many changes --> should now generate LHS of apparent horizon eqn

git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinAnalysis/AHFinderDirect/trunk@522 f88db872-0e4f-0410-b76b-b9085cfa78c5

1 files changed, 26 insertions, 18 deletions

diff --git a/src/gr/horizon.maple b/src/gr/horizon.maple
index d610844..86bc9cf 100644
--- a/src/gr/horizon.maple
+++ b/src/gr/horizon.maple
@@ -1,10 +1,10 @@
-# LHS.maple - evaluate $H$ = LHS of horizon function
+# horizon.maple - evaluate $H$ = LHS of horizon function
 # $Id$
 #
 # horizon - overall driver
-# non_unit_normal - compute s_d
-# non_unit_normal_deriv - compute partial_d_s_d
-# horizon_function - compute HA,HB,HC,HD,H = fn(s_d)
+## non_unit_normal - compute s_d
+## non_unit_normal_deriv - compute partial_d_s_d
+## horizon_function - compute HA,HB,HC,HD,H = fn(s_d)
 #
 
 ################################################################################
@@ -15,6 +15,12 @@
 # This function is a driver to compute, and optionally generate C code
 # for, the LHS of the apparent horizon equation, H.
 #
+# Inputs:
+#	h
+#
+# Outputs:
+#	H = H__fnd(h, ...)
+#
 horizon :=
 proc(cg_flag::boolean)
 
@@ -35,9 +41,9 @@ end proc;
 non_unit_normal :=
 proc()
 global
-       @include "../maple/coords.minc",
-       @include "../maple/gfa.minc",
-       @include "../gr/gr_gfas.minc";
+  @include "../maple/coords.minc",
+  @include "../maple/gfa.minc",
+  @include "../gr/gr_gfas.minc";
 local i, u;
 
 printf("%a...\n", procname);
@@ -64,11 +70,11 @@ end proc;
 # C code.
 #
 non_unit_normal_deriv :=
-proc(cg_flag::boolean)
+proc()
 global
-       @include "../maple/coords.minc",
-       @include "../maple/gfa.minc",
-       @include "../gr/gr_gfas.minc";
+  @include "../maple/coords.minc",
+  @include "../maple/gfa.minc",
+  @include "../gr/gr_gfas.minc";
 local temp, i, j, k, u, v;
 
 printf("%a...\n", procname);
@@ -105,16 +111,17 @@ end proc;
 #
 # This function computes the LHS of the apparent horizon equation
 # as a function of 1st and 2nd angular partial derivatives of the
-# apparent horizon radius $h$, in the Maple gridfn array H.fnd ,
-# using equation (15) in my 1996 apparent horizon finding paper.
+# apparent horizon radius $h$, in the Maple gridfn array H__fnd,
+# using equation (15) in my 1996 apparent horizon finding paper,
+# and using partial_d_g_uu[k,i,j] instead of Diff(g_uu[i,j], x_xyz[k]).
 # This function also optionally generates C code for this computation.
 #
 horizon_function :=
 proc(cg_flag::boolean)
 global
-       @include "../maple/coords.minc",
-       @include "../maple/gfa.minc",
-       @include "../gr/gr_gfas.minc";
+  @include "../maple/coords.minc",
+  @include "../maple/gfa.minc",
+  @include "../gr/gr_gfas.minc";
 local i,j,k,l;
 
 printf("%a...\n", procname);
@@ -122,6 +129,7 @@ printf("%a...\n", procname);
 assert_fnd_exists(g_uu);
 assert_fnd_exists(K_uu);
 assert_fnd_exists(partial_d_ln_sqrt_g);
+assert_fnd_exists(partial_d_g_uu);
 assert_fnd_exists(s_d, fnd);
 assert_fnd_exists(partial_d_s_d, fnd);
 
@@ -135,11 +143,11 @@ HA__fnd := - msum('g_uu[i,k]*s_d__fnd[k] * g_uu[j,l]*s_d__fnd[l]
 					 * partial_d_s_d__fnd[i,j]',
 		  'i'=1..N, 'j'=1..N, 'k'=1..N, 'l'=1..N)
 	   - (1/2)*msum('g_uu[i,j]*s_d__fnd[j]
-			* Diff(g_uu[k,l],x_xyz[i]) * s_d__fnd[k]*s_d__fnd[l]',
+			* partial_d_g_uu[i,k,l] * s_d__fnd[k]*s_d__fnd[l]',
 			'i'=1..N, 'j'=1..N, 'k'=1..N, 'l'=1..N);
 
 # (15b) in my paper
-HB__fnd := + msum('Diff(g_uu[i,j],x_xyz[i])*s_d__fnd[j]', 'i'=1..N, 'j'=1..N)
+HB__fnd := + msum('partial_d_g_uu[i,i,j]*s_d__fnd[j]', 'i'=1..N, 'j'=1..N)
 	   + msum('g_uu[i,j]*partial_d_s_d__fnd[i,j]', 'i'=1..N, 'j'=1..N)
 	   + msum('g_uu[i,j]*partial_d_ln_sqrt_g[i]*s_d__fnd[j]',
 		  'i'=1..N, 'j'=1..N);