add new functions partial_{mu,nu,phi}_wrt_{x,y,z}

git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinAnalysis/AHFinderDirect/trunk@527 f88db872-0e4f-0410-b76b-b9085cfa78c5

2 files changed, 37 insertions, 17 deletions

diff --git a/src/patch/coords.cc b/src/patch/coords.cc
index d906345..b33a6af 100644
--- a/src/patch/coords.cc
+++ b/src/patch/coords.cc
@@ -7,6 +7,7 @@
 //
 // (r,(mu,nu,phi)) <--> (x,y,z)
 // ((mu,nu,phi)) --> the 3rd
+//
 // usual polar spherical (r,theta,phi) <--> (x,y,z)
 // ((mu,nu,phi)) <--> usual polar spherical (theta,phi)
 //
@@ -241,26 +242,34 @@ return mu_of_yz(y, z);
 
 namespace local_coords
 	  {
-fp r_of_xyz(fp x, fp y, fp z)
-{
-return hypot3(x, y, z);
-}
+fp r_of_xyz(fp x, fp y, fp z) { return hypot3(x, y, z); }
+fp mu_of_yz(fp y, fp z)  { return arctan_xy(z,y); }
+fp nu_of_xz(fp x, fp z)  { return arctan_xy(z,x); }
+fp phi_of_xy(fp x, fp y) { return arctan_xy(x,y); }
+	  }
 
-fp mu_of_yz(fp y, fp z)
-{
-return arctan_xy(z,y);
-}
+//******************************************************************************
 
-fp nu_of_xz(fp x, fp z)
-{
-return arctan_xy(z,x);
-}
+//
+// these functions compute the partial derivatives
+//	partial {mu,nu,phi} / partial {x,y,z}
+// as per the formulas on p.5 of my apparent horizon finding notes
+//
+fp partial_mu_wrt_x(fp x, fp y, fp z) { return 0.0; }
+fp partial_mu_wrt_y(fp x, fp y, fp z) { return  z / (y*y + z*z); }
+fp partial_mu_wrt_z(fp x, fp y, fp z) { return -y / (y*y + z*z); }
 
-fp phi_of_xy(fp x, fp y)
-{
-return arctan_xy(x,y);
-}
-	  }
+//**************************************
+
+fp partial_nu_wrt_x(fp x, fp y, fp z) { return  z / (x*x + z*z); }
+fp partial_nu_wrt_y(fp x, fp y, fp z) { return 0.0; }
+fp partial_nu_wrt_z(fp x, fp y, fp z) { return -x / (x*x + z*z); }
+
+//**************************************
+
+fp partial_phi_wrt_x(fp x, fp y, fp z) { return -y / (x*x + y*y); }
+fp partial_phi_wrt_y(fp x, fp y, fp z) { return  x / (x*x + y*y); }
+fp partial_phi_wrt_z(fp x, fp y, fp z) { return 0.0; }
 
 //******************************************************************************
 
diff --git a/src/patch/coords.hh b/src/patch/coords.hh
index 7a0b624..ecf1124 100644
--- a/src/patch/coords.hh
+++ b/src/patch/coords.hh
@@ -137,6 +137,17 @@ fp phi_of_mu_nu(fp mu, fp nu );
 fp nu_of_mu_phi(fp mu, fp phi);
 fp mu_of_nu_phi(fp nu, fp phi);
 
+// partial {mu,nu,phi} / partial {x,y,z}
+fp partial_mu_wrt_x(fp x, fp y, fp z);
+fp partial_mu_wrt_y(fp x, fp y, fp z);
+fp partial_mu_wrt_z(fp x, fp y, fp z);
+fp partial_nu_wrt_x(fp x, fp y, fp z);
+fp partial_nu_wrt_y(fp x, fp y, fp z);
+fp partial_nu_wrt_z(fp x, fp y, fp z);
+fp partial_phi_wrt_x(fp x, fp y, fp z);
+fp partial_phi_wrt_y(fp x, fp y, fp z);
+fp partial_phi_wrt_z(fp x, fp y, fp z);
+
 // usual polar spherical (r,theta,phi) <--> (x,y,z)
 void xyz_of_r_theta_phi(fp r, fp theta, fp phi,   fp& x, fp& y, fp& z);
 // ... already have r_of_xyz()