -#define PDstandard4th21(u,i,j,k) (p1o144dxdy*(-64*((u)[CCTK_GFINDEX3D(cctkGH,(int)(-1 + i),(int)(1 + j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(-1 + j),(int)(k))]) + 64*((u)[CCTK_GFINDEX3D(cctkGH,(int)(-1 + i),(int)(-1 + j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(1 + j),(int)(k))]) + 8*((u)[CCTK_GFINDEX3D(cctkGH,(int)(-1 + i),(int)(2 + j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(-2 + j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(-2 + i),(int)(1 + j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(2 + i),(int)(-1 + j),(int)(k))]) - 8*((u)[CCTK_GFINDEX3D(cctkGH,(int)(-1 + i),(int)(-2 + j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(2 + j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(-2 + i),(int)(-1 + j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(2 + i),(int)(1 + j),(int)(k))]) + (u)[CCTK_GFINDEX3D(cctkGH,(int)(-2 + i),(int)(-2 + j),(int)(k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(-2 + i),(int)(2 + j),(int)(k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(2 + i),(int)(-2 + j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(2 + i),(int)(2 + j),(int)(k))])) -#define PDstandard4th23(u,i,j,k) (p1o144dydz*(-64*((u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(-1 + j),(int)(1 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(1 + j),(int)(-1 + k))]) + 64*((u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(-1 + j),(int)(-1 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(1 + j),(int)(1 + k))]) + 8*((u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(-1 + j),(int)(2 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(1 + j),(int)(-2 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(-2 + j),(int)(1 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(2 + j),(int)(-1 + k))]) - 8*((u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(-1 + j),(int)(-2 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(1 + j),(int)(2 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(-2 + j),(int)(-1 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(2 + j),(int)(1 + k))]) + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(-2 + j),(int)(-2 + k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(-2 + j),(int)(2 + k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(2 + j),(int)(-2 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(2 + j),(int)(2 + k))])) -#define PDstandard4th31(u,i,j,k) (p1o144dxdz*(-64*((u)[CCTK_GFINDEX3D(cctkGH,(int)(-1 + i),(int)(j),(int)(1 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(j),(int)(-1 + k))]) + 64*((u)[CCTK_GFINDEX3D(cctkGH,(int)(-1 + i),(int)(j),(int)(-1 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(j),(int)(1 + k))]) + 8*((u)[CCTK_GFINDEX3D(cctkGH,(int)(-1 + i),(int)(j),(int)(2 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(j),(int)(-2 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(-2 + i),(int)(j),(int)(1 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(2 + i),(int)(j),(int)(-1 + k))]) - 8*((u)[CCTK_GFINDEX3D(cctkGH,(int)(-1 + i),(int)(j),(int)(-2 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(j),(int)(2 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(-2 + i),(int)(j),(int)(-1 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(2 + i),(int)(j),(int)(1 + k))]) + (u)[CCTK_GFINDEX3D(cctkGH,(int)(-2 + i),(int)(j),(int)(-2 + k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(-2 + i),(int)(j),(int)(2 + k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(2 + i),(int)(j),(int)(-2 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(2 + i),(int)(j),(int)(2 + k))])) -#define PDstandard4th32(u,i,j,k) (p1o144dydz*(-64*((u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(-1 + j),(int)(1 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(1 + j),(int)(-1 + k))]) + 64*((u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(-1 + j),(int)(-1 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(1 + j),(int)(1 + k))]) + 8*((u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(-1 + j),(int)(2 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(1 + j),(int)(-2 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(-2 + j),(int)(1 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(2 + j),(int)(-1 + k))]) - 8*((u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(-1 + j),(int)(-2 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(1 + j),(int)(2 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(-2 + j),(int)(-1 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(2 + j),(int)(1 + k))]) + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(-2 + j),(int)(-2 + k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(-2 + j),(int)(2 + k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(2 + j),(int)(-2 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(2 + j),(int)(2 + k))])) -#define PDplus1(u,i,j,k) (p1odx*((u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(j),(int)(k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(k))])) -#define PDplus2(u,i,j,k) (p1ody*((u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(1 + j),(int)(k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(k))])) -#define PDplus3(u,i,j,k) (p1odz*((u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(1 + k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(k))])) -#define PDminus1(u,i,j,k) (p1odx*(-(u)[CCTK_GFINDEX3D(cctkGH,(int)(-1 + i),(int)(j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(k))])) -#define PDminus2(u,i,j,k) (p1ody*(-(u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(-1 + j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(k))])) -#define PDminus3(u,i,j,k) (p1odz*(-(u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(-1 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(k))])) -#define PDplus11(u,i,j,k) (p1odx2*(-2*(u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(2 + i),(int)(j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(k))])) -#define PDplus12(u,i,j,k) (p1odxdy*((u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(1 + j),(int)(k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(j),(int)(k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(1 + j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(k))])) -#define PDplus13(u,i,j,k) (p1odxdz*((u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(j),(int)(1 + k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(j),(int)(k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(1 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(k))])) -#define PDplus21(u,i,j,k) (p1odxdy*((u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(1 + j),(int)(k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(j),(int)(k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(1 + j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(k))])) -#define PDplus22(u,i,j,k) (p1ody2*(-2*(u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(1 + j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(2 + j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(k))])) -#define PDplus23(u,i,j,k) (p1odydz*((u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(1 + j),(int)(1 + k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(1 + j),(int)(k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(1 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(k))])) -#define PDplus31(u,i,j,k) (p1odxdz*((u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(j),(int)(1 + k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(1 + i),(int)(j),(int)(k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(1 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(k))])) -#define PDplus32(u,i,j,k) (p1odydz*((u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(1 + j),(int)(1 + k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(1 + j),(int)(k))] - (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(1 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(k))])) -#define PDplus33(u,i,j,k) (p1odz2*(-2*(u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(1 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(2 + k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(k))])) -#define PDonesided2nd1(u,i,j,k) (pm1o2dx*((u)[CCTK_GFINDEX3D(cctkGH,(int)(i + 2*dir(1)),(int)(j),(int)(k))] - 4*(u)[CCTK_GFINDEX3D(cctkGH,(int)(i + dir(1)),(int)(j),(int)(k))] + 3*(u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(k))])*dir(1)) -#define PDonesided2nd2(u,i,j,k) (pm1o2dy*((u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j + 2*dir(2)),(int)(k))] - 4*(u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j + dir(2)),(int)(k))] + 3*(u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(k))])*dir(2)) -#define PDonesided2nd3(u,i,j,k) (pm1o2dz*(3*(u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(k))] + (u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(k + 2*dir(3)))] - 4*(u)[CCTK_GFINDEX3D(cctkGH,(int)(i),(int)(j),(int)(k + dir(3)))])*dir(3)) +#define PDstandard2nd1(u,i,j,k) (p1o2dx*(-(u)[index+di*(-1)+dj*(0)+dk*(0)] + (u)[index+di*(1)+dj*(0)+dk*(0)])) +#define PDstandard2nd2(u,i,j,k) (p1o2dy*(-(u)[index+di*(0)+dj*(-1)+dk*(0)] + (u)[index+di*(0)+dj*(1)+dk*(0)])) +#define PDstandard2nd3(u,i,j,k) (p1o2dz*(-(u)[index+di*(0)+dj*(0)+dk*(-1)] + (u)[index+di*(0)+dj*(0)+dk*(1)])) +#define PDstandard2nd11(u,i,j,k) (p1odx2*(-2*(u)[index+di*(0)+dj*(0)+dk*(0)] + (u)[index+di*(-1)+dj*(0)+dk*(0)] + (u)[index+di*(1)+dj*(0)+dk*(0)])) +#define PDstandard2nd22(u,i,j,k) (p1ody2*(-2*(u)[index+di*(0)+dj*(0)+dk*(0)] + (u)[index+di*(0)+dj*(-1)+dk*(0)] + (u)[index+di*(0)+dj*(1)+dk*(0)])) +#define PDstandard2nd33(u,i,j,k) (p1odz2*(-2*(u)[index+di*(0)+dj*(0)+dk*(0)] + (u)[index+di*(0)+dj*(0)+dk*(-1)] + (u)[index+di*(0)+dj*(0)+dk*(1)])) +#define PDstandard2nd12(u,i,j,k) (p1o4dxdy*((u)[index+di*(-1)+dj*(-1)+dk*(0)] - (u)[index+di*(-1)+dj*(1)+dk*(0)] - (u)[index+di*(1)+dj*(-1)+dk*(0)] + (u)[index+di*(1)+dj*(1)+dk*(0)])) +#define PDstandard2nd13(u,i,j,k) (p1o4dxdz*((u)[index+di*(-1)+dj*(0)+dk*(-1)] - (u)[index+di*(-1)+dj*(0)+dk*(1)] - (u)[index+di*(1)+dj*(0)+dk*(-1)] + (u)[index+di*(1)+dj*(0)+dk*(1)])) +#define PDstandard2nd21(u,i,j,k) (p1o4dxdy*((u)[index+di*(-1)+dj*(-1)+dk*(0)] - (u)[index+di*(-1)+dj*(1)+dk*(0)] - (u)[index+di*(1)+dj*(-1)+dk*(0)] + (u)[index+di*(1)+dj*(1)+dk*(0)])) +#define PDstandard2nd23(u,i,j,k) (p1o4dydz*((u)[index+di*(0)+dj*(-1)+dk*(-1)] - (u)[index+di*(0)+dj*(-1)+dk*(1)] - (u)[index+di*(0)+dj*(1)+dk*(-1)] + (u)[index+di*(0)+dj*(1)+dk*(1)])) +#define PDstandard2nd31(u,i,j,k) (p1o4dxdz*((u)[index+di*(-1)+dj*(0)+dk*(-1)] - (u)[index+di*(-1)+dj*(0)+dk*(1)] - (u)[index+di*(1)+dj*(0)+dk*(-1)] + (u)[index+di*(1)+dj*(0)+dk*(1)])) +#define PDstandard2nd32(u,i,j,k) (p1o4dydz*((u)[index+di*(0)+dj*(-1)+dk*(-1)] - (u)[index+di*(0)+dj*(-1)+dk*(1)] - (u)[index+di*(0)+dj*(1)+dk*(-1)] + (u)[index+di*(0)+dj*(1)+dk*(1)])) +#define PDstandard4th1(u,i,j,k) (p1o12dx*(-8*(u)[index+di*(-1)+dj*(0)+dk*(0)] + 8*(u)[index+di*(1)+dj*(0)+dk*(0)] + (u)[index+di*(-2)+dj*(0)+dk*(0)] - (u)[index+di*(2)+dj*(0)+dk*(0)])) +#define PDstandard4th2(u,i,j,k) (p1o12dy*(-8*(u)[index+di*(0)+dj*(-1)+dk*(0)] + 8*(u)[index+di*(0)+dj*(1)+dk*(0)] + (u)[index+di*(0)+dj*(-2)+dk*(0)] - (u)[index+di*(0)+dj*(2)+dk*(0)])) +#define PDstandard4th3(u,i,j,k) (p1o12dz*(-8*(u)[index+di*(0)+dj*(0)+dk*(-1)] + 8*(u)[index+di*(0)+dj*(0)+dk*(1)] + (u)[index+di*(0)+dj*(0)+dk*(-2)] - (u)[index+di*(0)+dj*(0)+dk*(2)])) +#define PDstandard4th11(u,i,j,k) (pm1o12dx2*(30*(u)[index+di*(0)+dj*(0)+dk*(0)] - 16*((u)[index+di*(-1)+dj*(0)+dk*(0)] + (u)[index+di*(1)+dj*(0)+dk*(0)]) + (u)[index+di*(-2)+dj*(0)+dk*(0)] + (u)[index+di*(2)+dj*(0)+dk*(0)])) +#define PDstandard4th22(u,i,j,k) (pm1o12dy2*(30*(u)[index+di*(0)+dj*(0)+dk*(0)] - 16*((u)[index+di*(0)+dj*(-1)+dk*(0)] + (u)[index+di*(0)+dj*(1)+dk*(0)]) + (u)[index+di*(0)+dj*(-2)+dk*(0)] + (u)[index+di*(0)+dj*(2)+dk*(0)])) +#define PDstandard4th33(u,i,j,k) (pm1o12dz2*(30*(u)[index+di*(0)+dj*(0)+dk*(0)] - 16*((u)[index+di*(0)+dj*(0)+dk*(-1)] + (u)[index+di*(0)+dj*(0)+dk*(1)]) + (u)[index+di*(0)+dj*(0)+dk*(-2)] + (u)[index+di*(0)+dj*(0)+dk*(2)])) +#define PDstandard4th12(u,i,j,k) (p1o144dxdy*(-64*((u)[index+di*(-1)+dj*(1)+dk*(0)] + (u)[index+di*(1)+dj*(-1)+dk*(0)]) + 64*((u)[index+di*(-1)+dj*(-1)+dk*(0)] + (u)[index+di*(1)+dj*(1)+dk*(0)]) + 8*((u)[index+di*(-1)+dj*(2)+dk*(0)] + (u)[index+di*(1)+dj*(-2)+dk*(0)] + (u)[index+di*(-2)+dj*(1)+dk*(0)] + (u)[index+di*(2)+dj*(-1)+dk*(0)]) - 8*((u)[index+di*(-1)+dj*(-2)+dk*(0)] + (u)[index+di*(1)+dj*(2)+dk*(0)] + (u)[index+di*(-2)+dj*(-1)+dk*(0)] + (u)[index+di*(2)+dj*(1)+dk*(0)]) + (u)[index+di*(-2)+dj*(-2)+dk*(0)] - (u)[index+di*(-2)+dj*(2)+dk*(0)] - (u)[index+di*(2)+dj*(-2)+dk*(0)] + (u)[index+di*(2)+dj*(2)+dk*(0)])) +#define PDstandard4th13(u,i,j,k) (p1o144dxdz*(-64*((u)[index+di*(-1)+dj*(0)+dk*(1)] + (u)[index+di*(1)+dj*(0)+dk*(-1)]) + 64*((u)[index+di*(-1)+dj*(0)+dk*(-1)] + (u)[index+di*(1)+dj*(0)+dk*(1)]) + 8*((u)[index+di*(-1)+dj*(0)+dk*(2)] + (u)[index+di*(1)+dj*(0)+dk*(-2)] + (u)[index+di*(-2)+dj*(0)+dk*(1)] + (u)[index+di*(2)+dj*(0)+dk*(-1)]) - 8*((u)[index+di*(-1)+dj*(0)+dk*(-2)] + (u)[index+di*(1)+dj*(0)+dk*(2)] + (u)[index+di*(-2)+dj*(0)+dk*(-1)] + (u)[index+di*(2)+dj*(0)+dk*(1)]) + (u)[index+di*(-2)+dj*(0)+dk*(-2)] - (u)[index+di*(-2)+dj*(0)+dk*(2)] - (u)[index+di*(2)+dj*(0)+dk*(-2)] + (u)[index+di*(2)+dj*(0)+dk*(2)])) +#define PDstandard4th21(u,i,j,k) (p1o144dxdy*(-64*((u)[index+di*(-1)+dj*(1)+dk*(0)] + (u)[index+di*(1)+dj*(-1)+dk*(0)]) + 64*((u)[index+di*(-1)+dj*(-1)+dk*(0)] + (u)[index+di*(1)+dj*(1)+dk*(0)]) + 8*((u)[index+di*(-1)+dj*(2)+dk*(0)] + (u)[index+di*(1)+dj*(-2)+dk*(0)] + (u)[index+di*(-2)+dj*(1)+dk*(0)] + (u)[index+di*(2)+dj*(-1)+dk*(0)]) - 8*((u)[index+di*(-1)+dj*(-2)+dk*(0)] + (u)[index+di*(1)+dj*(2)+dk*(0)] + (u)[index+di*(-2)+dj*(-1)+dk*(0)] + (u)[index+di*(2)+dj*(1)+dk*(0)]) + (u)[index+di*(-2)+dj*(-2)+dk*(0)] - (u)[index+di*(-2)+dj*(2)+dk*(0)] - (u)[index+di*(2)+dj*(-2)+dk*(0)] + (u)[index+di*(2)+dj*(2)+dk*(0)])) +#define PDstandard4th23(u,i,j,k) (p1o144dydz*(-64*((u)[index+di*(0)+dj*(-1)+dk*(1)] + (u)[index+di*(0)+dj*(1)+dk*(-1)]) + 64*((u)[index+di*(0)+dj*(-1)+dk*(-1)] + (u)[index+di*(0)+dj*(1)+dk*(1)]) + 8*((u)[index+di*(0)+dj*(-1)+dk*(2)] + (u)[index+di*(0)+dj*(1)+dk*(-2)] + (u)[index+di*(0)+dj*(-2)+dk*(1)] + (u)[index+di*(0)+dj*(2)+dk*(-1)]) - 8*((u)[index+di*(0)+dj*(-1)+dk*(-2)] + (u)[index+di*(0)+dj*(1)+dk*(2)] + (u)[index+di*(0)+dj*(-2)+dk*(-1)] + (u)[index+di*(0)+dj*(2)+dk*(1)]) + (u)[index+di*(0)+dj*(-2)+dk*(-2)] - (u)[index+di*(0)+dj*(-2)+dk*(2)] - (u)[index+di*(0)+dj*(2)+dk*(-2)] + (u)[index+di*(0)+dj*(2)+dk*(2)])) +#define PDstandard4th31(u,i,j,k) (p1o144dxdz*(-64*((u)[index+di*(-1)+dj*(0)+dk*(1)] + (u)[index+di*(1)+dj*(0)+dk*(-1)]) + 64*((u)[index+di*(-1)+dj*(0)+dk*(-1)] + (u)[index+di*(1)+dj*(0)+dk*(1)]) + 8*((u)[index+di*(-1)+dj*(0)+dk*(2)] + (u)[index+di*(1)+dj*(0)+dk*(-2)] + (u)[index+di*(-2)+dj*(0)+dk*(1)] + (u)[index+di*(2)+dj*(0)+dk*(-1)]) - 8*((u)[index+di*(-1)+dj*(0)+dk*(-2)] + (u)[index+di*(1)+dj*(0)+dk*(2)] + (u)[index+di*(-2)+dj*(0)+dk*(-1)] + (u)[index+di*(2)+dj*(0)+dk*(1)]) + (u)[index+di*(-2)+dj*(0)+dk*(-2)] - (u)[index+di*(-2)+dj*(0)+dk*(2)] - (u)[index+di*(2)+dj*(0)+dk*(-2)] + (u)[index+di*(2)+dj*(0)+dk*(2)])) +#define PDstandard4th32(u,i,j,k) (p1o144dydz*(-64*((u)[index+di*(0)+dj*(-1)+dk*(1)] + (u)[index+di*(0)+dj*(1)+dk*(-1)]) + 64*((u)[index+di*(0)+dj*(-1)+dk*(-1)] + (u)[index+di*(0)+dj*(1)+dk*(1)]) + 8*((u)[index+di*(0)+dj*(-1)+dk*(2)] + (u)[index+di*(0)+dj*(1)+dk*(-2)] + (u)[index+di*(0)+dj*(-2)+dk*(1)] + (u)[index+di*(0)+dj*(2)+dk*(-1)]) - 8*((u)[index+di*(0)+dj*(-1)+dk*(-2)] + (u)[index+di*(0)+dj*(1)+dk*(2)] + (u)[index+di*(0)+dj*(-2)+dk*(-1)] + (u)[index+di*(0)+dj*(2)+dk*(1)]) + (u)[index+di*(0)+dj*(-2)+dk*(-2)] - (u)[index+di*(0)+dj*(-2)+dk*(2)] - (u)[index+di*(0)+dj*(2)+dk*(-2)] + (u)[index+di*(0)+dj*(2)+dk*(2)])) +#define PDplus1(u,i,j,k) (p1odx*(-(u)[index+di*(0)+dj*(0)+dk*(0)] + (u)[index+di*(1)+dj*(0)+dk*(0)])) +#define PDplus2(u,i,j,k) (p1ody*(-(u)[index+di*(0)+dj*(0)+dk*(0)] + (u)[index+di*(0)+dj*(1)+dk*(0)])) +#define PDplus3(u,i,j,k) (p1odz*(-(u)[index+di*(0)+dj*(0)+dk*(0)] + (u)[index+di*(0)+dj*(0)+dk*(1)])) +#define PDminus1(u,i,j,k) (p1odx*((u)[index+di*(0)+dj*(0)+dk*(0)] - (u)[index+di*(-1)+dj*(0)+dk*(0)])) +#define PDminus2(u,i,j,k) (p1ody*((u)[index+di*(0)+dj*(0)+dk*(0)] - (u)[index+di*(0)+dj*(-1)+dk*(0)])) +#define PDminus3(u,i,j,k) (p1odz*((u)[index+di*(0)+dj*(0)+dk*(0)] - (u)[index+di*(0)+dj*(0)+dk*(-1)])) +#define PDplus11(u,i,j,k) (p1odx2*((u)[index+di*(0)+dj*(0)+dk*(0)] - 2*(u)[index+di*(1)+dj*(0)+dk*(0)] + (u)[index+di*(2)+dj*(0)+dk*(0)])) +#define PDplus12(u,i,j,k) (p1odxdy*((u)[index+di*(0)+dj*(0)+dk*(0)] - (u)[index+di*(0)+dj*(1)+dk*(0)] - (u)[index+di*(1)+dj*(0)+dk*(0)] + (u)[index+di*(1)+dj*(1)+dk*(0)])) +#define PDplus13(u,i,j,k) (p1odxdz*((u)[index+di*(0)+dj*(0)+dk*(0)] - (u)[index+di*(0)+dj*(0)+dk*(1)] - (u)[index+di*(1)+dj*(0)+dk*(0)] + (u)[index+di*(1)+dj*(0)+dk*(1)])) +#define PDplus21(u,i,j,k) (p1odxdy*((u)[index+di*(0)+dj*(0)+dk*(0)] - (u)[index+di*(0)+dj*(1)+dk*(0)] - (u)[index+di*(1)+dj*(0)+dk*(0)] + (u)[index+di*(1)+dj*(1)+dk*(0)])) +#define PDplus22(u,i,j,k) (p1ody2*((u)[index+di*(0)+dj*(0)+dk*(0)] - 2*(u)[index+di*(0)+dj*(1)+dk*(0)] + (u)[index+di*(0)+dj*(2)+dk*(0)])) +#define PDplus23(u,i,j,k) (p1odydz*((u)[index+di*(0)+dj*(0)+dk*(0)] - (u)[index+di*(0)+dj*(0)+dk*(1)] - (u)[index+di*(0)+dj*(1)+dk*(0)] + (u)[index+di*(0)+dj*(1)+dk*(1)])) +#define PDplus31(u,i,j,k) (p1odxdz*((u)[index+di*(0)+dj*(0)+dk*(0)] - (u)[index+di*(0)+dj*(0)+dk*(1)] - (u)[index+di*(1)+dj*(0)+dk*(0)] + (u)[index+di*(1)+dj*(0)+dk*(1)])) +#define PDplus32(u,i,j,k) (p1odydz*((u)[index+di*(0)+dj*(0)+dk*(0)] - (u)[index+di*(0)+dj*(0)+dk*(1)] - (u)[index+di*(0)+dj*(1)+dk*(0)] + (u)[index+di*(0)+dj*(1)+dk*(1)])) +#define PDplus33(u,i,j,k) (p1odz2*((u)[index+di*(0)+dj*(0)+dk*(0)] - 2*(u)[index+di*(0)+dj*(0)+dk*(1)] + (u)[index+di*(0)+dj*(0)+dk*(2)])) +#define PDonesided2nd1(u,i,j,k) (pm1o2dx*(3*(u)[index+di*(0)+dj*(0)+dk*(0)] + (u)[index+di*(2*dir(1))+dj*(0)+dk*(0)] - 4*(u)[index+di*(dir(1))+dj*(0)+dk*(0)])*dir(1)) +#define PDonesided2nd2(u,i,j,k) (pm1o2dy*(3*(u)[index+di*(0)+dj*(0)+dk*(0)] + (u)[index+di*(0)+dj*(2*dir(2))+dk*(0)] - 4*(u)[index+di*(0)+dj*(dir(2))+dk*(0)])*dir(2)) +#define PDonesided2nd3(u,i,j,k) (pm1o2dz*(3*(u)[index+di*(0)+dj*(0)+dk*(0)] + (u)[index+di*(0)+dj*(0)+dk*(2*dir(3))] - 4*(u)[index+di*(0)+dj*(0)+dk*(dir(3))])*dir(3)) diff --git a/src/psis_calc_2nd.c b/src/psis_calc_2nd.c index 861a1c4..f97fa78 100644 --- a/src/psis_calc_2nd.c +++ b/src/psis_calc_2nd.c @@ -19,52 +19,17 @@ #define CUB(x) ((x) * (x) * (x)) #define QAD(x) ((x) * (x) * (x) * (x)) -void psis_calc_2nd_Body(cGH const * const cctkGH, CCTK_INT const dir, CCTK_INT const face, CCTK_REAL const normal[3], CCTK_REAL const tangentA[3], CCTK_REAL const tangentB[3], CCTK_INT const min[3], CCTK_INT const max[3], CCTK_INT const n_subblock_gfs, CCTK_REAL * const subblock_gfs[]) +void psis_calc_2nd_Body(cGH const * restrict const cctkGH, int const dir, int const face, CCTK_REAL const normal[3], CCTK_REAL const tangentA[3], CCTK_REAL const tangentB[3], int const min[3], int const max[3], int const n_subblock_gfs, CCTK_REAL * restrict const subblock_gfs[]) { DECLARE_CCTK_ARGUMENTS; DECLARE_CCTK_PARAMETERS; /* Declare the variables used for looping over grid points */ - CCTK_INT i = INITVALUE, j = INITVALUE, k = INITVALUE; - CCTK_INT index = INITVALUE; - CCTK_INT subblock_index = INITVALUE; + CCTK_INT i, j, k; + // CCTK_INT index = INITVALUE; /* Declare finite differencing variables */ - CCTK_REAL dx = INITVALUE, dy = INITVALUE, dz = INITVALUE; - CCTK_REAL dxi = INITVALUE, dyi = INITVALUE, dzi = INITVALUE; - CCTK_REAL khalf = INITVALUE, kthird = INITVALUE, ktwothird = INITVALUE, kfourthird = INITVALUE, keightthird = INITVALUE; - CCTK_REAL hdxi = INITVALUE, hdyi = INITVALUE, hdzi = INITVALUE; - - - /* Declare predefined quantities */ - CCTK_REAL p1o12dx = INITVALUE; - CCTK_REAL p1o12dy = INITVALUE; - CCTK_REAL p1o12dz = INITVALUE; - CCTK_REAL p1o144dxdy = INITVALUE; - CCTK_REAL p1o144dxdz = INITVALUE; - CCTK_REAL p1o144dydz = INITVALUE; - CCTK_REAL p1o2dx = INITVALUE; - CCTK_REAL p1o2dy = INITVALUE; - CCTK_REAL p1o2dz = INITVALUE; - CCTK_REAL p1o4dxdy = INITVALUE; - CCTK_REAL p1o4dxdz = INITVALUE; - CCTK_REAL p1o4dydz = INITVALUE; - CCTK_REAL p1odx = INITVALUE; - CCTK_REAL p1odx2 = INITVALUE; - CCTK_REAL p1odxdy = INITVALUE; - CCTK_REAL p1odxdz = INITVALUE; - CCTK_REAL p1ody = INITVALUE; - CCTK_REAL p1ody2 = INITVALUE; - CCTK_REAL p1odydz = INITVALUE; - CCTK_REAL p1odz = INITVALUE; - CCTK_REAL p1odz2 = INITVALUE; - CCTK_REAL pm1o12dx2 = INITVALUE; - CCTK_REAL pm1o12dy2 = INITVALUE; - CCTK_REAL pm1o12dz2 = INITVALUE; - CCTK_REAL pm1o2dx = INITVALUE; - CCTK_REAL pm1o2dy = INITVALUE; - CCTK_REAL pm1o2dz = INITVALUE; if (verbose > 1) { @@ -79,49 +44,52 @@ void psis_calc_2nd_Body(cGH const * const cctkGH, CCTK_INT const dir, CCTK_INT c /* Include user-supplied include files */ /* Initialise finite differencing variables */ - dx = CCTK_DELTA_SPACE(0); - dy = CCTK_DELTA_SPACE(1); - dz = CCTK_DELTA_SPACE(2); - dxi = 1.0 / dx; - dyi = 1.0 / dy; - dzi = 1.0 / dz; - khalf = 0.5; - kthird = 1/3.0; - ktwothird = 2.0/3.0; - kfourthird = 4.0/3.0; - keightthird = 8.0/3.0; - hdxi = 0.5 * dxi; - hdyi = 0.5 * dyi; - hdzi = 0.5 * dzi; + CCTK_REAL const dx = CCTK_DELTA_SPACE(0); + CCTK_REAL const dy = CCTK_DELTA_SPACE(1); + CCTK_REAL const dz = CCTK_DELTA_SPACE(2); + int const di = 1; + int const dj = CCTK_GFINDEX3D(cctkGH,0,1,0) - CCTK_GFINDEX3D(cctkGH,0,0,0); + int const dk = CCTK_GFINDEX3D(cctkGH,0,0,1) - CCTK_GFINDEX3D(cctkGH,0,0,0); + CCTK_REAL const dxi = 1.0 / dx; + CCTK_REAL const dyi = 1.0 / dy; + CCTK_REAL const dzi = 1.0 / dz; + CCTK_REAL const khalf = 0.5; + CCTK_REAL const kthird = 1/3.0; + CCTK_REAL const ktwothird = 2.0/3.0; + CCTK_REAL const kfourthird = 4.0/3.0; + CCTK_REAL const keightthird = 8.0/3.0; + CCTK_REAL const hdxi = 0.5 * dxi; + CCTK_REAL const hdyi = 0.5 * dyi; + CCTK_REAL const hdzi = 0.5 * dzi; /* Initialize predefined quantities */ - p1o12dx = INV(dx)/12.; - p1o12dy = INV(dy)/12.; - p1o12dz = INV(dz)/12.; - p1o144dxdy = (INV(dx)*INV(dy))/144.; - p1o144dxdz = (INV(dx)*INV(dz))/144.; - p1o144dydz = (INV(dy)*INV(dz))/144.; - p1o2dx = khalf*INV(dx); - p1o2dy = khalf*INV(dy); - p1o2dz = khalf*INV(dz); - p1o4dxdy = (INV(dx)*INV(dy))/4.; - p1o4dxdz = (INV(dx)*INV(dz))/4.; - p1o4dydz = (INV(dy)*INV(dz))/4.; - p1odx = INV(dx); - p1odx2 = pow(dx,-2); - p1odxdy = INV(dx)*INV(dy); - p1odxdz = INV(dx)*INV(dz); - p1ody = INV(dy); - p1ody2 = pow(dy,-2); - p1odydz = INV(dy)*INV(dz); - p1odz = INV(dz); - p1odz2 = pow(dz,-2); - pm1o12dx2 = -pow(dx,-2)/12.; - pm1o12dy2 = -pow(dy,-2)/12.; - pm1o12dz2 = -pow(dz,-2)/12.; - pm1o2dx = -(khalf*INV(dx)); - pm1o2dy = -(khalf*INV(dy)); - pm1o2dz = -(khalf*INV(dz)); + CCTK_REAL const p1o12dx = INV(dx)/12.; + CCTK_REAL const p1o12dy = INV(dy)/12.; + CCTK_REAL const p1o12dz = INV(dz)/12.; + CCTK_REAL const p1o144dxdy = (INV(dx)*INV(dy))/144.; + CCTK_REAL const p1o144dxdz = (INV(dx)*INV(dz))/144.; + CCTK_REAL const p1o144dydz = (INV(dy)*INV(dz))/144.; + CCTK_REAL const p1o2dx = khalf*INV(dx); + CCTK_REAL const p1o2dy = khalf*INV(dy); + CCTK_REAL const p1o2dz = khalf*INV(dz); + CCTK_REAL const p1o4dxdy = (INV(dx)*INV(dy))/4.; + CCTK_REAL const p1o4dxdz = (INV(dx)*INV(dz))/4.; + CCTK_REAL const p1o4dydz = (INV(dy)*INV(dz))/4.; + CCTK_REAL const p1odx = INV(dx); + CCTK_REAL const p1odx2 = pow(dx,-2); + CCTK_REAL const p1odxdy = INV(dx)*INV(dy); + CCTK_REAL const p1odxdz = INV(dx)*INV(dz); + CCTK_REAL const p1ody = INV(dy); + CCTK_REAL const p1ody2 = pow(dy,-2); + CCTK_REAL const p1odydz = INV(dy)*INV(dz); + CCTK_REAL const p1odz = INV(dz); + CCTK_REAL const p1odz2 = pow(dz,-2); + CCTK_REAL const pm1o12dx2 = -pow(dx,-2)/12.; + CCTK_REAL const pm1o12dy2 = -pow(dy,-2)/12.; + CCTK_REAL const pm1o12dz2 = -pow(dz,-2)/12.; + CCTK_REAL const pm1o2dx = -(khalf*INV(dx)); + CCTK_REAL const pm1o2dy = -(khalf*INV(dy)); + CCTK_REAL const pm1o2dz = -(khalf*INV(dz)); /* Loop over the grid points */ for (k = min[2]; k < max[2]; k++) @@ -130,1122 +98,1195 @@ void psis_calc_2nd_Body(cGH const * const cctkGH, CCTK_INT const dir, CCTK_INT c { for (i = min[0]; i < max[0]; i++) { - index = CCTK_GFINDEX3D(cctkGH,i,j,k) ; - subblock_index = i - min[0] + (max[0] - min[0]) * (j - min[1] + (max[1]-min[1]) * (k - min[2])) ; - - /* Declare shorthands */ - CCTK_REAL detg = INITVALUE; - CCTK_REAL gamma111 = INITVALUE, gamma121 = INITVALUE, gamma122 = INITVALUE, gamma131 = INITVALUE, gamma132 = INITVALUE, gamma133 = INITVALUE; - CCTK_REAL gamma211 = INITVALUE, gamma221 = INITVALUE, gamma222 = INITVALUE, gamma231 = INITVALUE, gamma232 = INITVALUE, gamma233 = INITVALUE; - CCTK_REAL gamma311 = INITVALUE, gamma321 = INITVALUE, gamma322 = INITVALUE, gamma331 = INITVALUE, gamma332 = INITVALUE, gamma333 = INITVALUE; - CCTK_REAL gInv11 = INITVALUE, gInv12 = INITVALUE, gInv13 = INITVALUE, gInv21 = INITVALUE, gInv22 = INITVALUE, gInv23 = INITVALUE; - CCTK_REAL gInv31 = INITVALUE, gInv32 = INITVALUE, gInv33 = INITVALUE; - CCTK_REAL im1 = INITVALUE, im2 = INITVALUE, im3 = INITVALUE; - CCTK_REAL imbar1 = INITVALUE, imbar2 = INITVALUE, imbar3 = INITVALUE; - CCTK_REAL invdetg = INITVALUE; - CCTK_REAL isqrt2 = INITVALUE; - CCTK_REAL n1 = INITVALUE, n2 = INITVALUE, n3 = INITVALUE; - CCTK_REAL nn = INITVALUE; - CCTK_REAL omega11 = INITVALUE, omega12 = INITVALUE, omega13 = INITVALUE, omega22 = INITVALUE, omega23 = INITVALUE, omega33 = INITVALUE; - CCTK_REAL R1111 = INITVALUE, R1112 = INITVALUE, R1113 = INITVALUE, R1121 = INITVALUE, R1122 = INITVALUE, R1123 = INITVALUE; - CCTK_REAL R1131 = INITVALUE, R1132 = INITVALUE, R1133 = INITVALUE, R1211 = INITVALUE, R1212 = INITVALUE, R1213 = INITVALUE; - CCTK_REAL R1221 = INITVALUE, R1222 = INITVALUE, R1223 = INITVALUE, R1231 = INITVALUE, R1232 = INITVALUE, R1233 = INITVALUE; - CCTK_REAL R1311 = INITVALUE, R1312 = INITVALUE, R1313 = INITVALUE, R1321 = INITVALUE, R1322 = INITVALUE, R1323 = INITVALUE; - CCTK_REAL R1331 = INITVALUE, R1332 = INITVALUE, R1333 = INITVALUE, R2111 = INITVALUE, R2112 = INITVALUE, R2113 = INITVALUE; - CCTK_REAL R2121 = INITVALUE, R2122 = INITVALUE, R2123 = INITVALUE, R2131 = INITVALUE, R2132 = INITVALUE, R2133 = INITVALUE; - CCTK_REAL R2211 = INITVALUE, R2212 = INITVALUE, R2213 = INITVALUE, R2221 = INITVALUE, R2222 = INITVALUE, R2223 = INITVALUE; - CCTK_REAL R2231 = INITVALUE, R2232 = INITVALUE, R2233 = INITVALUE, R2311 = INITVALUE, R2312 = INITVALUE, R2313 = INITVALUE; - CCTK_REAL R2321 = INITVALUE, R2322 = INITVALUE, R2323 = INITVALUE, R2331 = INITVALUE, R2332 = INITVALUE, R2333 = INITVALUE; - CCTK_REAL R3111 = INITVALUE, R3112 = INITVALUE, R3113 = INITVALUE, R3121 = INITVALUE, R3122 = INITVALUE, R3123 = INITVALUE; - CCTK_REAL R3131 = INITVALUE, R3132 = INITVALUE, R3133 = INITVALUE, R3211 = INITVALUE, R3212 = INITVALUE, R3213 = INITVALUE; - CCTK_REAL R3221 = INITVALUE, R3222 = INITVALUE, R3223 = INITVALUE, R3231 = INITVALUE, R3232 = INITVALUE, R3233 = INITVALUE; - CCTK_REAL R3311 = INITVALUE, R3312 = INITVALUE, R3313 = INITVALUE, R3321 = INITVALUE, R3322 = INITVALUE, R3323 = INITVALUE; - CCTK_REAL R3331 = INITVALUE, R3332 = INITVALUE, R3333 = INITVALUE; - CCTK_REAL R4p1111 = INITVALUE, R4p1112 = INITVALUE, R4p1113 = INITVALUE, R4p1121 = INITVALUE, R4p1122 = INITVALUE, R4p1123 = INITVALUE; - CCTK_REAL R4p1131 = INITVALUE, R4p1132 = INITVALUE, R4p1133 = INITVALUE, R4p1211 = INITVALUE, R4p1212 = INITVALUE, R4p1213 = INITVALUE; - CCTK_REAL R4p1221 = INITVALUE, R4p1222 = INITVALUE, R4p1223 = INITVALUE, R4p1231 = INITVALUE, R4p1232 = INITVALUE, R4p1233 = INITVALUE; - CCTK_REAL R4p1311 = INITVALUE, R4p1312 = INITVALUE, R4p1313 = INITVALUE, R4p1321 = INITVALUE, R4p1322 = INITVALUE, R4p1323 = INITVALUE; - CCTK_REAL R4p1331 = INITVALUE, R4p1332 = INITVALUE, R4p1333 = INITVALUE, R4p2111 = INITVALUE, R4p2112 = INITVALUE, R4p2113 = INITVALUE; - CCTK_REAL R4p2121 = INITVALUE, R4p2122 = INITVALUE, R4p2123 = INITVALUE, R4p2131 = INITVALUE, R4p2132 = INITVALUE, R4p2133 = INITVALUE; - CCTK_REAL R4p2211 = INITVALUE, R4p2212 = INITVALUE, R4p2213 = INITVALUE, R4p2221 = INITVALUE, R4p2222 = INITVALUE, R4p2223 = INITVALUE; - CCTK_REAL R4p2231 = INITVALUE, R4p2232 = INITVALUE, R4p2233 = INITVALUE, R4p2311 = INITVALUE, R4p2312 = INITVALUE, R4p2313 = INITVALUE; - CCTK_REAL R4p2321 = INITVALUE, R4p2322 = INITVALUE, R4p2323 = INITVALUE, R4p2331 = INITVALUE, R4p2332 = INITVALUE, R4p2333 = INITVALUE; - CCTK_REAL R4p3111 = INITVALUE, R4p3112 = INITVALUE, R4p3113 = INITVALUE, R4p3121 = INITVALUE, R4p3122 = INITVALUE, R4p3123 = INITVALUE; - CCTK_REAL R4p3131 = INITVALUE, R4p3132 = INITVALUE, R4p3133 = INITVALUE, R4p3211 = INITVALUE, R4p3212 = INITVALUE, R4p3213 = INITVALUE; - CCTK_REAL R4p3221 = INITVALUE, R4p3222 = INITVALUE, R4p3223 = INITVALUE, R4p3231 = INITVALUE, R4p3232 = INITVALUE, R4p3233 = INITVALUE; - CCTK_REAL R4p3311 = INITVALUE, R4p3312 = INITVALUE, R4p3313 = INITVALUE, R4p3321 = INITVALUE, R4p3322 = INITVALUE, R4p3323 = INITVALUE; - CCTK_REAL R4p3331 = INITVALUE, R4p3332 = INITVALUE, R4p3333 = INITVALUE; - CCTK_REAL rm1 = INITVALUE, rm2 = INITVALUE, rm3 = INITVALUE; - CCTK_REAL rmbar1 = INITVALUE, rmbar2 = INITVALUE, rmbar3 = INITVALUE; - CCTK_REAL Ro111 = INITVALUE, Ro112 = INITVALUE, Ro113 = INITVALUE, Ro121 = INITVALUE, Ro122 = INITVALUE, Ro123 = INITVALUE; - CCTK_REAL Ro131 = INITVALUE, Ro132 = INITVALUE, Ro133 = INITVALUE, Ro211 = INITVALUE, Ro212 = INITVALUE, Ro213 = INITVALUE; - CCTK_REAL Ro221 = INITVALUE, Ro222 = INITVALUE, Ro223 = INITVALUE, Ro231 = INITVALUE, Ro232 = INITVALUE, Ro233 = INITVALUE; - CCTK_REAL Ro311 = INITVALUE, Ro312 = INITVALUE, Ro313 = INITVALUE, Ro321 = INITVALUE, Ro322 = INITVALUE, Ro323 = INITVALUE; - CCTK_REAL Ro331 = INITVALUE, Ro332 = INITVALUE, Ro333 = INITVALUE; - CCTK_REAL Rojo11 = INITVALUE, Rojo12 = INITVALUE, Rojo13 = INITVALUE, Rojo21 = INITVALUE, Rojo22 = INITVALUE, Rojo23 = INITVALUE; - CCTK_REAL Rojo31 = INITVALUE, Rojo32 = INITVALUE, Rojo33 = INITVALUE; - CCTK_REAL va1 = INITVALUE, va2 = INITVALUE, va3 = INITVALUE; - CCTK_REAL vb1 = INITVALUE, vb2 = INITVALUE, vb3 = INITVALUE; - CCTK_REAL vc1 = INITVALUE, vc2 = INITVALUE, vc3 = INITVALUE; - CCTK_REAL xmoved = INITVALUE; - CCTK_REAL ymoved = INITVALUE; - CCTK_REAL zmoved = INITVALUE; - - /* Declare local copies of grid functions */ - CCTK_REAL gxxL = INITVALUE; - CCTK_REAL gxyL = INITVALUE; - CCTK_REAL gxzL = INITVALUE; - CCTK_REAL gyyL = INITVALUE; - CCTK_REAL gyzL = INITVALUE; - CCTK_REAL gzzL = INITVALUE; - CCTK_REAL kxxL = INITVALUE; - CCTK_REAL kxyL = INITVALUE; - CCTK_REAL kxzL = INITVALUE; - CCTK_REAL kyyL = INITVALUE; - CCTK_REAL kyzL = INITVALUE; - CCTK_REAL kzzL = INITVALUE; - CCTK_REAL Psi4iL = INITVALUE; - CCTK_REAL Psi4rL = INITVALUE; - CCTK_REAL xL = INITVALUE; - CCTK_REAL yL = INITVALUE; - CCTK_REAL zL = INITVALUE; - /* Declare precomputed derivatives*/ - + int const index = CCTK_GFINDEX3D(cctkGH,i,j,k) ; /* Declare derivatives */ - CCTK_REAL PDstandard2nd1gxx = INITVALUE; - CCTK_REAL PDstandard2nd2gxx = INITVALUE; - CCTK_REAL PDstandard2nd3gxx = INITVALUE; - CCTK_REAL PDstandard2nd22gxx = INITVALUE; - CCTK_REAL PDstandard2nd33gxx = INITVALUE; - CCTK_REAL PDstandard2nd23gxx = INITVALUE; - CCTK_REAL PDstandard2nd1gxy = INITVALUE; - CCTK_REAL PDstandard2nd2gxy = INITVALUE; - CCTK_REAL PDstandard2nd3gxy = INITVALUE; - CCTK_REAL PDstandard2nd33gxy = INITVALUE; - CCTK_REAL PDstandard2nd12gxy = INITVALUE; - CCTK_REAL PDstandard2nd13gxy = INITVALUE; - CCTK_REAL PDstandard2nd23gxy = INITVALUE; - CCTK_REAL PDstandard2nd1gxz = INITVALUE; - CCTK_REAL PDstandard2nd2gxz = INITVALUE; - CCTK_REAL PDstandard2nd3gxz = INITVALUE; - CCTK_REAL PDstandard2nd22gxz = INITVALUE; - CCTK_REAL PDstandard2nd12gxz = INITVALUE; - CCTK_REAL PDstandard2nd13gxz = INITVALUE; - CCTK_REAL PDstandard2nd23gxz = INITVALUE; - CCTK_REAL PDstandard2nd1gyy = INITVALUE; - CCTK_REAL PDstandard2nd2gyy = INITVALUE; - CCTK_REAL PDstandard2nd3gyy = INITVALUE; - CCTK_REAL PDstandard2nd11gyy = INITVALUE; - CCTK_REAL PDstandard2nd33gyy = INITVALUE; - CCTK_REAL PDstandard2nd13gyy = INITVALUE; - CCTK_REAL PDstandard2nd1gyz = INITVALUE; - CCTK_REAL PDstandard2nd2gyz = INITVALUE; - CCTK_REAL PDstandard2nd3gyz = INITVALUE; - CCTK_REAL PDstandard2nd11gyz = INITVALUE; - CCTK_REAL PDstandard2nd12gyz = INITVALUE; - CCTK_REAL PDstandard2nd13gyz = INITVALUE; - CCTK_REAL PDstandard2nd23gyz = INITVALUE; - CCTK_REAL PDstandard2nd1gzz = INITVALUE; - CCTK_REAL PDstandard2nd2gzz = INITVALUE; - CCTK_REAL PDstandard2nd3gzz = INITVALUE; - CCTK_REAL PDstandard2nd11gzz = INITVALUE; - CCTK_REAL PDstandard2nd22gzz = INITVALUE; - CCTK_REAL PDstandard2nd12gzz = INITVALUE; - CCTK_REAL PDstandard2nd2kxx = INITVALUE; - CCTK_REAL PDstandard2nd3kxx = INITVALUE; - CCTK_REAL PDstandard2nd1kxy = INITVALUE; - CCTK_REAL PDstandard2nd2kxy = INITVALUE; - CCTK_REAL PDstandard2nd3kxy = INITVALUE; - CCTK_REAL PDstandard2nd1kxz = INITVALUE; - CCTK_REAL PDstandard2nd2kxz = INITVALUE; - CCTK_REAL PDstandard2nd3kxz = INITVALUE; - CCTK_REAL PDstandard2nd1kyy = INITVALUE; - CCTK_REAL PDstandard2nd3kyy = INITVALUE; - CCTK_REAL PDstandard2nd1kyz = INITVALUE; - CCTK_REAL PDstandard2nd2kyz = INITVALUE; - CCTK_REAL PDstandard2nd3kyz = INITVALUE; - CCTK_REAL PDstandard2nd1kzz = INITVALUE; - CCTK_REAL PDstandard2nd2kzz = INITVALUE; + // CCTK_REAL PDstandard2nd1gxx = INITVALUE; + // CCTK_REAL PDstandard2nd2gxx = INITVALUE; + // CCTK_REAL PDstandard2nd3gxx = INITVALUE; + // CCTK_REAL PDstandard2nd22gxx = INITVALUE; + // CCTK_REAL PDstandard2nd33gxx = INITVALUE; + // CCTK_REAL PDstandard2nd23gxx = INITVALUE; + // CCTK_REAL PDstandard2nd1gxy = INITVALUE; + // CCTK_REAL PDstandard2nd2gxy = INITVALUE; + // CCTK_REAL PDstandard2nd3gxy = INITVALUE; + // CCTK_REAL PDstandard2nd33gxy = INITVALUE; + // CCTK_REAL PDstandard2nd12gxy = INITVALUE; + // CCTK_REAL PDstandard2nd13gxy = INITVALUE; + // CCTK_REAL PDstandard2nd23gxy = INITVALUE; + // CCTK_REAL PDstandard2nd1gxz = INITVALUE; + // CCTK_REAL PDstandard2nd2gxz = INITVALUE; + // CCTK_REAL PDstandard2nd3gxz = INITVALUE; + // CCTK_REAL PDstandard2nd22gxz = INITVALUE; + // CCTK_REAL PDstandard2nd12gxz = INITVALUE; + // CCTK_REAL PDstandard2nd13gxz = INITVALUE; + // CCTK_REAL PDstandard2nd23gxz = INITVALUE; + // CCTK_REAL PDstandard2nd1gyy = INITVALUE; + // CCTK_REAL PDstandard2nd2gyy = INITVALUE; + // CCTK_REAL PDstandard2nd3gyy = INITVALUE; + // CCTK_REAL PDstandard2nd11gyy = INITVALUE; + // CCTK_REAL PDstandard2nd33gyy = INITVALUE; + // CCTK_REAL PDstandard2nd13gyy = INITVALUE; + // CCTK_REAL PDstandard2nd1gyz = INITVALUE; + // CCTK_REAL PDstandard2nd2gyz = INITVALUE; + // CCTK_REAL PDstandard2nd3gyz = INITVALUE; + // CCTK_REAL PDstandard2nd11gyz = INITVALUE; + // CCTK_REAL PDstandard2nd12gyz = INITVALUE; + // CCTK_REAL PDstandard2nd13gyz = INITVALUE; + // CCTK_REAL PDstandard2nd23gyz = INITVALUE; + // CCTK_REAL PDstandard2nd1gzz = INITVALUE; + // CCTK_REAL PDstandard2nd2gzz = INITVALUE; + // CCTK_REAL PDstandard2nd3gzz = INITVALUE; + // CCTK_REAL PDstandard2nd11gzz = INITVALUE; + // CCTK_REAL PDstandard2nd22gzz = INITVALUE; + // CCTK_REAL PDstandard2nd12gzz = INITVALUE; + // CCTK_REAL PDstandard2nd2kxx = INITVALUE; + // CCTK_REAL PDstandard2nd3kxx = INITVALUE; + // CCTK_REAL PDstandard2nd1kxy = INITVALUE; + // CCTK_REAL PDstandard2nd2kxy = INITVALUE; + // CCTK_REAL PDstandard2nd3kxy = INITVALUE; + // CCTK_REAL PDstandard2nd1kxz = INITVALUE; + // CCTK_REAL PDstandard2nd2kxz = INITVALUE; + // CCTK_REAL PDstandard2nd3kxz = INITVALUE; + // CCTK_REAL PDstandard2nd1kyy = INITVALUE; + // CCTK_REAL PDstandard2nd3kyy = INITVALUE; + // CCTK_REAL PDstandard2nd1kyz = INITVALUE; + // CCTK_REAL PDstandard2nd2kyz = INITVALUE; + // CCTK_REAL PDstandard2nd3kyz = INITVALUE; + // CCTK_REAL PDstandard2nd1kzz = INITVALUE; + // CCTK_REAL PDstandard2nd2kzz = INITVALUE; /* Assign local copies of grid functions */ - gxxL = gxx[index]; - gxyL = gxy[index]; - gxzL = gxz[index]; - gyyL = gyy[index]; - gyzL = gyz[index]; - gzzL = gzz[index]; - kxxL = kxx[index]; - kxyL = kxy[index]; - kxzL = kxz[index]; - kyyL = kyy[index]; - kyzL = kyz[index]; - kzzL = kzz[index]; - xL = x[index]; - yL = y[index]; - zL = z[index]; - - /* Assign local copies of subblock grid functions */ + CCTK_REAL gxxL = gxx[index]; + CCTK_REAL gxyL = gxy[index]; + CCTK_REAL gxzL = gxz[index]; + CCTK_REAL gyyL = gyy[index]; + CCTK_REAL gyzL = gyz[index]; + CCTK_REAL gzzL = gzz[index]; + CCTK_REAL kxxL = kxx[index]; + CCTK_REAL kxyL = kxy[index]; + CCTK_REAL kxzL = kxz[index]; + CCTK_REAL kyyL = kyy[index]; + CCTK_REAL kyzL = kyz[index]; + CCTK_REAL kzzL = kzz[index]; + CCTK_REAL xL = x[index]; + CCTK_REAL yL = y[index]; + CCTK_REAL zL = z[index]; /* Include user supplied include files */ - /* Precompute derivatives (new style) */ - PDstandard2nd1gxx = PDstandard2nd1(gxx, i, j, k); - PDstandard2nd2gxx = PDstandard2nd2(gxx, i, j, k); - PDstandard2nd3gxx = PDstandard2nd3(gxx, i, j, k); - PDstandard2nd22gxx = PDstandard2nd22(gxx, i, j, k); - PDstandard2nd33gxx = PDstandard2nd33(gxx, i, j, k); - PDstandard2nd23gxx = PDstandard2nd23(gxx, i, j, k); - PDstandard2nd1gxy = PDstandard2nd1(gxy, i, j, k); - PDstandard2nd2gxy = PDstandard2nd2(gxy, i, j, k); - PDstandard2nd3gxy = PDstandard2nd3(gxy, i, j, k); - PDstandard2nd33gxy = PDstandard2nd33(gxy, i, j, k); - PDstandard2nd12gxy = PDstandard2nd12(gxy, i, j, k); - PDstandard2nd13gxy = PDstandard2nd13(gxy, i, j, k); - PDstandard2nd23gxy = PDstandard2nd23(gxy, i, j, k); - PDstandard2nd1gxz = PDstandard2nd1(gxz, i, j, k); - PDstandard2nd2gxz = PDstandard2nd2(gxz, i, j, k); - PDstandard2nd3gxz = PDstandard2nd3(gxz, i, j, k); - PDstandard2nd22gxz = PDstandard2nd22(gxz, i, j, k); - PDstandard2nd12gxz = PDstandard2nd12(gxz, i, j, k); - PDstandard2nd13gxz = PDstandard2nd13(gxz, i, j, k); - PDstandard2nd23gxz = PDstandard2nd23(gxz, i, j, k); - PDstandard2nd1gyy = PDstandard2nd1(gyy, i, j, k); - PDstandard2nd2gyy = PDstandard2nd2(gyy, i, j, k); - PDstandard2nd3gyy = PDstandard2nd3(gyy, i, j, k); - PDstandard2nd11gyy = PDstandard2nd11(gyy, i, j, k); - PDstandard2nd33gyy = PDstandard2nd33(gyy, i, j, k); - PDstandard2nd13gyy = PDstandard2nd13(gyy, i, j, k); - PDstandard2nd1gyz = PDstandard2nd1(gyz, i, j, k); - PDstandard2nd2gyz = PDstandard2nd2(gyz, i, j, k); - PDstandard2nd3gyz = PDstandard2nd3(gyz, i, j, k); - PDstandard2nd11gyz = PDstandard2nd11(gyz, i, j, k); - PDstandard2nd12gyz = PDstandard2nd12(gyz, i, j, k); - PDstandard2nd13gyz = PDstandard2nd13(gyz, i, j, k); - PDstandard2nd23gyz = PDstandard2nd23(gyz, i, j, k); - PDstandard2nd1gzz = PDstandard2nd1(gzz, i, j, k); - PDstandard2nd2gzz = PDstandard2nd2(gzz, i, j, k); - PDstandard2nd3gzz = PDstandard2nd3(gzz, i, j, k); - PDstandard2nd11gzz = PDstandard2nd11(gzz, i, j, k); - PDstandard2nd22gzz = PDstandard2nd22(gzz, i, j, k); - PDstandard2nd12gzz = PDstandard2nd12(gzz, i, j, k); - PDstandard2nd2kxx = PDstandard2nd2(kxx, i, j, k); - PDstandard2nd3kxx = PDstandard2nd3(kxx, i, j, k); - PDstandard2nd1kxy = PDstandard2nd1(kxy, i, j, k); - PDstandard2nd2kxy = PDstandard2nd2(kxy, i, j, k); - PDstandard2nd3kxy = PDstandard2nd3(kxy, i, j, k); - PDstandard2nd1kxz = PDstandard2nd1(kxz, i, j, k); - PDstandard2nd2kxz = PDstandard2nd2(kxz, i, j, k); - PDstandard2nd3kxz = PDstandard2nd3(kxz, i, j, k); - PDstandard2nd1kyy = PDstandard2nd1(kyy, i, j, k); - PDstandard2nd3kyy = PDstandard2nd3(kyy, i, j, k); - PDstandard2nd1kyz = PDstandard2nd1(kyz, i, j, k); - PDstandard2nd2kyz = PDstandard2nd2(kyz, i, j, k); - PDstandard2nd3kyz = PDstandard2nd3(kyz, i, j, k); - PDstandard2nd1kzz = PDstandard2nd1(kzz, i, j, k); - PDstandard2nd2kzz = PDstandard2nd2(kzz, i, j, k); - - /* Precompute derivatives (old style) */ + /* Precompute derivatives */ + CCTK_REAL const PDstandard2nd1gxx = PDstandard2nd1(gxx, i, j, k); + CCTK_REAL const PDstandard2nd2gxx = PDstandard2nd2(gxx, i, j, k); + CCTK_REAL const PDstandard2nd3gxx = PDstandard2nd3(gxx, i, j, k); + CCTK_REAL const PDstandard2nd22gxx = PDstandard2nd22(gxx, i, j, k); + CCTK_REAL const PDstandard2nd33gxx = PDstandard2nd33(gxx, i, j, k); + CCTK_REAL const PDstandard2nd23gxx = PDstandard2nd23(gxx, i, j, k); + CCTK_REAL const PDstandard2nd1gxy = PDstandard2nd1(gxy, i, j, k); + CCTK_REAL const PDstandard2nd2gxy = PDstandard2nd2(gxy, i, j, k); + CCTK_REAL const PDstandard2nd3gxy = PDstandard2nd3(gxy, i, j, k); + CCTK_REAL const PDstandard2nd33gxy = PDstandard2nd33(gxy, i, j, k); + CCTK_REAL const PDstandard2nd12gxy = PDstandard2nd12(gxy, i, j, k); + CCTK_REAL const PDstandard2nd13gxy = PDstandard2nd13(gxy, i, j, k); + CCTK_REAL const PDstandard2nd23gxy = PDstandard2nd23(gxy, i, j, k); + CCTK_REAL const PDstandard2nd1gxz = PDstandard2nd1(gxz, i, j, k); + CCTK_REAL const PDstandard2nd2gxz = PDstandard2nd2(gxz, i, j, k); + CCTK_REAL const PDstandard2nd3gxz = PDstandard2nd3(gxz, i, j, k); + CCTK_REAL const PDstandard2nd22gxz = PDstandard2nd22(gxz, i, j, k); + CCTK_REAL const PDstandard2nd12gxz = PDstandard2nd12(gxz, i, j, k); + CCTK_REAL const PDstandard2nd13gxz = PDstandard2nd13(gxz, i, j, k); + CCTK_REAL const PDstandard2nd23gxz = PDstandard2nd23(gxz, i, j, k); + CCTK_REAL const PDstandard2nd1gyy = PDstandard2nd1(gyy, i, j, k); + CCTK_REAL const PDstandard2nd2gyy = PDstandard2nd2(gyy, i, j, k); + CCTK_REAL const PDstandard2nd3gyy = PDstandard2nd3(gyy, i, j, k); + CCTK_REAL const PDstandard2nd11gyy = PDstandard2nd11(gyy, i, j, k); + CCTK_REAL const PDstandard2nd33gyy = PDstandard2nd33(gyy, i, j, k); + CCTK_REAL const PDstandard2nd13gyy = PDstandard2nd13(gyy, i, j, k); + CCTK_REAL const PDstandard2nd1gyz = PDstandard2nd1(gyz, i, j, k); + CCTK_REAL const PDstandard2nd2gyz = PDstandard2nd2(gyz, i, j, k); + CCTK_REAL const PDstandard2nd3gyz = PDstandard2nd3(gyz, i, j, k); + CCTK_REAL const PDstandard2nd11gyz = PDstandard2nd11(gyz, i, j, k); + CCTK_REAL const PDstandard2nd12gyz = PDstandard2nd12(gyz, i, j, k); + CCTK_REAL const PDstandard2nd13gyz = PDstandard2nd13(gyz, i, j, k); + CCTK_REAL const PDstandard2nd23gyz = PDstandard2nd23(gyz, i, j, k); + CCTK_REAL const PDstandard2nd1gzz = PDstandard2nd1(gzz, i, j, k); + CCTK_REAL const PDstandard2nd2gzz = PDstandard2nd2(gzz, i, j, k); + CCTK_REAL const PDstandard2nd3gzz = PDstandard2nd3(gzz, i, j, k); + CCTK_REAL const PDstandard2nd11gzz = PDstandard2nd11(gzz, i, j, k); + CCTK_REAL const PDstandard2nd22gzz = PDstandard2nd22(gzz, i, j, k); + CCTK_REAL const PDstandard2nd12gzz = PDstandard2nd12(gzz, i, j, k); + CCTK_REAL const PDstandard2nd2kxx = PDstandard2nd2(kxx, i, j, k); + CCTK_REAL const PDstandard2nd3kxx = PDstandard2nd3(kxx, i, j, k); + CCTK_REAL const PDstandard2nd1kxy = PDstandard2nd1(kxy, i, j, k); + CCTK_REAL const PDstandard2nd2kxy = PDstandard2nd2(kxy, i, j, k); + CCTK_REAL const PDstandard2nd3kxy = PDstandard2nd3(kxy, i, j, k); + CCTK_REAL const PDstandard2nd1kxz = PDstandard2nd1(kxz, i, j, k); + CCTK_REAL const PDstandard2nd2kxz = PDstandard2nd2(kxz, i, j, k); + CCTK_REAL const PDstandard2nd3kxz = PDstandard2nd3(kxz, i, j, k); + CCTK_REAL const PDstandard2nd1kyy = PDstandard2nd1(kyy, i, j, k); + CCTK_REAL const PDstandard2nd3kyy = PDstandard2nd3(kyy, i, j, k); + CCTK_REAL const PDstandard2nd1kyz = PDstandard2nd1(kyz, i, j, k); + CCTK_REAL const PDstandard2nd2kyz = PDstandard2nd2(kyz, i, j, k); + CCTK_REAL const PDstandard2nd3kyz = PDstandard2nd3(kyz, i, j, k); + CCTK_REAL const PDstandard2nd1kzz = PDstandard2nd1(kzz, i, j, k); + CCTK_REAL const PDstandard2nd2kzz = PDstandard2nd2(kzz, i, j, k); /* Calculate temporaries and grid functions */ - detg = 2*gxyL*gxzL*gyzL + gzzL*(gxxL*gyyL - SQR(gxyL)) - gyyL*SQR(gxzL) - gxxL*SQR(gyzL); - - invdetg = INV(detg); - - gInv11 = invdetg*(gyyL*gzzL - SQR(gyzL)); - - gInv12 = (gxzL*gyzL - gxyL*gzzL)*invdetg; - - gInv13 = (-(gxzL*gyyL) + gxyL*gyzL)*invdetg; - - gInv21 = (gxzL*gyzL - gxyL*gzzL)*invdetg; - - gInv22 = invdetg*(gxxL*gzzL - SQR(gxzL)); - - gInv23 = (gxyL*gxzL - gxxL*gyzL)*invdetg; - - gInv31 = (-(gxzL*gyyL) + gxyL*gyzL)*invdetg; - - gInv32 = (gxyL*gxzL - gxxL*gyzL)*invdetg; - - gInv33 = invdetg*(gxxL*gyyL - SQR(gxyL)); + CCTK_REAL detg = 2*gxyL*gxzL*gyzL + gzzL*(gxxL*gyyL - SQR(gxyL)) - + gyyL*SQR(gxzL) - gxxL*SQR(gyzL); - gamma111 = khalf*(gInv11*PDstandard2nd1gxx + 2*(gInv12*PDstandard2nd1gxy + gInv13*PDstandard2nd1gxz) - - gInv12*PDstandard2nd2gxx - gInv13*PDstandard2nd3gxx); + CCTK_REAL invdetg = INV(detg); - gamma211 = khalf*(gInv21*PDstandard2nd1gxx + 2*(gInv22*PDstandard2nd1gxy + gInv23*PDstandard2nd1gxz) - - gInv22*PDstandard2nd2gxx - gInv23*PDstandard2nd3gxx); + CCTK_REAL gInv11 = invdetg*(gyyL*gzzL - SQR(gyzL)); - gamma311 = khalf*(gInv31*PDstandard2nd1gxx + 2*(gInv32*PDstandard2nd1gxy + gInv33*PDstandard2nd1gxz) - - gInv32*PDstandard2nd2gxx - gInv33*PDstandard2nd3gxx); + CCTK_REAL gInv12 = (gxzL*gyzL - gxyL*gzzL)*invdetg; - gamma121 = khalf*(gInv12*PDstandard2nd1gyy + gInv11*PDstandard2nd2gxx + - gInv13*(PDstandard2nd1gyz + PDstandard2nd2gxz - PDstandard2nd3gxy)); + CCTK_REAL gInv13 = (-(gxzL*gyyL) + gxyL*gyzL)*invdetg; - gamma221 = khalf*(gInv22*PDstandard2nd1gyy + gInv21*PDstandard2nd2gxx + - gInv23*(PDstandard2nd1gyz + PDstandard2nd2gxz - PDstandard2nd3gxy)); + CCTK_REAL gInv21 = (gxzL*gyzL - gxyL*gzzL)*invdetg; - gamma321 = khalf*(gInv32*PDstandard2nd1gyy + gInv31*PDstandard2nd2gxx + - gInv33*(PDstandard2nd1gyz + PDstandard2nd2gxz - PDstandard2nd3gxy)); + CCTK_REAL gInv22 = invdetg*(gxxL*gzzL - SQR(gxzL)); - gamma131 = khalf*(gInv13*PDstandard2nd1gzz + gInv11*PDstandard2nd3gxx + - gInv12*(PDstandard2nd1gyz - PDstandard2nd2gxz + PDstandard2nd3gxy)); + CCTK_REAL gInv23 = (gxyL*gxzL - gxxL*gyzL)*invdetg; - gamma231 = khalf*(gInv23*PDstandard2nd1gzz + gInv21*PDstandard2nd3gxx + - gInv22*(PDstandard2nd1gyz - PDstandard2nd2gxz + PDstandard2nd3gxy)); + CCTK_REAL gInv31 = (-(gxzL*gyyL) + gxyL*gyzL)*invdetg; - gamma331 = khalf*(gInv33*PDstandard2nd1gzz + gInv31*PDstandard2nd3gxx + - gInv32*(PDstandard2nd1gyz - PDstandard2nd2gxz + PDstandard2nd3gxy)); + CCTK_REAL gInv32 = (gxyL*gxzL - gxxL*gyzL)*invdetg; - gamma122 = khalf*(gInv11*(-PDstandard2nd1gyy + 2*PDstandard2nd2gxy) + gInv12*PDstandard2nd2gyy + - gInv13*(2*PDstandard2nd2gyz - PDstandard2nd3gyy)); + CCTK_REAL gInv33 = invdetg*(gxxL*gyyL - SQR(gxyL)); - gamma222 = khalf*(gInv21*(-PDstandard2nd1gyy + 2*PDstandard2nd2gxy) + gInv22*PDstandard2nd2gyy + - gInv23*(2*PDstandard2nd2gyz - PDstandard2nd3gyy)); + CCTK_REAL gamma111 = khalf*(gInv11*PDstandard2nd1gxx + + 2*(gInv12*PDstandard2nd1gxy + gInv13*PDstandard2nd1gxz) - + gInv12*PDstandard2nd2gxx - gInv13*PDstandard2nd3gxx); - gamma322 = khalf*(gInv31*(-PDstandard2nd1gyy + 2*PDstandard2nd2gxy) + gInv32*PDstandard2nd2gyy + - gInv33*(2*PDstandard2nd2gyz - PDstandard2nd3gyy)); + CCTK_REAL gamma211 = khalf*(gInv21*PDstandard2nd1gxx + + 2*(gInv22*PDstandard2nd1gxy + gInv23*PDstandard2nd1gxz) - + gInv22*PDstandard2nd2gxx - gInv23*PDstandard2nd3gxx); - gamma132 = khalf*(gInv13*PDstandard2nd2gzz + gInv11*(-PDstandard2nd1gyz + PDstandard2nd2gxz + PDstandard2nd3gxy) + - gInv12*PDstandard2nd3gyy); + CCTK_REAL gamma311 = khalf*(gInv31*PDstandard2nd1gxx + + 2*(gInv32*PDstandard2nd1gxy + gInv33*PDstandard2nd1gxz) - + gInv32*PDstandard2nd2gxx - gInv33*PDstandard2nd3gxx); - gamma232 = khalf*(gInv23*PDstandard2nd2gzz + gInv21*(-PDstandard2nd1gyz + PDstandard2nd2gxz + PDstandard2nd3gxy) + - gInv22*PDstandard2nd3gyy); + CCTK_REAL gamma121 = khalf*(gInv12*PDstandard2nd1gyy + + gInv11*PDstandard2nd2gxx + gInv13*(PDstandard2nd1gyz + + PDstandard2nd2gxz - PDstandard2nd3gxy)); - gamma332 = khalf*(gInv33*PDstandard2nd2gzz + gInv31*(-PDstandard2nd1gyz + PDstandard2nd2gxz + PDstandard2nd3gxy) + - gInv32*PDstandard2nd3gyy); + CCTK_REAL gamma221 = khalf*(gInv22*PDstandard2nd1gyy + + gInv21*PDstandard2nd2gxx + gInv23*(PDstandard2nd1gyz + + PDstandard2nd2gxz - PDstandard2nd3gxy)); - gamma133 = khalf*(-(gInv11*PDstandard2nd1gzz) - gInv12*PDstandard2nd2gzz + 2*gInv11*PDstandard2nd3gxz + - 2*gInv12*PDstandard2nd3gyz + gInv13*PDstandard2nd3gzz); + CCTK_REAL gamma321 = khalf*(gInv32*PDstandard2nd1gyy + + gInv31*PDstandard2nd2gxx + gInv33*(PDstandard2nd1gyz + + PDstandard2nd2gxz - PDstandard2nd3gxy)); - gamma233 = khalf*(-(gInv21*PDstandard2nd1gzz) - gInv22*PDstandard2nd2gzz + 2*gInv21*PDstandard2nd3gxz + - 2*gInv22*PDstandard2nd3gyz + gInv23*PDstandard2nd3gzz); + CCTK_REAL gamma131 = khalf*(gInv13*PDstandard2nd1gzz + + gInv11*PDstandard2nd3gxx + gInv12*(PDstandard2nd1gyz - + PDstandard2nd2gxz + PDstandard2nd3gxy)); - gamma333 = khalf*(-(gInv31*PDstandard2nd1gzz) - gInv32*PDstandard2nd2gzz + 2*gInv31*PDstandard2nd3gxz + - 2*gInv32*PDstandard2nd3gyz + gInv33*PDstandard2nd3gzz); + CCTK_REAL gamma231 = khalf*(gInv23*PDstandard2nd1gzz + + gInv21*PDstandard2nd3gxx + gInv22*(PDstandard2nd1gyz - + PDstandard2nd2gxz + PDstandard2nd3gxy)); - xmoved = xL - xorig; + CCTK_REAL gamma331 = khalf*(gInv33*PDstandard2nd1gzz + + gInv31*PDstandard2nd3gxx + gInv32*(PDstandard2nd1gyz - + PDstandard2nd2gxz + PDstandard2nd3gxy)); - ymoved = yL - yorig; + CCTK_REAL gamma122 = khalf*(gInv11*(-PDstandard2nd1gyy + + 2*PDstandard2nd2gxy) + gInv12*PDstandard2nd2gyy + + gInv13*(2*PDstandard2nd2gyz - PDstandard2nd3gyy)); - zmoved = zL - zorig; + CCTK_REAL gamma222 = khalf*(gInv21*(-PDstandard2nd1gyy + + 2*PDstandard2nd2gxy) + gInv22*PDstandard2nd2gyy + + gInv23*(2*PDstandard2nd2gyz - PDstandard2nd3gyy)); - va1 = -ymoved; + CCTK_REAL gamma322 = khalf*(gInv31*(-PDstandard2nd1gyy + + 2*PDstandard2nd2gxy) + gInv32*PDstandard2nd2gyy + + gInv33*(2*PDstandard2nd2gyz - PDstandard2nd3gyy)); - va2 = offset + xmoved; + CCTK_REAL gamma132 = khalf*(gInv13*PDstandard2nd2gzz + + gInv11*(-PDstandard2nd1gyz + PDstandard2nd2gxz + PDstandard2nd3gxy) + + gInv12*PDstandard2nd3gyy); - va3 = 0; + CCTK_REAL gamma232 = khalf*(gInv23*PDstandard2nd2gzz + + gInv21*(-PDstandard2nd1gyz + PDstandard2nd2gxz + PDstandard2nd3gxy) + + gInv22*PDstandard2nd3gyy); - vb1 = offset + xmoved; + CCTK_REAL gamma332 = khalf*(gInv33*PDstandard2nd2gzz + + gInv31*(-PDstandard2nd1gyz + PDstandard2nd2gxz + PDstandard2nd3gxy) + + gInv32*PDstandard2nd3gyy); - vb2 = ymoved; + CCTK_REAL gamma133 = khalf*(-(gInv11*PDstandard2nd1gzz) - + gInv12*PDstandard2nd2gzz + 2*gInv11*PDstandard2nd3gxz + + 2*gInv12*PDstandard2nd3gyz + gInv13*PDstandard2nd3gzz); - vb3 = zmoved; + CCTK_REAL gamma233 = khalf*(-(gInv21*PDstandard2nd1gzz) - + gInv22*PDstandard2nd2gzz + 2*gInv21*PDstandard2nd3gxz + + 2*gInv22*PDstandard2nd3gyz + gInv23*PDstandard2nd3gzz); - vc1 = ((-(gInv13*va2) + gInv12*va3)*vb1 + (gInv13*va1 - gInv11*va3)*vb2 + (-(gInv12*va1) + gInv11*va2)*vb3)* - pow(detg,0.5); + CCTK_REAL gamma333 = khalf*(-(gInv31*PDstandard2nd1gzz) - + gInv32*PDstandard2nd2gzz + 2*gInv31*PDstandard2nd3gxz + + 2*gInv32*PDstandard2nd3gyz + gInv33*PDstandard2nd3gzz); - vc2 = ((-(gInv23*va2) + gInv22*va3)*vb1 + (gInv23*va1 - gInv21*va3)*vb2 + (-(gInv22*va1) + gInv21*va2)*vb3)* - pow(detg,0.5); + CCTK_REAL xmoved = xL - xorig; - vc3 = ((-(gInv33*va2) + gInv32*va3)*vb1 + (gInv33*va1 - gInv31*va3)*vb2 + (-(gInv32*va1) + gInv31*va2)*vb3)* - pow(detg,0.5); + CCTK_REAL ymoved = yL - yorig; - omega11 = 2*(gyzL*va2*va3 + va1*(gxyL*va2 + gxzL*va3)) + gxxL*SQR(va1) + gyyL*SQR(va2) + gzzL*SQR(va3); + CCTK_REAL zmoved = zL - zorig; - va1 = va1*pow(omega11,-khalf); + CCTK_REAL va1 = -ymoved; - va2 = va2*pow(omega11,-khalf); + CCTK_REAL va2 = offset + xmoved; - va3 = va3*pow(omega11,-khalf); + CCTK_REAL va3 = 0; - omega12 = (gxxL*va1 + gxyL*va2 + gxzL*va3)*vb1 + (gxyL*va1 + gyyL*va2 + gyzL*va3)*vb2 + - (gxzL*va1 + gyzL*va2 + gzzL*va3)*vb3; + CCTK_REAL vb1 = offset + xmoved; - vb1 = -(omega12*va1) + vb1; + CCTK_REAL vb2 = ymoved; - vb2 = -(omega12*va2) + vb2; + CCTK_REAL vb3 = zmoved; - vb3 = -(omega12*va3) + vb3; + CCTK_REAL vc1 = ((-(gInv13*va2) + gInv12*va3)*vb1 + (gInv13*va1 - + gInv11*va3)*vb2 + (-(gInv12*va1) + gInv11*va2)*vb3)*pow(detg,0.5); - omega22 = 2*(gyzL*vb2*vb3 + vb1*(gxyL*vb2 + gxzL*vb3)) + gxxL*SQR(vb1) + gyyL*SQR(vb2) + gzzL*SQR(vb3); + CCTK_REAL vc2 = ((-(gInv23*va2) + gInv22*va3)*vb1 + (gInv23*va1 - + gInv21*va3)*vb2 + (-(gInv22*va1) + gInv21*va2)*vb3)*pow(detg,0.5); - vb1 = vb1*pow(omega22,-khalf); + CCTK_REAL vc3 = ((-(gInv33*va2) + gInv32*va3)*vb1 + (gInv33*va1 - + gInv31*va3)*vb2 + (-(gInv32*va1) + gInv31*va2)*vb3)*pow(detg,0.5); - vb2 = vb2*pow(omega22,-khalf); + CCTK_REAL omega11 = 2*(gyzL*va2*va3 + va1*(gxyL*va2 + gxzL*va3)) + + gxxL*SQR(va1) + gyyL*SQR(va2) + gzzL*SQR(va3); - vb3 = vb3*pow(omega22,-khalf); + va1 = va1*pow(omega11,-khalf); - omega13 = (gxxL*va1 + gxyL*va2 + gxzL*va3)*vc1 + (gxyL*va1 + gyyL*va2 + gyzL*va3)*vc2 + - (gxzL*va1 + gyzL*va2 + gzzL*va3)*vc3; + va2 = va2*pow(omega11,-khalf); - omega23 = (gxxL*vb1 + gxyL*vb2 + gxzL*vb3)*vc1 + (gxyL*vb1 + gyyL*vb2 + gyzL*vb3)*vc2 + - (gxzL*vb1 + gyzL*vb2 + gzzL*vb3)*vc3; + va3 = va3*pow(omega11,-khalf); - vc1 = -(omega13*va1) - omega23*vb1 + vc1; + CCTK_REAL omega12 = (gxxL*va1 + gxyL*va2 + gxzL*va3)*vb1 + (gxyL*va1 + + gyyL*va2 + gyzL*va3)*vb2 + (gxzL*va1 + gyzL*va2 + gzzL*va3)*vb3; - vc2 = -(omega13*va2) - omega23*vb2 + vc2; + vb1 = -(omega12*va1) + vb1; - vc3 = -(omega13*va3) - omega23*vb3 + vc3; + vb2 = -(omega12*va2) + vb2; - omega33 = 2*(gyzL*vc2*vc3 + vc1*(gxyL*vc2 + gxzL*vc3)) + gxxL*SQR(vc1) + gyyL*SQR(vc2) + gzzL*SQR(vc3); + vb3 = -(omega12*va3) + vb3; - vc1 = vc1*pow(omega33,-khalf); + CCTK_REAL omega22 = 2*(gyzL*vb2*vb3 + vb1*(gxyL*vb2 + gxzL*vb3)) + + gxxL*SQR(vb1) + gyyL*SQR(vb2) + gzzL*SQR(vb3); - vc2 = vc2*pow(omega33,-khalf); + vb1 = vb1*pow(omega22,-khalf); - vc3 = vc3*pow(omega33,-khalf); + vb2 = vb2*pow(omega22,-khalf); - isqrt2 = 0.707106781186547524; + vb3 = vb3*pow(omega22,-khalf); - n1 = -(isqrt2*vb1); + CCTK_REAL omega13 = (gxxL*va1 + gxyL*va2 + gxzL*va3)*vc1 + (gxyL*va1 + + gyyL*va2 + gyzL*va3)*vc2 + (gxzL*va1 + gyzL*va2 + gzzL*va3)*vc3; - n2 = -(isqrt2*vb2); + CCTK_REAL omega23 = (gxxL*vb1 + gxyL*vb2 + gxzL*vb3)*vc1 + (gxyL*vb1 + + gyyL*vb2 + gyzL*vb3)*vc2 + (gxzL*vb1 + gyzL*vb2 + gzzL*vb3)*vc3; - n3 = -(isqrt2*vb3); + vc1 = -(omega13*va1) - omega23*vb1 + vc1; - rm1 = isqrt2*vc1; + vc2 = -(omega13*va2) - omega23*vb2 + vc2; - rm2 = isqrt2*vc2; + vc3 = -(omega13*va3) - omega23*vb3 + vc3; - rm3 = isqrt2*vc3; + CCTK_REAL omega33 = 2*(gyzL*vc2*vc3 + vc1*(gxyL*vc2 + gxzL*vc3)) + + gxxL*SQR(vc1) + gyyL*SQR(vc2) + gzzL*SQR(vc3); - im1 = isqrt2*va1; + vc1 = vc1*pow(omega33,-khalf); - im2 = isqrt2*va2; + vc2 = vc2*pow(omega33,-khalf); - im3 = isqrt2*va3; + vc3 = vc3*pow(omega33,-khalf); - rmbar1 = isqrt2*vc1; + CCTK_REAL isqrt2 = 0.707106781186547524; - rmbar2 = isqrt2*vc2; + CCTK_REAL n1 = -(isqrt2*vb1); - rmbar3 = isqrt2*vc3; + CCTK_REAL n2 = -(isqrt2*vb2); - imbar1 = -(isqrt2*va1); + CCTK_REAL n3 = -(isqrt2*vb3); - imbar2 = -(isqrt2*va2); + CCTK_REAL rm1 = isqrt2*vc1; - imbar3 = -(isqrt2*va3); + CCTK_REAL rm2 = isqrt2*vc2; - nn = isqrt2; + CCTK_REAL rm3 = isqrt2*vc3; - R1111 = 0; + CCTK_REAL im1 = isqrt2*va1; - R1112 = 0; + CCTK_REAL im2 = isqrt2*va2; - R1113 = 0; + CCTK_REAL im3 = isqrt2*va3; - R1121 = 0; + CCTK_REAL rmbar1 = isqrt2*vc1; - R1122 = 0; + CCTK_REAL rmbar2 = isqrt2*vc2; - R1123 = 0; + CCTK_REAL rmbar3 = isqrt2*vc3; - R1131 = 0; + CCTK_REAL imbar1 = -(isqrt2*va1); - R1132 = 0; + CCTK_REAL imbar2 = -(isqrt2*va2); - R1133 = 0; + CCTK_REAL imbar3 = -(isqrt2*va3); - R1211 = 0; + CCTK_REAL nn = isqrt2; - R1212 = khalf*((4*gamma121*gamma221 - 2*gamma111*gamma222)*gxyL + (4*gamma121*gamma321 - 2*gamma111*gamma322)*gxzL + - (4*gamma221*gamma321 - 2*gamma211*gamma322)*gyzL - - 2*(gamma111*gamma122*gxxL + gamma122*gamma211*gxyL + gamma122*gamma311*gxzL + gamma211*gamma222*gyyL + - gamma222*gamma311*gyzL + gamma311*gamma322*gzzL) - PDstandard2nd11gyy + 2*PDstandard2nd12gxy - - PDstandard2nd22gxx + 2*gxxL*SQR(gamma121) + 2*gyyL*SQR(gamma221) + 2*gzzL*SQR(gamma321)); + CCTK_REAL R1111 = 0; - R1213 = (gamma121*gamma131 - gamma111*gamma132)*gxxL + - (-(gamma132*gamma211) + gamma131*gamma221 + gamma121*gamma231 - gamma111*gamma232)*gxyL + - (-(gamma132*gamma311) + gamma131*gamma321 + gamma121*gamma331 - gamma111*gamma332)*gxzL + - (gamma221*gamma231 - gamma211*gamma232)*gyyL + - (-(gamma232*gamma311) + gamma231*gamma321 + gamma221*gamma331 - gamma211*gamma332)*gyzL + - (gamma321*gamma331 - gamma311*gamma332)*gzzL + - khalf*(-PDstandard2nd11gyz + PDstandard2nd12gxz + PDstandard2nd13gxy - PDstandard2nd23gxx); + CCTK_REAL R1112 = 0; - R1221 = (-2*gamma121*gamma221 + gamma111*gamma222)*gxyL + (-2*gamma121*gamma321 + gamma111*gamma322)*gxzL + - gamma122*(gamma111*gxxL + gamma211*gxyL + gamma311*gxzL) + (-2*gamma221*gamma321 + gamma211*gamma322)*gyzL + - gamma222*(gamma211*gyyL + gamma311*gyzL) - PDstandard2nd12gxy + khalf*(PDstandard2nd11gyy + PDstandard2nd22gxx) - - gxxL*SQR(gamma121) - gyyL*SQR(gamma221) + gzzL*(gamma311*gamma322 - SQR(gamma321)); + CCTK_REAL R1113 = 0; - R1222 = 0; + CCTK_REAL R1121 = 0; - R1223 = (gamma122*gamma131 - gamma121*gamma132)*gxxL + - (-(gamma132*gamma221) + gamma131*gamma222 + gamma122*gamma231 - gamma121*gamma232)*gxyL + - (-(gamma132*gamma321) + gamma131*gamma322 + gamma122*gamma331 - gamma121*gamma332)*gxzL + - (gamma222*gamma231 - gamma221*gamma232)*gyyL + - (-(gamma232*gamma321) + gamma231*gamma322 + gamma222*gamma331 - gamma221*gamma332)*gyzL + - (gamma322*gamma331 - gamma321*gamma332)*gzzL + - khalf*(-PDstandard2nd12gyz + PDstandard2nd13gyy + PDstandard2nd22gxz - PDstandard2nd23gxy); + CCTK_REAL R1122 = 0; - R1231 = (-(gamma121*gamma131) + gamma111*gamma132)*gxxL + - (gamma132*gamma211 - gamma131*gamma221 - gamma121*gamma231 + gamma111*gamma232)*gxyL + - (gamma132*gamma311 - gamma131*gamma321 - gamma121*gamma331 + gamma111*gamma332)*gxzL + - (-(gamma221*gamma231) + gamma211*gamma232)*gyyL + - (gamma232*gamma311 - gamma231*gamma321 - gamma221*gamma331 + gamma211*gamma332)*gyzL + - (-(gamma321*gamma331) + gamma311*gamma332)*gzzL + - khalf*(PDstandard2nd11gyz - PDstandard2nd12gxz - PDstandard2nd13gxy + PDstandard2nd23gxx); + CCTK_REAL R1123 = 0; - R1232 = (-(gamma122*gamma131) + gamma121*gamma132)*gxxL + - (gamma132*gamma221 - gamma131*gamma222 - gamma122*gamma231 + gamma121*gamma232)*gxyL + - (gamma132*gamma321 - gamma131*gamma322 - gamma122*gamma331 + gamma121*gamma332)*gxzL + - (-(gamma222*gamma231) + gamma221*gamma232)*gyyL + - (gamma232*gamma321 - gamma231*gamma322 - gamma222*gamma331 + gamma221*gamma332)*gyzL + - (-(gamma322*gamma331) + gamma321*gamma332)*gzzL + - khalf*(PDstandard2nd12gyz - PDstandard2nd13gyy - PDstandard2nd22gxz + PDstandard2nd23gxy); + CCTK_REAL R1131 = 0; - R1233 = 0; + CCTK_REAL R1132 = 0; - R1311 = 0; + CCTK_REAL R1133 = 0; - R1312 = (gamma121*gamma131 - gamma111*gamma132)*gxxL + - (-(gamma132*gamma211) + gamma131*gamma221 + gamma121*gamma231 - gamma111*gamma232)*gxyL + - (-(gamma132*gamma311) + gamma131*gamma321 + gamma121*gamma331 - gamma111*gamma332)*gxzL + - (gamma221*gamma231 - gamma211*gamma232)*gyyL + - (-(gamma232*gamma311) + gamma231*gamma321 + gamma221*gamma331 - gamma211*gamma332)*gyzL + - (gamma321*gamma331 - gamma311*gamma332)*gzzL + - khalf*(-PDstandard2nd11gyz + PDstandard2nd12gxz + PDstandard2nd13gxy - PDstandard2nd23gxx); + CCTK_REAL R1211 = 0; - R1313 = khalf*((4*gamma131*gamma231 - 2*gamma111*gamma233)*gxyL + (4*gamma131*gamma331 - 2*gamma111*gamma333)*gxzL + - (4*gamma231*gamma331 - 2*gamma211*gamma333)*gyzL - - 2*(gamma111*gamma133*gxxL + gamma133*gamma211*gxyL + gamma133*gamma311*gxzL + gamma211*gamma233*gyyL + - gamma233*gamma311*gyzL + gamma311*gamma333*gzzL) - PDstandard2nd11gzz + 2*PDstandard2nd13gxz - - PDstandard2nd33gxx + 2*gxxL*SQR(gamma131) + 2*gyyL*SQR(gamma231) + 2*gzzL*SQR(gamma331)); + CCTK_REAL R1212 = khalf*((4*gamma121*gamma221 - + 2*gamma111*gamma222)*gxyL + (4*gamma121*gamma321 - + 2*gamma111*gamma322)*gxzL + (4*gamma221*gamma321 - + 2*gamma211*gamma322)*gyzL - 2*(gamma111*gamma122*gxxL + + gamma122*gamma211*gxyL + gamma122*gamma311*gxzL + + gamma211*gamma222*gyyL + gamma222*gamma311*gyzL + + gamma311*gamma322*gzzL) - PDstandard2nd11gyy + 2*PDstandard2nd12gxy - + PDstandard2nd22gxx + 2*gxxL*SQR(gamma121) + 2*gyyL*SQR(gamma221) + + 2*gzzL*SQR(gamma321)); - R1321 = (-(gamma121*gamma131) + gamma111*gamma132)*gxxL + - (gamma132*gamma211 - gamma131*gamma221 - gamma121*gamma231 + gamma111*gamma232)*gxyL + - (gamma132*gamma311 - gamma131*gamma321 - gamma121*gamma331 + gamma111*gamma332)*gxzL + - (-(gamma221*gamma231) + gamma211*gamma232)*gyyL + - (gamma232*gamma311 - gamma231*gamma321 - gamma221*gamma331 + gamma211*gamma332)*gyzL + - (-(gamma321*gamma331) + gamma311*gamma332)*gzzL + - khalf*(PDstandard2nd11gyz - PDstandard2nd12gxz - PDstandard2nd13gxy + PDstandard2nd23gxx); + CCTK_REAL R1213 = (gamma121*gamma131 - gamma111*gamma132)*gxxL + + (-(gamma132*gamma211) + gamma131*gamma221 + gamma121*gamma231 - + gamma111*gamma232)*gxyL + (-(gamma132*gamma311) + gamma131*gamma321 + + gamma121*gamma331 - gamma111*gamma332)*gxzL + (gamma221*gamma231 - + gamma211*gamma232)*gyyL + (-(gamma232*gamma311) + gamma231*gamma321 + + gamma221*gamma331 - gamma211*gamma332)*gyzL + (gamma321*gamma331 - + gamma311*gamma332)*gzzL + khalf*(-PDstandard2nd11gyz + + PDstandard2nd12gxz + PDstandard2nd13gxy - PDstandard2nd23gxx); - R1322 = 0; + CCTK_REAL R1221 = (-2*gamma121*gamma221 + gamma111*gamma222)*gxyL + + (-2*gamma121*gamma321 + gamma111*gamma322)*gxzL + + gamma122*(gamma111*gxxL + gamma211*gxyL + gamma311*gxzL) + + (-2*gamma221*gamma321 + gamma211*gamma322)*gyzL + + gamma222*(gamma211*gyyL + gamma311*gyzL) - PDstandard2nd12gxy + + khalf*(PDstandard2nd11gyy + PDstandard2nd22gxx) - gxxL*SQR(gamma121) - + gyyL*SQR(gamma221) + gzzL*(gamma311*gamma322 - SQR(gamma321)); - R1323 = (gamma131*gamma132 - gamma121*gamma133)*gxxL + - (-(gamma133*gamma221) + gamma132*gamma231 + gamma131*gamma232 - gamma121*gamma233)*gxyL + - (-(gamma133*gamma321) + gamma132*gamma331 + gamma131*gamma332 - gamma121*gamma333)*gxzL + - (gamma231*gamma232 - gamma221*gamma233)*gyyL + - (-(gamma233*gamma321) + gamma232*gamma331 + gamma231*gamma332 - gamma221*gamma333)*gyzL + - (gamma331*gamma332 - gamma321*gamma333)*gzzL + - khalf*(-PDstandard2nd12gzz + PDstandard2nd13gyz + PDstandard2nd23gxz - PDstandard2nd33gxy); - - R1331 = (-2*gamma131*gamma231 + gamma111*gamma233)*gxyL + (-2*gamma131*gamma331 + gamma111*gamma333)*gxzL + - gamma133*(gamma111*gxxL + gamma211*gxyL + gamma311*gxzL) + (-2*gamma231*gamma331 + gamma211*gamma333)*gyzL + - gamma233*(gamma211*gyyL + gamma311*gyzL) - PDstandard2nd13gxz + khalf*(PDstandard2nd11gzz + PDstandard2nd33gxx) - - gxxL*SQR(gamma131) - gyyL*SQR(gamma231) + gzzL*(gamma311*gamma333 - SQR(gamma331)); - - R1332 = (-(gamma131*gamma132) + gamma121*gamma133)*gxxL + - (gamma133*gamma221 - gamma132*gamma231 - gamma131*gamma232 + gamma121*gamma233)*gxyL + - (gamma133*gamma321 - gamma132*gamma331 - gamma131*gamma332 + gamma121*gamma333)*gxzL + - (-(gamma231*gamma232) + gamma221*gamma233)*gyyL + - (gamma233*gamma321 - gamma232*gamma331 - gamma231*gamma332 + gamma221*gamma333)*gyzL + - (-(gamma331*gamma332) + gamma321*gamma333)*gzzL + - khalf*(PDstandard2nd12gzz - PDstandard2nd13gyz - PDstandard2nd23gxz + PDstandard2nd33gxy); - - R1333 = 0; - - R2111 = 0; - - R2112 = (-2*gamma121*gamma221 + gamma111*gamma222)*gxyL + (-2*gamma121*gamma321 + gamma111*gamma322)*gxzL + - gamma122*(gamma111*gxxL + gamma211*gxyL + gamma311*gxzL) + (-2*gamma221*gamma321 + gamma211*gamma322)*gyzL + - gamma222*(gamma211*gyyL + gamma311*gyzL) - PDstandard2nd12gxy + khalf*(PDstandard2nd11gyy + PDstandard2nd22gxx) - - gxxL*SQR(gamma121) - gyyL*SQR(gamma221) + gzzL*(gamma311*gamma322 - SQR(gamma321)); - - R2113 = (-(gamma121*gamma131) + gamma111*gamma132)*gxxL + - (gamma132*gamma211 - gamma131*gamma221 - gamma121*gamma231 + gamma111*gamma232)*gxyL + - (gamma132*gamma311 - gamma131*gamma321 - gamma121*gamma331 + gamma111*gamma332)*gxzL + - (-(gamma221*gamma231) + gamma211*gamma232)*gyyL + - (gamma232*gamma311 - gamma231*gamma321 - gamma221*gamma331 + gamma211*gamma332)*gyzL + - (-(gamma321*gamma331) + gamma311*gamma332)*gzzL + - khalf*(PDstandard2nd11gyz - PDstandard2nd12gxz - PDstandard2nd13gxy + PDstandard2nd23gxx); - - R2121 = khalf*((4*gamma121*gamma221 - 2*gamma111*gamma222)*gxyL + (4*gamma121*gamma321 - 2*gamma111*gamma322)*gxzL + - (4*gamma221*gamma321 - 2*gamma211*gamma322)*gyzL - - 2*(gamma111*gamma122*gxxL + gamma122*gamma211*gxyL + gamma122*gamma311*gxzL + gamma211*gamma222*gyyL + - gamma222*gamma311*gyzL + gamma311*gamma322*gzzL) - PDstandard2nd11gyy + 2*PDstandard2nd12gxy - - PDstandard2nd22gxx + 2*gxxL*SQR(gamma121) + 2*gyyL*SQR(gamma221) + 2*gzzL*SQR(gamma321)); - - R2122 = 0; - - R2123 = (-(gamma122*gamma131) + gamma121*gamma132)*gxxL + - (gamma132*gamma221 - gamma131*gamma222 - gamma122*gamma231 + gamma121*gamma232)*gxyL + - (gamma132*gamma321 - gamma131*gamma322 - gamma122*gamma331 + gamma121*gamma332)*gxzL + - (-(gamma222*gamma231) + gamma221*gamma232)*gyyL + - (gamma232*gamma321 - gamma231*gamma322 - gamma222*gamma331 + gamma221*gamma332)*gyzL + - (-(gamma322*gamma331) + gamma321*gamma332)*gzzL + - khalf*(PDstandard2nd12gyz - PDstandard2nd13gyy - PDstandard2nd22gxz + PDstandard2nd23gxy); - - R2131 = (gamma121*gamma131 - gamma111*gamma132)*gxxL + - (-(gamma132*gamma211) + gamma131*gamma221 + gamma121*gamma231 - gamma111*gamma232)*gxyL + - (-(gamma132*gamma311) + gamma131*gamma321 + gamma121*gamma331 - gamma111*gamma332)*gxzL + - (gamma221*gamma231 - gamma211*gamma232)*gyyL + - (-(gamma232*gamma311) + gamma231*gamma321 + gamma221*gamma331 - gamma211*gamma332)*gyzL + - (gamma321*gamma331 - gamma311*gamma332)*gzzL + - khalf*(-PDstandard2nd11gyz + PDstandard2nd12gxz + PDstandard2nd13gxy - PDstandard2nd23gxx); - - R2132 = (gamma122*gamma131 - gamma121*gamma132)*gxxL + - (-(gamma132*gamma221) + gamma131*gamma222 + gamma122*gamma231 - gamma121*gamma232)*gxyL + - (-(gamma132*gamma321) + gamma131*gamma322 + gamma122*gamma331 - gamma121*gamma332)*gxzL + - (gamma222*gamma231 - gamma221*gamma232)*gyyL + - (-(gamma232*gamma321) + gamma231*gamma322 + gamma222*gamma331 - gamma221*gamma332)*gyzL + - (gamma322*gamma331 - gamma321*gamma332)*gzzL + - khalf*(-PDstandard2nd12gyz + PDstandard2nd13gyy + PDstandard2nd22gxz - PDstandard2nd23gxy); - - R2133 = 0; - - R2211 = 0; - - R2212 = 0; - - R2213 = 0; - - R2221 = 0; - - R2222 = 0; - - R2223 = 0; - - R2231 = 0; - - R2232 = 0; - - R2233 = 0; - - R2311 = 0; - - R2312 = (gamma122*gamma131 - gamma121*gamma132)*gxxL + - (-(gamma132*gamma221) + gamma131*gamma222 + gamma122*gamma231 - gamma121*gamma232)*gxyL + - (-(gamma132*gamma321) + gamma131*gamma322 + gamma122*gamma331 - gamma121*gamma332)*gxzL + - (gamma222*gamma231 - gamma221*gamma232)*gyyL + - (-(gamma232*gamma321) + gamma231*gamma322 + gamma222*gamma331 - gamma221*gamma332)*gyzL + - (gamma322*gamma331 - gamma321*gamma332)*gzzL + - khalf*(-PDstandard2nd12gyz + PDstandard2nd13gyy + PDstandard2nd22gxz - PDstandard2nd23gxy); - - R2313 = (gamma131*gamma132 - gamma121*gamma133)*gxxL + - (-(gamma133*gamma221) + gamma132*gamma231 + gamma131*gamma232 - gamma121*gamma233)*gxyL + - (-(gamma133*gamma321) + gamma132*gamma331 + gamma131*gamma332 - gamma121*gamma333)*gxzL + - (gamma231*gamma232 - gamma221*gamma233)*gyyL + - (-(gamma233*gamma321) + gamma232*gamma331 + gamma231*gamma332 - gamma221*gamma333)*gyzL + - (gamma331*gamma332 - gamma321*gamma333)*gzzL + - khalf*(-PDstandard2nd12gzz + PDstandard2nd13gyz + PDstandard2nd23gxz - PDstandard2nd33gxy); - - R2321 = (-(gamma122*gamma131) + gamma121*gamma132)*gxxL + - (gamma132*gamma221 - gamma131*gamma222 - gamma122*gamma231 + gamma121*gamma232)*gxyL + - (gamma132*gamma321 - gamma131*gamma322 - gamma122*gamma331 + gamma121*gamma332)*gxzL + - (-(gamma222*gamma231) + gamma221*gamma232)*gyyL + - (gamma232*gamma321 - gamma231*gamma322 - gamma222*gamma331 + gamma221*gamma332)*gyzL + - (-(gamma322*gamma331) + gamma321*gamma332)*gzzL + - khalf*(PDstandard2nd12gyz - PDstandard2nd13gyy - PDstandard2nd22gxz + PDstandard2nd23gxy); - - R2322 = 0; - - R2323 = khalf*((4*gamma132*gamma232 - 2*gamma122*gamma233)*gxyL + (4*gamma132*gamma332 - 2*gamma122*gamma333)*gxzL + - (4*gamma232*gamma332 - 2*gamma222*gamma333)*gyzL - - 2*(gamma122*gamma133*gxxL + gamma133*gamma222*gxyL + gamma133*gamma322*gxzL + gamma222*gamma233*gyyL + - gamma233*gamma322*gyzL + gamma322*gamma333*gzzL) - PDstandard2nd22gzz + 2*PDstandard2nd23gyz - - PDstandard2nd33gyy + 2*gxxL*SQR(gamma132) + 2*gyyL*SQR(gamma232) + 2*gzzL*SQR(gamma332)); - - R2331 = (-(gamma131*gamma132) + gamma121*gamma133)*gxxL + - (gamma133*gamma221 - gamma132*gamma231 - gamma131*gamma232 + gamma121*gamma233)*gxyL + - (gamma133*gamma321 - gamma132*gamma331 - gamma131*gamma332 + gamma121*gamma333)*gxzL + - (-(gamma231*gamma232) + gamma221*gamma233)*gyyL + - (gamma233*gamma321 - gamma232*gamma331 - gamma231*gamma332 + gamma221*gamma333)*gyzL + - (-(gamma331*gamma332) + gamma321*gamma333)*gzzL + - khalf*(PDstandard2nd12gzz - PDstandard2nd13gyz - PDstandard2nd23gxz + PDstandard2nd33gxy); - - R2332 = (-2*gamma132*gamma232 + gamma122*gamma233)*gxyL + (-2*gamma132*gamma332 + gamma122*gamma333)*gxzL + - gamma133*(gamma122*gxxL + gamma222*gxyL + gamma322*gxzL) + (-2*gamma232*gamma332 + gamma222*gamma333)*gyzL + - gamma233*(gamma222*gyyL + gamma322*gyzL) - PDstandard2nd23gyz + khalf*(PDstandard2nd22gzz + PDstandard2nd33gyy) - - gxxL*SQR(gamma132) - gyyL*SQR(gamma232) + gzzL*(gamma322*gamma333 - SQR(gamma332)); - - R2333 = 0; - - R3111 = 0; - - R3112 = (-(gamma121*gamma131) + gamma111*gamma132)*gxxL + - (gamma132*gamma211 - gamma131*gamma221 - gamma121*gamma231 + gamma111*gamma232)*gxyL + - (gamma132*gamma311 - gamma131*gamma321 - gamma121*gamma331 + gamma111*gamma332)*gxzL + - (-(gamma221*gamma231) + gamma211*gamma232)*gyyL + - (gamma232*gamma311 - gamma231*gamma321 - gamma221*gamma331 + gamma211*gamma332)*gyzL + - (-(gamma321*gamma331) + gamma311*gamma332)*gzzL + - khalf*(PDstandard2nd11gyz - PDstandard2nd12gxz - PDstandard2nd13gxy + PDstandard2nd23gxx); - - R3113 = (-2*gamma131*gamma231 + gamma111*gamma233)*gxyL + (-2*gamma131*gamma331 + gamma111*gamma333)*gxzL + - gamma133*(gamma111*gxxL + gamma211*gxyL + gamma311*gxzL) + (-2*gamma231*gamma331 + gamma211*gamma333)*gyzL + - gamma233*(gamma211*gyyL + gamma311*gyzL) - PDstandard2nd13gxz + khalf*(PDstandard2nd11gzz + PDstandard2nd33gxx) - - gxxL*SQR(gamma131) - gyyL*SQR(gamma231) + gzzL*(gamma311*gamma333 - SQR(gamma331)); - - R3121 = (gamma121*gamma131 - gamma111*gamma132)*gxxL + - (-(gamma132*gamma211) + gamma131*gamma221 + gamma121*gamma231 - gamma111*gamma232)*gxyL + - (-(gamma132*gamma311) + gamma131*gamma321 + gamma121*gamma331 - gamma111*gamma332)*gxzL + - (gamma221*gamma231 - gamma211*gamma232)*gyyL + - (-(gamma232*gamma311) + gamma231*gamma321 + gamma221*gamma331 - gamma211*gamma332)*gyzL + - (gamma321*gamma331 - gamma311*gamma332)*gzzL + - khalf*(-PDstandard2nd11gyz + PDstandard2nd12gxz + PDstandard2nd13gxy - PDstandard2nd23gxx); + CCTK_REAL R1222 = 0; - R3122 = 0; + CCTK_REAL R1223 = (gamma122*gamma131 - gamma121*gamma132)*gxxL + + (-(gamma132*gamma221) + gamma131*gamma222 + gamma122*gamma231 - + gamma121*gamma232)*gxyL + (-(gamma132*gamma321) + gamma131*gamma322 + + gamma122*gamma331 - gamma121*gamma332)*gxzL + (gamma222*gamma231 - + gamma221*gamma232)*gyyL + (-(gamma232*gamma321) + gamma231*gamma322 + + gamma222*gamma331 - gamma221*gamma332)*gyzL + (gamma322*gamma331 - + gamma321*gamma332)*gzzL + khalf*(-PDstandard2nd12gyz + + PDstandard2nd13gyy + PDstandard2nd22gxz - PDstandard2nd23gxy); - R3123 = (-(gamma131*gamma132) + gamma121*gamma133)*gxxL + - (gamma133*gamma221 - gamma132*gamma231 - gamma131*gamma232 + gamma121*gamma233)*gxyL + - (gamma133*gamma321 - gamma132*gamma331 - gamma131*gamma332 + gamma121*gamma333)*gxzL + - (-(gamma231*gamma232) + gamma221*gamma233)*gyyL + - (gamma233*gamma321 - gamma232*gamma331 - gamma231*gamma332 + gamma221*gamma333)*gyzL + - (-(gamma331*gamma332) + gamma321*gamma333)*gzzL + - khalf*(PDstandard2nd12gzz - PDstandard2nd13gyz - PDstandard2nd23gxz + PDstandard2nd33gxy); + CCTK_REAL R1231 = (-(gamma121*gamma131) + gamma111*gamma132)*gxxL + + (gamma132*gamma211 - gamma131*gamma221 - gamma121*gamma231 + + gamma111*gamma232)*gxyL + (gamma132*gamma311 - gamma131*gamma321 - + gamma121*gamma331 + gamma111*gamma332)*gxzL + (-(gamma221*gamma231) + + gamma211*gamma232)*gyyL + (gamma232*gamma311 - gamma231*gamma321 - + gamma221*gamma331 + gamma211*gamma332)*gyzL + (-(gamma321*gamma331) + + gamma311*gamma332)*gzzL + khalf*(PDstandard2nd11gyz - + PDstandard2nd12gxz - PDstandard2nd13gxy + PDstandard2nd23gxx); + + CCTK_REAL R1232 = (-(gamma122*gamma131) + gamma121*gamma132)*gxxL + + (gamma132*gamma221 - gamma131*gamma222 - gamma122*gamma231 + + gamma121*gamma232)*gxyL + (gamma132*gamma321 - gamma131*gamma322 - + gamma122*gamma331 + gamma121*gamma332)*gxzL + (-(gamma222*gamma231) + + gamma221*gamma232)*gyyL + (gamma232*gamma321 - gamma231*gamma322 - + gamma222*gamma331 + gamma221*gamma332)*gyzL + (-(gamma322*gamma331) + + gamma321*gamma332)*gzzL + khalf*(PDstandard2nd12gyz - + PDstandard2nd13gyy - PDstandard2nd22gxz + PDstandard2nd23gxy); + + CCTK_REAL R1233 = 0; + + CCTK_REAL R1311 = 0; + + CCTK_REAL R1312 = (gamma121*gamma131 - gamma111*gamma132)*gxxL + + (-(gamma132*gamma211) + gamma131*gamma221 + gamma121*gamma231 - + gamma111*gamma232)*gxyL + (-(gamma132*gamma311) + gamma131*gamma321 + + gamma121*gamma331 - gamma111*gamma332)*gxzL + (gamma221*gamma231 - + gamma211*gamma232)*gyyL + (-(gamma232*gamma311) + gamma231*gamma321 + + gamma221*gamma331 - gamma211*gamma332)*gyzL + (gamma321*gamma331 - + gamma311*gamma332)*gzzL + khalf*(-PDstandard2nd11gyz + + PDstandard2nd12gxz + PDstandard2nd13gxy - PDstandard2nd23gxx); + + CCTK_REAL R1313 = khalf*((4*gamma131*gamma231 - + 2*gamma111*gamma233)*gxyL + (4*gamma131*gamma331 - + 2*gamma111*gamma333)*gxzL + (4*gamma231*gamma331 - + 2*gamma211*gamma333)*gyzL - 2*(gamma111*gamma133*gxxL + + gamma133*gamma211*gxyL + gamma133*gamma311*gxzL + + gamma211*gamma233*gyyL + gamma233*gamma311*gyzL + + gamma311*gamma333*gzzL) - PDstandard2nd11gzz + 2*PDstandard2nd13gxz - + PDstandard2nd33gxx + 2*gxxL*SQR(gamma131) + 2*gyyL*SQR(gamma231) + + 2*gzzL*SQR(gamma331)); + + CCTK_REAL R1321 = (-(gamma121*gamma131) + gamma111*gamma132)*gxxL + + (gamma132*gamma211 - gamma131*gamma221 - gamma121*gamma231 + + gamma111*gamma232)*gxyL + (gamma132*gamma311 - gamma131*gamma321 - + gamma121*gamma331 + gamma111*gamma332)*gxzL + (-(gamma221*gamma231) + + gamma211*gamma232)*gyyL + (gamma232*gamma311 - gamma231*gamma321 - + gamma221*gamma331 + gamma211*gamma332)*gyzL + (-(gamma321*gamma331) + + gamma311*gamma332)*gzzL + khalf*(PDstandard2nd11gyz - + PDstandard2nd12gxz - PDstandard2nd13gxy + PDstandard2nd23gxx); + + CCTK_REAL R1322 = 0; + + CCTK_REAL R1323 = (gamma131*gamma132 - gamma121*gamma133)*gxxL + + (-(gamma133*gamma221) + gamma132*gamma231 + gamma131*gamma232 - + gamma121*gamma233)*gxyL + (-(gamma133*gamma321) + gamma132*gamma331 + + gamma131*gamma332 - gamma121*gamma333)*gxzL + (gamma231*gamma232 - + gamma221*gamma233)*gyyL + (-(gamma233*gamma321) + gamma232*gamma331 + + gamma231*gamma332 - gamma221*gamma333)*gyzL + (gamma331*gamma332 - + gamma321*gamma333)*gzzL + khalf*(-PDstandard2nd12gzz + + PDstandard2nd13gyz + PDstandard2nd23gxz - PDstandard2nd33gxy); + + CCTK_REAL R1331 = (-2*gamma131*gamma231 + gamma111*gamma233)*gxyL + + (-2*gamma131*gamma331 + gamma111*gamma333)*gxzL + + gamma133*(gamma111*gxxL + gamma211*gxyL + gamma311*gxzL) + + (-2*gamma231*gamma331 + gamma211*gamma333)*gyzL + + gamma233*(gamma211*gyyL + gamma311*gyzL) - PDstandard2nd13gxz + + khalf*(PDstandard2nd11gzz + PDstandard2nd33gxx) - gxxL*SQR(gamma131) - + gyyL*SQR(gamma231) + gzzL*(gamma311*gamma333 - SQR(gamma331)); + + CCTK_REAL R1332 = (-(gamma131*gamma132) + gamma121*gamma133)*gxxL + + (gamma133*gamma221 - gamma132*gamma231 - gamma131*gamma232 + + gamma121*gamma233)*gxyL + (gamma133*gamma321 - gamma132*gamma331 - + gamma131*gamma332 + gamma121*gamma333)*gxzL + (-(gamma231*gamma232) + + gamma221*gamma233)*gyyL + (gamma233*gamma321 - gamma232*gamma331 - + gamma231*gamma332 + gamma221*gamma333)*gyzL + (-(gamma331*gamma332) + + gamma321*gamma333)*gzzL + khalf*(PDstandard2nd12gzz - + PDstandard2nd13gyz - PDstandard2nd23gxz + PDstandard2nd33gxy); + + CCTK_REAL R1333 = 0; + + CCTK_REAL R2111 = 0; + + CCTK_REAL R2112 = (-2*gamma121*gamma221 + gamma111*gamma222)*gxyL + + (-2*gamma121*gamma321 + gamma111*gamma322)*gxzL + + gamma122*(gamma111*gxxL + gamma211*gxyL + gamma311*gxzL) + + (-2*gamma221*gamma321 + gamma211*gamma322)*gyzL + + gamma222*(gamma211*gyyL + gamma311*gyzL) - PDstandard2nd12gxy + + khalf*(PDstandard2nd11gyy + PDstandard2nd22gxx) - gxxL*SQR(gamma121) - + gyyL*SQR(gamma221) + gzzL*(gamma311*gamma322 - SQR(gamma321)); + + CCTK_REAL R2113 = (-(gamma121*gamma131) + gamma111*gamma132)*gxxL + + (gamma132*gamma211 - gamma131*gamma221 - gamma121*gamma231 + + gamma111*gamma232)*gxyL + (gamma132*gamma311 - gamma131*gamma321 - + gamma121*gamma331 + gamma111*gamma332)*gxzL + (-(gamma221*gamma231) + + gamma211*gamma232)*gyyL + (gamma232*gamma311 - gamma231*gamma321 - + gamma221*gamma331 + gamma211*gamma332)*gyzL + (-(gamma321*gamma331) + + gamma311*gamma332)*gzzL + khalf*(PDstandard2nd11gyz - + PDstandard2nd12gxz - PDstandard2nd13gxy + PDstandard2nd23gxx); + + CCTK_REAL R2121 = khalf*((4*gamma121*gamma221 - + 2*gamma111*gamma222)*gxyL + (4*gamma121*gamma321 - + 2*gamma111*gamma322)*gxzL + (4*gamma221*gamma321 - + 2*gamma211*gamma322)*gyzL - 2*(gamma111*gamma122*gxxL + + gamma122*gamma211*gxyL + gamma122*gamma311*gxzL + + gamma211*gamma222*gyyL + gamma222*gamma311*gyzL + + gamma311*gamma322*gzzL) - PDstandard2nd11gyy + 2*PDstandard2nd12gxy - + PDstandard2nd22gxx + 2*gxxL*SQR(gamma121) + 2*gyyL*SQR(gamma221) + + 2*gzzL*SQR(gamma321)); + + CCTK_REAL R2122 = 0; + + CCTK_REAL R2123 = (-(gamma122*gamma131) + gamma121*gamma132)*gxxL + + (gamma132*gamma221 - gamma131*gamma222 - gamma122*gamma231 + + gamma121*gamma232)*gxyL + (gamma132*gamma321 - gamma131*gamma322 - + gamma122*gamma331 + gamma121*gamma332)*gxzL + (-(gamma222*gamma231) + + gamma221*gamma232)*gyyL + (gamma232*gamma321 - gamma231*gamma322 - + gamma222*gamma331 + gamma221*gamma332)*gyzL + (-(gamma322*gamma331) + + gamma321*gamma332)*gzzL + khalf*(PDstandard2nd12gyz - + PDstandard2nd13gyy - PDstandard2nd22gxz + PDstandard2nd23gxy); + + CCTK_REAL R2131 = (gamma121*gamma131 - gamma111*gamma132)*gxxL + + (-(gamma132*gamma211) + gamma131*gamma221 + gamma121*gamma231 - + gamma111*gamma232)*gxyL + (-(gamma132*gamma311) + gamma131*gamma321 + + gamma121*gamma331 - gamma111*gamma332)*gxzL + (gamma221*gamma231 - + gamma211*gamma232)*gyyL + (-(gamma232*gamma311) + gamma231*gamma321 + + gamma221*gamma331 - gamma211*gamma332)*gyzL + (gamma321*gamma331 - + gamma311*gamma332)*gzzL + khalf*(-PDstandard2nd11gyz + + PDstandard2nd12gxz + PDstandard2nd13gxy - PDstandard2nd23gxx); + + CCTK_REAL R2132 = (gamma122*gamma131 - gamma121*gamma132)*gxxL + + (-(gamma132*gamma221) + gamma131*gamma222 + gamma122*gamma231 - + gamma121*gamma232)*gxyL + (-(gamma132*gamma321) + gamma131*gamma322 + + gamma122*gamma331 - gamma121*gamma332)*gxzL + (gamma222*gamma231 - + gamma221*gamma232)*gyyL + (-(gamma232*gamma321) + gamma231*gamma322 + + gamma222*gamma331 - gamma221*gamma332)*gyzL + (gamma322*gamma331 - + gamma321*gamma332)*gzzL + khalf*(-PDstandard2nd12gyz + + PDstandard2nd13gyy + PDstandard2nd22gxz - PDstandard2nd23gxy); + + CCTK_REAL R2133 = 0; + + CCTK_REAL R2211 = 0; + + CCTK_REAL R2212 = 0; + + CCTK_REAL R2213 = 0; + + CCTK_REAL R2221 = 0; + + CCTK_REAL R2222 = 0; + + CCTK_REAL R2223 = 0; + + CCTK_REAL R2231 = 0; + + CCTK_REAL R2232 = 0; + + CCTK_REAL R2233 = 0; + + CCTK_REAL R2311 = 0; + + CCTK_REAL R2312 = (gamma122*gamma131 - gamma121*gamma132)*gxxL + + (-(gamma132*gamma221) + gamma131*gamma222 + gamma122*gamma231 - + gamma121*gamma232)*gxyL + (-(gamma132*gamma321) + gamma131*gamma322 + + gamma122*gamma331 - gamma121*gamma332)*gxzL + (gamma222*gamma231 - + gamma221*gamma232)*gyyL + (-(gamma232*gamma321) + gamma231*gamma322 + + gamma222*gamma331 - gamma221*gamma332)*gyzL + (gamma322*gamma331 - + gamma321*gamma332)*gzzL + khalf*(-PDstandard2nd12gyz + + PDstandard2nd13gyy + PDstandard2nd22gxz - PDstandard2nd23gxy); + + CCTK_REAL R2313 = (gamma131*gamma132 - gamma121*gamma133)*gxxL + + (-(gamma133*gamma221) + gamma132*gamma231 + gamma131*gamma232 - + gamma121*gamma233)*gxyL + (-(gamma133*gamma321) + gamma132*gamma331 + + gamma131*gamma332 - gamma121*gamma333)*gxzL + (gamma231*gamma232 - + gamma221*gamma233)*gyyL + (-(gamma233*gamma321) + gamma232*gamma331 + + gamma231*gamma332 - gamma221*gamma333)*gyzL + (gamma331*gamma332 - + gamma321*gamma333)*gzzL + khalf*(-PDstandard2nd12gzz + + PDstandard2nd13gyz + PDstandard2nd23gxz - PDstandard2nd33gxy); + + CCTK_REAL R2321 = (-(gamma122*gamma131) + gamma121*gamma132)*gxxL + + (gamma132*gamma221 - gamma131*gamma222 - gamma122*gamma231 + + gamma121*gamma232)*gxyL + (gamma132*gamma321 - gamma131*gamma322 - + gamma122*gamma331 + gamma121*gamma332)*gxzL + (-(gamma222*gamma231) + + gamma221*gamma232)*gyyL + (gamma232*gamma321 - gamma231*gamma322 - + gamma222*gamma331 + gamma221*gamma332)*gyzL + (-(gamma322*gamma331) + + gamma321*gamma332)*gzzL + khalf*(PDstandard2nd12gyz - + PDstandard2nd13gyy - PDstandard2nd22gxz + PDstandard2nd23gxy); + + CCTK_REAL R2322 = 0; + + CCTK_REAL R2323 = khalf*((4*gamma132*gamma232 - + 2*gamma122*gamma233)*gxyL + (4*gamma132*gamma332 - + 2*gamma122*gamma333)*gxzL + (4*gamma232*gamma332 - + 2*gamma222*gamma333)*gyzL - 2*(gamma122*gamma133*gxxL + + gamma133*gamma222*gxyL + gamma133*gamma322*gxzL + + gamma222*gamma233*gyyL + gamma233*gamma322*gyzL + + gamma322*gamma333*gzzL) - PDstandard2nd22gzz + 2*PDstandard2nd23gyz - + PDstandard2nd33gyy + 2*gxxL*SQR(gamma132) + 2*gyyL*SQR(gamma232) + + 2*gzzL*SQR(gamma332)); + + CCTK_REAL R2331 = (-(gamma131*gamma132) + gamma121*gamma133)*gxxL + + (gamma133*gamma221 - gamma132*gamma231 - gamma131*gamma232 + + gamma121*gamma233)*gxyL + (gamma133*gamma321 - gamma132*gamma331 - + gamma131*gamma332 + gamma121*gamma333)*gxzL + (-(gamma231*gamma232) + + gamma221*gamma233)*gyyL + (gamma233*gamma321 - gamma232*gamma331 - + gamma231*gamma332 + gamma221*gamma333)*gyzL + (-(gamma331*gamma332) + + gamma321*gamma333)*gzzL + khalf*(PDstandard2nd12gzz - + PDstandard2nd13gyz - PDstandard2nd23gxz + PDstandard2nd33gxy); + + CCTK_REAL R2332 = (-2*gamma132*gamma232 + gamma122*gamma233)*gxyL + + (-2*gamma132*gamma332 + gamma122*gamma333)*gxzL + + gamma133*(gamma122*gxxL + gamma222*gxyL + gamma322*gxzL) + + (-2*gamma232*gamma332 + gamma222*gamma333)*gyzL + + gamma233*(gamma222*gyyL + gamma322*gyzL) - PDstandard2nd23gyz + + khalf*(PDstandard2nd22gzz + PDstandard2nd33gyy) - gxxL*SQR(gamma132) - + gyyL*SQR(gamma232) + gzzL*(gamma322*gamma333 - SQR(gamma332)); + + CCTK_REAL R2333 = 0; + + CCTK_REAL R3111 = 0; + + CCTK_REAL R3112 = (-(gamma121*gamma131) + gamma111*gamma132)*gxxL + + (gamma132*gamma211 - gamma131*gamma221 - gamma121*gamma231 + + gamma111*gamma232)*gxyL + (gamma132*gamma311 - gamma131*gamma321 - + gamma121*gamma331 + gamma111*gamma332)*gxzL + (-(gamma221*gamma231) + + gamma211*gamma232)*gyyL + (gamma232*gamma311 - gamma231*gamma321 - + gamma221*gamma331 + gamma211*gamma332)*gyzL + (-(gamma321*gamma331) + + gamma311*gamma332)*gzzL + khalf*(PDstandard2nd11gyz - + PDstandard2nd12gxz - PDstandard2nd13gxy + PDstandard2nd23gxx); + + CCTK_REAL R3113 = (-2*gamma131*gamma231 + gamma111*gamma233)*gxyL + + (-2*gamma131*gamma331 + gamma111*gamma333)*gxzL + + gamma133*(gamma111*gxxL + gamma211*gxyL + gamma311*gxzL) + + (-2*gamma231*gamma331 + gamma211*gamma333)*gyzL + + gamma233*(gamma211*gyyL + gamma311*gyzL) - PDstandard2nd13gxz + + khalf*(PDstandard2nd11gzz + PDstandard2nd33gxx) - gxxL*SQR(gamma131) - + gyyL*SQR(gamma231) + gzzL*(gamma311*gamma333 - SQR(gamma331)); + + CCTK_REAL R3121 = (gamma121*gamma131 - gamma111*gamma132)*gxxL + + (-(gamma132*gamma211) + gamma131*gamma221 + gamma121*gamma231 - + gamma111*gamma232)*gxyL + (-(gamma132*gamma311) + gamma131*gamma321 + + gamma121*gamma331 - gamma111*gamma332)*gxzL + (gamma221*gamma231 - + gamma211*gamma232)*gyyL + (-(gamma232*gamma311) + gamma231*gamma321 + + gamma221*gamma331 - gamma211*gamma332)*gyzL + (gamma321*gamma331 - + gamma311*gamma332)*gzzL + khalf*(-PDstandard2nd11gyz + + PDstandard2nd12gxz + PDstandard2nd13gxy - PDstandard2nd23gxx); + + CCTK_REAL R3122 = 0; + + CCTK_REAL R3123 = (-(gamma131*gamma132) + gamma121*gamma133)*gxxL + + (gamma133*gamma221 - gamma132*gamma231 - gamma131*gamma232 + + gamma121*gamma233)*gxyL + (gamma133*gamma321 - gamma132*gamma331 - + gamma131*gamma332 + gamma121*gamma333)*gxzL + (-(gamma231*gamma232) + + gamma221*gamma233)*gyyL + (gamma233*gamma321 - gamma232*gamma331 - + gamma231*gamma332 + gamma221*gamma333)*gyzL + (-(gamma331*gamma332) + + gamma321*gamma333)*gzzL + khalf*(PDstandard2nd12gzz - + PDstandard2nd13gyz - PDstandard2nd23gxz + PDstandard2nd33gxy); + + CCTK_REAL R3131 = khalf*((4*gamma131*gamma231 - + 2*gamma111*gamma233)*gxyL + (4*gamma131*gamma331 - + 2*gamma111*gamma333)*gxzL + (4*gamma231*gamma331 - + 2*gamma211*gamma333)*gyzL - 2*(gamma111*gamma133*gxxL + + gamma133*gamma211*gxyL + gamma133*gamma311*gxzL + + gamma211*gamma233*gyyL + gamma233*gamma311*gyzL + + gamma311*gamma333*gzzL) - PDstandard2nd11gzz + 2*PDstandard2nd13gxz - + PDstandard2nd33gxx + 2*gxxL*SQR(gamma131) + 2*gyyL*SQR(gamma231) + + 2*gzzL*SQR(gamma331)); + + CCTK_REAL R3132 = (gamma131*gamma132 - gamma121*gamma133)*gxxL + + (-(gamma133*gamma221) + gamma132*gamma231 + gamma131*gamma232 - + gamma121*gamma233)*gxyL + (-(gamma133*gamma321) + gamma132*gamma331 + + gamma131*gamma332 - gamma121*gamma333)*gxzL + (gamma231*gamma232 - + gamma221*gamma233)*gyyL + (-(gamma233*gamma321) + gamma232*gamma331 + + gamma231*gamma332 - gamma221*gamma333)*gyzL + (gamma331*gamma332 - + gamma321*gamma333)*gzzL + khalf*(-PDstandard2nd12gzz + + PDstandard2nd13gyz + PDstandard2nd23gxz - PDstandard2nd33gxy); + + CCTK_REAL R3133 = 0; + + CCTK_REAL R3211 = 0; + + CCTK_REAL R3212 = (-(gamma122*gamma131) + gamma121*gamma132)*gxxL + + (gamma132*gamma221 - gamma131*gamma222 - gamma122*gamma231 + + gamma121*gamma232)*gxyL + (gamma132*gamma321 - gamma131*gamma322 - + gamma122*gamma331 + gamma121*gamma332)*gxzL + (-(gamma222*gamma231) + + gamma221*gamma232)*gyyL + (gamma232*gamma321 - gamma231*gamma322 - + gamma222*gamma331 + gamma221*gamma332)*gyzL + (-(gamma322*gamma331) + + gamma321*gamma332)*gzzL + khalf*(PDstandard2nd12gyz - + PDstandard2nd13gyy - PDstandard2nd22gxz + PDstandard2nd23gxy); + + CCTK_REAL R3213 = (-(gamma131*gamma132) + gamma121*gamma133)*gxxL + + (gamma133*gamma221 - gamma132*gamma231 - gamma131*gamma232 + + gamma121*gamma233)*gxyL + (gamma133*gamma321 - gamma132*gamma331 - + gamma131*gamma332 + gamma121*gamma333)*gxzL + (-(gamma231*gamma232) + + gamma221*gamma233)*gyyL + (gamma233*gamma321 - gamma232*gamma331 - + gamma231*gamma332 + gamma221*gamma333)*gyzL + (-(gamma331*gamma332) + + gamma321*gamma333)*gzzL + khalf*(PDstandard2nd12gzz - + PDstandard2nd13gyz - PDstandard2nd23gxz + PDstandard2nd33gxy); - R3131 = khalf*((4*gamma131*gamma231 - 2*gamma111*gamma233)*gxyL + (4*gamma131*gamma331 - 2*gamma111*gamma333)*gxzL + - (4*gamma231*gamma331 - 2*gamma211*gamma333)*gyzL - - 2*(gamma111*gamma133*gxxL + gamma133*gamma211*gxyL + gamma133*gamma311*gxzL + gamma211*gamma233*gyyL + - gamma233*gamma311*gyzL + gamma311*gamma333*gzzL) - PDstandard2nd11gzz + 2*PDstandard2nd13gxz - - PDstandard2nd33gxx + 2*gxxL*SQR(gamma131) + 2*gyyL*SQR(gamma231) + 2*gzzL*SQR(gamma331)); + CCTK_REAL R3221 = (gamma122*gamma131 - gamma121*gamma132)*gxxL + + (-(gamma132*gamma221) + gamma131*gamma222 + gamma122*gamma231 - + gamma121*gamma232)*gxyL + (-(gamma132*gamma321) + gamma131*gamma322 + + gamma122*gamma331 - gamma121*gamma332)*gxzL + (gamma222*gamma231 - + gamma221*gamma232)*gyyL + (-(gamma232*gamma321) + gamma231*gamma322 + + gamma222*gamma331 - gamma221*gamma332)*gyzL + (gamma322*gamma331 - + gamma321*gamma332)*gzzL + khalf*(-PDstandard2nd12gyz + + PDstandard2nd13gyy + PDstandard2nd22gxz - PDstandard2nd23gxy); - R3132 = (gamma131*gamma132 - gamma121*gamma133)*gxxL + - (-(gamma133*gamma221) + gamma132*gamma231 + gamma131*gamma232 - gamma121*gamma233)*gxyL + - (-(gamma133*gamma321) + gamma132*gamma331 + gamma131*gamma332 - gamma121*gamma333)*gxzL + - (gamma231*gamma232 - gamma221*gamma233)*gyyL + - (-(gamma233*gamma321) + gamma232*gamma331 + gamma231*gamma332 - gamma221*gamma333)*gyzL + - (gamma331*gamma332 - gamma321*gamma333)*gzzL + - khalf*(-PDstandard2nd12gzz + PDstandard2nd13gyz + PDstandard2nd23gxz - PDstandard2nd33gxy); + CCTK_REAL R3222 = 0; - R3133 = 0; + CCTK_REAL R3223 = (-2*gamma132*gamma232 + gamma122*gamma233)*gxyL + + (-2*gamma132*gamma332 + gamma122*gamma333)*gxzL + + gamma133*(gamma122*gxxL + gamma222*gxyL + gamma322*gxzL) + + (-2*gamma232*gamma332 + gamma222*gamma333)*gyzL + + gamma233*(gamma222*gyyL + gamma322*gyzL) - PDstandard2nd23gyz + + khalf*(PDstandard2nd22gzz + PDstandard2nd33gyy) - gxxL*SQR(gamma132) - + gyyL*SQR(gamma232) + gzzL*(gamma322*gamma333 - SQR(gamma332)); - R3211 = 0; + CCTK_REAL R3231 = (gamma131*gamma132 - gamma121*gamma133)*gxxL + + (-(gamma133*gamma221) + gamma132*gamma231 + gamma131*gamma232 - + gamma121*gamma233)*gxyL + (-(gamma133*gamma321) + gamma132*gamma331 + + gamma131*gamma332 - gamma121*gamma333)*gxzL + (gamma231*gamma232 - + gamma221*gamma233)*gyyL + (-(gamma233*gamma321) + gamma232*gamma331 + + gamma231*gamma332 - gamma221*gamma333)*gyzL + (gamma331*gamma332 - + gamma321*gamma333)*gzzL + khalf*(-PDstandard2nd12gzz + + PDstandard2nd13gyz + PDstandard2nd23gxz - PDstandard2nd33gxy); - R3212 = (-(gamma122*gamma131) + gamma121*gamma132)*gxxL + - (gamma132*gamma221 - gamma131*gamma222 - gamma122*gamma231 + gamma121*gamma232)*gxyL + - (gamma132*gamma321 - gamma131*gamma322 - gamma122*gamma331 + gamma121*gamma332)*gxzL + - (-(gamma222*gamma231) + gamma221*gamma232)*gyyL + - (gamma232*gamma321 - gamma231*gamma322 - gamma222*gamma331 + gamma221*gamma332)*gyzL + - (-(gamma322*gamma331) + gamma321*gamma332)*gzzL + - khalf*(PDstandard2nd12gyz - PDstandard2nd13gyy - PDstandard2nd22gxz + PDstandard2nd23gxy); + CCTK_REAL R3232 = khalf*((4*gamma132*gamma232 - + 2*gamma122*gamma233)*gxyL + (4*gamma132*gamma332 - + 2*gamma122*gamma333)*gxzL + (4*gamma232*gamma332 - + 2*gamma222*gamma333)*gyzL - 2*(gamma122*gamma133*gxxL + + gamma133*gamma222*gxyL + gamma133*gamma322*gxzL + + gamma222*gamma233*gyyL + gamma233*gamma322*gyzL + + gamma322*gamma333*gzzL) - PDstandard2nd22gzz + 2*PDstandard2nd23gyz - + PDstandard2nd33gyy + 2*gxxL*SQR(gamma132) + 2*gyyL*SQR(gamma232) + + 2*gzzL*SQR(gamma332)); - R3213 = (-(gamma131*gamma132) + gamma121*gamma133)*gxxL + - (gamma133*gamma221 - gamma132*gamma231 - gamma131*gamma232 + gamma121*gamma233)*gxyL + - (gamma133*gamma321 - gamma132*gamma331 - gamma131*gamma332 + gamma121*gamma333)*gxzL + - (-(gamma231*gamma232) + gamma221*gamma233)*gyyL + - (gamma233*gamma321 - gamma232*gamma331 - gamma231*gamma332 + gamma221*gamma333)*gyzL + - (-(gamma331*gamma332) + gamma321*gamma333)*gzzL + - khalf*(PDstandard2nd12gzz - PDstandard2nd13gyz - PDstandard2nd23gxz + PDstandard2nd33gxy); + CCTK_REAL R3233 = 0; - R3221 = (gamma122*gamma131 - gamma121*gamma132)*gxxL + - (-(gamma132*gamma221) + gamma131*gamma222 + gamma122*gamma231 - gamma121*gamma232)*gxyL + - (-(gamma132*gamma321) + gamma131*gamma322 + gamma122*gamma331 - gamma121*gamma332)*gxzL + - (gamma222*gamma231 - gamma221*gamma232)*gyyL + - (-(gamma232*gamma321) + gamma231*gamma322 + gamma222*gamma331 - gamma221*gamma332)*gyzL + - (gamma322*gamma331 - gamma321*gamma332)*gzzL + - khalf*(-PDstandard2nd12gyz + PDstandard2nd13gyy + PDstandard2nd22gxz - PDstandard2nd23gxy); + CCTK_REAL R3311 = 0; - R3222 = 0; + CCTK_REAL R3312 = 0; - R3223 = (-2*gamma132*gamma232 + gamma122*gamma233)*gxyL + (-2*gamma132*gamma332 + gamma122*gamma333)*gxzL + - gamma133*(gamma122*gxxL + gamma222*gxyL + gamma322*gxzL) + (-2*gamma232*gamma332 + gamma222*gamma333)*gyzL + - gamma233*(gamma222*gyyL + gamma322*gyzL) - PDstandard2nd23gyz + khalf*(PDstandard2nd22gzz + PDstandard2nd33gyy) - - gxxL*SQR(gamma132) - gyyL*SQR(gamma232) + gzzL*(gamma322*gamma333 - SQR(gamma332)); + CCTK_REAL R3313 = 0; - R3231 = (gamma131*gamma132 - gamma121*gamma133)*gxxL + - (-(gamma133*gamma221) + gamma132*gamma231 + gamma131*gamma232 - gamma121*gamma233)*gxyL + - (-(gamma133*gamma321) + gamma132*gamma331 + gamma131*gamma332 - gamma121*gamma333)*gxzL + - (gamma231*gamma232 - gamma221*gamma233)*gyyL + - (-(gamma233*gamma321) + gamma232*gamma331 + gamma231*gamma332 - gamma221*gamma333)*gyzL + - (gamma331*gamma332 - gamma321*gamma333)*gzzL + - khalf*(-PDstandard2nd12gzz + PDstandard2nd13gyz + PDstandard2nd23gxz - PDstandard2nd33gxy); + CCTK_REAL R3321 = 0; - R3232 = khalf*((4*gamma132*gamma232 - 2*gamma122*gamma233)*gxyL + (4*gamma132*gamma332 - 2*gamma122*gamma333)*gxzL + - (4*gamma232*gamma332 - 2*gamma222*gamma333)*gyzL - - 2*(gamma122*gamma133*gxxL + gamma133*gamma222*gxyL + gamma133*gamma322*gxzL + gamma222*gamma233*gyyL + - gamma233*gamma322*gyzL + gamma322*gamma333*gzzL) - PDstandard2nd22gzz + 2*PDstandard2nd23gyz - - PDstandard2nd33gyy + 2*gxxL*SQR(gamma132) + 2*gyyL*SQR(gamma232) + 2*gzzL*SQR(gamma332)); + CCTK_REAL R3322 = 0; - R3233 = 0; + CCTK_REAL R3323 = 0; - R3311 = 0; + CCTK_REAL R3331 = 0; - R3312 = 0; + CCTK_REAL R3332 = 0; - R3313 = 0; + CCTK_REAL R3333 = 0; - R3321 = 0; + CCTK_REAL R4p1111 = R1111; - R3322 = 0; + CCTK_REAL R4p1112 = R1112; - R3323 = 0; + CCTK_REAL R4p1113 = R1113; - R3331 = 0; + CCTK_REAL R4p1121 = R1121; - R3332 = 0; + CCTK_REAL R4p1122 = R1122; - R3333 = 0; + CCTK_REAL R4p1123 = R1123; - R4p1111 = R1111; + CCTK_REAL R4p1131 = R1131; - R4p1112 = R1112; + CCTK_REAL R4p1132 = R1132; - R4p1113 = R1113; + CCTK_REAL R4p1133 = R1133; - R4p1121 = R1121; + CCTK_REAL R4p1211 = R1211; - R4p1122 = R1122; + CCTK_REAL R4p1212 = kxxL*kyyL + R1212 - SQR(kxyL); - R4p1123 = R1123; + CCTK_REAL R4p1213 = -(kxyL*kxzL) + kxxL*kyzL + R1213; - R4p1131 = R1131; + CCTK_REAL R4p1221 = -(kxxL*kyyL) + R1221 + SQR(kxyL); - R4p1132 = R1132; + CCTK_REAL R4p1222 = R1222; - R4p1133 = R1133; + CCTK_REAL R4p1223 = -(kxzL*kyyL) + kxyL*kyzL + R1223; - R4p1211 = R1211; + CCTK_REAL R4p1231 = kxyL*kxzL - kxxL*kyzL + R1231; - R4p1212 = kxxL*kyyL + R1212 - SQR(kxyL); + CCTK_REAL R4p1232 = kxzL*kyyL - kxyL*kyzL + R1232; - R4p1213 = -(kxyL*kxzL) + kxxL*kyzL + R1213; + CCTK_REAL R4p1233 = R1233; - R4p1221 = -(kxxL*kyyL) + R1221 + SQR(kxyL); + CCTK_REAL R4p1311 = R1311; - R4p1222 = R1222; + CCTK_REAL R4p1312 = -(kxyL*kxzL) + kxxL*kyzL + R1312; - R4p1223 = -(kxzL*kyyL) + kxyL*kyzL + R1223; + CCTK_REAL R4p1313 = kxxL*kzzL + R1313 - SQR(kxzL); - R4p1231 = kxyL*kxzL - kxxL*kyzL + R1231; + CCTK_REAL R4p1321 = kxyL*kxzL - kxxL*kyzL + R1321; - R4p1232 = kxzL*kyyL - kxyL*kyzL + R1232; + CCTK_REAL R4p1322 = R1322; - R4p1233 = R1233; + CCTK_REAL R4p1323 = -(kxzL*kyzL) + kxyL*kzzL + R1323; - R4p1311 = R1311; + CCTK_REAL R4p1331 = -(kxxL*kzzL) + R1331 + SQR(kxzL); - R4p1312 = -(kxyL*kxzL) + kxxL*kyzL + R1312; + CCTK_REAL R4p1332 = kxzL*kyzL - kxyL*kzzL + R1332; - R4p1313 = kxxL*kzzL + R1313 - SQR(kxzL); + CCTK_REAL R4p1333 = R1333; - R4p1321 = kxyL*kxzL - kxxL*kyzL + R1321; + CCTK_REAL R4p2111 = R2111; - R4p1322 = R1322; + CCTK_REAL R4p2112 = -(kxxL*kyyL) + R2112 + SQR(kxyL); - R4p1323 = -(kxzL*kyzL) + kxyL*kzzL + R1323; + CCTK_REAL R4p2113 = kxyL*kxzL - kxxL*kyzL + R2113; - R4p1331 = -(kxxL*kzzL) + R1331 + SQR(kxzL); + CCTK_REAL R4p2121 = kxxL*kyyL + R2121 - SQR(kxyL); - R4p1332 = kxzL*kyzL - kxyL*kzzL + R1332; + CCTK_REAL R4p2122 = R2122; - R4p1333 = R1333; + CCTK_REAL R4p2123 = kxzL*kyyL - kxyL*kyzL + R2123; - R4p2111 = R2111; + CCTK_REAL R4p2131 = -(kxyL*kxzL) + kxxL*kyzL + R2131; - R4p2112 = -(kxxL*kyyL) + R2112 + SQR(kxyL); + CCTK_REAL R4p2132 = -(kxzL*kyyL) + kxyL*kyzL + R2132; - R4p2113 = kxyL*kxzL - kxxL*kyzL + R2113; + CCTK_REAL R4p2133 = R2133; - R4p2121 = kxxL*kyyL + R2121 - SQR(kxyL); + CCTK_REAL R4p2211 = R2211; - R4p2122 = R2122; + CCTK_REAL R4p2212 = R2212; - R4p2123 = kxzL*kyyL - kxyL*kyzL + R2123; + CCTK_REAL R4p2213 = R2213; - R4p2131 = -(kxyL*kxzL) + kxxL*kyzL + R2131; + CCTK_REAL R4p2221 = R2221; - R4p2132 = -(kxzL*kyyL) + kxyL*kyzL + R2132; + CCTK_REAL R4p2222 = R2222; - R4p2133 = R2133; + CCTK_REAL R4p2223 = R2223; - R4p2211 = R2211; + CCTK_REAL R4p2231 = R2231; - R4p2212 = R2212; + CCTK_REAL R4p2232 = R2232; - R4p2213 = R2213; + CCTK_REAL R4p2233 = R2233; - R4p2221 = R2221; + CCTK_REAL R4p2311 = R2311; - R4p2222 = R2222; + CCTK_REAL R4p2312 = -(kxzL*kyyL) + kxyL*kyzL + R2312; - R4p2223 = R2223; + CCTK_REAL R4p2313 = -(kxzL*kyzL) + kxyL*kzzL + R2313; - R4p2231 = R2231; + CCTK_REAL R4p2321 = kxzL*kyyL - kxyL*kyzL + R2321; - R4p2232 = R2232; + CCTK_REAL R4p2322 = R2322; - R4p2233 = R2233; + CCTK_REAL R4p2323 = kyyL*kzzL + R2323 - SQR(kyzL); - R4p2311 = R2311; + CCTK_REAL R4p2331 = kxzL*kyzL - kxyL*kzzL + R2331; - R4p2312 = -(kxzL*kyyL) + kxyL*kyzL + R2312; + CCTK_REAL R4p2332 = -(kyyL*kzzL) + R2332 + SQR(kyzL); - R4p2313 = -(kxzL*kyzL) + kxyL*kzzL + R2313; + CCTK_REAL R4p2333 = R2333; - R4p2321 = kxzL*kyyL - kxyL*kyzL + R2321; + CCTK_REAL R4p3111 = R3111; - R4p2322 = R2322; + CCTK_REAL R4p3112 = kxyL*kxzL - kxxL*kyzL + R3112; - R4p2323 = kyyL*kzzL + R2323 - SQR(kyzL); + CCTK_REAL R4p3113 = -(kxxL*kzzL) + R3113 + SQR(kxzL); - R4p2331 = kxzL*kyzL - kxyL*kzzL + R2331; + CCTK_REAL R4p3121 = -(kxyL*kxzL) + kxxL*kyzL + R3121; - R4p2332 = -(kyyL*kzzL) + R2332 + SQR(kyzL); + CCTK_REAL R4p3122 = R3122; - R4p2333 = R2333; + CCTK_REAL R4p3123 = kxzL*kyzL - kxyL*kzzL + R3123; - R4p3111 = R3111; + CCTK_REAL R4p3131 = kxxL*kzzL + R3131 - SQR(kxzL); - R4p3112 = kxyL*kxzL - kxxL*kyzL + R3112; + CCTK_REAL R4p3132 = -(kxzL*kyzL) + kxyL*kzzL + R3132; - R4p3113 = -(kxxL*kzzL) + R3113 + SQR(kxzL); + CCTK_REAL R4p3133 = R3133; - R4p3121 = -(kxyL*kxzL) + kxxL*kyzL + R3121; + CCTK_REAL R4p3211 = R3211; - R4p3122 = R3122; + CCTK_REAL R4p3212 = kxzL*kyyL - kxyL*kyzL + R3212; - R4p3123 = kxzL*kyzL - kxyL*kzzL + R3123; + CCTK_REAL R4p3213 = kxzL*kyzL - kxyL*kzzL + R3213; - R4p3131 = kxxL*kzzL + R3131 - SQR(kxzL); + CCTK_REAL R4p3221 = -(kxzL*kyyL) + kxyL*kyzL + R3221; - R4p3132 = -(kxzL*kyzL) + kxyL*kzzL + R3132; + CCTK_REAL R4p3222 = R3222; - R4p3133 = R3133; + CCTK_REAL R4p3223 = -(kyyL*kzzL) + R3223 + SQR(kyzL); - R4p3211 = R3211; + CCTK_REAL R4p3231 = -(kxzL*kyzL) + kxyL*kzzL + R3231; - R4p3212 = kxzL*kyyL - kxyL*kyzL + R3212; + CCTK_REAL R4p3232 = kyyL*kzzL + R3232 - SQR(kyzL); - R4p3213 = kxzL*kyzL - kxyL*kzzL + R3213; + CCTK_REAL R4p3233 = R3233; - R4p3221 = -(kxzL*kyyL) + kxyL*kyzL + R3221; + CCTK_REAL R4p3311 = R3311; - R4p3222 = R3222; + CCTK_REAL R4p3312 = R3312; - R4p3223 = -(kyyL*kzzL) + R3223 + SQR(kyzL); + CCTK_REAL R4p3313 = R3313; - R4p3231 = -(kxzL*kyzL) + kxyL*kzzL + R3231; + CCTK_REAL R4p3321 = R3321; - R4p3232 = kyyL*kzzL + R3232 - SQR(kyzL); + CCTK_REAL R4p3322 = R3322; - R4p3233 = R3233; + CCTK_REAL R4p3323 = R3323; - R4p3311 = R3311; + CCTK_REAL R4p3331 = R3331; - R4p3312 = R3312; + CCTK_REAL R4p3332 = R3332; - R4p3313 = R3313; + CCTK_REAL R4p3333 = R3333; - R4p3321 = R3321; + CCTK_REAL Ro111 = 0; - R4p3322 = R3322; + CCTK_REAL Ro112 = gamma121*kxxL + (-gamma111 + gamma221)*kxyL + + gamma321*kxzL - gamma211*kyyL - gamma311*kyzL + PDstandard2nd1kxy - + PDstandard2nd2kxx; - R4p3323 = R3323; + CCTK_REAL Ro113 = gamma131*kxxL + gamma231*kxyL + (-gamma111 + + gamma331)*kxzL - gamma211*kyzL - gamma311*kzzL + PDstandard2nd1kxz - + PDstandard2nd3kxx; - R4p3331 = R3331; + CCTK_REAL Ro121 = -(gamma121*kxxL) + gamma111*kxyL - gamma221*kxyL - + gamma321*kxzL + gamma211*kyyL + gamma311*kyzL - PDstandard2nd1kxy + + PDstandard2nd2kxx; - R4p3332 = R3332; + CCTK_REAL Ro122 = 0; - R4p3333 = R3333; + CCTK_REAL Ro123 = gamma131*kxyL - gamma121*kxzL + gamma231*kyyL - + gamma221*kyzL + gamma331*kyzL - gamma321*kzzL + PDstandard2nd2kxz - + PDstandard2nd3kxy; - Ro111 = 0; + CCTK_REAL Ro131 = -(gamma131*kxxL) - gamma231*kxyL + gamma111*kxzL - + gamma331*kxzL + gamma211*kyzL + gamma311*kzzL - PDstandard2nd1kxz + + PDstandard2nd3kxx; - Ro112 = gamma121*kxxL + (-gamma111 + gamma221)*kxyL + gamma321*kxzL - gamma211*kyyL - gamma311*kyzL + - PDstandard2nd1kxy - PDstandard2nd2kxx; + CCTK_REAL Ro132 = -(gamma131*kxyL) + gamma121*kxzL - gamma231*kyyL + + gamma221*kyzL - gamma331*kyzL + gamma321*kzzL - PDstandard2nd2kxz + + PDstandard2nd3kxy; - Ro113 = gamma131*kxxL + gamma231*kxyL + (-gamma111 + gamma331)*kxzL - gamma211*kyzL - gamma311*kzzL + - PDstandard2nd1kxz - PDstandard2nd3kxx; + CCTK_REAL Ro133 = 0; - Ro121 = -(gamma121*kxxL) + gamma111*kxyL - gamma221*kxyL - gamma321*kxzL + gamma211*kyyL + gamma311*kyzL - - PDstandard2nd1kxy + PDstandard2nd2kxx; + CCTK_REAL Ro211 = 0; - Ro122 = 0; + CCTK_REAL Ro212 = gamma122*kxxL + (-gamma121 + gamma222)*kxyL + + gamma322*kxzL - gamma221*kyyL - gamma321*kyzL + PDstandard2nd1kyy - + PDstandard2nd2kxy; - Ro123 = gamma131*kxyL - gamma121*kxzL + gamma231*kyyL - gamma221*kyzL + gamma331*kyzL - gamma321*kzzL + - PDstandard2nd2kxz - PDstandard2nd3kxy; + CCTK_REAL Ro213 = gamma132*kxxL + gamma232*kxyL + (-gamma121 + + gamma332)*kxzL - gamma221*kyzL - gamma321*kzzL + PDstandard2nd1kyz - + PDstandard2nd3kxy; - Ro131 = -(gamma131*kxxL) - gamma231*kxyL + gamma111*kxzL - gamma331*kxzL + gamma211*kyzL + gamma311*kzzL - - PDstandard2nd1kxz + PDstandard2nd3kxx; + CCTK_REAL Ro221 = -(gamma122*kxxL) + gamma121*kxyL - gamma222*kxyL - + gamma322*kxzL + gamma221*kyyL + gamma321*kyzL - PDstandard2nd1kyy + + PDstandard2nd2kxy; - Ro132 = -(gamma131*kxyL) + gamma121*kxzL - gamma231*kyyL + gamma221*kyzL - gamma331*kyzL + gamma321*kzzL - - PDstandard2nd2kxz + PDstandard2nd3kxy; + CCTK_REAL Ro222 = 0; - Ro133 = 0; + CCTK_REAL Ro223 = gamma132*kxyL - gamma122*kxzL + gamma232*kyyL - + gamma222*kyzL + gamma332*kyzL - gamma322*kzzL + PDstandard2nd2kyz - + PDstandard2nd3kyy; - Ro211 = 0; + CCTK_REAL Ro231 = -(gamma132*kxxL) - gamma232*kxyL + gamma121*kxzL - + gamma332*kxzL + gamma221*kyzL + gamma321*kzzL - PDstandard2nd1kyz + + PDstandard2nd3kxy; - Ro212 = gamma122*kxxL + (-gamma121 + gamma222)*kxyL + gamma322*kxzL - gamma221*kyyL - gamma321*kyzL + - PDstandard2nd1kyy - PDstandard2nd2kxy; + CCTK_REAL Ro232 = -(gamma132*kxyL) + gamma122*kxzL - gamma232*kyyL + + gamma222*kyzL - gamma332*kyzL + gamma322*kzzL - PDstandard2nd2kyz + + PDstandard2nd3kyy; - Ro213 = gamma132*kxxL + gamma232*kxyL + (-gamma121 + gamma332)*kxzL - gamma221*kyzL - gamma321*kzzL + - PDstandard2nd1kyz - PDstandard2nd3kxy; + CCTK_REAL Ro233 = 0; - Ro221 = -(gamma122*kxxL) + gamma121*kxyL - gamma222*kxyL - gamma322*kxzL + gamma221*kyyL + gamma321*kyzL - - PDstandard2nd1kyy + PDstandard2nd2kxy; + CCTK_REAL Ro311 = 0; - Ro222 = 0; + CCTK_REAL Ro312 = gamma132*kxxL + (-gamma131 + gamma232)*kxyL + + gamma332*kxzL - gamma231*kyyL - gamma331*kyzL + PDstandard2nd1kyz - + PDstandard2nd2kxz; - Ro223 = gamma132*kxyL - gamma122*kxzL + gamma232*kyyL - gamma222*kyzL + gamma332*kyzL - gamma322*kzzL + - PDstandard2nd2kyz - PDstandard2nd3kyy; + CCTK_REAL Ro313 = gamma133*kxxL + gamma233*kxyL + (-gamma131 + + gamma333)*kxzL - gamma231*kyzL - gamma331*kzzL + PDstandard2nd1kzz - + PDstandard2nd3kxz; - Ro231 = -(gamma132*kxxL) - gamma232*kxyL + gamma121*kxzL - gamma332*kxzL + gamma221*kyzL + gamma321*kzzL - - PDstandard2nd1kyz + PDstandard2nd3kxy; + CCTK_REAL Ro321 = -(gamma132*kxxL) + gamma131*kxyL - gamma232*kxyL - + gamma332*kxzL + gamma231*kyyL + gamma331*kyzL - PDstandard2nd1kyz + + PDstandard2nd2kxz; - Ro232 = -(gamma132*kxyL) + gamma122*kxzL - gamma232*kyyL + gamma222*kyzL - gamma332*kyzL + gamma322*kzzL - - PDstandard2nd2kyz + PDstandard2nd3kyy; - - Ro233 = 0; - - Ro311 = 0; - - Ro312 = gamma132*kxxL + (-gamma131 + gamma232)*kxyL + gamma332*kxzL - gamma231*kyyL - gamma331*kyzL + - PDstandard2nd1kyz - PDstandard2nd2kxz; - - Ro313 = gamma133*kxxL + gamma233*kxyL + (-gamma131 + gamma333)*kxzL - gamma231*kyzL - gamma331*kzzL + - PDstandard2nd1kzz - PDstandard2nd3kxz; - - Ro321 = -(gamma132*kxxL) + gamma131*kxyL - gamma232*kxyL - gamma332*kxzL + gamma231*kyyL + gamma331*kyzL - - PDstandard2nd1kyz + PDstandard2nd2kxz; - - Ro322 = 0; - - Ro323 = gamma133*kxyL - gamma132*kxzL + gamma233*kyyL - gamma232*kyzL + gamma333*kyzL - gamma332*kzzL + - PDstandard2nd2kzz - PDstandard2nd3kyz; - - Ro331 = -(gamma133*kxxL) - gamma233*kxyL + gamma131*kxzL - gamma333*kxzL + gamma231*kyzL + gamma331*kzzL - - PDstandard2nd1kzz + PDstandard2nd3kxz; - - Ro332 = -(gamma133*kxyL) + gamma132*kxzL - gamma233*kyyL + gamma232*kyzL - gamma333*kyzL + gamma332*kzzL - - PDstandard2nd2kzz + PDstandard2nd3kyz; - - Ro333 = 0; - - Rojo11 = gInv11*R1111 + gInv12*R1112 + gInv13*R1113 + gInv21*R1211 + gInv23*(-(kxyL*kxzL) + kxxL*kyzL + R1213) + - gInv31*R1311 + gInv32*(-(kxyL*kxzL) + kxxL*kyzL + R1312) + gInv22*(kxxL*kyyL + R1212 - SQR(kxyL)) + - gInv33*(kxxL*kzzL + R1313 - SQR(kxzL)); - - Rojo12 = gInv11*R1121 + gInv13*(kxyL*kxzL - kxxL*kyzL + R1123) + gInv21*R1221 + gInv22*R1222 + gInv23*R1223 + - gInv31*R1321 + gInv32*(-(kxzL*kyyL) + kxyL*kyzL + R1322) + gInv33*(-(kxzL*kyzL) + kxyL*kzzL + R1323) + - gInv12*(-(kxxL*kyyL) + R1122 + SQR(kxyL)); - - Rojo13 = gInv11*R1131 + gInv12*(kxyL*kxzL - kxxL*kyzL + R1132) + gInv21*R1231 + - gInv22*(kxzL*kyyL - kxyL*kyzL + R1232) + gInv23*(kxzL*kyzL - kxyL*kzzL + R1233) + gInv31*R1331 + gInv32*R1332 + - gInv33*R1333 + gInv13*(-(kxxL*kzzL) + R1133 + SQR(kxzL)); - - Rojo21 = gInv11*R2111 + gInv12*R2112 + gInv13*R2113 + gInv22*R2212 + gInv23*(-(kxzL*kyyL) + kxyL*kyzL + R2213) + - gInv31*(kxyL*kxzL - kxxL*kyzL + R2311) + gInv32*R2312 + gInv33*(-(kxzL*kyzL) + kxyL*kzzL + R2313) + - gInv21*(-(kxxL*kyyL) + R2211 + SQR(kxyL)); - - Rojo22 = gInv12*R2122 + gInv13*(kxzL*kyyL - kxyL*kyzL + R2123) + gInv21*R2221 + gInv22*R2222 + gInv23*R2223 + - gInv31*(kxzL*kyyL - kxyL*kyzL + R2321) + gInv32*R2322 + gInv11*(kxxL*kyyL + R2121 - SQR(kxyL)) + - gInv33*(kyyL*kzzL + R2323 - SQR(kyzL)); - - Rojo23 = gInv11*(-(kxyL*kxzL) + kxxL*kyzL + R2131) + gInv12*R2132 + gInv13*(kxzL*kyzL - kxyL*kzzL + R2133) + - gInv21*(-(kxzL*kyyL) + kxyL*kyzL + R2231) + gInv22*R2232 + gInv31*R2331 + gInv32*R2332 + gInv33*R2333 + - gInv23*(-(kyyL*kzzL) + R2233 + SQR(kyzL)); - - Rojo31 = gInv11*R3111 + gInv12*R3112 + gInv13*R3113 + gInv21*(kxyL*kxzL - kxxL*kyzL + R3211) + - gInv22*(kxzL*kyyL - kxyL*kyzL + R3212) + gInv23*R3213 + gInv32*(kxzL*kyzL - kxyL*kzzL + R3312) + gInv33*R3313 + - gInv31*(-(kxxL*kzzL) + R3311 + SQR(kxzL)); - - Rojo32 = gInv11*(-(kxyL*kxzL) + kxxL*kyzL + R3121) + gInv12*(-(kxzL*kyyL) + kxyL*kyzL + R3122) + gInv13*R3123 + - gInv21*R3221 + gInv22*R3222 + gInv23*R3223 + gInv31*(kxzL*kyzL - kxyL*kzzL + R3321) + gInv33*R3323 + - gInv32*(-(kyyL*kzzL) + R3322 + SQR(kyzL)); - - Rojo33 = gInv12*(-(kxzL*kyzL) + kxyL*kzzL + R3132) + gInv13*R3133 + gInv21*(-(kxzL*kyzL) + kxyL*kzzL + R3231) + - gInv23*R3233 + gInv31*R3331 + gInv32*R3332 + gInv33*R3333 + gInv11*(kxxL*kzzL + R3131 - SQR(kxzL)) + - gInv22*(kyyL*kzzL + R3232 - SQR(kyzL)); - - Psi4rL = n1*(-(imbar1*(imbar2*(n1*(R4p1112 + R4p1211) + n2*(R4p1122 + R4p1221) + n3*(R4p1132 + R4p1231)) + - imbar3*(n1*(R4p1113 + R4p1311) + n2*(R4p1123 + R4p1321) + n3*(R4p1133 + R4p1331)))) - - imbar2*imbar3*(n1*(R4p1213 + R4p1312) + n2*(R4p1223 + R4p1322) + n3*(R4p1233 + R4p1332)) + - n1*R4p1112*rmbar1*rmbar2 + n2*R4p1122*rmbar1*rmbar2 + n3*R4p1132*rmbar1*rmbar2 + n1*R4p1211*rmbar1*rmbar2 + - n2*R4p1221*rmbar1*rmbar2 + n3*R4p1231*rmbar1*rmbar2 + n1*R4p1113*rmbar1*rmbar3 + n2*R4p1123*rmbar1*rmbar3 + - n3*R4p1133*rmbar1*rmbar3 + n1*R4p1311*rmbar1*rmbar3 + n2*R4p1321*rmbar1*rmbar3 + n3*R4p1331*rmbar1*rmbar3 + - n1*R4p1213*rmbar2*rmbar3 + n2*R4p1223*rmbar2*rmbar3 + n3*R4p1233*rmbar2*rmbar3 + n1*R4p1312*rmbar2*rmbar3 + - n2*R4p1322*rmbar2*rmbar3 + n3*R4p1332*rmbar2*rmbar3 - (n1*R4p1111 + n2*R4p1121 + n3*R4p1131)*SQR(imbar1) - - (n1*R4p1212 + n2*R4p1222 + n3*R4p1232)*SQR(imbar2) - n1*R4p1313*SQR(imbar3) - n2*R4p1323*SQR(imbar3) - - n3*R4p1333*SQR(imbar3) + n1*R4p1111*SQR(rmbar1) + n2*R4p1121*SQR(rmbar1) + n3*R4p1131*SQR(rmbar1) + - n1*R4p1212*SQR(rmbar2) + n2*R4p1222*SQR(rmbar2) + n3*R4p1232*SQR(rmbar2) + n1*R4p1313*SQR(rmbar3) + - n2*R4p1323*SQR(rmbar3) + n3*R4p1333*SQR(rmbar3)) + - n2*(-(imbar1*(imbar2*(n1*(R4p2112 + R4p2211) + n2*(R4p2122 + R4p2221) + n3*(R4p2132 + R4p2231)) + - imbar3*(n1*(R4p2113 + R4p2311) + n2*(R4p2123 + R4p2321) + n3*(R4p2133 + R4p2331)))) - - imbar2*imbar3*(n1*(R4p2213 + R4p2312) + n2*(R4p2223 + R4p2322) + n3*(R4p2233 + R4p2332)) + - n1*R4p2112*rmbar1*rmbar2 + n2*R4p2122*rmbar1*rmbar2 + n3*R4p2132*rmbar1*rmbar2 + n1*R4p2211*rmbar1*rmbar2 + - n2*R4p2221*rmbar1*rmbar2 + n3*R4p2231*rmbar1*rmbar2 + n1*R4p2113*rmbar1*rmbar3 + n2*R4p2123*rmbar1*rmbar3 + - n3*R4p2133*rmbar1*rmbar3 + n1*R4p2311*rmbar1*rmbar3 + n2*R4p2321*rmbar1*rmbar3 + n3*R4p2331*rmbar1*rmbar3 + - n1*R4p2213*rmbar2*rmbar3 + n2*R4p2223*rmbar2*rmbar3 + n3*R4p2233*rmbar2*rmbar3 + n1*R4p2312*rmbar2*rmbar3 + - n2*R4p2322*rmbar2*rmbar3 + n3*R4p2332*rmbar2*rmbar3 - (n1*R4p2111 + n2*R4p2121 + n3*R4p2131)*SQR(imbar1) - - (n1*R4p2212 + n2*R4p2222 + n3*R4p2232)*SQR(imbar2) - n1*R4p2313*SQR(imbar3) - n2*R4p2323*SQR(imbar3) - - n3*R4p2333*SQR(imbar3) + n1*R4p2111*SQR(rmbar1) + n2*R4p2121*SQR(rmbar1) + n3*R4p2131*SQR(rmbar1) + - n1*R4p2212*SQR(rmbar2) + n2*R4p2222*SQR(rmbar2) + n3*R4p2232*SQR(rmbar2) + n1*R4p2313*SQR(rmbar3) + - n2*R4p2323*SQR(rmbar3) + n3*R4p2333*SQR(rmbar3)) + - n3*(-(imbar1*(imbar2*(n1*(R4p3112 + R4p3211) + n2*(R4p3122 + R4p3221) + n3*(R4p3132 + R4p3231)) + - imbar3*(n1*(R4p3113 + R4p3311) + n2*(R4p3123 + R4p3321) + n3*(R4p3133 + R4p3331)))) - - imbar2*imbar3*(n1*(R4p3213 + R4p3312) + n2*(R4p3223 + R4p3322) + n3*(R4p3233 + R4p3332)) + - n1*R4p3112*rmbar1*rmbar2 + n2*R4p3122*rmbar1*rmbar2 + n3*R4p3132*rmbar1*rmbar2 + n1*R4p3211*rmbar1*rmbar2 + - n2*R4p3221*rmbar1*rmbar2 + n3*R4p3231*rmbar1*rmbar2 + n1*R4p3113*rmbar1*rmbar3 + n2*R4p3123*rmbar1*rmbar3 + - n3*R4p3133*rmbar1*rmbar3 + n1*R4p3311*rmbar1*rmbar3 + n2*R4p3321*rmbar1*rmbar3 + n3*R4p3331*rmbar1*rmbar3 + - n1*R4p3213*rmbar2*rmbar3 + n2*R4p3223*rmbar2*rmbar3 + n3*R4p3233*rmbar2*rmbar3 + n1*R4p3312*rmbar2*rmbar3 + - n2*R4p3322*rmbar2*rmbar3 + n3*R4p3332*rmbar2*rmbar3 - (n1*R4p3111 + n2*R4p3121 + n3*R4p3131)*SQR(imbar1) - - (n1*R4p3212 + n2*R4p3222 + n3*R4p3232)*SQR(imbar2) - n1*R4p3313*SQR(imbar3) - n2*R4p3323*SQR(imbar3) - - n3*R4p3333*SQR(imbar3) + n1*R4p3111*SQR(rmbar1) + n2*R4p3121*SQR(rmbar1) + n3*R4p3131*SQR(rmbar1) + - n1*R4p3212*SQR(rmbar2) + n2*R4p3222*SQR(rmbar2) + n3*R4p3232*SQR(rmbar2) + n1*R4p3313*SQR(rmbar3) + - n2*R4p3323*SQR(rmbar3) + n3*R4p3333*SQR(rmbar3)) - - SQR(nn)*((imbar2*imbar3 - rmbar2*rmbar3)*Rojo23 + imbar1*(imbar2*(Rojo12 + Rojo21) + imbar3*(Rojo13 + Rojo31)) - - rmbar1*(rmbar2*(Rojo12 + Rojo21) + rmbar3*(Rojo13 + Rojo31)) + imbar2*imbar3*Rojo32 - rmbar2*rmbar3*Rojo32 + - Rojo11*SQR(imbar1) + Rojo22*SQR(imbar2) + Rojo33*SQR(imbar3) - Rojo11*SQR(rmbar1) - Rojo22*SQR(rmbar2) - - Rojo33*SQR(rmbar3)) + 2*nn*(-(n1*(imbar2*imbar3*Ro213 - rmbar2*rmbar3*Ro213 + - imbar1*(imbar2*(Ro112 + Ro211) + imbar3*(Ro113 + Ro311)) - - rmbar1*(rmbar2*(Ro112 + Ro211) + rmbar3*(Ro113 + Ro311)) + imbar2*imbar3*Ro312 - rmbar2*rmbar3*Ro312 + - Ro111*SQR(imbar1) + Ro212*SQR(imbar2) + Ro313*SQR(imbar3) - Ro111*SQR(rmbar1) - Ro212*SQR(rmbar2) - - Ro313*SQR(rmbar3))) - n2*(imbar2*imbar3*Ro223 - rmbar2*rmbar3*Ro223 + - imbar1*(imbar2*(Ro122 + Ro221) + imbar3*(Ro123 + Ro321)) - - rmbar1*(rmbar2*(Ro122 + Ro221) + rmbar3*(Ro123 + Ro321)) + imbar2*imbar3*Ro322 - rmbar2*rmbar3*Ro322 + - Ro121*SQR(imbar1) + Ro222*SQR(imbar2) + Ro323*SQR(imbar3) - Ro121*SQR(rmbar1) - Ro222*SQR(rmbar2) - - Ro323*SQR(rmbar3)) - n3*(imbar2*imbar3*Ro233 - rmbar2*rmbar3*Ro233 + - imbar1*(imbar2*(Ro132 + Ro231) + imbar3*(Ro133 + Ro331)) - - rmbar1*(rmbar2*(Ro132 + Ro231) + rmbar3*(Ro133 + Ro331)) + imbar2*imbar3*Ro332 - rmbar2*rmbar3*Ro332 + - Ro131*SQR(imbar1) + Ro232*SQR(imbar2) + Ro333*SQR(imbar3) - Ro131*SQR(rmbar1) - Ro232*SQR(rmbar2) - - Ro333*SQR(rmbar3))); - - Psi4iL = -(n1*(im1*(n1*(2*R4p1111*rm1 + R4p1112*rm2 + R4p1211*rm2 + R4p1113*rm3 + R4p1311*rm3) + - n2*(2*R4p1121*rm1 + R4p1122*rm2 + R4p1221*rm2 + R4p1123*rm3 + R4p1321*rm3) + - n3*(2*R4p1131*rm1 + R4p1132*rm2 + R4p1231*rm2 + R4p1133*rm3 + R4p1331*rm3)) + - im2*(n1*(R4p1112*rm1 + R4p1211*rm1 + 2*R4p1212*rm2 + R4p1213*rm3 + R4p1312*rm3) + - n2*(R4p1122*rm1 + R4p1221*rm1 + 2*R4p1222*rm2 + R4p1223*rm3 + R4p1322*rm3) + - n3*(R4p1132*rm1 + R4p1231*rm1 + 2*R4p1232*rm2 + R4p1233*rm3 + R4p1332*rm3)) + - im3*(n1*(R4p1113*rm1 + R4p1311*rm1 + R4p1213*rm2 + R4p1312*rm2 + 2*R4p1313*rm3) + - n2*(R4p1123*rm1 + R4p1321*rm1 + R4p1223*rm2 + R4p1322*rm2 + 2*R4p1323*rm3) + - n3*(R4p1133*rm1 + R4p1331*rm1 + R4p1233*rm2 + R4p1332*rm2 + 2*R4p1333*rm3)))) - - n2*(im1*(n1*(2*R4p2111*rm1 + R4p2112*rm2 + R4p2211*rm2 + R4p2113*rm3 + R4p2311*rm3) + - n2*(2*R4p2121*rm1 + R4p2122*rm2 + R4p2221*rm2 + R4p2123*rm3 + R4p2321*rm3) + - n3*(2*R4p2131*rm1 + R4p2132*rm2 + R4p2231*rm2 + R4p2133*rm3 + R4p2331*rm3)) + - im2*(n1*(R4p2112*rm1 + R4p2211*rm1 + 2*R4p2212*rm2 + R4p2213*rm3 + R4p2312*rm3) + - n2*(R4p2122*rm1 + R4p2221*rm1 + 2*R4p2222*rm2 + R4p2223*rm3 + R4p2322*rm3) + - n3*(R4p2132*rm1 + R4p2231*rm1 + 2*R4p2232*rm2 + R4p2233*rm3 + R4p2332*rm3)) + - im3*(n1*(R4p2113*rm1 + R4p2311*rm1 + R4p2213*rm2 + R4p2312*rm2 + 2*R4p2313*rm3) + - n2*(R4p2123*rm1 + R4p2321*rm1 + R4p2223*rm2 + R4p2322*rm2 + 2*R4p2323*rm3) + - n3*(R4p2133*rm1 + R4p2331*rm1 + R4p2233*rm2 + R4p2332*rm2 + 2*R4p2333*rm3))) - - n3*(im1*(n1*(2*R4p3111*rm1 + R4p3112*rm2 + R4p3211*rm2 + R4p3113*rm3 + R4p3311*rm3) + - n2*(2*R4p3121*rm1 + R4p3122*rm2 + R4p3221*rm2 + R4p3123*rm3 + R4p3321*rm3) + - n3*(2*R4p3131*rm1 + R4p3132*rm2 + R4p3231*rm2 + R4p3133*rm3 + R4p3331*rm3)) + - im2*(n1*(R4p3112*rm1 + R4p3211*rm1 + 2*R4p3212*rm2 + R4p3213*rm3 + R4p3312*rm3) + - n2*(R4p3122*rm1 + R4p3221*rm1 + 2*R4p3222*rm2 + R4p3223*rm3 + R4p3322*rm3) + - n3*(R4p3132*rm1 + R4p3231*rm1 + 2*R4p3232*rm2 + R4p3233*rm3 + R4p3332*rm3)) + - im3*(n1*(R4p3113*rm1 + R4p3311*rm1 + R4p3213*rm2 + R4p3312*rm2 + 2*R4p3313*rm3) + - n2*(R4p3123*rm1 + R4p3321*rm1 + R4p3223*rm2 + R4p3322*rm2 + 2*R4p3323*rm3) + - n3*(R4p3133*rm1 + R4p3331*rm1 + R4p3233*rm2 + R4p3332*rm2 + 2*R4p3333*rm3))) - - 2*nn*(im1*(n1*(2*rm1*Ro111 + rm2*(Ro112 + Ro211) + rm3*(Ro113 + Ro311)) + - n2*(2*rm1*Ro121 + rm2*(Ro122 + Ro221) + rm3*(Ro123 + Ro321)) + - n3*(2*rm1*Ro131 + rm2*(Ro132 + Ro231) + rm3*(Ro133 + Ro331))) + - im2*(n1*(rm1*(Ro112 + Ro211) + 2*rm2*Ro212 + rm3*(Ro213 + Ro312)) + - n2*(rm1*(Ro122 + Ro221) + 2*rm2*Ro222 + rm3*(Ro223 + Ro322)) + - n3*(rm1*(Ro132 + Ro231) + 2*rm2*Ro232 + rm3*(Ro233 + Ro332))) + - im3*(n1*(rm1*(Ro113 + Ro311) + rm2*(Ro213 + Ro312) + 2*rm3*Ro313) + - n2*(rm1*(Ro123 + Ro321) + rm2*(Ro223 + Ro322) + 2*rm3*Ro323) + - n3*(rm1*(Ro133 + Ro331) + rm2*(Ro233 + Ro332) + 2*rm3*Ro333))) - - (im1*(2*rm1*Rojo11 + rm2*(Rojo12 + Rojo21) + rm3*(Rojo13 + Rojo31)) + - im2*(rm1*(Rojo12 + Rojo21) + 2*rm2*Rojo22 + rm3*(Rojo23 + Rojo32)) + - im3*(rm1*(Rojo13 + Rojo31) + rm2*(Rojo23 + Rojo32) + 2*rm3*Rojo33))*SQR(nn); + CCTK_REAL Ro322 = 0; + + CCTK_REAL Ro323 = gamma133*kxyL - gamma132*kxzL + gamma233*kyyL - + gamma232*kyzL + gamma333*kyzL - gamma332*kzzL + PDstandard2nd2kzz - + PDstandard2nd3kyz; + + CCTK_REAL Ro331 = -(gamma133*kxxL) - gamma233*kxyL + gamma131*kxzL - + gamma333*kxzL + gamma231*kyzL + gamma331*kzzL - PDstandard2nd1kzz + + PDstandard2nd3kxz; + + CCTK_REAL Ro332 = -(gamma133*kxyL) + gamma132*kxzL - gamma233*kyyL + + gamma232*kyzL - gamma333*kyzL + gamma332*kzzL - PDstandard2nd2kzz + + PDstandard2nd3kyz; + + CCTK_REAL Ro333 = 0; + + CCTK_REAL Rojo11 = gInv11*R1111 + gInv12*R1112 + gInv13*R1113 + + gInv21*R1211 + gInv23*(-(kxyL*kxzL) + kxxL*kyzL + R1213) + gInv31*R1311 + + gInv32*(-(kxyL*kxzL) + kxxL*kyzL + R1312) + gInv22*(kxxL*kyyL + R1212 + - SQR(kxyL)) + gInv33*(kxxL*kzzL + R1313 - SQR(kxzL)); + + CCTK_REAL Rojo12 = gInv11*R1121 + gInv13*(kxyL*kxzL - kxxL*kyzL + + R1123) + gInv21*R1221 + gInv22*R1222 + gInv23*R1223 + gInv31*R1321 + + gInv32*(-(kxzL*kyyL) + kxyL*kyzL + R1322) + gInv33*(-(kxzL*kyzL) + + kxyL*kzzL + R1323) + gInv12*(-(kxxL*kyyL) + R1122 + SQR(kxyL)); + + CCTK_REAL Rojo13 = gInv11*R1131 + gInv12*(kxyL*kxzL - kxxL*kyzL + + R1132) + gInv21*R1231 + gInv22*(kxzL*kyyL - kxyL*kyzL + R1232) + + gInv23*(kxzL*kyzL - kxyL*kzzL + R1233) + gInv31*R1331 + gInv32*R1332 + + gInv33*R1333 + gInv13*(-(kxxL*kzzL) + R1133 + SQR(kxzL)); + + CCTK_REAL Rojo21 = gInv11*R2111 + gInv12*R2112 + gInv13*R2113 + + gInv22*R2212 + gInv23*(-(kxzL*kyyL) + kxyL*kyzL + R2213) + + gInv31*(kxyL*kxzL - kxxL*kyzL + R2311) + gInv32*R2312 + + gInv33*(-(kxzL*kyzL) + kxyL*kzzL + R2313) + gInv21*(-(kxxL*kyyL) + + R2211 + SQR(kxyL)); + + CCTK_REAL Rojo22 = gInv12*R2122 + gInv13*(kxzL*kyyL - kxyL*kyzL + + R2123) + gInv21*R2221 + gInv22*R2222 + gInv23*R2223 + gInv31*(kxzL*kyyL + - kxyL*kyzL + R2321) + gInv32*R2322 + gInv11*(kxxL*kyyL + R2121 - + SQR(kxyL)) + gInv33*(kyyL*kzzL + R2323 - SQR(kyzL)); + + CCTK_REAL Rojo23 = gInv11*(-(kxyL*kxzL) + kxxL*kyzL + R2131) + + gInv12*R2132 + gInv13*(kxzL*kyzL - kxyL*kzzL + R2133) + + gInv21*(-(kxzL*kyyL) + kxyL*kyzL + R2231) + gInv22*R2232 + gInv31*R2331 + + gInv32*R2332 + gInv33*R2333 + gInv23*(-(kyyL*kzzL) + R2233 + + SQR(kyzL)); + + CCTK_REAL Rojo31 = gInv11*R3111 + gInv12*R3112 + gInv13*R3113 + + gInv21*(kxyL*kxzL - kxxL*kyzL + R3211) + gInv22*(kxzL*kyyL - kxyL*kyzL + + R3212) + gInv23*R3213 + gInv32*(kxzL*kyzL - kxyL*kzzL + R3312) + + gInv33*R3313 + gInv31*(-(kxxL*kzzL) + R3311 + SQR(kxzL)); + + CCTK_REAL Rojo32 = gInv11*(-(kxyL*kxzL) + kxxL*kyzL + R3121) + + gInv12*(-(kxzL*kyyL) + kxyL*kyzL + R3122) + gInv13*R3123 + gInv21*R3221 + + gInv22*R3222 + gInv23*R3223 + gInv31*(kxzL*kyzL - kxyL*kzzL + R3321) + + gInv33*R3323 + gInv32*(-(kyyL*kzzL) + R3322 + SQR(kyzL)); + + CCTK_REAL Rojo33 = gInv12*(-(kxzL*kyzL) + kxyL*kzzL + R3132) + + gInv13*R3133 + gInv21*(-(kxzL*kyzL) + kxyL*kzzL + R3231) + gInv23*R3233 + + gInv31*R3331 + gInv32*R3332 + gInv33*R3333 + gInv11*(kxxL*kzzL + + R3131 - SQR(kxzL)) + gInv22*(kyyL*kzzL + R3232 - SQR(kyzL)); + + CCTK_REAL Psi4rL = n1*(-(imbar1*(imbar2*(n1*(R4p1112 + R4p1211) + + n2*(R4p1122 + R4p1221) + n3*(R4p1132 + R4p1231)) + imbar3*(n1*(R4p1113 + + R4p1311) + n2*(R4p1123 + R4p1321) + n3*(R4p1133 + R4p1331)))) - + imbar2*imbar3*(n1*(R4p1213 + R4p1312) + n2*(R4p1223 + R4p1322) + + n3*(R4p1233 + R4p1332)) + n1*R4p1112*rmbar1*rmbar2 + + n2*R4p1122*rmbar1*rmbar2 + n3*R4p1132*rmbar1*rmbar2 + + n1*R4p1211*rmbar1*rmbar2 + n2*R4p1221*rmbar1*rmbar2 + + n3*R4p1231*rmbar1*rmbar2 + n1*R4p1113*rmbar1*rmbar3 + + n2*R4p1123*rmbar1*rmbar3 + n3*R4p1133*rmbar1*rmbar3 + + n1*R4p1311*rmbar1*rmbar3 + n2*R4p1321*rmbar1*rmbar3 + + n3*R4p1331*rmbar1*rmbar3 + n1*R4p1213*rmbar2*rmbar3 + + n2*R4p1223*rmbar2*rmbar3 + n3*R4p1233*rmbar2*rmbar3 + + n1*R4p1312*rmbar2*rmbar3 + n2*R4p1322*rmbar2*rmbar3 + + n3*R4p1332*rmbar2*rmbar3 - (n1*R4p1111 + n2*R4p1121 + + n3*R4p1131)*SQR(imbar1) - (n1*R4p1212 + n2*R4p1222 + + n3*R4p1232)*SQR(imbar2) - n1*R4p1313*SQR(imbar3) - + n2*R4p1323*SQR(imbar3) - n3*R4p1333*SQR(imbar3) + + n1*R4p1111*SQR(rmbar1) + n2*R4p1121*SQR(rmbar1) + + n3*R4p1131*SQR(rmbar1) + n1*R4p1212*SQR(rmbar2) + + n2*R4p1222*SQR(rmbar2) + n3*R4p1232*SQR(rmbar2) + + n1*R4p1313*SQR(rmbar3) + n2*R4p1323*SQR(rmbar3) + + n3*R4p1333*SQR(rmbar3)) + n2*(-(imbar1*(imbar2*(n1*(R4p2112 + R4p2211) + + n2*(R4p2122 + R4p2221) + n3*(R4p2132 + R4p2231)) + + imbar3*(n1*(R4p2113 + R4p2311) + n2*(R4p2123 + R4p2321) + n3*(R4p2133 + + R4p2331)))) - imbar2*imbar3*(n1*(R4p2213 + R4p2312) + n2*(R4p2223 + + R4p2322) + n3*(R4p2233 + R4p2332)) + n1*R4p2112*rmbar1*rmbar2 + + n2*R4p2122*rmbar1*rmbar2 + n3*R4p2132*rmbar1*rmbar2 + + n1*R4p2211*rmbar1*rmbar2 + n2*R4p2221*rmbar1*rmbar2 + + n3*R4p2231*rmbar1*rmbar2 + n1*R4p2113*rmbar1*rmbar3 + + n2*R4p2123*rmbar1*rmbar3 + n3*R4p2133*rmbar1*rmbar3 + + n1*R4p2311*rmbar1*rmbar3 + n2*R4p2321*rmbar1*rmbar3 + + n3*R4p2331*rmbar1*rmbar3 + n1*R4p2213*rmbar2*rmbar3 + + n2*R4p2223*rmbar2*rmbar3 + n3*R4p2233*rmbar2*rmbar3 + + n1*R4p2312*rmbar2*rmbar3 + n2*R4p2322*rmbar2*rmbar3 + + n3*R4p2332*rmbar2*rmbar3 - (n1*R4p2111 + n2*R4p2121 + + n3*R4p2131)*SQR(imbar1) - (n1*R4p2212 + n2*R4p2222 + + n3*R4p2232)*SQR(imbar2) - n1*R4p2313*SQR(imbar3) - + n2*R4p2323*SQR(imbar3) - n3*R4p2333*SQR(imbar3) + + n1*R4p2111*SQR(rmbar1) + n2*R4p2121*SQR(rmbar1) + + n3*R4p2131*SQR(rmbar1) + n1*R4p2212*SQR(rmbar2) + + n2*R4p2222*SQR(rmbar2) + n3*R4p2232*SQR(rmbar2) + + n1*R4p2313*SQR(rmbar3) + n2*R4p2323*SQR(rmbar3) + + n3*R4p2333*SQR(rmbar3)) + n3*(-(imbar1*(imbar2*(n1*(R4p3112 + R4p3211) + + n2*(R4p3122 + R4p3221) + n3*(R4p3132 + R4p3231)) + + imbar3*(n1*(R4p3113 + R4p3311) + n2*(R4p3123 + R4p3321) + n3*(R4p3133 + + R4p3331)))) - imbar2*imbar3*(n1*(R4p3213 + R4p3312) + n2*(R4p3223 + + R4p3322) + n3*(R4p3233 + R4p3332)) + n1*R4p3112*rmbar1*rmbar2 + + n2*R4p3122*rmbar1*rmbar2 + n3*R4p3132*rmbar1*rmbar2 + + n1*R4p3211*rmbar1*rmbar2 + n2*R4p3221*rmbar1*rmbar2 + + n3*R4p3231*rmbar1*rmbar2 + n1*R4p3113*rmbar1*rmbar3 + + n2*R4p3123*rmbar1*rmbar3 + n3*R4p3133*rmbar1*rmbar3 + + n1*R4p3311*rmbar1*rmbar3 + n2*R4p3321*rmbar1*rmbar3 + + n3*R4p3331*rmbar1*rmbar3 + n1*R4p3213*rmbar2*rmbar3 + + n2*R4p3223*rmbar2*rmbar3 + n3*R4p3233*rmbar2*rmbar3 + + n1*R4p3312*rmbar2*rmbar3 + n2*R4p3322*rmbar2*rmbar3 + + n3*R4p3332*rmbar2*rmbar3 - (n1*R4p3111 + n2*R4p3121 + + n3*R4p3131)*SQR(imbar1) - (n1*R4p3212 + n2*R4p3222 + + n3*R4p3232)*SQR(imbar2) - n1*R4p3313*SQR(imbar3) - + n2*R4p3323*SQR(imbar3) - n3*R4p3333*SQR(imbar3) + + n1*R4p3111*SQR(rmbar1) + n2*R4p3121*SQR(rmbar1) + + n3*R4p3131*SQR(rmbar1) + n1*R4p3212*SQR(rmbar2) + + n2*R4p3222*SQR(rmbar2) + n3*R4p3232*SQR(rmbar2) + + n1*R4p3313*SQR(rmbar3) + n2*R4p3323*SQR(rmbar3) + + n3*R4p3333*SQR(rmbar3)) - SQR(nn)*((imbar2*imbar3 - + rmbar2*rmbar3)*Rojo23 + imbar1*(imbar2*(Rojo12 + Rojo21) + + imbar3*(Rojo13 + Rojo31)) - rmbar1*(rmbar2*(Rojo12 + Rojo21) + + rmbar3*(Rojo13 + Rojo31)) + imbar2*imbar3*Rojo32 - rmbar2*rmbar3*Rojo32 + + Rojo11*SQR(imbar1) + Rojo22*SQR(imbar2) + Rojo33*SQR(imbar3) - + Rojo11*SQR(rmbar1) - Rojo22*SQR(rmbar2) - Rojo33*SQR(rmbar3)) + + 2*nn*(-(n1*(imbar2*imbar3*Ro213 - rmbar2*rmbar3*Ro213 + + imbar1*(imbar2*(Ro112 + Ro211) + imbar3*(Ro113 + Ro311)) - + rmbar1*(rmbar2*(Ro112 + Ro211) + rmbar3*(Ro113 + Ro311)) + + imbar2*imbar3*Ro312 - rmbar2*rmbar3*Ro312 + Ro111*SQR(imbar1) + + Ro212*SQR(imbar2) + Ro313*SQR(imbar3) - Ro111*SQR(rmbar1) - + Ro212*SQR(rmbar2) - Ro313*SQR(rmbar3))) - n2*(imbar2*imbar3*Ro223 - + rmbar2*rmbar3*Ro223 + imbar1*(imbar2*(Ro122 + Ro221) + imbar3*(Ro123 + + Ro321)) - rmbar1*(rmbar2*(Ro122 + Ro221) + rmbar3*(Ro123 + Ro321)) + + imbar2*imbar3*Ro322 - rmbar2*rmbar3*Ro322 + Ro121*SQR(imbar1) + + Ro222*SQR(imbar2) + Ro323*SQR(imbar3) - Ro121*SQR(rmbar1) - + Ro222*SQR(rmbar2) - Ro323*SQR(rmbar3)) - n3*(imbar2*imbar3*Ro233 - + rmbar2*rmbar3*Ro233 + imbar1*(imbar2*(Ro132 + Ro231) + imbar3*(Ro133 + + Ro331)) - rmbar1*(rmbar2*(Ro132 + Ro231) + rmbar3*(Ro133 + Ro331)) + + imbar2*imbar3*Ro332 - rmbar2*rmbar3*Ro332 + Ro131*SQR(imbar1) + + Ro232*SQR(imbar2) + Ro333*SQR(imbar3) - Ro131*SQR(rmbar1) - + Ro232*SQR(rmbar2) - Ro333*SQR(rmbar3))); + + CCTK_REAL Psi4iL = -(n1*(im1*(n1*(2*R4p1111*rm1 + R4p1112*rm2 + + R4p1211*rm2 + R4p1113*rm3 + R4p1311*rm3) + n2*(2*R4p1121*rm1 + + R4p1122*rm2 + R4p1221*rm2 + R4p1123*rm3 + R4p1321*rm3) + + n3*(2*R4p1131*rm1 + R4p1132*rm2 + R4p1231*rm2 + R4p1133*rm3 + + R4p1331*rm3)) + im2*(n1*(R4p1112*rm1 + R4p1211*rm1 + 2*R4p1212*rm2 + + R4p1213*rm3 + R4p1312*rm3) + n2*(R4p1122*rm1 + R4p1221*rm1 + + 2*R4p1222*rm2 + R4p1223*rm3 + R4p1322*rm3) + n3*(R4p1132*rm1 + + R4p1231*rm1 + 2*R4p1232*rm2 + R4p1233*rm3 + R4p1332*rm3)) + + im3*(n1*(R4p1113*rm1 + R4p1311*rm1 + R4p1213*rm2 + R4p1312*rm2 + + 2*R4p1313*rm3) + n2*(R4p1123*rm1 + R4p1321*rm1 + R4p1223*rm2 + + R4p1322*rm2 + 2*R4p1323*rm3) + n3*(R4p1133*rm1 + R4p1331*rm1 + + R4p1233*rm2 + R4p1332*rm2 + 2*R4p1333*rm3)))) - + n2*(im1*(n1*(2*R4p2111*rm1 + R4p2112*rm2 + R4p2211*rm2 + R4p2113*rm3 + + R4p2311*rm3) + n2*(2*R4p2121*rm1 + R4p2122*rm2 + R4p2221*rm2 + + R4p2123*rm3 + R4p2321*rm3) + n3*(2*R4p2131*rm1 + R4p2132*rm2 + + R4p2231*rm2 + R4p2133*rm3 + R4p2331*rm3)) + im2*(n1*(R4p2112*rm1 + + R4p2211*rm1 + 2*R4p2212*rm2 + R4p2213*rm3 + R4p2312*rm3) + + n2*(R4p2122*rm1 + R4p2221*rm1 + 2*R4p2222*rm2 + R4p2223*rm3 + + R4p2322*rm3) + n3*(R4p2132*rm1 + R4p2231*rm1 + 2*R4p2232*rm2 + + R4p2233*rm3 + R4p2332*rm3)) + im3*(n1*(R4p2113*rm1 + R4p2311*rm1 + + R4p2213*rm2 + R4p2312*rm2 + 2*R4p2313*rm3) + n2*(R4p2123*rm1 + + R4p2321*rm1 + R4p2223*rm2 + R4p2322*rm2 + 2*R4p2323*rm3) + + n3*(R4p2133*rm1 + R4p2331*rm1 + R4p2233*rm2 + R4p2332*rm2 + + 2*R4p2333*rm3))) - n3*(im1*(n1*(2*R4p3111*rm1 + R4p3112*rm2 + + R4p3211*rm2 + R4p3113*rm3 + R4p3311*rm3) + n2*(2*R4p3121*rm1 + + R4p3122*rm2 + R4p3221*rm2 + R4p3123*rm3 + R4p3321*rm3) + + n3*(2*R4p3131*rm1 + R4p3132*rm2 + R4p3231*rm2 + R4p3133*rm3 + + R4p3331*rm3)) + im2*(n1*(R4p3112*rm1 + R4p3211*rm1 + 2*R4p3212*rm2 + + R4p3213*rm3 + R4p3312*rm3) + n2*(R4p3122*rm1 + R4p3221*rm1 + + 2*R4p3222*rm2 + R4p3223*rm3 + R4p3322*rm3) + n3*(R4p3132*rm1 + + R4p3231*rm1 + 2*R4p3232*rm2 + R4p3233*rm3 + R4p3332*rm3)) + + im3*(n1*(R4p3113*rm1 + R4p3311*rm1 + R4p3213*rm2 + R4p3312*rm2 + + 2*R4p3313*rm3) + n2*(R4p3123*rm1 + R4p3321*rm1 + R4p3223*rm2 + + R4p3322*rm2 + 2*R4p3323*rm3) + n3*(R4p3133*rm1 + R4p3331*rm1 + + R4p3233*rm2 + R4p3332*rm2 + 2*R4p3333*rm3))) - + 2*nn*(im1*(n1*(2*rm1*Ro111 + rm2*(Ro112 + Ro211) + rm3*(Ro113 + Ro311)) + + n2*(2*rm1*Ro121 + rm2*(Ro122 + Ro221) + rm3*(Ro123 + Ro321)) + + n3*(2*rm1*Ro131 + rm2*(Ro132 + Ro231) + rm3*(Ro133 + Ro331))) + + im2*(n1*(rm1*(Ro112 + Ro211) + 2*rm2*Ro212 + rm3*(Ro213 + Ro312)) + + n2*(rm1*(Ro122 + Ro221) + 2*rm2*Ro222 + rm3*(Ro223 + Ro322)) + + n3*(rm1*(Ro132 + Ro231) + 2*rm2*Ro232 + rm3*(Ro233 + Ro332))) + + im3*(n1*(rm1*(Ro113 + Ro311) + rm2*(Ro213 + Ro312) + 2*rm3*Ro313) + + n2*(rm1*(Ro123 + Ro321) + rm2*(Ro223 + Ro322) + 2*rm3*Ro323) + + n3*(rm1*(Ro133 + Ro331) + rm2*(Ro233 + Ro332) + 2*rm3*Ro333))) - + (im1*(2*rm1*Rojo11 + rm2*(Rojo12 + Rojo21) + rm3*(Rojo13 + Rojo31)) + + im2*(rm1*(Rojo12 + Rojo21) + 2*rm2*Rojo22 + rm3*(Rojo23 + Rojo32)) + + im3*(rm1*(Rojo13 + Rojo31) + rm2*(Rojo23 + Rojo32) + + 2*rm3*Rojo33))*SQR(nn); /* Copy local copies back to grid functions */ Psi4i[index] = Psi4iL; Psi4r[index] = Psi4rL; - - /* Copy local copies back to subblock grid functions */ } } } diff --git a/src/psis_calc_4th.c b/src/psis_calc_4th.c index 3cf8e8f..3be80e2 100644 --- a/src/psis_calc_4th.c +++ b/src/psis_calc_4th.c @@ -19,52 +19,17 @@ #define CUB(x) ((x) * (x) * (x)) #define QAD(x) ((x) * (x) * (x) * (x)) -void psis_calc_4th_Body(cGH const * const cctkGH, CCTK_INT const dir, CCTK_INT const face, CCTK_REAL const normal[3], CCTK_REAL const tangentA[3], CCTK_REAL const tangentB[3], CCTK_INT const min[3], CCTK_INT const max[3], CCTK_INT const n_subblock_gfs, CCTK_REAL * const subblock_gfs[]) +void psis_calc_4th_Body(cGH const * restrict const cctkGH, int const dir, int const face, CCTK_REAL const normal[3], CCTK_REAL const tangentA[3], CCTK_REAL const tangentB[3], int const min[3], int const max[3], int const n_subblock_gfs, CCTK_REAL * restrict const subblock_gfs[]) { DECLARE_CCTK_ARGUMENTS; DECLARE_CCTK_PARAMETERS; /* Declare the variables used for looping over grid points */ - CCTK_INT i = INITVALUE, j = INITVALUE, k = INITVALUE; - CCTK_INT index = INITVALUE; - CCTK_INT subblock_index = INITVALUE; + CCTK_INT i, j, k; + // CCTK_INT index = INITVALUE; /* Declare finite differencing variables */ - CCTK_REAL dx = INITVALUE, dy = INITVALUE, dz = INITVALUE; - CCTK_REAL dxi = INITVALUE, dyi = INITVALUE, dzi = INITVALUE; - CCTK_REAL khalf = INITVALUE, kthird = INITVALUE, ktwothird = INITVALUE, kfourthird = INITVALUE, keightthird = INITVALUE; - CCTK_REAL hdxi = INITVALUE, hdyi = INITVALUE, hdzi = INITVALUE; - - - /* Declare predefined quantities */ - CCTK_REAL p1o12dx = INITVALUE; - CCTK_REAL p1o12dy = INITVALUE; - CCTK_REAL p1o12dz = INITVALUE; - CCTK_REAL p1o144dxdy = INITVALUE; - CCTK_REAL p1o144dxdz = INITVALUE; - CCTK_REAL p1o144dydz = INITVALUE; - CCTK_REAL p1o2dx = INITVALUE; - CCTK_REAL p1o2dy = INITVALUE; - CCTK_REAL p1o2dz = INITVALUE; - CCTK_REAL p1o4dxdy = INITVALUE; - CCTK_REAL p1o4dxdz = INITVALUE; - CCTK_REAL p1o4dydz = INITVALUE; - CCTK_REAL p1odx = INITVALUE; - CCTK_REAL p1odx2 = INITVALUE; - CCTK_REAL p1odxdy = INITVALUE; - CCTK_REAL p1odxdz = INITVALUE; - CCTK_REAL p1ody = INITVALUE; - CCTK_REAL p1ody2 = INITVALUE; - CCTK_REAL p1odydz = INITVALUE; - CCTK_REAL p1odz = INITVALUE; - CCTK_REAL p1odz2 = INITVALUE; - CCTK_REAL pm1o12dx2 = INITVALUE; - CCTK_REAL pm1o12dy2 = INITVALUE; - CCTK_REAL pm1o12dz2 = INITVALUE; - CCTK_REAL pm1o2dx = INITVALUE; - CCTK_REAL pm1o2dy = INITVALUE; - CCTK_REAL pm1o2dz = INITVALUE; if (verbose > 1) { @@ -79,49 +44,52 @@ void psis_calc_4th_Body(cGH const * const cctkGH, CCTK_INT const dir, CCTK_INT c /* Include user-supplied include files */ /* Initialise finite differencing variables */ - dx = CCTK_DELTA_SPACE(0); - dy = CCTK_DELTA_SPACE(1); - dz = CCTK_DELTA_SPACE(2); - dxi = 1.0 / dx; - dyi = 1.0 / dy; - dzi = 1.0 / dz; - khalf = 0.5; - kthird = 1/3.0; - ktwothird = 2.0/3.0; - kfourthird = 4.0/3.0; - keightthird = 8.0/3.0; - hdxi = 0.5 * dxi; - hdyi = 0.5 * dyi; - hdzi = 0.5 * dzi; + CCTK_REAL const dx = CCTK_DELTA_SPACE(0); + CCTK_REAL const dy = CCTK_DELTA_SPACE(1); + CCTK_REAL const dz = CCTK_DELTA_SPACE(2); + int const di = 1; + int const dj = CCTK_GFINDEX3D(cctkGH,0,1,0) - CCTK_GFINDEX3D(cctkGH,0,0,0); + int const dk = CCTK_GFINDEX3D(cctkGH,0,0,1) - CCTK_GFINDEX3D(cctkGH,0,0,0); + CCTK_REAL const dxi = 1.0 / dx; + CCTK_REAL const dyi = 1.0 / dy; + CCTK_REAL const dzi = 1.0 / dz; + CCTK_REAL const khalf = 0.5; + CCTK_REAL const kthird = 1/3.0; + CCTK_REAL const ktwothird = 2.0/3.0; + CCTK_REAL const kfourthird = 4.0/3.0; + CCTK_REAL const keightthird = 8.0/3.0; + CCTK_REAL const hdxi = 0.5 * dxi; + CCTK_REAL const hdyi = 0.5 * dyi; + CCTK_REAL const hdzi = 0.5 * dzi; /* Initialize predefined quantities */ - p1o12dx = INV(dx)/12.; - p1o12dy = INV(dy)/12.; - p1o12dz = INV(dz)/12.; - p1o144dxdy = (INV(dx)*INV(dy))/144.; - p1o144dxdz = (INV(dx)*INV(dz))/144.; - p1o144dydz = (INV(dy)*INV(dz))/144.; - p1o2dx = khalf*INV(dx); - p1o2dy = khalf*INV(dy); - p1o2dz = khalf*INV(dz); - p1o4dxdy = (INV(dx)*INV(dy))/4.; - p1o4dxdz = (INV(dx)*INV(dz))/4.; - p1o4dydz = (INV(dy)*INV(dz))/4.; - p1odx = INV(dx); - p1odx2 = pow(dx,-2); - p1odxdy = INV(dx)*INV(dy); - p1odxdz = INV(dx)*INV(dz); - p1ody = INV(dy); - p1ody2 = pow(dy,-2); - p1odydz = INV(dy)*INV(dz); - p1odz = INV(dz); - p1odz2 = pow(dz,-2); - pm1o12dx2 = -pow(dx,-2)/12.; - pm1o12dy2 = -pow(dy,-2)/12.; - pm1o12dz2 = -pow(dz,-2)/12.; - pm1o2dx = -(khalf*INV(dx)); - pm1o2dy = -(khalf*INV(dy)); - pm1o2dz = -(khalf*INV(dz)); + CCTK_REAL const p1o12dx = INV(dx)/12.; + CCTK_REAL const p1o12dy = INV(dy)/12.; + CCTK_REAL const p1o12dz = INV(dz)/12.; + CCTK_REAL const p1o144dxdy = (INV(dx)*INV(dy))/144.; + CCTK_REAL const p1o144dxdz = (INV(dx)*INV(dz))/144.; + CCTK_REAL const p1o144dydz = (INV(dy)*INV(dz))/144.; + CCTK_REAL const p1o2dx = khalf*INV(dx); + CCTK_REAL const p1o2dy = khalf*INV(dy); + CCTK_REAL const p1o2dz = khalf*INV(dz); + CCTK_REAL const p1o4dxdy = (INV(dx)*INV(dy))/4.; + CCTK_REAL const p1o4dxdz = (INV(dx)*INV(dz))/4.; + CCTK_REAL const p1o4dydz = (INV(dy)*INV(dz))/4.; + CCTK_REAL const p1odx = INV(dx); + CCTK_REAL const p1odx2 = pow(dx,-2); + CCTK_REAL const p1odxdy = INV(dx)*INV(dy); + CCTK_REAL const p1odxdz = INV(dx)*INV(dz); + CCTK_REAL const p1ody = INV(dy); + CCTK_REAL const p1ody2 = pow(dy,-2); + CCTK_REAL const p1odydz = INV(dy)*INV(dz); + CCTK_REAL const p1odz = INV(dz); + CCTK_REAL const p1odz2 = pow(dz,-2); + CCTK_REAL const pm1o12dx2 = -pow(dx,-2)/12.; + CCTK_REAL const pm1o12dy2 = -pow(dy,-2)/12.; + CCTK_REAL const pm1o12dz2 = -pow(dz,-2)/12.; + CCTK_REAL const pm1o2dx = -(khalf*INV(dx)); + CCTK_REAL const pm1o2dy = -(khalf*INV(dy)); + CCTK_REAL const pm1o2dz = -(khalf*INV(dz)); /* Loop over the grid points */ for (k = min[2]; k < max[2]; k++) @@ -130,1122 +98,1195 @@ void psis_calc_4th_Body(cGH const * const cctkGH, CCTK_INT const dir, CCTK_INT c { for (i = min[0]; i < max[0]; i++) { - index = CCTK_GFINDEX3D(cctkGH,i,j,k) ; - subblock_index = i - min[0] + (max[0] - min[0]) * (j - min[1] + (max[1]-min[1]) * (k - min[2])) ; - - /* Declare shorthands */ - CCTK_REAL detg = INITVALUE; - CCTK_REAL gamma111 = INITVALUE, gamma121 = INITVALUE, gamma122 = INITVALUE, gamma131 = INITVALUE, gamma132 = INITVALUE, gamma133 = INITVALUE; - CCTK_REAL gamma211 = INITVALUE, gamma221 = INITVALUE, gamma222 = INITVALUE, gamma231 = INITVALUE, gamma232 = INITVALUE, gamma233 = INITVALUE; - CCTK_REAL gamma311 = INITVALUE, gamma321 = INITVALUE, gamma322 = INITVALUE, gamma331 = INITVALUE, gamma332 = INITVALUE, gamma333 = INITVALUE; - CCTK_REAL gInv11 = INITVALUE, gInv12 = INITVALUE, gInv13 = INITVALUE, gInv21 = INITVALUE, gInv22 = INITVALUE, gInv23 = INITVALUE; - CCTK_REAL gInv31 = INITVALUE, gInv32 = INITVALUE, gInv33 = INITVALUE; - CCTK_REAL im1 = INITVALUE, im2 = INITVALUE, im3 = INITVALUE; - CCTK_REAL imbar1 = INITVALUE, imbar2 = INITVALUE, imbar3 = INITVALUE; - CCTK_REAL invdetg = INITVALUE; - CCTK_REAL isqrt2 = INITVALUE; - CCTK_REAL n1 = INITVALUE, n2 = INITVALUE, n3 = INITVALUE; - CCTK_REAL nn = INITVALUE; - CCTK_REAL omega11 = INITVALUE, omega12 = INITVALUE, omega13 = INITVALUE, omega22 = INITVALUE, omega23 = INITVALUE, omega33 = INITVALUE; - CCTK_REAL R1111 = INITVALUE, R1112 = INITVALUE, R1113 = INITVALUE, R1121 = INITVALUE, R1122 = INITVALUE, R1123 = INITVALUE; - CCTK_REAL R1131 = INITVALUE, R1132 = INITVALUE, R1133 = INITVALUE, R1211 = INITVALUE, R1212 = INITVALUE, R1213 = INITVALUE; - CCTK_REAL R1221 = INITVALUE, R1222 = INITVALUE, R1223 = INITVALUE, R1231 = INITVALUE, R1232 = INITVALUE, R1233 = INITVALUE; - CCTK_REAL R1311 = INITVALUE, R1312 = INITVALUE, R1313 = INITVALUE, R1321 = INITVALUE, R1322 = INITVALUE, R1323 = INITVALUE; - CCTK_REAL R1331 = INITVALUE, R1332 = INITVALUE, R1333 = INITVALUE, R2111 = INITVALUE, R2112 = INITVALUE, R2113 = INITVALUE; - CCTK_REAL R2121 = INITVALUE, R2122 = INITVALUE, R2123 = INITVALUE, R2131 = INITVALUE, R2132 = INITVALUE, R2133 = INITVALUE; - CCTK_REAL R2211 = INITVALUE, R2212 = INITVALUE, R2213 = INITVALUE, R2221 = INITVALUE, R2222 = INITVALUE, R2223 = INITVALUE; - CCTK_REAL R2231 = INITVALUE, R2232 = INITVALUE, R2233 = INITVALUE, R2311 = INITVALUE, R2312 = INITVALUE, R2313 = INITVALUE; - CCTK_REAL R2321 = INITVALUE, R2322 = INITVALUE, R2323 = INITVALUE, R2331 = INITVALUE, R2332 = INITVALUE, R2333 = INITVALUE; - CCTK_REAL R3111 = INITVALUE, R3112 = INITVALUE, R3113 = INITVALUE, R3121 = INITVALUE, R3122 = INITVALUE, R3123 = INITVALUE; - CCTK_REAL R3131 = INITVALUE, R3132 = INITVALUE, R3133 = INITVALUE, R3211 = INITVALUE, R3212 = INITVALUE, R3213 = INITVALUE; - CCTK_REAL R3221 = INITVALUE, R3222 = INITVALUE, R3223 = INITVALUE, R3231 = INITVALUE, R3232 = INITVALUE, R3233 = INITVALUE; - CCTK_REAL R3311 = INITVALUE, R3312 = INITVALUE, R3313 = INITVALUE, R3321 = INITVALUE, R3322 = INITVALUE, R3323 = INITVALUE; - CCTK_REAL R3331 = INITVALUE, R3332 = INITVALUE, R3333 = INITVALUE; - CCTK_REAL R4p1111 = INITVALUE, R4p1112 = INITVALUE, R4p1113 = INITVALUE, R4p1121 = INITVALUE, R4p1122 = INITVALUE, R4p1123 = INITVALUE; - CCTK_REAL R4p1131 = INITVALUE, R4p1132 = INITVALUE, R4p1133 = INITVALUE, R4p1211 = INITVALUE, R4p1212 = INITVALUE, R4p1213 = INITVALUE; - CCTK_REAL R4p1221 = INITVALUE, R4p1222 = INITVALUE, R4p1223 = INITVALUE, R4p1231 = INITVALUE, R4p1232 = INITVALUE, R4p1233 = INITVALUE; - CCTK_REAL R4p1311 = INITVALUE, R4p1312 = INITVALUE, R4p1313 = INITVALUE, R4p1321 = INITVALUE, R4p1322 = INITVALUE, R4p1323 = INITVALUE; - CCTK_REAL R4p1331 = INITVALUE, R4p1332 = INITVALUE, R4p1333 = INITVALUE, R4p2111 = INITVALUE, R4p2112 = INITVALUE, R4p2113 = INITVALUE; - CCTK_REAL R4p2121 = INITVALUE, R4p2122 = INITVALUE, R4p2123 = INITVALUE, R4p2131 = INITVALUE, R4p2132 = INITVALUE, R4p2133 = INITVALUE; - CCTK_REAL R4p2211 = INITVALUE, R4p2212 = INITVALUE, R4p2213 = INITVALUE, R4p2221 = INITVALUE, R4p2222 = INITVALUE, R4p2223 = INITVALUE; - CCTK_REAL R4p2231 = INITVALUE, R4p2232 = INITVALUE, R4p2233 = INITVALUE, R4p2311 = INITVALUE, R4p2312 = INITVALUE, R4p2313 = INITVALUE; - CCTK_REAL R4p2321 = INITVALUE, R4p2322 = INITVALUE, R4p2323 = INITVALUE, R4p2331 = INITVALUE, R4p2332 = INITVALUE, R4p2333 = INITVALUE; - CCTK_REAL R4p3111 = INITVALUE, R4p3112 = INITVALUE, R4p3113 = INITVALUE, R4p3121 = INITVALUE, R4p3122 = INITVALUE, R4p3123 = INITVALUE; - CCTK_REAL R4p3131 = INITVALUE, R4p3132 = INITVALUE, R4p3133 = INITVALUE, R4p3211 = INITVALUE, R4p3212 = INITVALUE, R4p3213 = INITVALUE; - CCTK_REAL R4p3221 = INITVALUE, R4p3222 = INITVALUE, R4p3223 = INITVALUE, R4p3231 = INITVALUE, R4p3232 = INITVALUE, R4p3233 = INITVALUE; - CCTK_REAL R4p3311 = INITVALUE, R4p3312 = INITVALUE, R4p3313 = INITVALUE, R4p3321 = INITVALUE, R4p3322 = INITVALUE, R4p3323 = INITVALUE; - CCTK_REAL R4p3331 = INITVALUE, R4p3332 = INITVALUE, R4p3333 = INITVALUE; - CCTK_REAL rm1 = INITVALUE, rm2 = INITVALUE, rm3 = INITVALUE; - CCTK_REAL rmbar1 = INITVALUE, rmbar2 = INITVALUE, rmbar3 = INITVALUE; - CCTK_REAL Ro111 = INITVALUE, Ro112 = INITVALUE, Ro113 = INITVALUE, Ro121 = INITVALUE, Ro122 = INITVALUE, Ro123 = INITVALUE; - CCTK_REAL Ro131 = INITVALUE, Ro132 = INITVALUE, Ro133 = INITVALUE, Ro211 = INITVALUE, Ro212 = INITVALUE, Ro213 = INITVALUE; - CCTK_REAL Ro221 = INITVALUE, Ro222 = INITVALUE, Ro223 = INITVALUE, Ro231 = INITVALUE, Ro232 = INITVALUE, Ro233 = INITVALUE; - CCTK_REAL Ro311 = INITVALUE, Ro312 = INITVALUE, Ro313 = INITVALUE, Ro321 = INITVALUE, Ro322 = INITVALUE, Ro323 = INITVALUE; - CCTK_REAL Ro331 = INITVALUE, Ro332 = INITVALUE, Ro333 = INITVALUE; - CCTK_REAL Rojo11 = INITVALUE, Rojo12 = INITVALUE, Rojo13 = INITVALUE, Rojo21 = INITVALUE, Rojo22 = INITVALUE, Rojo23 = INITVALUE; - CCTK_REAL Rojo31 = INITVALUE, Rojo32 = INITVALUE, Rojo33 = INITVALUE; - CCTK_REAL va1 = INITVALUE, va2 = INITVALUE, va3 = INITVALUE; - CCTK_REAL vb1 = INITVALUE, vb2 = INITVALUE, vb3 = INITVALUE; - CCTK_REAL vc1 = INITVALUE, vc2 = INITVALUE, vc3 = INITVALUE; - CCTK_REAL xmoved = INITVALUE; - CCTK_REAL ymoved = INITVALUE; - CCTK_REAL zmoved = INITVALUE; - - /* Declare local copies of grid functions */ - CCTK_REAL gxxL = INITVALUE; - CCTK_REAL gxyL = INITVALUE; - CCTK_REAL gxzL = INITVALUE; - CCTK_REAL gyyL = INITVALUE; - CCTK_REAL gyzL = INITVALUE; - CCTK_REAL gzzL = INITVALUE; - CCTK_REAL kxxL = INITVALUE; - CCTK_REAL kxyL = INITVALUE; - CCTK_REAL kxzL = INITVALUE; - CCTK_REAL kyyL = INITVALUE; - CCTK_REAL kyzL = INITVALUE; - CCTK_REAL kzzL = INITVALUE; - CCTK_REAL Psi4iL = INITVALUE; - CCTK_REAL Psi4rL = INITVALUE; - CCTK_REAL xL = INITVALUE; - CCTK_REAL yL = INITVALUE; - CCTK_REAL zL = INITVALUE; - /* Declare precomputed derivatives*/ - + int const index = CCTK_GFINDEX3D(cctkGH,i,j,k) ; /* Declare derivatives */ - CCTK_REAL PDstandard4th1gxx = INITVALUE; - CCTK_REAL PDstandard4th2gxx = INITVALUE; - CCTK_REAL PDstandard4th3gxx = INITVALUE; - CCTK_REAL PDstandard4th22gxx = INITVALUE; - CCTK_REAL PDstandard4th33gxx = INITVALUE; - CCTK_REAL PDstandard4th23gxx = INITVALUE; - CCTK_REAL PDstandard4th1gxy = INITVALUE; - CCTK_REAL PDstandard4th2gxy = INITVALUE; - CCTK_REAL PDstandard4th3gxy = INITVALUE; - CCTK_REAL PDstandard4th33gxy = INITVALUE; - CCTK_REAL PDstandard4th12gxy = INITVALUE; - CCTK_REAL PDstandard4th13gxy = INITVALUE; - CCTK_REAL PDstandard4th23gxy = INITVALUE; - CCTK_REAL PDstandard4th1gxz = INITVALUE; - CCTK_REAL PDstandard4th2gxz = INITVALUE; - CCTK_REAL PDstandard4th3gxz = INITVALUE; - CCTK_REAL PDstandard4th22gxz = INITVALUE; - CCTK_REAL PDstandard4th12gxz = INITVALUE; - CCTK_REAL PDstandard4th13gxz = INITVALUE; - CCTK_REAL PDstandard4th23gxz = INITVALUE; - CCTK_REAL PDstandard4th1gyy = INITVALUE; - CCTK_REAL PDstandard4th2gyy = INITVALUE; - CCTK_REAL PDstandard4th3gyy = INITVALUE; - CCTK_REAL PDstandard4th11gyy = INITVALUE; - CCTK_REAL PDstandard4th33gyy = INITVALUE; - CCTK_REAL PDstandard4th13gyy = INITVALUE; - CCTK_REAL PDstandard4th1gyz = INITVALUE; - CCTK_REAL PDstandard4th2gyz = INITVALUE; - CCTK_REAL PDstandard4th3gyz = INITVALUE; - CCTK_REAL PDstandard4th11gyz = INITVALUE; - CCTK_REAL PDstandard4th12gyz = INITVALUE; - CCTK_REAL PDstandard4th13gyz = INITVALUE; - CCTK_REAL PDstandard4th23gyz = INITVALUE; - CCTK_REAL PDstandard4th1gzz = INITVALUE; - CCTK_REAL PDstandard4th2gzz = INITVALUE; - CCTK_REAL PDstandard4th3gzz = INITVALUE; - CCTK_REAL PDstandard4th11gzz = INITVALUE; - CCTK_REAL PDstandard4th22gzz = INITVALUE; - CCTK_REAL PDstandard4th12gzz = INITVALUE; - CCTK_REAL PDstandard4th2kxx = INITVALUE; - CCTK_REAL PDstandard4th3kxx = INITVALUE; - CCTK_REAL PDstandard4th1kxy = INITVALUE; - CCTK_REAL PDstandard4th2kxy = INITVALUE; - CCTK_REAL PDstandard4th3kxy = INITVALUE; - CCTK_REAL PDstandard4th1kxz = INITVALUE; - CCTK_REAL PDstandard4th2kxz = INITVALUE; - CCTK_REAL PDstandard4th3kxz = INITVALUE; - CCTK_REAL PDstandard4th1kyy = INITVALUE; - CCTK_REAL PDstandard4th3kyy = INITVALUE; - CCTK_REAL PDstandard4th1kyz = INITVALUE; - CCTK_REAL PDstandard4th2kyz = INITVALUE; - CCTK_REAL PDstandard4th3kyz = INITVALUE; - CCTK_REAL PDstandard4th1kzz = INITVALUE; - CCTK_REAL PDstandard4th2kzz = INITVALUE; + // CCTK_REAL PDstandard4th1gxx = INITVALUE; + // CCTK_REAL PDstandard4th2gxx = INITVALUE; + // CCTK_REAL PDstandard4th3gxx = INITVALUE; + // CCTK_REAL PDstandard4th22gxx = INITVALUE; + // CCTK_REAL PDstandard4th33gxx = INITVALUE; + // CCTK_REAL PDstandard4th23gxx = INITVALUE; + // CCTK_REAL PDstandard4th1gxy = INITVALUE; + // CCTK_REAL PDstandard4th2gxy = INITVALUE; + // CCTK_REAL PDstandard4th3gxy = INITVALUE; + // CCTK_REAL PDstandard4th33gxy = INITVALUE; + // CCTK_REAL PDstandard4th12gxy = INITVALUE; + // CCTK_REAL PDstandard4th13gxy = INITVALUE; + // CCTK_REAL PDstandard4th23gxy = INITVALUE; + // CCTK_REAL PDstandard4th1gxz = INITVALUE; + // CCTK_REAL PDstandard4th2gxz = INITVALUE; + // CCTK_REAL PDstandard4th3gxz = INITVALUE; + // CCTK_REAL PDstandard4th22gxz = INITVALUE; + // CCTK_REAL PDstandard4th12gxz = INITVALUE; + // CCTK_REAL PDstandard4th13gxz = INITVALUE; + // CCTK_REAL PDstandard4th23gxz = INITVALUE; + // CCTK_REAL PDstandard4th1gyy = INITVALUE; + // CCTK_REAL PDstandard4th2gyy = INITVALUE; + // CCTK_REAL PDstandard4th3gyy = INITVALUE; + // CCTK_REAL PDstandard4th11gyy = INITVALUE; + // CCTK_REAL PDstandard4th33gyy = INITVALUE; + // CCTK_REAL PDstandard4th13gyy = INITVALUE; + // CCTK_REAL PDstandard4th1gyz = INITVALUE; + // CCTK_REAL PDstandard4th2gyz = INITVALUE; + // CCTK_REAL PDstandard4th3gyz = INITVALUE; + // CCTK_REAL PDstandard4th11gyz = INITVALUE; + // CCTK_REAL PDstandard4th12gyz = INITVALUE; + // CCTK_REAL PDstandard4th13gyz = INITVALUE; + // CCTK_REAL PDstandard4th23gyz = INITVALUE; + // CCTK_REAL PDstandard4th1gzz = INITVALUE; + // CCTK_REAL PDstandard4th2gzz = INITVALUE; + // CCTK_REAL PDstandard4th3gzz = INITVALUE; + // CCTK_REAL PDstandard4th11gzz = INITVALUE; + // CCTK_REAL PDstandard4th22gzz = INITVALUE; + // CCTK_REAL PDstandard4th12gzz = INITVALUE; + // CCTK_REAL PDstandard4th2kxx = INITVALUE; + // CCTK_REAL PDstandard4th3kxx = INITVALUE; + // CCTK_REAL PDstandard4th1kxy = INITVALUE; + // CCTK_REAL PDstandard4th2kxy = INITVALUE; + // CCTK_REAL PDstandard4th3kxy = INITVALUE; + // CCTK_REAL PDstandard4th1kxz = INITVALUE; + // CCTK_REAL PDstandard4th2kxz = INITVALUE; + // CCTK_REAL PDstandard4th3kxz = INITVALUE; + // CCTK_REAL PDstandard4th1kyy = INITVALUE; + // CCTK_REAL PDstandard4th3kyy = INITVALUE; + // CCTK_REAL PDstandard4th1kyz = INITVALUE; + // CCTK_REAL PDstandard4th2kyz = INITVALUE; + // CCTK_REAL PDstandard4th3kyz = INITVALUE; + // CCTK_REAL PDstandard4th1kzz = INITVALUE; + // CCTK_REAL PDstandard4th2kzz = INITVALUE; /* Assign local copies of grid functions */ - gxxL = gxx[index]; - gxyL = gxy[index]; - gxzL = gxz[index]; - gyyL = gyy[index]; - gyzL = gyz[index]; - gzzL = gzz[index]; - kxxL = kxx[index]; - kxyL = kxy[index]; - kxzL = kxz[index]; - kyyL = kyy[index]; - kyzL = kyz[index]; - kzzL = kzz[index]; - xL = x[index]; - yL = y[index]; - zL = z[index]; - - /* Assign local copies of subblock grid functions */ + CCTK_REAL gxxL = gxx[index]; + CCTK_REAL gxyL = gxy[index]; + CCTK_REAL gxzL = gxz[index]; + CCTK_REAL gyyL = gyy[index]; + CCTK_REAL gyzL = gyz[index]; + CCTK_REAL gzzL = gzz[index]; + CCTK_REAL kxxL = kxx[index]; + CCTK_REAL kxyL = kxy[index]; + CCTK_REAL kxzL = kxz[index]; + CCTK_REAL kyyL = kyy[index]; + CCTK_REAL kyzL = kyz[index]; + CCTK_REAL kzzL = kzz[index]; + CCTK_REAL xL = x[index]; + CCTK_REAL yL = y[index]; + CCTK_REAL zL = z[index]; /* Include user supplied include files */ - /* Precompute derivatives (new style) */ - PDstandard4th1gxx = PDstandard4th1(gxx, i, j, k); - PDstandard4th2gxx = PDstandard4th2(gxx, i, j, k); - PDstandard4th3gxx = PDstandard4th3(gxx, i, j, k); - PDstandard4th22gxx = PDstandard4th22(gxx, i, j, k); - PDstandard4th33gxx = PDstandard4th33(gxx, i, j, k); - PDstandard4th23gxx = PDstandard4th23(gxx, i, j, k); - PDstandard4th1gxy = PDstandard4th1(gxy, i, j, k); - PDstandard4th2gxy = PDstandard4th2(gxy, i, j, k); - PDstandard4th3gxy = PDstandard4th3(gxy, i, j, k); - PDstandard4th33gxy = PDstandard4th33(gxy, i, j, k); - PDstandard4th12gxy = PDstandard4th12(gxy, i, j, k); - PDstandard4th13gxy = PDstandard4th13(gxy, i, j, k); - PDstandard4th23gxy = PDstandard4th23(gxy, i, j, k); - PDstandard4th1gxz = PDstandard4th1(gxz, i, j, k); - PDstandard4th2gxz = PDstandard4th2(gxz, i, j, k); - PDstandard4th3gxz = PDstandard4th3(gxz, i, j, k); - PDstandard4th22gxz = PDstandard4th22(gxz, i, j, k); - PDstandard4th12gxz = PDstandard4th12(gxz, i, j, k); - PDstandard4th13gxz = PDstandard4th13(gxz, i, j, k); - PDstandard4th23gxz = PDstandard4th23(gxz, i, j, k); - PDstandard4th1gyy = PDstandard4th1(gyy, i, j, k); - PDstandard4th2gyy = PDstandard4th2(gyy, i, j, k); - PDstandard4th3gyy = PDstandard4th3(gyy, i, j, k); - PDstandard4th11gyy = PDstandard4th11(gyy, i, j, k); - PDstandard4th33gyy = PDstandard4th33(gyy, i, j, k); - PDstandard4th13gyy = PDstandard4th13(gyy, i, j, k); - PDstandard4th1gyz = PDstandard4th1(gyz, i, j, k); - PDstandard4th2gyz = PDstandard4th2(gyz, i, j, k); - PDstandard4th3gyz = PDstandard4th3(gyz, i, j, k); - PDstandard4th11gyz = PDstandard4th11(gyz, i, j, k); - PDstandard4th12gyz = PDstandard4th12(gyz, i, j, k); - PDstandard4th13gyz = PDstandard4th13(gyz, i, j, k); - PDstandard4th23gyz = PDstandard4th23(gyz, i, j, k); - PDstandard4th1gzz = PDstandard4th1(gzz, i, j, k); - PDstandard4th2gzz = PDstandard4th2(gzz, i, j, k); - PDstandard4th3gzz = PDstandard4th3(gzz, i, j, k); - PDstandard4th11gzz = PDstandard4th11(gzz, i, j, k); - PDstandard4th22gzz = PDstandard4th22(gzz, i, j, k); - PDstandard4th12gzz = PDstandard4th12(gzz, i, j, k); - PDstandard4th2kxx = PDstandard4th2(kxx, i, j, k); - PDstandard4th3kxx = PDstandard4th3(kxx, i, j, k); - PDstandard4th1kxy = PDstandard4th1(kxy, i, j, k); - PDstandard4th2kxy = PDstandard4th2(kxy, i, j, k); - PDstandard4th3kxy = PDstandard4th3(kxy, i, j, k); - PDstandard4th1kxz = PDstandard4th1(kxz, i, j, k); - PDstandard4th2kxz = PDstandard4th2(kxz, i, j, k); - PDstandard4th3kxz = PDstandard4th3(kxz, i, j, k); - PDstandard4th1kyy = PDstandard4th1(kyy, i, j, k); - PDstandard4th3kyy = PDstandard4th3(kyy, i, j, k); - PDstandard4th1kyz = PDstandard4th1(kyz, i, j, k); - PDstandard4th2kyz = PDstandard4th2(kyz, i, j, k); - PDstandard4th3kyz = PDstandard4th3(kyz, i, j, k); - PDstandard4th1kzz = PDstandard4th1(kzz, i, j, k); - PDstandard4th2kzz = PDstandard4th2(kzz, i, j, k); - - /* Precompute derivatives (old style) */ + /* Precompute derivatives */ + CCTK_REAL const PDstandard4th1gxx = PDstandard4th1(gxx, i, j, k); + CCTK_REAL const PDstandard4th2gxx = PDstandard4th2(gxx, i, j, k); + CCTK_REAL const PDstandard4th3gxx = PDstandard4th3(gxx, i, j, k); + CCTK_REAL const PDstandard4th22gxx = PDstandard4th22(gxx, i, j, k); + CCTK_REAL const PDstandard4th33gxx = PDstandard4th33(gxx, i, j, k); + CCTK_REAL const PDstandard4th23gxx = PDstandard4th23(gxx, i, j, k); + CCTK_REAL const PDstandard4th1gxy = PDstandard4th1(gxy, i, j, k); + CCTK_REAL const PDstandard4th2gxy = PDstandard4th2(gxy, i, j, k); + CCTK_REAL const PDstandard4th3gxy = PDstandard4th3(gxy, i, j, k); + CCTK_REAL const PDstandard4th33gxy = PDstandard4th33(gxy, i, j, k); + CCTK_REAL const PDstandard4th12gxy = PDstandard4th12(gxy, i, j, k); + CCTK_REAL const PDstandard4th13gxy = PDstandard4th13(gxy, i, j, k); + CCTK_REAL const PDstandard4th23gxy = PDstandard4th23(gxy, i, j, k); + CCTK_REAL const PDstandard4th1gxz = PDstandard4th1(gxz, i, j, k); + CCTK_REAL const PDstandard4th2gxz = PDstandard4th2(gxz, i, j, k); + CCTK_REAL const PDstandard4th3gxz = PDstandard4th3(gxz, i, j, k); + CCTK_REAL const PDstandard4th22gxz = PDstandard4th22(gxz, i, j, k); + CCTK_REAL const PDstandard4th12gxz = PDstandard4th12(gxz, i, j, k); + CCTK_REAL const PDstandard4th13gxz = PDstandard4th13(gxz, i, j, k); + CCTK_REAL const PDstandard4th23gxz = PDstandard4th23(gxz, i, j, k); + CCTK_REAL const PDstandard4th1gyy = PDstandard4th1(gyy, i, j, k); + CCTK_REAL const PDstandard4th2gyy = PDstandard4th2(gyy, i, j, k); + CCTK_REAL const PDstandard4th3gyy = PDstandard4th3(gyy, i, j, k); + CCTK_REAL const PDstandard4th11gyy = PDstandard4th11(gyy, i, j, k); + CCTK_REAL const PDstandard4th33gyy = PDstandard4th33(gyy, i, j, k); + CCTK_REAL const PDstandard4th13gyy = PDstandard4th13(gyy, i, j, k); + CCTK_REAL const PDstandard4th1gyz = PDstandard4th1(gyz, i, j, k); + CCTK_REAL const PDstandard4th2gyz = PDstandard4th2(gyz, i, j, k); + CCTK_REAL const PDstandard4th3gyz = PDstandard4th3(gyz, i, j, k); + CCTK_REAL const PDstandard4th11gyz = PDstandard4th11(gyz, i, j, k); + CCTK_REAL const PDstandard4th12gyz = PDstandard4th12(gyz, i, j, k); + CCTK_REAL const PDstandard4th13gyz = PDstandard4th13(gyz, i, j, k); + CCTK_REAL const PDstandard4th23gyz = PDstandard4th23(gyz, i, j, k); + CCTK_REAL const PDstandard4th1gzz = PDstandard4th1(gzz, i, j, k); + CCTK_REAL const PDstandard4th2gzz = PDstandard4th2(gzz, i, j, k); + CCTK_REAL const PDstandard4th3gzz = PDstandard4th3(gzz, i, j, k); + CCTK_REAL const PDstandard4th11gzz = PDstandard4th11(gzz, i, j, k); + CCTK_REAL const PDstandard4th22gzz = PDstandard4th22(gzz, i, j, k); + CCTK_REAL const PDstandard4th12gzz = PDstandard4th12(gzz, i, j, k); + CCTK_REAL const PDstandard4th2kxx = PDstandard4th2(kxx, i, j, k); + CCTK_REAL const PDstandard4th3kxx = PDstandard4th3(kxx, i, j, k); + CCTK_REAL const PDstandard4th1kxy = PDstandard4th1(kxy, i, j, k); + CCTK_REAL const PDstandard4th2kxy = PDstandard4th2(kxy, i, j, k); + CCTK_REAL const PDstandard4th3kxy = PDstandard4th3(kxy, i, j, k); + CCTK_REAL const PDstandard4th1kxz = PDstandard4th1(kxz, i, j, k); + CCTK_REAL const PDstandard4th2kxz = PDstandard4th2(kxz, i, j, k); + CCTK_REAL const PDstandard4th3kxz = PDstandard4th3(kxz, i, j, k); + CCTK_REAL const PDstandard4th1kyy = PDstandard4th1(kyy, i, j, k); + CCTK_REAL const PDstandard4th3kyy = PDstandard4th3(kyy, i, j, k); + CCTK_REAL const PDstandard4th1kyz = PDstandard4th1(kyz, i, j, k); + CCTK_REAL const PDstandard4th2kyz = PDstandard4th2(kyz, i, j, k); + CCTK_REAL const PDstandard4th3kyz = PDstandard4th3(kyz, i, j, k); + CCTK_REAL const PDstandard4th1kzz = PDstandard4th1(kzz, i, j, k); + CCTK_REAL const PDstandard4th2kzz = PDstandard4th2(kzz, i, j, k); /* Calculate temporaries and grid functions */ - detg = 2*gxyL*gxzL*gyzL + gzzL*(gxxL*gyyL - SQR(gxyL)) - gyyL*SQR(gxzL) - gxxL*SQR(gyzL); - - invdetg = INV(detg); - - gInv11 = invdetg*(gyyL*gzzL - SQR(gyzL)); - - gInv12 = (gxzL*gyzL - gxyL*gzzL)*invdetg; - - gInv13 = (-(gxzL*gyyL) + gxyL*gyzL)*invdetg; - - gInv21 = (gxzL*gyzL - gxyL*gzzL)*invdetg; - - gInv22 = invdetg*(gxxL*gzzL - SQR(gxzL)); - - gInv23 = (gxyL*gxzL - gxxL*gyzL)*invdetg; - - gInv31 = (-(gxzL*gyyL) + gxyL*gyzL)*invdetg; - - gInv32 = (gxyL*gxzL - gxxL*gyzL)*invdetg; - - gInv33 = invdetg*(gxxL*gyyL - SQR(gxyL)); + CCTK_REAL detg = 2*gxyL*gxzL*gyzL + gzzL*(gxxL*gyyL - SQR(gxyL)) - + gyyL*SQR(gxzL) - gxxL*SQR(gyzL); - gamma111 = khalf*(gInv11*PDstandard4th1gxx + 2*(gInv12*PDstandard4th1gxy + gInv13*PDstandard4th1gxz) - - gInv12*PDstandard4th2gxx - gInv13*PDstandard4th3gxx); + CCTK_REAL invdetg = INV(detg); - gamma211 = khalf*(gInv21*PDstandard4th1gxx + 2*(gInv22*PDstandard4th1gxy + gInv23*PDstandard4th1gxz) - - gInv22*PDstandard4th2gxx - gInv23*PDstandard4th3gxx); + CCTK_REAL gInv11 = invdetg*(gyyL*gzzL - SQR(gyzL)); - gamma311 = khalf*(gInv31*PDstandard4th1gxx + 2*(gInv32*PDstandard4th1gxy + gInv33*PDstandard4th1gxz) - - gInv32*PDstandard4th2gxx - gInv33*PDstandard4th3gxx); + CCTK_REAL gInv12 = (gxzL*gyzL - gxyL*gzzL)*invdetg; - gamma121 = khalf*(gInv12*PDstandard4th1gyy + gInv11*PDstandard4th2gxx + - gInv13*(PDstandard4th1gyz + PDstandard4th2gxz - PDstandard4th3gxy)); + CCTK_REAL gInv13 = (-(gxzL*gyyL) + gxyL*gyzL)*invdetg; - gamma221 = khalf*(gInv22*PDstandard4th1gyy + gInv21*PDstandard4th2gxx + - gInv23*(PDstandard4th1gyz + PDstandard4th2gxz - PDstandard4th3gxy)); + CCTK_REAL gInv21 = (gxzL*gyzL - gxyL*gzzL)*invdetg; - gamma321 = khalf*(gInv32*PDstandard4th1gyy + gInv31*PDstandard4th2gxx + - gInv33*(PDstandard4th1gyz + PDstandard4th2gxz - PDstandard4th3gxy)); + CCTK_REAL gInv22 = invdetg*(gxxL*gzzL - SQR(gxzL)); - gamma131 = khalf*(gInv13*PDstandard4th1gzz + gInv11*PDstandard4th3gxx + - gInv12*(PDstandard4th1gyz - PDstandard4th2gxz + PDstandard4th3gxy)); + CCTK_REAL gInv23 = (gxyL*gxzL - gxxL*gyzL)*invdetg; - gamma231 = khalf*(gInv23*PDstandard4th1gzz + gInv21*PDstandard4th3gxx + - gInv22*(PDstandard4th1gyz - PDstandard4th2gxz + PDstandard4th3gxy)); + CCTK_REAL gInv31 = (-(gxzL*gyyL) + gxyL*gyzL)*invdetg; - gamma331 = khalf*(gInv33*PDstandard4th1gzz + gInv31*PDstandard4th3gxx + - gInv32*(PDstandard4th1gyz - PDstandard4th2gxz + PDstandard4th3gxy)); + CCTK_REAL gInv32 = (gxyL*gxzL - gxxL*gyzL)*invdetg; - gamma122 = khalf*(gInv11*(-PDstandard4th1gyy + 2*PDstandard4th2gxy) + gInv12*PDstandard4th2gyy + - gInv13*(2*PDstandard4th2gyz - PDstandard4th3gyy)); + CCTK_REAL gInv33 = invdetg*(gxxL*gyyL - SQR(gxyL)); - gamma222 = khalf*(gInv21*(-PDstandard4th1gyy + 2*PDstandard4th2gxy) + gInv22*PDstandard4th2gyy + - gInv23*(2*PDstandard4th2gyz - PDstandard4th3gyy)); + CCTK_REAL gamma111 = khalf*(gInv11*PDstandard4th1gxx + + 2*(gInv12*PDstandard4th1gxy + gInv13*PDstandard4th1gxz) - + gInv12*PDstandard4th2gxx - gInv13*PDstandard4th3gxx); - gamma322 = khalf*(gInv31*(-PDstandard4th1gyy + 2*PDstandard4th2gxy) + gInv32*PDstandard4th2gyy + - gInv33*(2*PDstandard4th2gyz - PDstandard4th3gyy)); + CCTK_REAL gamma211 = khalf*(gInv21*PDstandard4th1gxx + + 2*(gInv22*PDstandard4th1gxy + gInv23*PDstandard4th1gxz) - + gInv22*PDstandard4th2gxx - gInv23*PDstandard4th3gxx); - gamma132 = khalf*(gInv13*PDstandard4th2gzz + gInv11*(-PDstandard4th1gyz + PDstandard4th2gxz + PDstandard4th3gxy) + - gInv12*PDstandard4th3gyy); + CCTK_REAL gamma311 = khalf*(gInv31*PDstandard4th1gxx + + 2*(gInv32*PDstandard4th1gxy + gInv33*PDstandard4th1gxz) - + gInv32*PDstandard4th2gxx - gInv33*PDstandard4th3gxx); - gamma232 = khalf*(gInv23*PDstandard4th2gzz + gInv21*(-PDstandard4th1gyz + PDstandard4th2gxz + PDstandard4th3gxy) + - gInv22*PDstandard4th3gyy); + CCTK_REAL gamma121 = khalf*(gInv12*PDstandard4th1gyy + + gInv11*PDstandard4th2gxx + gInv13*(PDstandard4th1gyz + + PDstandard4th2gxz - PDstandard4th3gxy)); - gamma332 = khalf*(gInv33*PDstandard4th2gzz + gInv31*(-PDstandard4th1gyz + PDstandard4th2gxz + PDstandard4th3gxy) + - gInv32*PDstandard4th3gyy); + CCTK_REAL gamma221 = khalf*(gInv22*PDstandard4th1gyy + + gInv21*PDstandard4th2gxx + gInv23*(PDstandard4th1gyz + + PDstandard4th2gxz - PDstandard4th3gxy)); - gamma133 = khalf*(-(gInv11*PDstandard4th1gzz) - gInv12*PDstandard4th2gzz + 2*gInv11*PDstandard4th3gxz + - 2*gInv12*PDstandard4th3gyz + gInv13*PDstandard4th3gzz); + CCTK_REAL gamma321 = khalf*(gInv32*PDstandard4th1gyy + + gInv31*PDstandard4th2gxx + gInv33*(PDstandard4th1gyz + + PDstandard4th2gxz - PDstandard4th3gxy)); - gamma233 = khalf*(-(gInv21*PDstandard4th1gzz) - gInv22*PDstandard4th2gzz + 2*gInv21*PDstandard4th3gxz + - 2*gInv22*PDstandard4th3gyz + gInv23*PDstandard4th3gzz); + CCTK_REAL gamma131 = khalf*(gInv13*PDstandard4th1gzz + + gInv11*PDstandard4th3gxx + gInv12*(PDstandard4th1gyz - + PDstandard4th2gxz + PDstandard4th3gxy)); - gamma333 = khalf*(-(gInv31*PDstandard4th1gzz) - gInv32*PDstandard4th2gzz + 2*gInv31*PDstandard4th3gxz + - 2*gInv32*PDstandard4th3gyz + gInv33*PDstandard4th3gzz); + CCTK_REAL gamma231 = khalf*(gInv23*PDstandard4th1gzz + + gInv21*PDstandard4th3gxx + gInv22*(PDstandard4th1gyz - + PDstandard4th2gxz + PDstandard4th3gxy)); - xmoved = xL - xorig; + CCTK_REAL gamma331 = khalf*(gInv33*PDstandard4th1gzz + + gInv31*PDstandard4th3gxx + gInv32*(PDstandard4th1gyz - + PDstandard4th2gxz + PDstandard4th3gxy)); - ymoved = yL - yorig; + CCTK_REAL gamma122 = khalf*(gInv11*(-PDstandard4th1gyy + + 2*PDstandard4th2gxy) + gInv12*PDstandard4th2gyy + + gInv13*(2*PDstandard4th2gyz - PDstandard4th3gyy)); - zmoved = zL - zorig; + CCTK_REAL gamma222 = khalf*(gInv21*(-PDstandard4th1gyy + + 2*PDstandard4th2gxy) + gInv22*PDstandard4th2gyy + + gInv23*(2*PDstandard4th2gyz - PDstandard4th3gyy)); - va1 = -ymoved; + CCTK_REAL gamma322 = khalf*(gInv31*(-PDstandard4th1gyy + + 2*PDstandard4th2gxy) + gInv32*PDstandard4th2gyy + + gInv33*(2*PDstandard4th2gyz - PDstandard4th3gyy)); - va2 = offset + xmoved; + CCTK_REAL gamma132 = khalf*(gInv13*PDstandard4th2gzz + + gInv11*(-PDstandard4th1gyz + PDstandard4th2gxz + PDstandard4th3gxy) + + gInv12*PDstandard4th3gyy); - va3 = 0; + CCTK_REAL gamma232 = khalf*(gInv23*PDstandard4th2gzz + + gInv21*(-PDstandard4th1gyz + PDstandard4th2gxz + PDstandard4th3gxy) + + gInv22*PDstandard4th3gyy); - vb1 = offset + xmoved; + CCTK_REAL gamma332 = khalf*(gInv33*PDstandard4th2gzz + + gInv31*(-PDstandard4th1gyz + PDstandard4th2gxz + PDstandard4th3gxy) + + gInv32*PDstandard4th3gyy); - vb2 = ymoved; + CCTK_REAL gamma133 = khalf*(-(gInv11*PDstandard4th1gzz) - + gInv12*PDstandard4th2gzz + 2*gInv11*PDstandard4th3gxz + + 2*gInv12*PDstandard4th3gyz + gInv13*PDstandard4th3gzz); - vb3 = zmoved; + CCTK_REAL gamma233 = khalf*(-(gInv21*PDstandard4th1gzz) - + gInv22*PDstandard4th2gzz + 2*gInv21*PDstandard4th3gxz + + 2*gInv22*PDstandard4th3gyz + gInv23*PDstandard4th3gzz); - vc1 = ((-(gInv13*va2) + gInv12*va3)*vb1 + (gInv13*va1 - gInv11*va3)*vb2 + (-(gInv12*va1) + gInv11*va2)*vb3)* - pow(detg,0.5); + CCTK_REAL gamma333 = khalf*(-(gInv31*PDstandard4th1gzz) - + gInv32*PDstandard4th2gzz + 2*gInv31*PDstandard4th3gxz + + 2*gInv32*PDstandard4th3gyz + gInv33*PDstandard4th3gzz); - vc2 = ((-(gInv23*va2) + gInv22*va3)*vb1 + (gInv23*va1 - gInv21*va3)*vb2 + (-(gInv22*va1) + gInv21*va2)*vb3)* - pow(detg,0.5); + CCTK_REAL xmoved = xL - xorig; - vc3 = ((-(gInv33*va2) + gInv32*va3)*vb1 + (gInv33*va1 - gInv31*va3)*vb2 + (-(gInv32*va1) + gInv31*va2)*vb3)* - pow(detg,0.5); + CCTK_REAL ymoved = yL - yorig; - omega11 = 2*(gyzL*va2*va3 + va1*(gxyL*va2 + gxzL*va3)) + gxxL*SQR(va1) + gyyL*SQR(va2) + gzzL*SQR(va3); + CCTK_REAL zmoved = zL - zorig; - va1 = va1*pow(omega11,-khalf); + CCTK_REAL va1 = -ymoved; - va2 = va2*pow(omega11,-khalf); + CCTK_REAL va2 = offset + xmoved; - va3 = va3*pow(omega11,-khalf); + CCTK_REAL va3 = 0; - omega12 = (gxxL*va1 + gxyL*va2 + gxzL*va3)*vb1 + (gxyL*va1 + gyyL*va2 + gyzL*va3)*vb2 + - (gxzL*va1 + gyzL*va2 + gzzL*va3)*vb3; + CCTK_REAL vb1 = offset + xmoved; - vb1 = -(omega12*va1) + vb1; + CCTK_REAL vb2 = ymoved; - vb2 = -(omega12*va2) + vb2; + CCTK_REAL vb3 = zmoved; - vb3 = -(omega12*va3) + vb3; + CCTK_REAL vc1 = ((-(gInv13*va2) + gInv12*va3)*vb1 + (gInv13*va1 - + gInv11*va3)*vb2 + (-(gInv12*va1) + gInv11*va2)*vb3)*pow(detg,0.5); - omega22 = 2*(gyzL*vb2*vb3 + vb1*(gxyL*vb2 + gxzL*vb3)) + gxxL*SQR(vb1) + gyyL*SQR(vb2) + gzzL*SQR(vb3); + CCTK_REAL vc2 = ((-(gInv23*va2) + gInv22*va3)*vb1 + (gInv23*va1 - + gInv21*va3)*vb2 + (-(gInv22*va1) + gInv21*va2)*vb3)*pow(detg,0.5); - vb1 = vb1*pow(omega22,-khalf); + CCTK_REAL vc3 = ((-(gInv33*va2) + gInv32*va3)*vb1 + (gInv33*va1 - + gInv31*va3)*vb2 + (-(gInv32*va1) + gInv31*va2)*vb3)*pow(detg,0.5); - vb2 = vb2*pow(omega22,-khalf); + CCTK_REAL omega11 = 2*(gyzL*va2*va3 + va1*(gxyL*va2 + gxzL*va3)) + + gxxL*SQR(va1) + gyyL*SQR(va2) + gzzL*SQR(va3); - vb3 = vb3*pow(omega22,-khalf); + va1 = va1*pow(omega11,-khalf); - omega13 = (gxxL*va1 + gxyL*va2 + gxzL*va3)*vc1 + (gxyL*va1 + gyyL*va2 + gyzL*va3)*vc2 + - (gxzL*va1 + gyzL*va2 + gzzL*va3)*vc3; + va2 = va2*pow(omega11,-khalf); - omega23 = (gxxL*vb1 + gxyL*vb2 + gxzL*vb3)*vc1 + (gxyL*vb1 + gyyL*vb2 + gyzL*vb3)*vc2 + - (gxzL*vb1 + gyzL*vb2 + gzzL*vb3)*vc3; + va3 = va3*pow(omega11,-khalf); - vc1 = -(omega13*va1) - omega23*vb1 + vc1; + CCTK_REAL omega12 = (gxxL*va1 + gxyL*va2 + gxzL*va3)*vb1 + (gxyL*va1 + + gyyL*va2 + gyzL*va3)*vb2 + (gxzL*va1 + gyzL*va2 + gzzL*va3)*vb3; - vc2 = -(omega13*va2) - omega23*vb2 + vc2; + vb1 = -(omega12*va1) + vb1; - vc3 = -(omega13*va3) - omega23*vb3 + vc3; + vb2 = -(omega12*va2) + vb2; - omega33 = 2*(gyzL*vc2*vc3 + vc1*(gxyL*vc2 + gxzL*vc3)) + gxxL*SQR(vc1) + gyyL*SQR(vc2) + gzzL*SQR(vc3); + vb3 = -(omega12*va3) + vb3; - vc1 = vc1*pow(omega33,-khalf); + CCTK_REAL omega22 = 2*(gyzL*vb2*vb3 + vb1*(gxyL*vb2 + gxzL*vb3)) + + gxxL*SQR(vb1) + gyyL*SQR(vb2) + gzzL*SQR(vb3); - vc2 = vc2*pow(omega33,-khalf); + vb1 = vb1*pow(omega22,-khalf); - vc3 = vc3*pow(omega33,-khalf); + vb2 = vb2*pow(omega22,-khalf); - isqrt2 = 0.707106781186547524; + vb3 = vb3*pow(omega22,-khalf); - n1 = -(isqrt2*vb1); + CCTK_REAL omega13 = (gxxL*va1 + gxyL*va2 + gxzL*va3)*vc1 + (gxyL*va1 + + gyyL*va2 + gyzL*va3)*vc2 + (gxzL*va1 + gyzL*va2 + gzzL*va3)*vc3; - n2 = -(isqrt2*vb2); + CCTK_REAL omega23 = (gxxL*vb1 + gxyL*vb2 + gxzL*vb3)*vc1 + (gxyL*vb1 + + gyyL*vb2 + gyzL*vb3)*vc2 + (gxzL*vb1 + gyzL*vb2 + gzzL*vb3)*vc3; - n3 = -(isqrt2*vb3); + vc1 = -(omega13*va1) - omega23*vb1 + vc1; - rm1 = isqrt2*vc1; + vc2 = -(omega13*va2) - omega23*vb2 + vc2; - rm2 = isqrt2*vc2; + vc3 = -(omega13*va3) - omega23*vb3 + vc3; - rm3 = isqrt2*vc3; + CCTK_REAL omega33 = 2*(gyzL*vc2*vc3 + vc1*(gxyL*vc2 + gxzL*vc3)) + + gxxL*SQR(vc1) + gyyL*SQR(vc2) + gzzL*SQR(vc3); - im1 = isqrt2*va1; + vc1 = vc1*pow(omega33,-khalf); - im2 = isqrt2*va2; + vc2 = vc2*pow(omega33,-khalf); - im3 = isqrt2*va3; + vc3 = vc3*pow(omega33,-khalf); - rmbar1 = isqrt2*vc1; + CCTK_REAL isqrt2 = 0.707106781186547524; - rmbar2 = isqrt2*vc2; + CCTK_REAL n1 = -(isqrt2*vb1); - rmbar3 = isqrt2*vc3; + CCTK_REAL n2 = -(isqrt2*vb2); - imbar1 = -(isqrt2*va1); + CCTK_REAL n3 = -(isqrt2*vb3); - imbar2 = -(isqrt2*va2); + CCTK_REAL rm1 = isqrt2*vc1; - imbar3 = -(isqrt2*va3); + CCTK_REAL rm2 = isqrt2*vc2; - nn = isqrt2; + CCTK_REAL rm3 = isqrt2*vc3; - R1111 = 0; + CCTK_REAL im1 = isqrt2*va1; - R1112 = 0; + CCTK_REAL im2 = isqrt2*va2; - R1113 = 0; + CCTK_REAL im3 = isqrt2*va3; - R1121 = 0; + CCTK_REAL rmbar1 = isqrt2*vc1; - R1122 = 0; + CCTK_REAL rmbar2 = isqrt2*vc2; - R1123 = 0; + CCTK_REAL rmbar3 = isqrt2*vc3; - R1131 = 0; + CCTK_REAL imbar1 = -(isqrt2*va1); - R1132 = 0; + CCTK_REAL imbar2 = -(isqrt2*va2); - R1133 = 0; + CCTK_REAL imbar3 = -(isqrt2*va3); - R1211 = 0; + CCTK_REAL nn = isqrt2; - R1212 = khalf*((4*gamma121*gamma221 - 2*gamma111*gamma222)*gxyL + (4*gamma121*gamma321 - 2*gamma111*gamma322)*gxzL + - (4*gamma221*gamma321 - 2*gamma211*gamma322)*gyzL - - 2*(gamma111*gamma122*gxxL + gamma122*gamma211*gxyL + gamma122*gamma311*gxzL + gamma211*gamma222*gyyL + - gamma222*gamma311*gyzL + gamma311*gamma322*gzzL) - PDstandard4th11gyy + 2*PDstandard4th12gxy - - PDstandard4th22gxx + 2*gxxL*SQR(gamma121) + 2*gyyL*SQR(gamma221) + 2*gzzL*SQR(gamma321)); + CCTK_REAL R1111 = 0; - R1213 = (gamma121*gamma131 - gamma111*gamma132)*gxxL + - (-(gamma132*gamma211) + gamma131*gamma221 + gamma121*gamma231 - gamma111*gamma232)*gxyL + - (-(gamma132*gamma311) + gamma131*gamma321 + gamma121*gamma331 - gamma111*gamma332)*gxzL + - (gamma221*gamma231 - gamma211*gamma232)*gyyL + - (-(gamma232*gamma311) + gamma231*gamma321 + gamma221*gamma331 - gamma211*gamma332)*gyzL + - (gamma321*gamma331 - gamma311*gamma332)*gzzL + - khalf*(-PDstandard4th11gyz + PDstandard4th12gxz + PDstandard4th13gxy - PDstandard4th23gxx); + CCTK_REAL R1112 = 0; - R1221 = (-2*gamma121*gamma221 + gamma111*gamma222)*gxyL + (-2*gamma121*gamma321 + gamma111*gamma322)*gxzL + - gamma122*(gamma111*gxxL + gamma211*gxyL + gamma311*gxzL) + (-2*gamma221*gamma321 + gamma211*gamma322)*gyzL + - gamma222*(gamma211*gyyL + gamma311*gyzL) - PDstandard4th12gxy + khalf*(PDstandard4th11gyy + PDstandard4th22gxx) - - gxxL*SQR(gamma121) - gyyL*SQR(gamma221) + gzzL*(gamma311*gamma322 - SQR(gamma321)); + CCTK_REAL R1113 = 0; - R1222 = 0; + CCTK_REAL R1121 = 0; - R1223 = (gamma122*gamma131 - gamma121*gamma132)*gxxL + - (-(gamma132*gamma221) + gamma131*gamma222 + gamma122*gamma231 - gamma121*gamma232)*gxyL + - (-(gamma132*gamma321) + gamma131*gamma322 + gamma122*gamma331 - gamma121*gamma332)*gxzL + - (gamma222*gamma231 - gamma221*gamma232)*gyyL + - (-(gamma232*gamma321) + gamma231*gamma322 + gamma222*gamma331 - gamma221*gamma332)*gyzL + - (gamma322*gamma331 - gamma321*gamma332)*gzzL + - khalf*(-PDstandard4th12gyz + PDstandard4th13gyy + PDstandard4th22gxz - PDstandard4th23gxy); + CCTK_REAL R1122 = 0; - R1231 = (-(gamma121*gamma131) + gamma111*gamma132)*gxxL + - (gamma132*gamma211 - gamma131*gamma221 - gamma121*gamma231 + gamma111*gamma232)*gxyL + - (gamma132*gamma311 - gamma131*gamma321 - gamma121*gamma331 + gamma111*gamma332)*gxzL + - (-(gamma221*gamma231) + gamma211*gamma232)*gyyL + - (gamma232*gamma311 - gamma231*gamma321 - gamma221*gamma331 + gamma211*gamma332)*gyzL + - (-(gamma321*gamma331) + gamma311*gamma332)*gzzL + - khalf*(PDstandard4th11gyz - PDstandard4th12gxz - PDstandard4th13gxy + PDstandard4th23gxx); + CCTK_REAL R1123 = 0; - R1232 = (-(gamma122*gamma131) + gamma121*gamma132)*gxxL + - (gamma132*gamma221 - gamma131*gamma222 - gamma122*gamma231 + gamma121*gamma232)*gxyL + - (gamma132*gamma321 - gamma131*gamma322 - gamma122*gamma331 + gamma121*gamma332)*gxzL + - (-(gamma222*gamma231) + gamma221*gamma232)*gyyL + - (gamma232*gamma321 - gamma231*gamma322 - gamma222*gamma331 + gamma221*gamma332)*gyzL + - (-(gamma322*gamma331) + gamma321*gamma332)*gzzL + - khalf*(PDstandard4th12gyz - PDstandard4th13gyy - PDstandard4th22gxz + PDstandard4th23gxy); + CCTK_REAL R1131 = 0; - R1233 = 0; + CCTK_REAL R1132 = 0; - R1311 = 0; + CCTK_REAL R1133 = 0; - R1312 = (gamma121*gamma131 - gamma111*gamma132)*gxxL + - (-(gamma132*gamma211) + gamma131*gamma221 + gamma121*gamma231 - gamma111*gamma232)*gxyL + - (-(gamma132*gamma311) + gamma131*gamma321 + gamma121*gamma331 - gamma111*gamma332)*gxzL + - (gamma221*gamma231 - gamma211*gamma232)*gyyL + - (-(gamma232*gamma311) + gamma231*gamma321 + gamma221*gamma331 - gamma211*gamma332)*gyzL + - (gamma321*gamma331 - gamma311*gamma332)*gzzL + - khalf*(-PDstandard4th11gyz + PDstandard4th12gxz + PDstandard4th13gxy - PDstandard4th23gxx); + CCTK_REAL R1211 = 0; - R1313 = khalf*((4*gamma131*gamma231 - 2*gamma111*gamma233)*gxyL + (4*gamma131*gamma331 - 2*gamma111*gamma333)*gxzL + - (4*gamma231*gamma331 - 2*gamma211*gamma333)*gyzL - - 2*(gamma111*gamma133*gxxL + gamma133*gamma211*gxyL + gamma133*gamma311*gxzL + gamma211*gamma233*gyyL + - gamma233*gamma311*gyzL + gamma311*gamma333*gzzL) - PDstandard4th11gzz + 2*PDstandard4th13gxz - - PDstandard4th33gxx + 2*gxxL*SQR(gamma131) + 2*gyyL*SQR(gamma231) + 2*gzzL*SQR(gamma331)); + CCTK_REAL R1212 = khalf*((4*gamma121*gamma221 - + 2*gamma111*gamma222)*gxyL + (4*gamma121*gamma321 - + 2*gamma111*gamma322)*gxzL + (4*gamma221*gamma321 - + 2*gamma211*gamma322)*gyzL - 2*(gamma111*gamma122*gxxL + + gamma122*gamma211*gxyL + gamma122*gamma311*gxzL + + gamma211*gamma222*gyyL + gamma222*gamma311*gyzL + + gamma311*gamma322*gzzL) - PDstandard4th11gyy + 2*PDstandard4th12gxy - + PDstandard4th22gxx + 2*gxxL*SQR(gamma121) + 2*gyyL*SQR(gamma221) + + 2*gzzL*SQR(gamma321)); - R1321 = (-(gamma121*gamma131) + gamma111*gamma132)*gxxL + - (gamma132*gamma211 - gamma131*gamma221 - gamma121*gamma231 + gamma111*gamma232)*gxyL + - (gamma132*gamma311 - gamma131*gamma321 - gamma121*gamma331 + gamma111*gamma332)*gxzL + - (-(gamma221*gamma231) + gamma211*gamma232)*gyyL + - (gamma232*gamma311 - gamma231*gamma321 - gamma221*gamma331 + gamma211*gamma332)*gyzL + - (-(gamma321*gamma331) + gamma311*gamma332)*gzzL + - khalf*(PDstandard4th11gyz - PDstandard4th12gxz - PDstandard4th13gxy + PDstandard4th23gxx); + CCTK_REAL R1213 = (gamma121*gamma131 - gamma111*gamma132)*gxxL + + (-(gamma132*gamma211) + gamma131*gamma221 + gamma121*gamma231 - + gamma111*gamma232)*gxyL + (-(gamma132*gamma311) + gamma131*gamma321 + + gamma121*gamma331 - gamma111*gamma332)*gxzL + (gamma221*gamma231 - + gamma211*gamma232)*gyyL + (-(gamma232*gamma311) + gamma231*gamma321 + + gamma221*gamma331 - gamma211*gamma332)*gyzL + (gamma321*gamma331 - + gamma311*gamma332)*gzzL + khalf*(-PDstandard4th11gyz + + PDstandard4th12gxz + PDstandard4th13gxy - PDstandard4th23gxx); - R1322 = 0; + CCTK_REAL R1221 = (-2*gamma121*gamma221 + gamma111*gamma222)*gxyL + + (-2*gamma121*gamma321 + gamma111*gamma322)*gxzL + + gamma122*(gamma111*gxxL + gamma211*gxyL + gamma311*gxzL) + + (-2*gamma221*gamma321 + gamma211*gamma322)*gyzL + + gamma222*(gamma211*gyyL + gamma311*gyzL) - PDstandard4th12gxy + + khalf*(PDstandard4th11gyy + PDstandard4th22gxx) - gxxL*SQR(gamma121) - + gyyL*SQR(gamma221) + gzzL*(gamma311*gamma322 - SQR(gamma321)); - R1323 = (gamma131*gamma132 - gamma121*gamma133)*gxxL + - (-(gamma133*gamma221) + gamma132*gamma231 + gamma131*gamma232 - gamma121*gamma233)*gxyL + - (-(gamma133*gamma321) + gamma132*gamma331 + gamma131*gamma332 - gamma121*gamma333)*gxzL + - (gamma231*gamma232 - gamma221*gamma233)*gyyL + - (-(gamma233*gamma321) + gamma232*gamma331 + gamma231*gamma332 - gamma221*gamma333)*gyzL + - (gamma331*gamma332 - gamma321*gamma333)*gzzL + - khalf*(-PDstandard4th12gzz + PDstandard4th13gyz + PDstandard4th23gxz - PDstandard4th33gxy); - - R1331 = (-2*gamma131*gamma231 + gamma111*gamma233)*gxyL + (-2*gamma131*gamma331 + gamma111*gamma333)*gxzL + - gamma133*(gamma111*gxxL + gamma211*gxyL + gamma311*gxzL) + (-2*gamma231*gamma331 + gamma211*gamma333)*gyzL + - gamma233*(gamma211*gyyL + gamma311*gyzL) - PDstandard4th13gxz + khalf*(PDstandard4th11gzz + PDstandard4th33gxx) - - gxxL*SQR(gamma131) - gyyL*SQR(gamma231) + gzzL*(gamma311*gamma333 - SQR(gamma331)); - - R1332 = (-(gamma131*gamma132) + gamma121*gamma133)*gxxL + - (gamma133*gamma221 - gamma132*gamma231 - gamma131*gamma232 + gamma121*gamma233)*gxyL + - (gamma133*gamma321 - gamma132*gamma331 - gamma131*gamma332 + gamma121*gamma333)*gxzL + - (-(gamma231*gamma232) + gamma221*gamma233)*gyyL + - (gamma233*gamma321 - gamma232*gamma331 - gamma231*gamma332 + gamma221*gamma333)*gyzL + - (-(gamma331*gamma332) + gamma321*gamma333)*gzzL + - khalf*(PDstandard4th12gzz - PDstandard4th13gyz - PDstandard4th23gxz + PDstandard4th33gxy); - - R1333 = 0; - - R2111 = 0; - - R2112 = (-2*gamma121*gamma221 + gamma111*gamma222)*gxyL + (-2*gamma121*gamma321 + gamma111*gamma322)*gxzL + - gamma122*(gamma111*gxxL + gamma211*gxyL + gamma311*gxzL) + (-2*gamma221*gamma321 + gamma211*gamma322)*gyzL + - gamma222*(gamma211*gyyL + gamma311*gyzL) - PDstandard4th12gxy + khalf*(PDstandard4th11gyy + PDstandard4th22gxx) - - gxxL*SQR(gamma121) - gyyL*SQR(gamma221) + gzzL*(gamma311*gamma322 - SQR(gamma321)); - - R2113 = (-(gamma121*gamma131) + gamma111*gamma132)*gxxL + - (gamma132*gamma211 - gamma131*gamma221 - gamma121*gamma231 + gamma111*gamma232)*gxyL + - (gamma132*gamma311 - gamma131*gamma321 - gamma121*gamma331 + gamma111*gamma332)*gxzL + - (-(gamma221*gamma231) + gamma211*gamma232)*gyyL + - (gamma232*gamma311 - gamma231*gamma321 - gamma221*gamma331 + gamma211*gamma332)*gyzL + - (-(gamma321*gamma331) + gamma311*gamma332)*gzzL + - khalf*(PDstandard4th11gyz - PDstandard4th12gxz - PDstandard4th13gxy + PDstandard4th23gxx); - - R2121 = khalf*((4*gamma121*gamma221 - 2*gamma111*gamma222)*gxyL + (4*gamma121*gamma321 - 2*gamma111*gamma322)*gxzL + - (4*gamma221*gamma321 - 2*gamma211*gamma322)*gyzL - - 2*(gamma111*gamma122*gxxL + gamma122*gamma211*gxyL + gamma122*gamma311*gxzL + gamma211*gamma222*gyyL + - gamma222*gamma311*gyzL + gamma311*gamma322*gzzL) - PDstandard4th11gyy + 2*PDstandard4th12gxy - - PDstandard4th22gxx + 2*gxxL*SQR(gamma121) + 2*gyyL*SQR(gamma221) + 2*gzzL*SQR(gamma321)); - - R2122 = 0; - - R2123 = (-(gamma122*gamma131) + gamma121*gamma132)*gxxL + - (gamma132*gamma221 - gamma131*gamma222 - gamma122*gamma231 + gamma121*gamma232)*gxyL + - (gamma132*gamma321 - gamma131*gamma322 - gamma122*gamma331 + gamma121*gamma332)*gxzL + - (-(gamma222*gamma231) + gamma221*gamma232)*gyyL + - (gamma232*gamma321 - gamma231*gamma322 - gamma222*gamma331 + gamma221*gamma332)*gyzL + - (-(gamma322*gamma331) + gamma321*gamma332)*gzzL + - khalf*(PDstandard4th12gyz - PDstandard4th13gyy - PDstandard4th22gxz + PDstandard4th23gxy); - - R2131 = (gamma121*gamma131 - gamma111*gamma132)*gxxL + - (-(gamma132*gamma211) + gamma131*gamma221 + gamma121*gamma231 - gamma111*gamma232)*gxyL + - (-(gamma132*gamma311) + gamma131*gamma321 + gamma121*gamma331 - gamma111*gamma332)*gxzL + - (gamma221*gamma231 - gamma211*gamma232)*gyyL + - (-(gamma232*gamma311) + gamma231*gamma321 + gamma221*gamma331 - gamma211*gamma332)*gyzL + - (gamma321*gamma331 - gamma311*gamma332)*gzzL + - khalf*(-PDstandard4th11gyz + PDstandard4th12gxz + PDstandard4th13gxy - PDstandard4th23gxx); - - R2132 = (gamma122*gamma131 - gamma121*gamma132)*gxxL + - (-(gamma132*gamma221) + gamma131*gamma222 + gamma122*gamma231 - gamma121*gamma232)*gxyL + - (-(gamma132*gamma321) + gamma131*gamma322 + gamma122*gamma331 - gamma121*gamma332)*gxzL + - (gamma222*gamma231 - gamma221*gamma232)*gyyL + - (-(gamma232*gamma321) + gamma231*gamma322 + gamma222*gamma331 - gamma221*gamma332)*gyzL + - (gamma322*gamma331 - gamma321*gamma332)*gzzL + - khalf*(-PDstandard4th12gyz + PDstandard4th13gyy + PDstandard4th22gxz - PDstandard4th23gxy); - - R2133 = 0; - - R2211 = 0; - - R2212 = 0; - - R2213 = 0; - - R2221 = 0; - - R2222 = 0; - - R2223 = 0; - - R2231 = 0; - - R2232 = 0; - - R2233 = 0; - - R2311 = 0; - - R2312 = (gamma122*gamma131 - gamma121*gamma132)*gxxL + - (-(gamma132*gamma221) + gamma131*gamma222 + gamma122*gamma231 - gamma121*gamma232)*gxyL + - (-(gamma132*gamma321) + gamma131*gamma322 + gamma122*gamma331 - gamma121*gamma332)*gxzL + - (gamma222*gamma231 - gamma221*gamma232)*gyyL + - (-(gamma232*gamma321) + gamma231*gamma322 + gamma222*gamma331 - gamma221*gamma332)*gyzL + - (gamma322*gamma331 - gamma321*gamma332)*gzzL + - khalf*(-PDstandard4th12gyz + PDstandard4th13gyy + PDstandard4th22gxz - PDstandard4th23gxy); - - R2313 = (gamma131*gamma132 - gamma121*gamma133)*gxxL + - (-(gamma133*gamma221) + gamma132*gamma231 + gamma131*gamma232 - gamma121*gamma233)*gxyL + - (-(gamma133*gamma321) + gamma132*gamma331 + gamma131*gamma332 - gamma121*gamma333)*gxzL + - (gamma231*gamma232 - gamma221*gamma233)*gyyL + - (-(gamma233*gamma321) + gamma232*gamma331 + gamma231*gamma332 - gamma221*gamma333)*gyzL + - (gamma331*gamma332 - gamma321*gamma333)*gzzL + - khalf*(-PDstandard4th12gzz + PDstandard4th13gyz + PDstandard4th23gxz - PDstandard4th33gxy); - - R2321 = (-(gamma122*gamma131) + gamma121*gamma132)*gxxL + - (gamma132*gamma221 - gamma131*gamma222 - gamma122*gamma231 + gamma121*gamma232)*gxyL + - (gamma132*gamma321 - gamma131*gamma322 - gamma122*gamma331 + gamma121*gamma332)*gxzL + - (-(gamma222*gamma231) + gamma221*gamma232)*gyyL + - (gamma232*gamma321 - gamma231*gamma322 - gamma222*gamma331 + gamma221*gamma332)*gyzL + - (-(gamma322*gamma331) + gamma321*gamma332)*gzzL + - khalf*(PDstandard4th12gyz - PDstandard4th13gyy - PDstandard4th22gxz + PDstandard4th23gxy); - - R2322 = 0; - - R2323 = khalf*((4*gamma132*gamma232 - 2*gamma122*gamma233)*gxyL + (4*gamma132*gamma332 - 2*gamma122*gamma333)*gxzL + - (4*gamma232*gamma332 - 2*gamma222*gamma333)*gyzL - - 2*(gamma122*gamma133*gxxL + gamma133*gamma222*gxyL + gamma133*gamma322*gxzL + gamma222*gamma233*gyyL + - gamma233*gamma322*gyzL + gamma322*gamma333*gzzL) - PDstandard4th22gzz + 2*PDstandard4th23gyz - - PDstandard4th33gyy + 2*gxxL*SQR(gamma132) + 2*gyyL*SQR(gamma232) + 2*gzzL*SQR(gamma332)); - - R2331 = (-(gamma131*gamma132) + gamma121*gamma133)*gxxL + - (gamma133*gamma221 - gamma132*gamma231 - gamma131*gamma232 + gamma121*gamma233)*gxyL + - (gamma133*gamma321 - gamma132*gamma331 - gamma131*gamma332 + gamma121*gamma333)*gxzL + - (-(gamma231*gamma232) + gamma221*gamma233)*gyyL + - (gamma233*gamma321 - gamma232*gamma331 - gamma231*gamma332 + gamma221*gamma333)*gyzL + - (-(gamma331*gamma332) + gamma321*gamma333)*gzzL + - khalf*(PDstandard4th12gzz - PDstandard4th13gyz - PDstandard4th23gxz + PDstandard4th33gxy); - - R2332 = (-2*gamma132*gamma232 + gamma122*gamma233)*gxyL + (-2*gamma132*gamma332 + gamma122*gamma333)*gxzL + - gamma133*(gamma122*gxxL + gamma222*gxyL + gamma322*gxzL) + (-2*gamma232*gamma332 + gamma222*gamma333)*gyzL + - gamma233*(gamma222*gyyL + gamma322*gyzL) - PDstandard4th23gyz + khalf*(PDstandard4th22gzz + PDstandard4th33gyy) - - gxxL*SQR(gamma132) - gyyL*SQR(gamma232) + gzzL*(gamma322*gamma333 - SQR(gamma332)); - - R2333 = 0; - - R3111 = 0; - - R3112 = (-(gamma121*gamma131) + gamma111*gamma132)*gxxL + - (gamma132*gamma211 - gamma131*gamma221 - gamma121*gamma231 + gamma111*gamma232)*gxyL + - (gamma132*gamma311 - gamma131*gamma321 - gamma121*gamma331 + gamma111*gamma332)*gxzL + - (-(gamma221*gamma231) + gamma211*gamma232)*gyyL + - (gamma232*gamma311 - gamma231*gamma321 - gamma221*gamma331 + gamma211*gamma332)*gyzL + - (-(gamma321*gamma331) + gamma311*gamma332)*gzzL + - khalf*(PDstandard4th11gyz - PDstandard4th12gxz - PDstandard4th13gxy + PDstandard4th23gxx); - - R3113 = (-2*gamma131*gamma231 + gamma111*gamma233)*gxyL + (-2*gamma131*gamma331 + gamma111*gamma333)*gxzL + - gamma133*(gamma111*gxxL + gamma211*gxyL + gamma311*gxzL) + (-2*gamma231*gamma331 + gamma211*gamma333)*gyzL + - gamma233*(gamma211*gyyL + gamma311*gyzL) - PDstandard4th13gxz + khalf*(PDstandard4th11gzz + PDstandard4th33gxx) - - gxxL*SQR(gamma131) - gyyL*SQR(gamma231) + gzzL*(gamma311*gamma333 - SQR(gamma331)); - - R3121 = (gamma121*gamma131 - gamma111*gamma132)*gxxL + - (-(gamma132*gamma211) + gamma131*gamma221 + gamma121*gamma231 - gamma111*gamma232)*gxyL + - (-(gamma132*gamma311) + gamma131*gamma321 + gamma121*gamma331 - gamma111*gamma332)*gxzL + - (gamma221*gamma231 - gamma211*gamma232)*gyyL + - (-(gamma232*gamma311) + gamma231*gamma321 + gamma221*gamma331 - gamma211*gamma332)*gyzL + - (gamma321*gamma331 - gamma311*gamma332)*gzzL + - khalf*(-PDstandard4th11gyz + PDstandard4th12gxz + PDstandard4th13gxy - PDstandard4th23gxx); + CCTK_REAL R1222 = 0; - R3122 = 0; + CCTK_REAL R1223 = (gamma122*gamma131 - gamma121*gamma132)*gxxL + + (-(gamma132*gamma221) + gamma131*gamma222 + gamma122*gamma231 - + gamma121*gamma232)*gxyL + (-(gamma132*gamma321) + gamma131*gamma322 + + gamma122*gamma331 - gamma121*gamma332)*gxzL + (gamma222*gamma231 - + gamma221*gamma232)*gyyL + (-(gamma232*gamma321) + gamma231*gamma322 + + gamma222*gamma331 - gamma221*gamma332)*gyzL + (gamma322*gamma331 - + gamma321*gamma332)*gzzL + khalf*(-PDstandard4th12gyz + + PDstandard4th13gyy + PDstandard4th22gxz - PDstandard4th23gxy); - R3123 = (-(gamma131*gamma132) + gamma121*gamma133)*gxxL + - (gamma133*gamma221 - gamma132*gamma231 - gamma131*gamma232 + gamma121*gamma233)*gxyL + - (gamma133*gamma321 - gamma132*gamma331 - gamma131*gamma332 + gamma121*gamma333)*gxzL + - (-(gamma231*gamma232) + gamma221*gamma233)*gyyL + - (gamma233*gamma321 - gamma232*gamma331 - gamma231*gamma332 + gamma221*gamma333)*gyzL + - (-(gamma331*gamma332) + gamma321*gamma333)*gzzL + - khalf*(PDstandard4th12gzz - PDstandard4th13gyz - PDstandard4th23gxz + PDstandard4th33gxy); + CCTK_REAL R1231 = (-(gamma121*gamma131) + gamma111*gamma132)*gxxL + + (gamma132*gamma211 - gamma131*gamma221 - gamma121*gamma231 + + gamma111*gamma232)*gxyL + (gamma132*gamma311 - gamma131*gamma321 - + gamma121*gamma331 + gamma111*gamma332)*gxzL + (-(gamma221*gamma231) + + gamma211*gamma232)*gyyL + (gamma232*gamma311 - gamma231*gamma321 - + gamma221*gamma331 + gamma211*gamma332)*gyzL + (-(gamma321*gamma331) + + gamma311*gamma332)*gzzL + khalf*(PDstandard4th11gyz - + PDstandard4th12gxz - PDstandard4th13gxy + PDstandard4th23gxx); + + CCTK_REAL R1232 = (-(gamma122*gamma131) + gamma121*gamma132)*gxxL + + (gamma132*gamma221 - gamma131*gamma222 - gamma122*gamma231 + + gamma121*gamma232)*gxyL + (gamma132*gamma321 - gamma131*gamma322 - + gamma122*gamma331 + gamma121*gamma332)*gxzL + (-(gamma222*gamma231) + + gamma221*gamma232)*gyyL + (gamma232*gamma321 - gamma231*gamma322 - + gamma222*gamma331 + gamma221*gamma332)*gyzL + (-(gamma322*gamma331) + + gamma321*gamma332)*gzzL + khalf*(PDstandard4th12gyz - + PDstandard4th13gyy - PDstandard4th22gxz + PDstandard4th23gxy); + + CCTK_REAL R1233 = 0; + + CCTK_REAL R1311 = 0; + + CCTK_REAL R1312 = (gamma121*gamma131 - gamma111*gamma132)*gxxL + + (-(gamma132*gamma211) + gamma131*gamma221 + gamma121*gamma231 - + gamma111*gamma232)*gxyL + (-(gamma132*gamma311) + gamma131*gamma321 + + gamma121*gamma331 - gamma111*gamma332)*gxzL + (gamma221*gamma231 - + gamma211*gamma232)*gyyL + (-(gamma232*gamma311) + gamma231*gamma321 + + gamma221*gamma331 - gamma211*gamma332)*gyzL + (gamma321*gamma331 - + gamma311*gamma332)*gzzL + khalf*(-PDstandard4th11gyz + + PDstandard4th12gxz + PDstandard4th13gxy - PDstandard4th23gxx); + + CCTK_REAL R1313 = khalf*((4*gamma131*gamma231 - + 2*gamma111*gamma233)*gxyL + (4*gamma131*gamma331 - + 2*gamma111*gamma333)*gxzL + (4*gamma231*gamma331 - + 2*gamma211*gamma333)*gyzL - 2*(gamma111*gamma133*gxxL + + gamma133*gamma211*gxyL + gamma133*gamma311*gxzL + + gamma211*gamma233*gyyL + gamma233*gamma311*gyzL + + gamma311*gamma333*gzzL) - PDstandard4th11gzz + 2*PDstandard4th13gxz - + PDstandard4th33gxx + 2*gxxL*SQR(gamma131) + 2*gyyL*SQR(gamma231) + + 2*gzzL*SQR(gamma331)); + + CCTK_REAL R1321 = (-(gamma121*gamma131) + gamma111*gamma132)*gxxL + + (gamma132*gamma211 - gamma131*gamma221 - gamma121*gamma231 + + gamma111*gamma232)*gxyL + (gamma132*gamma311 - gamma131*gamma321 - + gamma121*gamma331 + gamma111*gamma332)*gxzL + (-(gamma221*gamma231) + + gamma211*gamma232)*gyyL + (gamma232*gamma311 - gamma231*gamma321 - + gamma221*gamma331 + gamma211*gamma332)*gyzL + (-(gamma321*gamma331) + + gamma311*gamma332)*gzzL + khalf*(PDstandard4th11gyz - + PDstandard4th12gxz - PDstandard4th13gxy + PDstandard4th23gxx); + + CCTK_REAL R1322 = 0; + + CCTK_REAL R1323 = (gamma131*gamma132 - gamma121*gamma133)*gxxL + + (-(gamma133*gamma221) + gamma132*gamma231 + gamma131*gamma232 - + gamma121*gamma233)*gxyL + (-(gamma133*gamma321) + gamma132*gamma331 + + gamma131*gamma332 - gamma121*gamma333)*gxzL + (gamma231*gamma232 - + gamma221*gamma233)*gyyL + (-(gamma233*gamma321) + gamma232*gamma331 + + gamma231*gamma332 - gamma221*gamma333)*gyzL + (gamma331*gamma332 - + gamma321*gamma333)*gzzL + khalf*(-PDstandard4th12gzz + + PDstandard4th13gyz + PDstandard4th23gxz - PDstandard4th33gxy); + + CCTK_REAL R1331 = (-2*gamma131*gamma231 + gamma111*gamma233)*gxyL + + (-2*gamma131*gamma331 + gamma111*gamma333)*gxzL + + gamma133*(gamma111*gxxL + gamma211*gxyL + gamma311*gxzL) + + (-2*gamma231*gamma331 + gamma211*gamma333)*gyzL + + gamma233*(gamma211*gyyL + gamma311*gyzL) - PDstandard4th13gxz + + khalf*(PDstandard4th11gzz + PDstandard4th33gxx) - gxxL*SQR(gamma131) - + gyyL*SQR(gamma231) + gzzL*(gamma311*gamma333 - SQR(gamma331)); + + CCTK_REAL R1332 = (-(gamma131*gamma132) + gamma121*gamma133)*gxxL + + (gamma133*gamma221 - gamma132*gamma231 - gamma131*gamma232 + + gamma121*gamma233)*gxyL + (gamma133*gamma321 - gamma132*gamma331 - + gamma131*gamma332 + gamma121*gamma333)*gxzL + (-(gamma231*gamma232) + + gamma221*gamma233)*gyyL + (gamma233*gamma321 - gamma232*gamma331 - + gamma231*gamma332 + gamma221*gamma333)*gyzL + (-(gamma331*gamma332) + + gamma321*gamma333)*gzzL + khalf*(PDstandard4th12gzz - + PDstandard4th13gyz - PDstandard4th23gxz + PDstandard4th33gxy); + + CCTK_REAL R1333 = 0; + + CCTK_REAL R2111 = 0; + + CCTK_REAL R2112 = (-2*gamma121*gamma221 + gamma111*gamma222)*gxyL + + (-2*gamma121*gamma321 + gamma111*gamma322)*gxzL + + gamma122*(gamma111*gxxL + gamma211*gxyL + gamma311*gxzL) + + (-2*gamma221*gamma321 + gamma211*gamma322)*gyzL + + gamma222*(gamma211*gyyL + gamma311*gyzL) - PDstandard4th12gxy + + khalf*(PDstandard4th11gyy + PDstandard4th22gxx) - gxxL*SQR(gamma121) - + gyyL*SQR(gamma221) + gzzL*(gamma311*gamma322 - SQR(gamma321)); + + CCTK_REAL R2113 = (-(gamma121*gamma131) + gamma111*gamma132)*gxxL + + (gamma132*gamma211 - gamma131*gamma221 - gamma121*gamma231 + + gamma111*gamma232)*gxyL + (gamma132*gamma311 - gamma131*gamma321 - + gamma121*gamma331 + gamma111*gamma332)*gxzL + (-(gamma221*gamma231) + + gamma211*gamma232)*gyyL + (gamma232*gamma311 - gamma231*gamma321 - + gamma221*gamma331 + gamma211*gamma332)*gyzL + (-(gamma321*gamma331) + + gamma311*gamma332)*gzzL + khalf*(PDstandard4th11gyz - + PDstandard4th12gxz - PDstandard4th13gxy + PDstandard4th23gxx); + + CCTK_REAL R2121 = khalf*((4*gamma121*gamma221 - + 2*gamma111*gamma222)*gxyL + (4*gamma121*gamma321 - + 2*gamma111*gamma322)*gxzL + (4*gamma221*gamma321 - + 2*gamma211*gamma322)*gyzL - 2*(gamma111*gamma122*gxxL + + gamma122*gamma211*gxyL + gamma122*gamma311*gxzL + + gamma211*gamma222*gyyL + gamma222*gamma311*gyzL + + gamma311*gamma322*gzzL) - PDstandard4th11gyy + 2*PDstandard4th12gxy - + PDstandard4th22gxx + 2*gxxL*SQR(gamma121) + 2*gyyL*SQR(gamma221) + + 2*gzzL*SQR(gamma321)); + + CCTK_REAL R2122 = 0; + + CCTK_REAL R2123 = (-(gamma122*gamma131) + gamma121*gamma132)*gxxL + + (gamma132*gamma221 - gamma131*gamma222 - gamma122*gamma231 + + gamma121*gamma232)*gxyL + (gamma132*gamma321 - gamma131*gamma322 - + gamma122*gamma331 + gamma121*gamma332)*gxzL + (-(gamma222*gamma231) + + gamma221*gamma232)*gyyL + (gamma232*gamma321 - gamma231*gamma322 - + gamma222*gamma331 + gamma221*gamma332)*gyzL + (-(gamma322*gamma331) + + gamma321*gamma332)*gzzL + khalf*(PDstandard4th12gyz - + PDstandard4th13gyy - PDstandard4th22gxz + PDstandard4th23gxy); + + CCTK_REAL R2131 = (gamma121*gamma131 - gamma111*gamma132)*gxxL + + (-(gamma132*gamma211) + gamma131*gamma221 + gamma121*gamma231 - + gamma111*gamma232)*gxyL + (-(gamma132*gamma311) + gamma131*gamma321 + + gamma121*gamma331 - gamma111*gamma332)*gxzL + (gamma221*gamma231 - + gamma211*gamma232)*gyyL + (-(gamma232*gamma311) + gamma231*gamma321 + + gamma221*gamma331 - gamma211*gamma332)*gyzL + (gamma321*gamma331 - + gamma311*gamma332)*gzzL + khalf*(-PDstandard4th11gyz + + PDstandard4th12gxz + PDstandard4th13gxy - PDstandard4th23gxx); + + CCTK_REAL R2132 = (gamma122*gamma131 - gamma121*gamma132)*gxxL + + (-(gamma132*gamma221) + gamma131*gamma222 + gamma122*gamma231 - + gamma121*gamma232)*gxyL + (-(gamma132*gamma321) + gamma131*gamma322 + + gamma122*gamma331 - gamma121*gamma332)*gxzL + (gamma222*gamma231 - + gamma221*gamma232)*gyyL + (-(gamma232*gamma321) + gamma231*gamma322 + + gamma222*gamma331 - gamma221*gamma332)*gyzL + (gamma322*gamma331 - + gamma321*gamma332)*gzzL + khalf*(-PDstandard4th12gyz + + PDstandard4th13gyy + PDstandard4th22gxz - PDstandard4th23gxy); + + CCTK_REAL R2133 = 0; + + CCTK_REAL R2211 = 0; + + CCTK_REAL R2212 = 0; + + CCTK_REAL R2213 = 0; + + CCTK_REAL R2221 = 0; + + CCTK_REAL R2222 = 0; + + CCTK_REAL R2223 = 0; + + CCTK_REAL R2231 = 0; + + CCTK_REAL R2232 = 0; + + CCTK_REAL R2233 = 0; + + CCTK_REAL R2311 = 0; + + CCTK_REAL R2312 = (gamma122*gamma131 - gamma121*gamma132)*gxxL + + (-(gamma132*gamma221) + gamma131*gamma222 + gamma122*gamma231 - + gamma121*gamma232)*gxyL + (-(gamma132*gamma321) + gamma131*gamma322 + + gamma122*gamma331 - gamma121*gamma332)*gxzL + (gamma222*gamma231 - + gamma221*gamma232)*gyyL + (-(gamma232*gamma321) + gamma231*gamma322 + + gamma222*gamma331 - gamma221*gamma332)*gyzL + (gamma322*gamma331 - + gamma321*gamma332)*gzzL + khalf*(-PDstandard4th12gyz + + PDstandard4th13gyy + PDstandard4th22gxz - PDstandard4th23gxy); + + CCTK_REAL R2313 = (gamma131*gamma132 - gamma121*gamma133)*gxxL + + (-(gamma133*gamma221) + gamma132*gamma231 + gamma131*gamma232 - + gamma121*gamma233)*gxyL + (-(gamma133*gamma321) + gamma132*gamma331 + + gamma131*gamma332 - gamma121*gamma333)*gxzL + (gamma231*gamma232 - + gamma221*gamma233)*gyyL + (-(gamma233*gamma321) + gamma232*gamma331 + + gamma231*gamma332 - gamma221*gamma333)*gyzL + (gamma331*gamma332 - + gamma321*gamma333)*gzzL + khalf*(-PDstandard4th12gzz + + PDstandard4th13gyz + PDstandard4th23gxz - PDstandard4th33gxy); + + CCTK_REAL R2321 = (-(gamma122*gamma131) + gamma121*gamma132)*gxxL + + (gamma132*gamma221 - gamma131*gamma222 - gamma122*gamma231 + + gamma121*gamma232)*gxyL + (gamma132*gamma321 - gamma131*gamma322 - + gamma122*gamma331 + gamma121*gamma332)*gxzL + (-(gamma222*gamma231) + + gamma221*gamma232)*gyyL + (gamma232*gamma321 - gamma231*gamma322 - + gamma222*gamma331 + gamma221*gamma332)*gyzL + (-(gamma322*gamma331) + + gamma321*gamma332)*gzzL + khalf*(PDstandard4th12gyz - + PDstandard4th13gyy - PDstandard4th22gxz + PDstandard4th23gxy); + + CCTK_REAL R2322 = 0; + + CCTK_REAL R2323 = khalf*((4*gamma132*gamma232 - + 2*gamma122*gamma233)*gxyL + (4*gamma132*gamma332 - + 2*gamma122*gamma333)*gxzL + (4*gamma232*gamma332 - + 2*gamma222*gamma333)*gyzL - 2*(gamma122*gamma133*gxxL + + gamma133*gamma222*gxyL + gamma133*gamma322*gxzL + + gamma222*gamma233*gyyL + gamma233*gamma322*gyzL + + gamma322*gamma333*gzzL) - PDstandard4th22gzz + 2*PDstandard4th23gyz - + PDstandard4th33gyy + 2*gxxL*SQR(gamma132) + 2*gyyL*SQR(gamma232) + + 2*gzzL*SQR(gamma332)); + + CCTK_REAL R2331 = (-(gamma131*gamma132) + gamma121*gamma133)*gxxL + + (gamma133*gamma221 - gamma132*gamma231 - gamma131*gamma232 + + gamma121*gamma233)*gxyL + (gamma133*gamma321 - gamma132*gamma331 - + gamma131*gamma332 + gamma121*gamma333)*gxzL + (-(gamma231*gamma232) + + gamma221*gamma233)*gyyL + (gamma233*gamma321 - gamma232*gamma331 - + gamma231*gamma332 + gamma221*gamma333)*gyzL + (-(gamma331*gamma332) + + gamma321*gamma333)*gzzL + khalf*(PDstandard4th12gzz - + PDstandard4th13gyz - PDstandard4th23gxz + PDstandard4th33gxy); + + CCTK_REAL R2332 = (-2*gamma132*gamma232 + gamma122*gamma233)*gxyL + + (-2*gamma132*gamma332 + gamma122*gamma333)*gxzL + + gamma133*(gamma122*gxxL + gamma222*gxyL + gamma322*gxzL) + + (-2*gamma232*gamma332 + gamma222*gamma333)*gyzL + + gamma233*(gamma222*gyyL + gamma322*gyzL) - PDstandard4th23gyz + + khalf*(PDstandard4th22gzz + PDstandard4th33gyy) - gxxL*SQR(gamma132) - + gyyL*SQR(gamma232) + gzzL*(gamma322*gamma333 - SQR(gamma332)); + + CCTK_REAL R2333 = 0; + + CCTK_REAL R3111 = 0; + + CCTK_REAL R3112 = (-(gamma121*gamma131) + gamma111*gamma132)*gxxL + + (gamma132*gamma211 - gamma131*gamma221 - gamma121*gamma231 + + gamma111*gamma232)*gxyL + (gamma132*gamma311 - gamma131*gamma321 - + gamma121*gamma331 + gamma111*gamma332)*gxzL + (-(gamma221*gamma231) + + gamma211*gamma232)*gyyL + (gamma232*gamma311 - gamma231*gamma321 - + gamma221*gamma331 + gamma211*gamma332)*gyzL + (-(gamma321*gamma331) + + gamma311*gamma332)*gzzL + khalf*(PDstandard4th11gyz - + PDstandard4th12gxz - PDstandard4th13gxy + PDstandard4th23gxx); + + CCTK_REAL R3113 = (-2*gamma131*gamma231 + gamma111*gamma233)*gxyL + + (-2*gamma131*gamma331 + gamma111*gamma333)*gxzL + + gamma133*(gamma111*gxxL + gamma211*gxyL + gamma311*gxzL) + + (-2*gamma231*gamma331 + gamma211*gamma333)*gyzL + + gamma233*(gamma211*gyyL + gamma311*gyzL) - PDstandard4th13gxz + + khalf*(PDstandard4th11gzz + PDstandard4th33gxx) - gxxL*SQR(gamma131) - + gyyL*SQR(gamma231) + gzzL*(gamma311*gamma333 - SQR(gamma331)); + + CCTK_REAL R3121 = (gamma121*gamma131 - gamma111*gamma132)*gxxL + + (-(gamma132*gamma211) + gamma131*gamma221 + gamma121*gamma231 - + gamma111*gamma232)*gxyL + (-(gamma132*gamma311) + gamma131*gamma321 + + gamma121*gamma331 - gamma111*gamma332)*gxzL + (gamma221*gamma231 - + gamma211*gamma232)*gyyL + (-(gamma232*gamma311) + gamma231*gamma321 + + gamma221*gamma331 - gamma211*gamma332)*gyzL + (gamma321*gamma331 - + gamma311*gamma332)*gzzL + khalf*(-PDstandard4th11gyz + + PDstandard4th12gxz + PDstandard4th13gxy - PDstandard4th23gxx); + + CCTK_REAL R3122 = 0; + + CCTK_REAL R3123 = (-(gamma131*gamma132) + gamma121*gamma133)*gxxL + + (gamma133*gamma221 - gamma132*gamma231 - gamma131*gamma232 + + gamma121*gamma233)*gxyL + (gamma133*gamma321 - gamma132*gamma331 - + gamma131*gamma332 + gamma121*gamma333)*gxzL + (-(gamma231*gamma232) + + gamma221*gamma233)*gyyL + (gamma233*gamma321 - gamma232*gamma331 - + gamma231*gamma332 + gamma221*gamma333)*gyzL + (-(gamma331*gamma332) + + gamma321*gamma333)*gzzL + khalf*(PDstandard4th12gzz - + PDstandard4th13gyz - PDstandard4th23gxz + PDstandard4th33gxy); + + CCTK_REAL R3131 = khalf*((4*gamma131*gamma231 - + 2*gamma111*gamma233)*gxyL + (4*gamma131*gamma331 - + 2*gamma111*gamma333)*gxzL + (4*gamma231*gamma331 - + 2*gamma211*gamma333)*gyzL - 2*(gamma111*gamma133*gxxL + + gamma133*gamma211*gxyL + gamma133*gamma311*gxzL + + gamma211*gamma233*gyyL + gamma233*gamma311*gyzL + + gamma311*gamma333*gzzL) - PDstandard4th11gzz + 2*PDstandard4th13gxz - + PDstandard4th33gxx + 2*gxxL*SQR(gamma131) + 2*gyyL*SQR(gamma231) + + 2*gzzL*SQR(gamma331)); + + CCTK_REAL R3132 = (gamma131*gamma132 - gamma121*gamma133)*gxxL + + (-(gamma133*gamma221) + gamma132*gamma231 + gamma131*gamma232 - + gamma121*gamma233)*gxyL + (-(gamma133*gamma321) + gamma132*gamma331 + + gamma131*gamma332 - gamma121*gamma333)*gxzL + (gamma231*gamma232 - + gamma221*gamma233)*gyyL + (-(gamma233*gamma321) + gamma232*gamma331 + + gamma231*gamma332 - gamma221*gamma333)*gyzL + (gamma331*gamma332 - + gamma321*gamma333)*gzzL + khalf*(-PDstandard4th12gzz + + PDstandard4th13gyz + PDstandard4th23gxz - PDstandard4th33gxy); + + CCTK_REAL R3133 = 0; + + CCTK_REAL R3211 = 0; + + CCTK_REAL R3212 = (-(gamma122*gamma131) + gamma121*gamma132)*gxxL + + (gamma132*gamma221 - gamma131*gamma222 - gamma122*gamma231 + + gamma121*gamma232)*gxyL + (gamma132*gamma321 - gamma131*gamma322 - + gamma122*gamma331 + gamma121*gamma332)*gxzL + (-(gamma222*gamma231) + + gamma221*gamma232)*gyyL + (gamma232*gamma321 - gamma231*gamma322 - + gamma222*gamma331 + gamma221*gamma332)*gyzL + (-(gamma322*gamma331) + + gamma321*gamma332)*gzzL + khalf*(PDstandard4th12gyz - + PDstandard4th13gyy - PDstandard4th22gxz + PDstandard4th23gxy); + + CCTK_REAL R3213 = (-(gamma131*gamma132) + gamma121*gamma133)*gxxL + + (gamma133*gamma221 - gamma132*gamma231 - gamma131*gamma232 + + gamma121*gamma233)*gxyL + (gamma133*gamma321 - gamma132*gamma331 - + gamma131*gamma332 + gamma121*gamma333)*gxzL + (-(gamma231*gamma232) + + gamma221*gamma233)*gyyL + (gamma233*gamma321 - gamma232*gamma331 - + gamma231*gamma332 + gamma221*gamma333)*gyzL + (-(gamma331*gamma332) + + gamma321*gamma333)*gzzL + khalf*(PDstandard4th12gzz - + PDstandard4th13gyz - PDstandard4th23gxz + PDstandard4th33gxy); - R3131 = khalf*((4*gamma131*gamma231 - 2*gamma111*gamma233)*gxyL + (4*gamma131*gamma331 - 2*gamma111*gamma333)*gxzL + - (4*gamma231*gamma331 - 2*gamma211*gamma333)*gyzL - - 2*(gamma111*gamma133*gxxL + gamma133*gamma211*gxyL + gamma133*gamma311*gxzL + gamma211*gamma233*gyyL + - gamma233*gamma311*gyzL + gamma311*gamma333*gzzL) - PDstandard4th11gzz + 2*PDstandard4th13gxz - - PDstandard4th33gxx + 2*gxxL*SQR(gamma131) + 2*gyyL*SQR(gamma231) + 2*gzzL*SQR(gamma331)); + CCTK_REAL R3221 = (gamma122*gamma131 - gamma121*gamma132)*gxxL + + (-(gamma132*gamma221) + gamma131*gamma222 + gamma122*gamma231 - + gamma121*gamma232)*gxyL + (-(gamma132*gamma321) + gamma131*gamma322 + + gamma122*gamma331 - gamma121*gamma332)*gxzL + (gamma222*gamma231 - + gamma221*gamma232)*gyyL + (-(gamma232*gamma321) + gamma231*gamma322 + + gamma222*gamma331 - gamma221*gamma332)*gyzL + (gamma322*gamma331 - + gamma321*gamma332)*gzzL + khalf*(-PDstandard4th12gyz + + PDstandard4th13gyy + PDstandard4th22gxz - PDstandard4th23gxy); - R3132 = (gamma131*gamma132 - gamma121*gamma133)*gxxL + - (-(gamma133*gamma221) + gamma132*gamma231 + gamma131*gamma232 - gamma121*gamma233)*gxyL + - (-(gamma133*gamma321) + gamma132*gamma331 + gamma131*gamma332 - gamma121*gamma333)*gxzL + - (gamma231*gamma232 - gamma221*gamma233)*gyyL + - (-(gamma233*gamma321) + gamma232*gamma331 + gamma231*gamma332 - gamma221*gamma333)*gyzL + - (gamma331*gamma332 - gamma321*gamma333)*gzzL + - khalf*(-PDstandard4th12gzz + PDstandard4th13gyz + PDstandard4th23gxz - PDstandard4th33gxy); + CCTK_REAL R3222 = 0; - R3133 = 0; + CCTK_REAL R3223 = (-2*gamma132*gamma232 + gamma122*gamma233)*gxyL + + (-2*gamma132*gamma332 + gamma122*gamma333)*gxzL + + gamma133*(gamma122*gxxL + gamma222*gxyL + gamma322*gxzL) + + (-2*gamma232*gamma332 + gamma222*gamma333)*gyzL + + gamma233*(gamma222*gyyL + gamma322*gyzL) - PDstandard4th23gyz + + khalf*(PDstandard4th22gzz + PDstandard4th33gyy) - gxxL*SQR(gamma132) - + gyyL*SQR(gamma232) + gzzL*(gamma322*gamma333 - SQR(gamma332)); - R3211 = 0; + CCTK_REAL R3231 = (gamma131*gamma132 - gamma121*gamma133)*gxxL + + (-(gamma133*gamma221) + gamma132*gamma231 + gamma131*gamma232 - + gamma121*gamma233)*gxyL + (-(gamma133*gamma321) + gamma132*gamma331 + + gamma131*gamma332 - gamma121*gamma333)*gxzL + (gamma231*gamma232 - + gamma221*gamma233)*gyyL + (-(gamma233*gamma321) + gamma232*gamma331 + + gamma231*gamma332 - gamma221*gamma333)*gyzL + (gamma331*gamma332 - + gamma321*gamma333)*gzzL + khalf*(-PDstandard4th12gzz + + PDstandard4th13gyz + PDstandard4th23gxz - PDstandard4th33gxy); - R3212 = (-(gamma122*gamma131) + gamma121*gamma132)*gxxL + - (gamma132*gamma221 - gamma131*gamma222 - gamma122*gamma231 + gamma121*gamma232)*gxyL + - (gamma132*gamma321 - gamma131*gamma322 - gamma122*gamma331 + gamma121*gamma332)*gxzL + - (-(gamma222*gamma231) + gamma221*gamma232)*gyyL + - (gamma232*gamma321 - gamma231*gamma322 - gamma222*gamma331 + gamma221*gamma332)*gyzL + - (-(gamma322*gamma331) + gamma321*gamma332)*gzzL + - khalf*(PDstandard4th12gyz - PDstandard4th13gyy - PDstandard4th22gxz + PDstandard4th23gxy); + CCTK_REAL R3232 = khalf*((4*gamma132*gamma232 - + 2*gamma122*gamma233)*gxyL + (4*gamma132*gamma332 - + 2*gamma122*gamma333)*gxzL + (4*gamma232*gamma332 - + 2*gamma222*gamma333)*gyzL - 2*(gamma122*gamma133*gxxL + + gamma133*gamma222*gxyL + gamma133*gamma322*gxzL + + gamma222*gamma233*gyyL + gamma233*gamma322*gyzL + + gamma322*gamma333*gzzL) - PDstandard4th22gzz + 2*PDstandard4th23gyz - + PDstandard4th33gyy + 2*gxxL*SQR(gamma132) + 2*gyyL*SQR(gamma232) + + 2*gzzL*SQR(gamma332)); - R3213 = (-(gamma131*gamma132) + gamma121*gamma133)*gxxL + - (gamma133*gamma221 - gamma132*gamma231 - gamma131*gamma232 + gamma121*gamma233)*gxyL + - (gamma133*gamma321 - gamma132*gamma331 - gamma131*gamma332 + gamma121*gamma333)*gxzL + - (-(gamma231*gamma232) + gamma221*gamma233)*gyyL + - (gamma233*gamma321 - gamma232*gamma331 - gamma231*gamma332 + gamma221*gamma333)*gyzL + - (-(gamma331*gamma332) + gamma321*gamma333)*gzzL + - khalf*(PDstandard4th12gzz - PDstandard4th13gyz - PDstandard4th23gxz + PDstandard4th33gxy); + CCTK_REAL R3233 = 0; - R3221 = (gamma122*gamma131 - gamma121*gamma132)*gxxL + - (-(gamma132*gamma221) + gamma131*gamma222 + gamma122*gamma231 - gamma121*gamma232)*gxyL + - (-(gamma132*gamma321) + gamma131*gamma322 + gamma122*gamma331 - gamma121*gamma332)*gxzL + - (gamma222*gamma231 - gamma221*gamma232)*gyyL + - (-(gamma232*gamma321) + gamma231*gamma322 + gamma222*gamma331 - gamma221*gamma332)*gyzL + - (gamma322*gamma331 - gamma321*gamma332)*gzzL + - khalf*(-PDstandard4th12gyz + PDstandard4th13gyy + PDstandard4th22gxz - PDstandard4th23gxy); + CCTK_REAL R3311 = 0; - R3222 = 0; + CCTK_REAL R3312 = 0; - R3223 = (-2*gamma132*gamma232 + gamma122*gamma233)*gxyL + (-2*gamma132*gamma332 + gamma122*gamma333)*gxzL + - gamma133*(gamma122*gxxL + gamma222*gxyL + gamma322*gxzL) + (-2*gamma232*gamma332 + gamma222*gamma333)*gyzL + - gamma233*(gamma222*gyyL + gamma322*gyzL) - PDstandard4th23gyz + khalf*(PDstandard4th22gzz + PDstandard4th33gyy) - - gxxL*SQR(gamma132) - gyyL*SQR(gamma232) + gzzL*(gamma322*gamma333 - SQR(gamma332)); + CCTK_REAL R3313 = 0; - R3231 = (gamma131*gamma132 - gamma121*gamma133)*gxxL + - (-(gamma133*gamma221) + gamma132*gamma231 + gamma131*gamma232 - gamma121*gamma233)*gxyL + - (-(gamma133*gamma321) + gamma132*gamma331 + gamma131*gamma332 - gamma121*gamma333)*gxzL + - (gamma231*gamma232 - gamma221*gamma233)*gyyL + - (-(gamma233*gamma321) + gamma232*gamma331 + gamma231*gamma332 - gamma221*gamma333)*gyzL + - (gamma331*gamma332 - gamma321*gamma333)*gzzL + - khalf*(-PDstandard4th12gzz + PDstandard4th13gyz + PDstandard4th23gxz - PDstandard4th33gxy); + CCTK_REAL R3321 = 0; - R3232 = khalf*((4*gamma132*gamma232 - 2*gamma122*gamma233)*gxyL + (4*gamma132*gamma332 - 2*gamma122*gamma333)*gxzL + - (4*gamma232*gamma332 - 2*gamma222*gamma333)*gyzL - - 2*(gamma122*gamma133*gxxL + gamma133*gamma222*gxyL + gamma133*gamma322*gxzL + gamma222*gamma233*gyyL + - gamma233*gamma322*gyzL + gamma322*gamma333*gzzL) - PDstandard4th22gzz + 2*PDstandard4th23gyz - - PDstandard4th33gyy + 2*gxxL*SQR(gamma132) + 2*gyyL*SQR(gamma232) + 2*gzzL*SQR(gamma332)); + CCTK_REAL R3322 = 0; - R3233 = 0; + CCTK_REAL R3323 = 0; - R3311 = 0; + CCTK_REAL R3331 = 0; - R3312 = 0; + CCTK_REAL R3332 = 0; - R3313 = 0; + CCTK_REAL R3333 = 0; - R3321 = 0; + CCTK_REAL R4p1111 = R1111; - R3322 = 0; + CCTK_REAL R4p1112 = R1112; - R3323 = 0; + CCTK_REAL R4p1113 = R1113; - R3331 = 0; + CCTK_REAL R4p1121 = R1121; - R3332 = 0; + CCTK_REAL R4p1122 = R1122; - R3333 = 0; + CCTK_REAL R4p1123 = R1123; - R4p1111 = R1111; + CCTK_REAL R4p1131 = R1131; - R4p1112 = R1112; + CCTK_REAL R4p1132 = R1132; - R4p1113 = R1113; + CCTK_REAL R4p1133 = R1133; - R4p1121 = R1121; + CCTK_REAL R4p1211 = R1211; - R4p1122 = R1122; + CCTK_REAL R4p1212 = kxxL*kyyL + R1212 - SQR(kxyL); - R4p1123 = R1123; + CCTK_REAL R4p1213 = -(kxyL*kxzL) + kxxL*kyzL + R1213; - R4p1131 = R1131; + CCTK_REAL R4p1221 = -(kxxL*kyyL) + R1221 + SQR(kxyL); - R4p1132 = R1132; + CCTK_REAL R4p1222 = R1222; - R4p1133 = R1133; + CCTK_REAL R4p1223 = -(kxzL*kyyL) + kxyL*kyzL + R1223; - R4p1211 = R1211; + CCTK_REAL R4p1231 = kxyL*kxzL - kxxL*kyzL + R1231; - R4p1212 = kxxL*kyyL + R1212 - SQR(kxyL); + CCTK_REAL R4p1232 = kxzL*kyyL - kxyL*kyzL + R1232; - R4p1213 = -(kxyL*kxzL) + kxxL*kyzL + R1213; + CCTK_REAL R4p1233 = R1233; - R4p1221 = -(kxxL*kyyL) + R1221 + SQR(kxyL); + CCTK_REAL R4p1311 = R1311; - R4p1222 = R1222; + CCTK_REAL R4p1312 = -(kxyL*kxzL) + kxxL*kyzL + R1312; - R4p1223 = -(kxzL*kyyL) + kxyL*kyzL + R1223; + CCTK_REAL R4p1313 = kxxL*kzzL + R1313 - SQR(kxzL); - R4p1231 = kxyL*kxzL - kxxL*kyzL + R1231; + CCTK_REAL R4p1321 = kxyL*kxzL - kxxL*kyzL + R1321; - R4p1232 = kxzL*kyyL - kxyL*kyzL + R1232; + CCTK_REAL R4p1322 = R1322; - R4p1233 = R1233; + CCTK_REAL R4p1323 = -(kxzL*kyzL) + kxyL*kzzL + R1323; - R4p1311 = R1311; + CCTK_REAL R4p1331 = -(kxxL*kzzL) + R1331 + SQR(kxzL); - R4p1312 = -(kxyL*kxzL) + kxxL*kyzL + R1312; + CCTK_REAL R4p1332 = kxzL*kyzL - kxyL*kzzL + R1332; - R4p1313 = kxxL*kzzL + R1313 - SQR(kxzL); + CCTK_REAL R4p1333 = R1333; - R4p1321 = kxyL*kxzL - kxxL*kyzL + R1321; + CCTK_REAL R4p2111 = R2111; - R4p1322 = R1322; + CCTK_REAL R4p2112 = -(kxxL*kyyL) + R2112 + SQR(kxyL); - R4p1323 = -(kxzL*kyzL) + kxyL*kzzL + R1323; + CCTK_REAL R4p2113 = kxyL*kxzL - kxxL*kyzL + R2113; - R4p1331 = -(kxxL*kzzL) + R1331 + SQR(kxzL); + CCTK_REAL R4p2121 = kxxL*kyyL + R2121 - SQR(kxyL); - R4p1332 = kxzL*kyzL - kxyL*kzzL + R1332; + CCTK_REAL R4p2122 = R2122; - R4p1333 = R1333; + CCTK_REAL R4p2123 = kxzL*kyyL - kxyL*kyzL + R2123; - R4p2111 = R2111; + CCTK_REAL R4p2131 = -(kxyL*kxzL) + kxxL*kyzL + R2131; - R4p2112 = -(kxxL*kyyL) + R2112 + SQR(kxyL); + CCTK_REAL R4p2132 = -(kxzL*kyyL) + kxyL*kyzL + R2132; - R4p2113 = kxyL*kxzL - kxxL*kyzL + R2113; + CCTK_REAL R4p2133 = R2133; - R4p2121 = kxxL*kyyL + R2121 - SQR(kxyL); + CCTK_REAL R4p2211 = R2211; - R4p2122 = R2122; + CCTK_REAL R4p2212 = R2212; - R4p2123 = kxzL*kyyL - kxyL*kyzL + R2123; + CCTK_REAL R4p2213 = R2213; - R4p2131 = -(kxyL*kxzL) + kxxL*kyzL + R2131; + CCTK_REAL R4p2221 = R2221; - R4p2132 = -(kxzL*kyyL) + kxyL*kyzL + R2132; + CCTK_REAL R4p2222 = R2222; - R4p2133 = R2133; + CCTK_REAL R4p2223 = R2223; - R4p2211 = R2211; + CCTK_REAL R4p2231 = R2231; - R4p2212 = R2212; + CCTK_REAL R4p2232 = R2232; - R4p2213 = R2213; + CCTK_REAL R4p2233 = R2233; - R4p2221 = R2221; + CCTK_REAL R4p2311 = R2311; - R4p2222 = R2222; + CCTK_REAL R4p2312 = -(kxzL*kyyL) + kxyL*kyzL + R2312; - R4p2223 = R2223; + CCTK_REAL R4p2313 = -(kxzL*kyzL) + kxyL*kzzL + R2313; - R4p2231 = R2231; + CCTK_REAL R4p2321 = kxzL*kyyL - kxyL*kyzL + R2321; - R4p2232 = R2232; + CCTK_REAL R4p2322 = R2322; - R4p2233 = R2233; + CCTK_REAL R4p2323 = kyyL*kzzL + R2323 - SQR(kyzL); - R4p2311 = R2311; + CCTK_REAL R4p2331 = kxzL*kyzL - kxyL*kzzL + R2331; - R4p2312 = -(kxzL*kyyL) + kxyL*kyzL + R2312; + CCTK_REAL R4p2332 = -(kyyL*kzzL) + R2332 + SQR(kyzL); - R4p2313 = -(kxzL*kyzL) + kxyL*kzzL + R2313; + CCTK_REAL R4p2333 = R2333; - R4p2321 = kxzL*kyyL - kxyL*kyzL + R2321; + CCTK_REAL R4p3111 = R3111; - R4p2322 = R2322; + CCTK_REAL R4p3112 = kxyL*kxzL - kxxL*kyzL + R3112; - R4p2323 = kyyL*kzzL + R2323 - SQR(kyzL); + CCTK_REAL R4p3113 = -(kxxL*kzzL) + R3113 + SQR(kxzL); - R4p2331 = kxzL*kyzL - kxyL*kzzL + R2331; + CCTK_REAL R4p3121 = -(kxyL*kxzL) + kxxL*kyzL + R3121; - R4p2332 = -(kyyL*kzzL) + R2332 + SQR(kyzL); + CCTK_REAL R4p3122 = R3122; - R4p2333 = R2333; + CCTK_REAL R4p3123 = kxzL*kyzL - kxyL*kzzL + R3123; - R4p3111 = R3111; + CCTK_REAL R4p3131 = kxxL*kzzL + R3131 - SQR(kxzL); - R4p3112 = kxyL*kxzL - kxxL*kyzL + R3112; + CCTK_REAL R4p3132 = -(kxzL*kyzL) + kxyL*kzzL + R3132; - R4p3113 = -(kxxL*kzzL) + R3113 + SQR(kxzL); + CCTK_REAL R4p3133 = R3133; - R4p3121 = -(kxyL*kxzL) + kxxL*kyzL + R3121; + CCTK_REAL R4p3211 = R3211; - R4p3122 = R3122; + CCTK_REAL R4p3212 = kxzL*kyyL - kxyL*kyzL + R3212; - R4p3123 = kxzL*kyzL - kxyL*kzzL + R3123; + CCTK_REAL R4p3213 = kxzL*kyzL - kxyL*kzzL + R3213; - R4p3131 = kxxL*kzzL + R3131 - SQR(kxzL); + CCTK_REAL R4p3221 = -(kxzL*kyyL) + kxyL*kyzL + R3221; - R4p3132 = -(kxzL*kyzL) + kxyL*kzzL + R3132; + CCTK_REAL R4p3222 = R3222; - R4p3133 = R3133; + CCTK_REAL R4p3223 = -(kyyL*kzzL) + R3223 + SQR(kyzL); - R4p3211 = R3211; + CCTK_REAL R4p3231 = -(kxzL*kyzL) + kxyL*kzzL + R3231; - R4p3212 = kxzL*kyyL - kxyL*kyzL + R3212; + CCTK_REAL R4p3232 = kyyL*kzzL + R3232 - SQR(kyzL); - R4p3213 = kxzL*kyzL - kxyL*kzzL + R3213; + CCTK_REAL R4p3233 = R3233; - R4p3221 = -(kxzL*kyyL) + kxyL*kyzL + R3221; + CCTK_REAL R4p3311 = R3311; - R4p3222 = R3222; + CCTK_REAL R4p3312 = R3312; - R4p3223 = -(kyyL*kzzL) + R3223 + SQR(kyzL); + CCTK_REAL R4p3313 = R3313; - R4p3231 = -(kxzL*kyzL) + kxyL*kzzL + R3231; + CCTK_REAL R4p3321 = R3321; - R4p3232 = kyyL*kzzL + R3232 - SQR(kyzL); + CCTK_REAL R4p3322 = R3322; - R4p3233 = R3233; + CCTK_REAL R4p3323 = R3323; - R4p3311 = R3311; + CCTK_REAL R4p3331 = R3331; - R4p3312 = R3312; + CCTK_REAL R4p3332 = R3332; - R4p3313 = R3313; + CCTK_REAL R4p3333 = R3333; - R4p3321 = R3321; + CCTK_REAL Ro111 = 0; - R4p3322 = R3322; + CCTK_REAL Ro112 = gamma121*kxxL + (-gamma111 + gamma221)*kxyL + + gamma321*kxzL - gamma211*kyyL - gamma311*kyzL + PDstandard4th1kxy - + PDstandard4th2kxx; - R4p3323 = R3323; + CCTK_REAL Ro113 = gamma131*kxxL + gamma231*kxyL + (-gamma111 + + gamma331)*kxzL - gamma211*kyzL - gamma311*kzzL + PDstandard4th1kxz - + PDstandard4th3kxx; - R4p3331 = R3331; + CCTK_REAL Ro121 = -(gamma121*kxxL) + gamma111*kxyL - gamma221*kxyL - + gamma321*kxzL + gamma211*kyyL + gamma311*kyzL - PDstandard4th1kxy + + PDstandard4th2kxx; - R4p3332 = R3332; + CCTK_REAL Ro122 = 0; - R4p3333 = R3333; + CCTK_REAL Ro123 = gamma131*kxyL - gamma121*kxzL + gamma231*kyyL - + gamma221*kyzL + gamma331*kyzL - gamma321*kzzL + PDstandard4th2kxz - + PDstandard4th3kxy; - Ro111 = 0; + CCTK_REAL Ro131 = -(gamma131*kxxL) - gamma231*kxyL + gamma111*kxzL - + gamma331*kxzL + gamma211*kyzL + gamma311*kzzL - PDstandard4th1kxz + + PDstandard4th3kxx; - Ro112 = gamma121*kxxL + (-gamma111 + gamma221)*kxyL + gamma321*kxzL - gamma211*kyyL - gamma311*kyzL + - PDstandard4th1kxy - PDstandard4th2kxx; + CCTK_REAL Ro132 = -(gamma131*kxyL) + gamma121*kxzL - gamma231*kyyL + + gamma221*kyzL - gamma331*kyzL + gamma321*kzzL - PDstandard4th2kxz + + PDstandard4th3kxy; - Ro113 = gamma131*kxxL + gamma231*kxyL + (-gamma111 + gamma331)*kxzL - gamma211*kyzL - gamma311*kzzL + - PDstandard4th1kxz - PDstandard4th3kxx; + CCTK_REAL Ro133 = 0; - Ro121 = -(gamma121*kxxL) + gamma111*kxyL - gamma221*kxyL - gamma321*kxzL + gamma211*kyyL + gamma311*kyzL - - PDstandard4th1kxy + PDstandard4th2kxx; + CCTK_REAL Ro211 = 0; - Ro122 = 0; + CCTK_REAL Ro212 = gamma122*kxxL + (-gamma121 + gamma222)*kxyL + + gamma322*kxzL - gamma221*kyyL - gamma321*kyzL + PDstandard4th1kyy - + PDstandard4th2kxy; - Ro123 = gamma131*kxyL - gamma121*kxzL + gamma231*kyyL - gamma221*kyzL + gamma331*kyzL - gamma321*kzzL + - PDstandard4th2kxz - PDstandard4th3kxy; + CCTK_REAL Ro213 = gamma132*kxxL + gamma232*kxyL + (-gamma121 + + gamma332)*kxzL - gamma221*kyzL - gamma321*kzzL + PDstandard4th1kyz - + PDstandard4th3kxy; - Ro131 = -(gamma131*kxxL) - gamma231*kxyL + gamma111*kxzL - gamma331*kxzL + gamma211*kyzL + gamma311*kzzL - - PDstandard4th1kxz + PDstandard4th3kxx; + CCTK_REAL Ro221 = -(gamma122*kxxL) + gamma121*kxyL - gamma222*kxyL - + gamma322*kxzL + gamma221*kyyL + gamma321*kyzL - PDstandard4th1kyy + + PDstandard4th2kxy; - Ro132 = -(gamma131*kxyL) + gamma121*kxzL - gamma231*kyyL + gamma221*kyzL - gamma331*kyzL + gamma321*kzzL - - PDstandard4th2kxz + PDstandard4th3kxy; + CCTK_REAL Ro222 = 0; - Ro133 = 0; + CCTK_REAL Ro223 = gamma132*kxyL - gamma122*kxzL + gamma232*kyyL - + gamma222*kyzL + gamma332*kyzL - gamma322*kzzL + PDstandard4th2kyz - + PDstandard4th3kyy; - Ro211 = 0; + CCTK_REAL Ro231 = -(gamma132*kxxL) - gamma232*kxyL + gamma121*kxzL - + gamma332*kxzL + gamma221*kyzL + gamma321*kzzL - PDstandard4th1kyz + + PDstandard4th3kxy; - Ro212 = gamma122*kxxL + (-gamma121 + gamma222)*kxyL + gamma322*kxzL - gamma221*kyyL - gamma321*kyzL + - PDstandard4th1kyy - PDstandard4th2kxy; + CCTK_REAL Ro232 = -(gamma132*kxyL) + gamma122*kxzL - gamma232*kyyL + + gamma222*kyzL - gamma332*kyzL + gamma322*kzzL - PDstandard4th2kyz + + PDstandard4th3kyy; - Ro213 = gamma132*kxxL + gamma232*kxyL + (-gamma121 + gamma332)*kxzL - gamma221*kyzL - gamma321*kzzL + - PDstandard4th1kyz - PDstandard4th3kxy; + CCTK_REAL Ro233 = 0; - Ro221 = -(gamma122*kxxL) + gamma121*kxyL - gamma222*kxyL - gamma322*kxzL + gamma221*kyyL + gamma321*kyzL - - PDstandard4th1kyy + PDstandard4th2kxy; + CCTK_REAL Ro311 = 0; - Ro222 = 0; + CCTK_REAL Ro312 = gamma132*kxxL + (-gamma131 + gamma232)*kxyL + + gamma332*kxzL - gamma231*kyyL - gamma331*kyzL + PDstandard4th1kyz - + PDstandard4th2kxz; - Ro223 = gamma132*kxyL - gamma122*kxzL + gamma232*kyyL - gamma222*kyzL + gamma332*kyzL - gamma322*kzzL + - PDstandard4th2kyz - PDstandard4th3kyy; + CCTK_REAL Ro313 = gamma133*kxxL + gamma233*kxyL + (-gamma131 + + gamma333)*kxzL - gamma231*kyzL - gamma331*kzzL + PDstandard4th1kzz - + PDstandard4th3kxz; - Ro231 = -(gamma132*kxxL) - gamma232*kxyL + gamma121*kxzL - gamma332*kxzL + gamma221*kyzL + gamma321*kzzL - - PDstandard4th1kyz + PDstandard4th3kxy; + CCTK_REAL Ro321 = -(gamma132*kxxL) + gamma131*kxyL - gamma232*kxyL - + gamma332*kxzL + gamma231*kyyL + gamma331*kyzL - PDstandard4th1kyz + + PDstandard4th2kxz; - Ro232 = -(gamma132*kxyL) + gamma122*kxzL - gamma232*kyyL + gamma222*kyzL - gamma332*kyzL + gamma322*kzzL - - PDstandard4th2kyz + PDstandard4th3kyy; - - Ro233 = 0; - - Ro311 = 0; - - Ro312 = gamma132*kxxL + (-gamma131 + gamma232)*kxyL + gamma332*kxzL - gamma231*kyyL - gamma331*kyzL + - PDstandard4th1kyz - PDstandard4th2kxz; - - Ro313 = gamma133*kxxL + gamma233*kxyL + (-gamma131 + gamma333)*kxzL - gamma231*kyzL - gamma331*kzzL + - PDstandard4th1kzz - PDstandard4th3kxz; - - Ro321 = -(gamma132*kxxL) + gamma131*kxyL - gamma232*kxyL - gamma332*kxzL + gamma231*kyyL + gamma331*kyzL - - PDstandard4th1kyz + PDstandard4th2kxz; - - Ro322 = 0; - - Ro323 = gamma133*kxyL - gamma132*kxzL + gamma233*kyyL - gamma232*kyzL + gamma333*kyzL - gamma332*kzzL + - PDstandard4th2kzz - PDstandard4th3kyz; - - Ro331 = -(gamma133*kxxL) - gamma233*kxyL + gamma131*kxzL - gamma333*kxzL + gamma231*kyzL + gamma331*kzzL - - PDstandard4th1kzz + PDstandard4th3kxz; - - Ro332 = -(gamma133*kxyL) + gamma132*kxzL - gamma233*kyyL + gamma232*kyzL - gamma333*kyzL + gamma332*kzzL - - PDstandard4th2kzz + PDstandard4th3kyz; - - Ro333 = 0; - - Rojo11 = gInv11*R1111 + gInv12*R1112 + gInv13*R1113 + gInv21*R1211 + gInv23*(-(kxyL*kxzL) + kxxL*kyzL + R1213) + - gInv31*R1311 + gInv32*(-(kxyL*kxzL) + kxxL*kyzL + R1312) + gInv22*(kxxL*kyyL + R1212 - SQR(kxyL)) + - gInv33*(kxxL*kzzL + R1313 - SQR(kxzL)); - - Rojo12 = gInv11*R1121 + gInv13*(kxyL*kxzL - kxxL*kyzL + R1123) + gInv21*R1221 + gInv22*R1222 + gInv23*R1223 + - gInv31*R1321 + gInv32*(-(kxzL*kyyL) + kxyL*kyzL + R1322) + gInv33*(-(kxzL*kyzL) + kxyL*kzzL + R1323) + - gInv12*(-(kxxL*kyyL) + R1122 + SQR(kxyL)); - - Rojo13 = gInv11*R1131 + gInv12*(kxyL*kxzL - kxxL*kyzL + R1132) + gInv21*R1231 + - gInv22*(kxzL*kyyL - kxyL*kyzL + R1232) + gInv23*(kxzL*kyzL - kxyL*kzzL + R1233) + gInv31*R1331 + gInv32*R1332 + - gInv33*R1333 + gInv13*(-(kxxL*kzzL) + R1133 + SQR(kxzL)); - - Rojo21 = gInv11*R2111 + gInv12*R2112 + gInv13*R2113 + gInv22*R2212 + gInv23*(-(kxzL*kyyL) + kxyL*kyzL + R2213) + - gInv31*(kxyL*kxzL - kxxL*kyzL + R2311) + gInv32*R2312 + gInv33*(-(kxzL*kyzL) + kxyL*kzzL + R2313) + - gInv21*(-(kxxL*kyyL) + R2211 + SQR(kxyL)); - - Rojo22 = gInv12*R2122 + gInv13*(kxzL*kyyL - kxyL*kyzL + R2123) + gInv21*R2221 + gInv22*R2222 + gInv23*R2223 + - gInv31*(kxzL*kyyL - kxyL*kyzL + R2321) + gInv32*R2322 + gInv11*(kxxL*kyyL + R2121 - SQR(kxyL)) + - gInv33*(kyyL*kzzL + R2323 - SQR(kyzL)); - - Rojo23 = gInv11*(-(kxyL*kxzL) + kxxL*kyzL + R2131) + gInv12*R2132 + gInv13*(kxzL*kyzL - kxyL*kzzL + R2133) + - gInv21*(-(kxzL*kyyL) + kxyL*kyzL + R2231) + gInv22*R2232 + gInv31*R2331 + gInv32*R2332 + gInv33*R2333 + - gInv23*(-(kyyL*kzzL) + R2233 + SQR(kyzL)); - - Rojo31 = gInv11*R3111 + gInv12*R3112 + gInv13*R3113 + gInv21*(kxyL*kxzL - kxxL*kyzL + R3211) + - gInv22*(kxzL*kyyL - kxyL*kyzL + R3212) + gInv23*R3213 + gInv32*(kxzL*kyzL - kxyL*kzzL + R3312) + gInv33*R3313 + - gInv31*(-(kxxL*kzzL) + R3311 + SQR(kxzL)); - - Rojo32 = gInv11*(-(kxyL*kxzL) + kxxL*kyzL + R3121) + gInv12*(-(kxzL*kyyL) + kxyL*kyzL + R3122) + gInv13*R3123 + - gInv21*R3221 + gInv22*R3222 + gInv23*R3223 + gInv31*(kxzL*kyzL - kxyL*kzzL + R3321) + gInv33*R3323 + - gInv32*(-(kyyL*kzzL) + R3322 + SQR(kyzL)); - - Rojo33 = gInv12*(-(kxzL*kyzL) + kxyL*kzzL + R3132) + gInv13*R3133 + gInv21*(-(kxzL*kyzL) + kxyL*kzzL + R3231) + - gInv23*R3233 + gInv31*R3331 + gInv32*R3332 + gInv33*R3333 + gInv11*(kxxL*kzzL + R3131 - SQR(kxzL)) + - gInv22*(kyyL*kzzL + R3232 - SQR(kyzL)); - - Psi4rL = n1*(-(imbar1*(imbar2*(n1*(R4p1112 + R4p1211) + n2*(R4p1122 + R4p1221) + n3*(R4p1132 + R4p1231)) + - imbar3*(n1*(R4p1113 + R4p1311) + n2*(R4p1123 + R4p1321) + n3*(R4p1133 + R4p1331)))) - - imbar2*imbar3*(n1*(R4p1213 + R4p1312) + n2*(R4p1223 + R4p1322) + n3*(R4p1233 + R4p1332)) + - n1*R4p1112*rmbar1*rmbar2 + n2*R4p1122*rmbar1*rmbar2 + n3*R4p1132*rmbar1*rmbar2 + n1*R4p1211*rmbar1*rmbar2 + - n2*R4p1221*rmbar1*rmbar2 + n3*R4p1231*rmbar1*rmbar2 + n1*R4p1113*rmbar1*rmbar3 + n2*R4p1123*rmbar1*rmbar3 + - n3*R4p1133*rmbar1*rmbar3 + n1*R4p1311*rmbar1*rmbar3 + n2*R4p1321*rmbar1*rmbar3 + n3*R4p1331*rmbar1*rmbar3 + - n1*R4p1213*rmbar2*rmbar3 + n2*R4p1223*rmbar2*rmbar3 + n3*R4p1233*rmbar2*rmbar3 + n1*R4p1312*rmbar2*rmbar3 + - n2*R4p1322*rmbar2*rmbar3 + n3*R4p1332*rmbar2*rmbar3 - (n1*R4p1111 + n2*R4p1121 + n3*R4p1131)*SQR(imbar1) - - (n1*R4p1212 + n2*R4p1222 + n3*R4p1232)*SQR(imbar2) - n1*R4p1313*SQR(imbar3) - n2*R4p1323*SQR(imbar3) - - n3*R4p1333*SQR(imbar3) + n1*R4p1111*SQR(rmbar1) + n2*R4p1121*SQR(rmbar1) + n3*R4p1131*SQR(rmbar1) + - n1*R4p1212*SQR(rmbar2) + n2*R4p1222*SQR(rmbar2) + n3*R4p1232*SQR(rmbar2) + n1*R4p1313*SQR(rmbar3) + - n2*R4p1323*SQR(rmbar3) + n3*R4p1333*SQR(rmbar3)) + - n2*(-(imbar1*(imbar2*(n1*(R4p2112 + R4p2211) + n2*(R4p2122 + R4p2221) + n3*(R4p2132 + R4p2231)) + - imbar3*(n1*(R4p2113 + R4p2311) + n2*(R4p2123 + R4p2321) + n3*(R4p2133 + R4p2331)))) - - imbar2*imbar3*(n1*(R4p2213 + R4p2312) + n2*(R4p2223 + R4p2322) + n3*(R4p2233 + R4p2332)) + - n1*R4p2112*rmbar1*rmbar2 + n2*R4p2122*rmbar1*rmbar2 + n3*R4p2132*rmbar1*rmbar2 + n1*R4p2211*rmbar1*rmbar2 + - n2*R4p2221*rmbar1*rmbar2 + n3*R4p2231*rmbar1*rmbar2 + n1*R4p2113*rmbar1*rmbar3 + n2*R4p2123*rmbar1*rmbar3 + - n3*R4p2133*rmbar1*rmbar3 + n1*R4p2311*rmbar1*rmbar3 + n2*R4p2321*rmbar1*rmbar3 + n3*R4p2331*rmbar1*rmbar3 + - n1*R4p2213*rmbar2*rmbar3 + n2*R4p2223*rmbar2*rmbar3 + n3*R4p2233*rmbar2*rmbar3 + n1*R4p2312*rmbar2*rmbar3 + - n2*R4p2322*rmbar2*rmbar3 + n3*R4p2332*rmbar2*rmbar3 - (n1*R4p2111 + n2*R4p2121 + n3*R4p2131)*SQR(imbar1) - - (n1*R4p2212 + n2*R4p2222 + n3*R4p2232)*SQR(imbar2) - n1*R4p2313*SQR(imbar3) - n2*R4p2323*SQR(imbar3) - - n3*R4p2333*SQR(imbar3) + n1*R4p2111*SQR(rmbar1) + n2*R4p2121*SQR(rmbar1) + n3*R4p2131*SQR(rmbar1) + - n1*R4p2212*SQR(rmbar2) + n2*R4p2222*SQR(rmbar2) + n3*R4p2232*SQR(rmbar2) + n1*R4p2313*SQR(rmbar3) + - n2*R4p2323*SQR(rmbar3) + n3*R4p2333*SQR(rmbar3)) + - n3*(-(imbar1*(imbar2*(n1*(R4p3112 + R4p3211) + n2*(R4p3122 + R4p3221) + n3*(R4p3132 + R4p3231)) + - imbar3*(n1*(R4p3113 + R4p3311) + n2*(R4p3123 + R4p3321) + n3*(R4p3133 + R4p3331)))) - - imbar2*imbar3*(n1*(R4p3213 + R4p3312) + n2*(R4p3223 + R4p3322) + n3*(R4p3233 + R4p3332)) + - n1*R4p3112*rmbar1*rmbar2 + n2*R4p3122*rmbar1*rmbar2 + n3*R4p3132*rmbar1*rmbar2 + n1*R4p3211*rmbar1*rmbar2 + - n2*R4p3221*rmbar1*rmbar2 + n3*R4p3231*rmbar1*rmbar2 + n1*R4p3113*rmbar1*rmbar3 + n2*R4p3123*rmbar1*rmbar3 + - n3*R4p3133*rmbar1*rmbar3 + n1*R4p3311*rmbar1*rmbar3 + n2*R4p3321*rmbar1*rmbar3 + n3*R4p3331*rmbar1*rmbar3 + - n1*R4p3213*rmbar2*rmbar3 + n2*R4p3223*rmbar2*rmbar3 + n3*R4p3233*rmbar2*rmbar3 + n1*R4p3312*rmbar2*rmbar3 + - n2*R4p3322*rmbar2*rmbar3 + n3*R4p3332*rmbar2*rmbar3 - (n1*R4p3111 + n2*R4p3121 + n3*R4p3131)*SQR(imbar1) - - (n1*R4p3212 + n2*R4p3222 + n3*R4p3232)*SQR(imbar2) - n1*R4p3313*SQR(imbar3) - n2*R4p3323*SQR(imbar3) - - n3*R4p3333*SQR(imbar3) + n1*R4p3111*SQR(rmbar1) + n2*R4p3121*SQR(rmbar1) + n3*R4p3131*SQR(rmbar1) + - n1*R4p3212*SQR(rmbar2) + n2*R4p3222*SQR(rmbar2) + n3*R4p3232*SQR(rmbar2) + n1*R4p3313*SQR(rmbar3) + - n2*R4p3323*SQR(rmbar3) + n3*R4p3333*SQR(rmbar3)) - - SQR(nn)*((imbar2*imbar3 - rmbar2*rmbar3)*Rojo23 + imbar1*(imbar2*(Rojo12 + Rojo21) + imbar3*(Rojo13 + Rojo31)) - - rmbar1*(rmbar2*(Rojo12 + Rojo21) + rmbar3*(Rojo13 + Rojo31)) + imbar2*imbar3*Rojo32 - rmbar2*rmbar3*Rojo32 + - Rojo11*SQR(imbar1) + Rojo22*SQR(imbar2) + Rojo33*SQR(imbar3) - Rojo11*SQR(rmbar1) - Rojo22*SQR(rmbar2) - - Rojo33*SQR(rmbar3)) + 2*nn*(-(n1*(imbar2*imbar3*Ro213 - rmbar2*rmbar3*Ro213 + - imbar1*(imbar2*(Ro112 + Ro211) + imbar3*(Ro113 + Ro311)) - - rmbar1*(rmbar2*(Ro112 + Ro211) + rmbar3*(Ro113 + Ro311)) + imbar2*imbar3*Ro312 - rmbar2*rmbar3*Ro312 + - Ro111*SQR(imbar1) + Ro212*SQR(imbar2) + Ro313*SQR(imbar3) - Ro111*SQR(rmbar1) - Ro212*SQR(rmbar2) - - Ro313*SQR(rmbar3))) - n2*(imbar2*imbar3*Ro223 - rmbar2*rmbar3*Ro223 + - imbar1*(imbar2*(Ro122 + Ro221) + imbar3*(Ro123 + Ro321)) - - rmbar1*(rmbar2*(Ro122 + Ro221) + rmbar3*(Ro123 + Ro321)) + imbar2*imbar3*Ro322 - rmbar2*rmbar3*Ro322 + - Ro121*SQR(imbar1) + Ro222*SQR(imbar2) + Ro323*SQR(imbar3) - Ro121*SQR(rmbar1) - Ro222*SQR(rmbar2) - - Ro323*SQR(rmbar3)) - n3*(imbar2*imbar3*Ro233 - rmbar2*rmbar3*Ro233 + - imbar1*(imbar2*(Ro132 + Ro231) + imbar3*(Ro133 + Ro331)) - - rmbar1*(rmbar2*(Ro132 + Ro231) + rmbar3*(Ro133 + Ro331)) + imbar2*imbar3*Ro332 - rmbar2*rmbar3*Ro332 + - Ro131*SQR(imbar1) + Ro232*SQR(imbar2) + Ro333*SQR(imbar3) - Ro131*SQR(rmbar1) - Ro232*SQR(rmbar2) - - Ro333*SQR(rmbar3))); - - Psi4iL = -(n1*(im1*(n1*(2*R4p1111*rm1 + R4p1112*rm2 + R4p1211*rm2 + R4p1113*rm3 + R4p1311*rm3) + - n2*(2*R4p1121*rm1 + R4p1122*rm2 + R4p1221*rm2 + R4p1123*rm3 + R4p1321*rm3) + - n3*(2*R4p1131*rm1 + R4p1132*rm2 + R4p1231*rm2 + R4p1133*rm3 + R4p1331*rm3)) + - im2*(n1*(R4p1112*rm1 + R4p1211*rm1 + 2*R4p1212*rm2 + R4p1213*rm3 + R4p1312*rm3) + - n2*(R4p1122*rm1 + R4p1221*rm1 + 2*R4p1222*rm2 + R4p1223*rm3 + R4p1322*rm3) + - n3*(R4p1132*rm1 + R4p1231*rm1 + 2*R4p1232*rm2 + R4p1233*rm3 + R4p1332*rm3)) + - im3*(n1*(R4p1113*rm1 + R4p1311*rm1 + R4p1213*rm2 + R4p1312*rm2 + 2*R4p1313*rm3) + - n2*(R4p1123*rm1 + R4p1321*rm1 + R4p1223*rm2 + R4p1322*rm2 + 2*R4p1323*rm3) + - n3*(R4p1133*rm1 + R4p1331*rm1 + R4p1233*rm2 + R4p1332*rm2 + 2*R4p1333*rm3)))) - - n2*(im1*(n1*(2*R4p2111*rm1 + R4p2112*rm2 + R4p2211*rm2 + R4p2113*rm3 + R4p2311*rm3) + - n2*(2*R4p2121*rm1 + R4p2122*rm2 + R4p2221*rm2 + R4p2123*rm3 + R4p2321*rm3) + - n3*(2*R4p2131*rm1 + R4p2132*rm2 + R4p2231*rm2 + R4p2133*rm3 + R4p2331*rm3)) + - im2*(n1*(R4p2112*rm1 + R4p2211*rm1 + 2*R4p2212*rm2 + R4p2213*rm3 + R4p2312*rm3) + - n2*(R4p2122*rm1 + R4p2221*rm1 + 2*R4p2222*rm2 + R4p2223*rm3 + R4p2322*rm3) + - n3*(R4p2132*rm1 + R4p2231*rm1 + 2*R4p2232*rm2 + R4p2233*rm3 + R4p2332*rm3)) + - im3*(n1*(R4p2113*rm1 + R4p2311*rm1 + R4p2213*rm2 + R4p2312*rm2 + 2*R4p2313*rm3) + - n2*(R4p2123*rm1 + R4p2321*rm1 + R4p2223*rm2 + R4p2322*rm2 + 2*R4p2323*rm3) + - n3*(R4p2133*rm1 + R4p2331*rm1 + R4p2233*rm2 + R4p2332*rm2 + 2*R4p2333*rm3))) - - n3*(im1*(n1*(2*R4p3111*rm1 + R4p3112*rm2 + R4p3211*rm2 + R4p3113*rm3 + R4p3311*rm3) + - n2*(2*R4p3121*rm1 + R4p3122*rm2 + R4p3221*rm2 + R4p3123*rm3 + R4p3321*rm3) + - n3*(2*R4p3131*rm1 + R4p3132*rm2 + R4p3231*rm2 + R4p3133*rm3 + R4p3331*rm3)) + - im2*(n1*(R4p3112*rm1 + R4p3211*rm1 + 2*R4p3212*rm2 + R4p3213*rm3 + R4p3312*rm3) + - n2*(R4p3122*rm1 + R4p3221*rm1 + 2*R4p3222*rm2 + R4p3223*rm3 + R4p3322*rm3) + - n3*(R4p3132*rm1 + R4p3231*rm1 + 2*R4p3232*rm2 + R4p3233*rm3 + R4p3332*rm3)) + - im3*(n1*(R4p3113*rm1 + R4p3311*rm1 + R4p3213*rm2 + R4p3312*rm2 + 2*R4p3313*rm3) + - n2*(R4p3123*rm1 + R4p3321*rm1 + R4p3223*rm2 + R4p3322*rm2 + 2*R4p3323*rm3) + - n3*(R4p3133*rm1 + R4p3331*rm1 + R4p3233*rm2 + R4p3332*rm2 + 2*R4p3333*rm3))) - - 2*nn*(im1*(n1*(2*rm1*Ro111 + rm2*(Ro112 + Ro211) + rm3*(Ro113 + Ro311)) + - n2*(2*rm1*Ro121 + rm2*(Ro122 + Ro221) + rm3*(Ro123 + Ro321)) + - n3*(2*rm1*Ro131 + rm2*(Ro132 + Ro231) + rm3*(Ro133 + Ro331))) + - im2*(n1*(rm1*(Ro112 + Ro211) + 2*rm2*Ro212 + rm3*(Ro213 + Ro312)) + - n2*(rm1*(Ro122 + Ro221) + 2*rm2*Ro222 + rm3*(Ro223 + Ro322)) + - n3*(rm1*(Ro132 + Ro231) + 2*rm2*Ro232 + rm3*(Ro233 + Ro332))) + - im3*(n1*(rm1*(Ro113 + Ro311) + rm2*(Ro213 + Ro312) + 2*rm3*Ro313) + - n2*(rm1*(Ro123 + Ro321) + rm2*(Ro223 + Ro322) + 2*rm3*Ro323) + - n3*(rm1*(Ro133 + Ro331) + rm2*(Ro233 + Ro332) + 2*rm3*Ro333))) - - (im1*(2*rm1*Rojo11 + rm2*(Rojo12 + Rojo21) + rm3*(Rojo13 + Rojo31)) + - im2*(rm1*(Rojo12 + Rojo21) + 2*rm2*Rojo22 + rm3*(Rojo23 + Rojo32)) + - im3*(rm1*(Rojo13 + Rojo31) + rm2*(Rojo23 + Rojo32) + 2*rm3*Rojo33))*SQR(nn); + CCTK_REAL Ro322 = 0; + + CCTK_REAL Ro323 = gamma133*kxyL - gamma132*kxzL + gamma233*kyyL - + gamma232*kyzL + gamma333*kyzL - gamma332*kzzL + PDstandard4th2kzz - + PDstandard4th3kyz; + + CCTK_REAL Ro331 = -(gamma133*kxxL) - gamma233*kxyL + gamma131*kxzL - + gamma333*kxzL + gamma231*kyzL + gamma331*kzzL - PDstandard4th1kzz + + PDstandard4th3kxz; + + CCTK_REAL Ro332 = -(gamma133*kxyL) + gamma132*kxzL - gamma233*kyyL + + gamma232*kyzL - gamma333*kyzL + gamma332*kzzL - PDstandard4th2kzz + + PDstandard4th3kyz; + + CCTK_REAL Ro333 = 0; + + CCTK_REAL Rojo11 = gInv11*R1111 + gInv12*R1112 + gInv13*R1113 + + gInv21*R1211 + gInv23*(-(kxyL*kxzL) + kxxL*kyzL + R1213) + gInv31*R1311 + + gInv32*(-(kxyL*kxzL) + kxxL*kyzL + R1312) + gInv22*(kxxL*kyyL + R1212 + - SQR(kxyL)) + gInv33*(kxxL*kzzL + R1313 - SQR(kxzL)); + + CCTK_REAL Rojo12 = gInv11*R1121 + gInv13*(kxyL*kxzL - kxxL*kyzL + + R1123) + gInv21*R1221 + gInv22*R1222 + gInv23*R1223 + gInv31*R1321 + + gInv32*(-(kxzL*kyyL) + kxyL*kyzL + R1322) + gInv33*(-(kxzL*kyzL) + + kxyL*kzzL + R1323) + gInv12*(-(kxxL*kyyL) + R1122 + SQR(kxyL)); + + CCTK_REAL Rojo13 = gInv11*R1131 + gInv12*(kxyL*kxzL - kxxL*kyzL + + R1132) + gInv21*R1231 + gInv22*(kxzL*kyyL - kxyL*kyzL + R1232) + + gInv23*(kxzL*kyzL - kxyL*kzzL + R1233) + gInv31*R1331 + gInv32*R1332 + + gInv33*R1333 + gInv13*(-(kxxL*kzzL) + R1133 + SQR(kxzL)); + + CCTK_REAL Rojo21 = gInv11*R2111 + gInv12*R2112 + gInv13*R2113 + + gInv22*R2212 + gInv23*(-(kxzL*kyyL) + kxyL*kyzL + R2213) + + gInv31*(kxyL*kxzL - kxxL*kyzL + R2311) + gInv32*R2312 + + gInv33*(-(kxzL*kyzL) + kxyL*kzzL + R2313) + gInv21*(-(kxxL*kyyL) + + R2211 + SQR(kxyL)); + + CCTK_REAL Rojo22 = gInv12*R2122 + gInv13*(kxzL*kyyL - kxyL*kyzL + + R2123) + gInv21*R2221 + gInv22*R2222 + gInv23*R2223 + gInv31*(kxzL*kyyL + - kxyL*kyzL + R2321) + gInv32*R2322 + gInv11*(kxxL*kyyL + R2121 - + SQR(kxyL)) + gInv33*(kyyL*kzzL + R2323 - SQR(kyzL)); + + CCTK_REAL Rojo23 = gInv11*(-(kxyL*kxzL) + kxxL*kyzL + R2131) + + gInv12*R2132 + gInv13*(kxzL*kyzL - kxyL*kzzL + R2133) + + gInv21*(-(kxzL*kyyL) + kxyL*kyzL + R2231) + gInv22*R2232 + gInv31*R2331 + + gInv32*R2332 + gInv33*R2333 + gInv23*(-(kyyL*kzzL) + R2233 + + SQR(kyzL)); + + CCTK_REAL Rojo31 = gInv11*R3111 + gInv12*R3112 + gInv13*R3113 + + gInv21*(kxyL*kxzL - kxxL*kyzL + R3211) + gInv22*(kxzL*kyyL - kxyL*kyzL + + R3212) + gInv23*R3213 + gInv32*(kxzL*kyzL - kxyL*kzzL + R3312) + + gInv33*R3313 + gInv31*(-(kxxL*kzzL) + R3311 + SQR(kxzL)); + + CCTK_REAL Rojo32 = gInv11*(-(kxyL*kxzL) + kxxL*kyzL + R3121) + + gInv12*(-(kxzL*kyyL) + kxyL*kyzL + R3122) + gInv13*R3123 + gInv21*R3221 + + gInv22*R3222 + gInv23*R3223 + gInv31*(kxzL*kyzL - kxyL*kzzL + R3321) + + gInv33*R3323 + gInv32*(-(kyyL*kzzL) + R3322 + SQR(kyzL)); + + CCTK_REAL Rojo33 = gInv12*(-(kxzL*kyzL) + kxyL*kzzL + R3132) + + gInv13*R3133 + gInv21*(-(kxzL*kyzL) + kxyL*kzzL + R3231) + gInv23*R3233 + + gInv31*R3331 + gInv32*R3332 + gInv33*R3333 + gInv11*(kxxL*kzzL + + R3131 - SQR(kxzL)) + gInv22*(kyyL*kzzL + R3232 - SQR(kyzL)); + + CCTK_REAL Psi4rL = n1*(-(imbar1*(imbar2*(n1*(R4p1112 + R4p1211) + + n2*(R4p1122 + R4p1221) + n3*(R4p1132 + R4p1231)) + imbar3*(n1*(R4p1113 + + R4p1311) + n2*(R4p1123 + R4p1321) + n3*(R4p1133 + R4p1331)))) - + imbar2*imbar3*(n1*(R4p1213 + R4p1312) + n2*(R4p1223 + R4p1322) + + n3*(R4p1233 + R4p1332)) + n1*R4p1112*rmbar1*rmbar2 + + n2*R4p1122*rmbar1*rmbar2 + n3*R4p1132*rmbar1*rmbar2 + + n1*R4p1211*rmbar1*rmbar2 + n2*R4p1221*rmbar1*rmbar2 + + n3*R4p1231*rmbar1*rmbar2 + n1*R4p1113*rmbar1*rmbar3 + + n2*R4p1123*rmbar1*rmbar3 + n3*R4p1133*rmbar1*rmbar3 + + n1*R4p1311*rmbar1*rmbar3 + n2*R4p1321*rmbar1*rmbar3 + + n3*R4p1331*rmbar1*rmbar3 + n1*R4p1213*rmbar2*rmbar3 + + n2*R4p1223*rmbar2*rmbar3 + n3*R4p1233*rmbar2*rmbar3 + + n1*R4p1312*rmbar2*rmbar3 + n2*R4p1322*rmbar2*rmbar3 + + n3*R4p1332*rmbar2*rmbar3 - (n1*R4p1111 + n2*R4p1121 + + n3*R4p1131)*SQR(imbar1) - (n1*R4p1212 + n2*R4p1222 + + n3*R4p1232)*SQR(imbar2) - n1*R4p1313*SQR(imbar3) - + n2*R4p1323*SQR(imbar3) - n3*R4p1333*SQR(imbar3) + + n1*R4p1111*SQR(rmbar1) + n2*R4p1121*SQR(rmbar1) + + n3*R4p1131*SQR(rmbar1) + n1*R4p1212*SQR(rmbar2) + + n2*R4p1222*SQR(rmbar2) + n3*R4p1232*SQR(rmbar2) + + n1*R4p1313*SQR(rmbar3) + n2*R4p1323*SQR(rmbar3) + + n3*R4p1333*SQR(rmbar3)) + n2*(-(imbar1*(imbar2*(n1*(R4p2112 + R4p2211) + + n2*(R4p2122 + R4p2221) + n3*(R4p2132 + R4p2231)) + + imbar3*(n1*(R4p2113 + R4p2311) + n2*(R4p2123 + R4p2321) + n3*(R4p2133 + + R4p2331)))) - imbar2*imbar3*(n1*(R4p2213 + R4p2312) + n2*(R4p2223 + + R4p2322) + n3*(R4p2233 + R4p2332)) + n1*R4p2112*rmbar1*rmbar2 + + n2*R4p2122*rmbar1*rmbar2 + n3*R4p2132*rmbar1*rmbar2 + + n1*R4p2211*rmbar1*rmbar2 + n2*R4p2221*rmbar1*rmbar2 + + n3*R4p2231*rmbar1*rmbar2 + n1*R4p2113*rmbar1*rmbar3 + + n2*R4p2123*rmbar1*rmbar3 + n3*R4p2133*rmbar1*rmbar3 + + n1*R4p2311*rmbar1*rmbar3 + n2*R4p2321*rmbar1*rmbar3 + + n3*R4p2331*rmbar1*rmbar3 + n1*R4p2213*rmbar2*rmbar3 + + n2*R4p2223*rmbar2*rmbar3 + n3*R4p2233*rmbar2*rmbar3 + + n1*R4p2312*rmbar2*rmbar3 + n2*R4p2322*rmbar2*rmbar3 + + n3*R4p2332*rmbar2*rmbar3 - (n1*R4p2111 + n2*R4p2121 + + n3*R4p2131)*SQR(imbar1) - (n1*R4p2212 + n2*R4p2222 + + n3*R4p2232)*SQR(imbar2) - n1*R4p2313*SQR(imbar3) - + n2*R4p2323*SQR(imbar3) - n3*R4p2333*SQR(imbar3) + + n1*R4p2111*SQR(rmbar1) + n2*R4p2121*SQR(rmbar1) + + n3*R4p2131*SQR(rmbar1) + n1*R4p2212*SQR(rmbar2) + + n2*R4p2222*SQR(rmbar2) + n3*R4p2232*SQR(rmbar2) + + n1*R4p2313*SQR(rmbar3) + n2*R4p2323*SQR(rmbar3) + + n3*R4p2333*SQR(rmbar3)) + n3*(-(imbar1*(imbar2*(n1*(R4p3112 + R4p3211) + + n2*(R4p3122 + R4p3221) + n3*(R4p3132 + R4p3231)) + + imbar3*(n1*(R4p3113 + R4p3311) + n2*(R4p3123 + R4p3321) + n3*(R4p3133 + + R4p3331)))) - imbar2*imbar3*(n1*(R4p3213 + R4p3312) + n2*(R4p3223 + + R4p3322) + n3*(R4p3233 + R4p3332)) + n1*R4p3112*rmbar1*rmbar2 + + n2*R4p3122*rmbar1*rmbar2 + n3*R4p3132*rmbar1*rmbar2 + + n1*R4p3211*rmbar1*rmbar2 + n2*R4p3221*rmbar1*rmbar2 + + n3*R4p3231*rmbar1*rmbar2 + n1*R4p3113*rmbar1*rmbar3 + + n2*R4p3123*rmbar1*rmbar3 + n3*R4p3133*rmbar1*rmbar3 + + n1*R4p3311*rmbar1*rmbar3 + n2*R4p3321*rmbar1*rmbar3 + + n3*R4p3331*rmbar1*rmbar3 + n1*R4p3213*rmbar2*rmbar3 + + n2*R4p3223*rmbar2*rmbar3 + n3*R4p3233*rmbar2*rmbar3 + + n1*R4p3312*rmbar2*rmbar3 + n2*R4p3322*rmbar2*rmbar3 + + n3*R4p3332*rmbar2*rmbar3 - (n1*R4p3111 + n2*R4p3121 + + n3*R4p3131)*SQR(imbar1) - (n1*R4p3212 + n2*R4p3222 + + n3*R4p3232)*SQR(imbar2) - n1*R4p3313*SQR(imbar3) - + n2*R4p3323*SQR(imbar3) - n3*R4p3333*SQR(imbar3) + + n1*R4p3111*SQR(rmbar1) + n2*R4p3121*SQR(rmbar1) + + n3*R4p3131*SQR(rmbar1) + n1*R4p3212*SQR(rmbar2) + + n2*R4p3222*SQR(rmbar2) + n3*R4p3232*SQR(rmbar2) + + n1*R4p3313*SQR(rmbar3) + n2*R4p3323*SQR(rmbar3) + + n3*R4p3333*SQR(rmbar3)) - SQR(nn)*((imbar2*imbar3 - + rmbar2*rmbar3)*Rojo23 + imbar1*(imbar2*(Rojo12 + Rojo21) + + imbar3*(Rojo13 + Rojo31)) - rmbar1*(rmbar2*(Rojo12 + Rojo21) + + rmbar3*(Rojo13 + Rojo31)) + imbar2*imbar3*Rojo32 - rmbar2*rmbar3*Rojo32 + + Rojo11*SQR(imbar1) + Rojo22*SQR(imbar2) + Rojo33*SQR(imbar3) - + Rojo11*SQR(rmbar1) - Rojo22*SQR(rmbar2) - Rojo33*SQR(rmbar3)) + + 2*nn*(-(n1*(imbar2*imbar3*Ro213 - rmbar2*rmbar3*Ro213 + + imbar1*(imbar2*(Ro112 + Ro211) + imbar3*(Ro113 + Ro311)) - + rmbar1*(rmbar2*(Ro112 + Ro211) + rmbar3*(Ro113 + Ro311)) + + imbar2*imbar3*Ro312 - rmbar2*rmbar3*Ro312 + Ro111*SQR(imbar1) + + Ro212*SQR(imbar2) + Ro313*SQR(imbar3) - Ro111*SQR(rmbar1) - + Ro212*SQR(rmbar2) - Ro313*SQR(rmbar3))) - n2*(imbar2*imbar3*Ro223 - + rmbar2*rmbar3*Ro223 + imbar1*(imbar2*(Ro122 + Ro221) + imbar3*(Ro123 + + Ro321)) - rmbar1*(rmbar2*(Ro122 + Ro221) + rmbar3*(Ro123 + Ro321)) + + imbar2*imbar3*Ro322 - rmbar2*rmbar3*Ro322 + Ro121*SQR(imbar1) + + Ro222*SQR(imbar2) + Ro323*SQR(imbar3) - Ro121*SQR(rmbar1) - + Ro222*SQR(rmbar2) - Ro323*SQR(rmbar3)) - n3*(imbar2*imbar3*Ro233 - + rmbar2*rmbar3*Ro233 + imbar1*(imbar2*(Ro132 + Ro231) + imbar3*(Ro133 + + Ro331)) - rmbar1*(rmbar2*(Ro132 + Ro231) + rmbar3*(Ro133 + Ro331)) + + imbar2*imbar3*Ro332 - rmbar2*rmbar3*Ro332 + Ro131*SQR(imbar1) + + Ro232*SQR(imbar2) + Ro333*SQR(imbar3) - Ro131*SQR(rmbar1) - + Ro232*SQR(rmbar2) - Ro333*SQR(rmbar3))); + + CCTK_REAL Psi4iL = -(n1*(im1*(n1*(2*R4p1111*rm1 + R4p1112*rm2 + + R4p1211*rm2 + R4p1113*rm3 + R4p1311*rm3) + n2*(2*R4p1121*rm1 + + R4p1122*rm2 + R4p1221*rm2 + R4p1123*rm3 + R4p1321*rm3) + + n3*(2*R4p1131*rm1 + R4p1132*rm2 + R4p1231*rm2 + R4p1133*rm3 + + R4p1331*rm3)) + im2*(n1*(R4p1112*rm1 + R4p1211*rm1 + 2*R4p1212*rm2 + + R4p1213*rm3 + R4p1312*rm3) + n2*(R4p1122*rm1 + R4p1221*rm1 + + 2*R4p1222*rm2 + R4p1223*rm3 + R4p1322*rm3) + n3*(R4p1132*rm1 + + R4p1231*rm1 + 2*R4p1232*rm2 + R4p1233*rm3 + R4p1332*rm3)) + + im3*(n1*(R4p1113*rm1 + R4p1311*rm1 + R4p1213*rm2 + R4p1312*rm2 + + 2*R4p1313*rm3) + n2*(R4p1123*rm1 + R4p1321*rm1 + R4p1223*rm2 + + R4p1322*rm2 + 2*R4p1323*rm3) + n3*(R4p1133*rm1 + R4p1331*rm1 + + R4p1233*rm2 + R4p1332*rm2 + 2*R4p1333*rm3)))) - + n2*(im1*(n1*(2*R4p2111*rm1 + R4p2112*rm2 + R4p2211*rm2 + R4p2113*rm3 + + R4p2311*rm3) + n2*(2*R4p2121*rm1 + R4p2122*rm2 + R4p2221*rm2 + + R4p2123*rm3 + R4p2321*rm3) + n3*(2*R4p2131*rm1 + R4p2132*rm2 + + R4p2231*rm2 + R4p2133*rm3 + R4p2331*rm3)) + im2*(n1*(R4p2112*rm1 + + R4p2211*rm1 + 2*R4p2212*rm2 + R4p2213*rm3 + R4p2312*rm3) + + n2*(R4p2122*rm1 + R4p2221*rm1 + 2*R4p2222*rm2 + R4p2223*rm3 + + R4p2322*rm3) + n3*(R4p2132*rm1 + R4p2231*rm1 + 2*R4p2232*rm2 + + R4p2233*rm3 + R4p2332*rm3)) + im3*(n1*(R4p2113*rm1 + R4p2311*rm1 + + R4p2213*rm2 + R4p2312*rm2 + 2*R4p2313*rm3) + n2*(R4p2123*rm1 + + R4p2321*rm1 + R4p2223*rm2 + R4p2322*rm2 + 2*R4p2323*rm3) + + n3*(R4p2133*rm1 + R4p2331*rm1 + R4p2233*rm2 + R4p2332*rm2 + + 2*R4p2333*rm3))) - n3*(im1*(n1*(2*R4p3111*rm1 + R4p3112*rm2 + + R4p3211*rm2 + R4p3113*rm3 + R4p3311*rm3) + n2*(2*R4p3121*rm1 + + R4p3122*rm2 + R4p3221*rm2 + R4p3123*rm3 + R4p3321*rm3) + + n3*(2*R4p3131*rm1 + R4p3132*rm2 + R4p3231*rm2 + R4p3133*rm3 + + R4p3331*rm3)) + im2*(n1*(R4p3112*rm1 + R4p3211*rm1 + 2*R4p3212*rm2 + + R4p3213*rm3 + R4p3312*rm3) + n2*(R4p3122*rm1 + R4p3221*rm1 + + 2*R4p3222*rm2 + R4p3223*rm3 + R4p3322*rm3) + n3*(R4p3132*rm1 + + R4p3231*rm1 + 2*R4p3232*rm2 + R4p3233*rm3 + R4p3332*rm3)) + + im3*(n1*(R4p3113*rm1 + R4p3311*rm1 + R4p3213*rm2 + R4p3312*rm2 + + 2*R4p3313*rm3) + n2*(R4p3123*rm1 + R4p3321*rm1 + R4p3223*rm2 + + R4p3322*rm2 + 2*R4p3323*rm3) + n3*(R4p3133*rm1 + R4p3331*rm1 + + R4p3233*rm2 + R4p3332*rm2 + 2*R4p3333*rm3))) - + 2*nn*(im1*(n1*(2*rm1*Ro111 + rm2*(Ro112 + Ro211) + rm3*(Ro113 + Ro311)) + + n2*(2*rm1*Ro121 + rm2*(Ro122 + Ro221) + rm3*(Ro123 + Ro321)) + + n3*(2*rm1*Ro131 + rm2*(Ro132 + Ro231) + rm3*(Ro133 + Ro331))) + + im2*(n1*(rm1*(Ro112 + Ro211) + 2*rm2*Ro212 + rm3*(Ro213 + Ro312)) + + n2*(rm1*(Ro122 + Ro221) + 2*rm2*Ro222 + rm3*(Ro223 + Ro322)) + + n3*(rm1*(Ro132 + Ro231) + 2*rm2*Ro232 + rm3*(Ro233 + Ro332))) + + im3*(n1*(rm1*(Ro113 + Ro311) + rm2*(Ro213 + Ro312) + 2*rm3*Ro313) + + n2*(rm1*(Ro123 + Ro321) + rm2*(Ro223 + Ro322) + 2*rm3*Ro323) + + n3*(rm1*(Ro133 + Ro331) + rm2*(Ro233 + Ro332) + 2*rm3*Ro333))) - + (im1*(2*rm1*Rojo11 + rm2*(Rojo12 + Rojo21) + rm3*(Rojo13 + Rojo31)) + + im2*(rm1*(Rojo12 + Rojo21) + 2*rm2*Rojo22 + rm3*(Rojo23 + Rojo32)) + + im3*(rm1*(Rojo13 + Rojo31) + rm2*(Rojo23 + Rojo32) + + 2*rm3*Rojo33))*SQR(nn); /* Copy local copies back to grid functions */ Psi4i[index] = Psi4iL; Psi4r[index] = Psi4rL; - - /* Copy local copies back to subblock grid functions */ } } } |