move Jacobian.* to ../elliptic/

update other files to compute more of Jacobian coeffs


git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinAnalysis/AHFinderDirect/trunk@633 f88db872-0e4f-0410-b76b-b9085cfa78c5

1 files changed, 61 insertions, 109 deletions

diff --git a/src/gr/driver.cc b/src/gr/driver.cc
index 3982be2..0c04dfe 100644
--- a/src/gr/driver.cc
+++ b/src/gr/driver.cc
@@ -3,7 +3,7 @@
 //
 // <<<prototypes for functions local to this file>>>
 // AHFinderDirect_driver - top-level driver
-/// setup_ellipsoid_initial_guess - set up ellipsoid in h gridfn
+/// setup_Kerr_KerrSchild_initial_guess - set up Kerr/Kerr-Schild initial guess
 //
 
 #include <stdio.h>
@@ -32,6 +32,7 @@ using jtutil::error_exit;
 #include "../util/patch_interp.hh"
 #include "../util/ghost_zone.hh"
 #include "../util/patch_system.hh"
+#include "../util/Jacobian.hh"
 
 #include "gfn.hh"
 #include "AHFinderDirect.hh"
@@ -43,10 +44,9 @@ using jtutil::error_exit;
 //
 
 namespace {
-void setup_ellipsoid_initial_guess
-	(patch_system& ps,
-	 fp global_center_x, fp global_center_y, fp global_center_z,
-	 fp radius_x, fp radius_y, fp radius_z);
+void setup_Kerr_KerrSchild_horizon(patch_system& ps,
+				   fp mass, fp spin,
+				   fp xposn, fp yposn, fp zposn);
 	  };
 
 //******************************************************************************
@@ -113,42 +113,22 @@ cgi.coord_delta[2] = cctk_delta_space[2];
 cgi.gridfn_dims[0] = cctk_lsh[0];
 cgi.gridfn_dims[1] = cctk_lsh[1];
 cgi.gridfn_dims[2] = cctk_lsh[2];
-cgi.g_dd_11_data = static_cast<const fp *>(
-			CCTK_VarDataPtr(cctkGH, 0, "einstein::gxx")
-					  );
-cgi.g_dd_12_data = static_cast<const fp *>(
-			CCTK_VarDataPtr(cctkGH, 0, "einstein::gxy")
-					  );
-cgi.g_dd_13_data = static_cast<const fp *>(
-			CCTK_VarDataPtr(cctkGH, 0, "einstein::gxz")
-					  );
-cgi.g_dd_22_data = static_cast<const fp *>(
-			CCTK_VarDataPtr(cctkGH, 0, "einstein::gyy")
-					  );
-cgi.g_dd_23_data = static_cast<const fp *>(
-			CCTK_VarDataPtr(cctkGH, 0, "einstein::gyz")
-					  );
-cgi.g_dd_33_data = static_cast<const fp *>(
-			CCTK_VarDataPtr(cctkGH, 0, "einstein::gzz")
-					  );
-cgi.K_dd_11_data = static_cast<const fp *>(
-			CCTK_VarDataPtr(cctkGH, 0, "einstein::kxx")
-					  );
-cgi.K_dd_12_data = static_cast<const fp *>(
-			CCTK_VarDataPtr(cctkGH, 0, "einstein::kxy")
-					  );
-cgi.K_dd_13_data = static_cast<const fp *>(
-			CCTK_VarDataPtr(cctkGH, 0, "einstein::kxz")
-					  );
-cgi.K_dd_22_data = static_cast<const fp *>(
-			CCTK_VarDataPtr(cctkGH, 0, "einstein::kyy")
-					  );
-cgi.K_dd_23_data = static_cast<const fp *>(
-			CCTK_VarDataPtr(cctkGH, 0, "einstein::kyz")
-					  );
-cgi.K_dd_33_data = static_cast<const fp *>(
-			CCTK_VarDataPtr(cctkGH, 0, "einstein::kzz")
-					  );
+// n.b. The  cgi.[gK]_dd_??_data  are actually  const fp *  pointers,
+//	since we won't modify the 3-D gridfn data!  But  static_cast<...>
+//      won't change const modifiers, so we just cast to  fp*  and let
+//	the assignment take care of the const part...
+cgi.g_dd_11_data = static_cast<fp*>(CCTK_VarDataPtr(cctkGH,0, "einstein::gxx"));
+cgi.g_dd_12_data = static_cast<fp*>(CCTK_VarDataPtr(cctkGH,0, "einstein::gxy"));
+cgi.g_dd_13_data = static_cast<fp*>(CCTK_VarDataPtr(cctkGH,0, "einstein::gxz"));
+cgi.g_dd_22_data = static_cast<fp*>(CCTK_VarDataPtr(cctkGH,0, "einstein::gyy"));
+cgi.g_dd_23_data = static_cast<fp*>(CCTK_VarDataPtr(cctkGH,0, "einstein::gyz"));
+cgi.g_dd_33_data = static_cast<fp*>(CCTK_VarDataPtr(cctkGH,0, "einstein::gzz"));
+cgi.K_dd_11_data = static_cast<fp*>(CCTK_VarDataPtr(cctkGH,0, "einstein::kxx"));
+cgi.K_dd_12_data = static_cast<fp*>(CCTK_VarDataPtr(cctkGH,0, "einstein::kxy"));
+cgi.K_dd_13_data = static_cast<fp*>(CCTK_VarDataPtr(cctkGH,0, "einstein::kxz"));
+cgi.K_dd_22_data = static_cast<fp*>(CCTK_VarDataPtr(cctkGH,0, "einstein::kyy"));
+cgi.K_dd_23_data = static_cast<fp*>(CCTK_VarDataPtr(cctkGH,0, "einstein::kyz"));
+cgi.K_dd_33_data = static_cast<fp*>(CCTK_VarDataPtr(cctkGH,0, "einstein::kzz"));
 
 
 //
@@ -175,15 +155,14 @@ if	(STRING_EQUAL(initial_guess_method, "read from file"))
 			       initial_guess__read_from_file__file_name,
 			       false);		// no ghost zones
 	}
-else if (STRING_EQUAL(initial_guess_method, "ellipsoid"))
+else if (STRING_EQUAL(initial_guess_method, "Kerr/Kerr-Schild"))
    then {
-	setup_ellipsoid_initial_guess(ps,
-				      initial_guess__ellipsoid__center_global_x,
-				      initial_guess__ellipsoid__center_global_y,
-				      initial_guess__ellipsoid__center_global_z,
-				      initial_guess__ellipsoid__radius_x,
-				      initial_guess__ellipsoid__radius_y,
-				      initial_guess__ellipsoid__radius_z);
+	setup_Kerr_KerrSchild_horizon(ps,
+				      initial_guess__Kerr_KerrSchild__mass,
+				      initial_guess__Kerr_KerrSchild__spin,
+				      initial_guess__Kerr_KerrSchild__xposn,
+				      initial_guess__Kerr_KerrSchild__yposn,
+				      initial_guess__Kerr_KerrSchild__zposn);
 	ps.print_ghosted_gridfn_with_xyz(ghosted_gfns::gfn__h,
 					 true, ghosted_gfns::gfn__h,
 					 "h.dat",
@@ -204,6 +183,12 @@ if      (STRING_EQUAL(method, "horizon"))
 				 true, ghosted_gfns::gfn__h,
 				 "H.dat");
 	}
+if      (STRING_EQUAL(method, "horizon Jacobian"))
+   then {
+	Jacobian& Jac = create_Jacobian(ps, Jacobian_type);
+	horizon_function(ps, cgi, gii, true);
+	horizon_Jacobian(ps, Jac);
+	}
 else	CCTK_VWarn(-1, __LINE__, __FILE__, CCTK_THORNSTRING,
 		   "unknown method=\"%s\"!",
 		   method);					/*NOTREACHED*/
@@ -212,38 +197,30 @@ else	CCTK_VWarn(-1, __LINE__, __FILE__, CCTK_THORNSTRING,
 //******************************************************************************
 
 //
-// This function sets up an ellipsoid in the gridfn h, using the
-// formulas in "ellipsoid.maple" and the Maple-generated C code in
-// "ellipsoid.c":
-//
-// ellipsoid has center (A,B,C), radius (a,b,c)
-// angular coordinate system has center (U,V,W)
-//
-// direction cosines wrt angular coordinate center are (xcos,ycos,zcos)
-// i.e. a point has coordinates (U+xcos*r, V+ycos*r, W+zcos*r)
+// This function sets up the horizon of a Kerr black hole in Kerr-Schild
+// coordinates, on the nominal grid, in the  h  gridfn.
 //
-// then the equation of the ellipsoid is
-//	(U+xcos*r - A)^2     (V+ycos*r - B)^2     (W+zcos*r - C)^2
-//	-----------------  +  ----------------  +  -----------------  =  1
-//	        a^2                  b^2                   c^2
+// Kerr-Schild coordinates are described in MTW Exercise 33.8, page 903,
+// and the horizon is worked out on page 13 of my AHFinderDirect notes.
 //
-// to solve this, we introduce intermediate variables
-//	AU = A - U
-//	BV = B - V
-//	CW = C - W
+// Arguments:
+// (mass,spin) = Describe the Kerr black hole.
+// [xyz]_posn = The position of the Kerr black hole.
 //
 namespace {
-void setup_ellipsoid_initial_guess
-	(patch_system& ps,
-	 fp global_center_x, fp global_center_y, fp global_center_z,
-	 fp radius_x, fp radius_y, fp radius_z)
+void setup_Kerr_KerrSchild_horizon(patch_system& ps,
+				   fp mass, fp spin,
+				   fp xposn, fp yposn, fp zposn)
 {
 CCTK_VInfo(CCTK_THORNSTRING,
-	   "   h = ellipsoid: global_center=(%g,%g,%g)",
-	   global_center_x, global_center_y, global_center_z);
+	   "   setting up Kerr/Kerr-Schild horizon");
 CCTK_VInfo(CCTK_THORNSTRING,
-	   "                  radius=(%g,%g,%g)",
-	   radius_x, radius_y, radius_z);
+	   "      mass=%g, spin=%g, posn=(%g,%g,%g)",
+	   double(mass), double(spin),
+	   double(xposn), double(yposn), double(zposn));
+
+// horizon in Kerr-Schild is coordinate sphere $r = (1 + \sqrt{1-a^2}) m$
+const fp r = (1.0 + sqrt(1.0 - spin*spin)) * mass;
 
 	for (int pn = 0 ; pn < ps.N_patches() ; ++pn)
 	{
@@ -255,44 +232,19 @@ CCTK_VInfo(CCTK_THORNSTRING,
 		     isigma <= p.max_isigma() ;
 		     ++isigma)
 		{
-		const fp rho = p.rho_of_irho(irho);
+		const fp rho   = p.rho_of_irho(irho);
 		const fp sigma = p.sigma_of_isigma(isigma);
-		fp xcos, ycos, zcos;
-		p.xyzcos_of_rho_sigma(rho,sigma, xcos,ycos,zcos);
-
-		// set up variables used by Maple-generated code
-		const fp AU = global_center_x - ps.origin_x();
-		const fp BV = global_center_y - ps.origin_y();
-		const fp CW = global_center_z - ps.origin_z();
-		const fp a = radius_x;
-		const fp b = radius_y;
-		const fp c = radius_z;
-
-		// compute the solutions r_plus and r_minus
-		fp r_plus, r_minus;
-		#include "ellipsoid.c"
 
-		// exactly one of the solutions (call it r) should be positive
-		fp r;
-		if      ((r_plus > 0.0) && (r_minus < 0.0))
-		   then r = r_plus;
-		else if ((r_plus < 0.0) && (r_minus > 0.0))
-		   then r = r_minus;
-		else    CCTK_VWarn(-1, __LINE__, __FILE__, CCTK_THORNSTRING,
-				   "\n"
-"   expected exactly one r>0 solution, got 0 or 2!\n"
-"   %s patch (irho,isigma)=(%d,%d) ==> (rho,sigma)=(%g,%g)\n"
-"   direction cosines (xcos,ycos,zcos)=(%g,%g,%g)\n"
-"   ==> r_plus=%g r_minus=%g\n"
-				   ,
-				   p.name(), irho, isigma,
-				   double(rho), double(sigma),
-				   double(xcos), double(ycos), double(zcos),
-				   double(r_plus), double(r_minus));
-		   						/*NOTREACHED*/
+		fp theta, phi;
+		p.theta_phi_of_rho_sigma(rho,sigma, theta,phi);
+		fp Kerr_x, Kerr_y, Kerr_z;
+		p.xyz_of_r_rho_sigma(r,rho,sigma, Kerr_x,Kerr_y,Kerr_z);
 
-		// r = horizon radius at this grid point
-		p.ghosted_gridfn(ghosted_gfns::gfn__h, irho,isigma) = r;
+		const fp KS_x = Kerr_x - spin*sin(theta)*sin(phi);
+		const fp KS_y = Kerr_y + spin*sin(theta)*cos(phi);
+		const fp KS_z = Kerr_z;
+		p.ghosted_gridfn(ghosted_gfns::gfn__h,irho,isigma)
+			= jtutil::hypot3(KS_x, KS_y, KS_z);
 		}
 		}
 	}