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/*@@
@file CartToSphere.c
@date Thu Apr 25 16:04:53 2002
@author Tom Goodale
@desc
@enddesc
@version $Header
@@*/
#include "cctk.h"
#include <math.h>
#include "ADMAnalysis.h"
static const char *rcsid = "$Header$";
CCTK_FILEVERSION(CactusEinstein_ADMAnalysis_CartToSphere_c)
/********************************************************************
********************* Local Data Types ***********************
********************************************************************/
#define SQR(a) ((a)*(a))
/********************************************************************
********************* Local Routine Prototypes *********************
********************************************************************/
/********************************************************************
***************** Scheduled Routine Prototypes *********************
********************************************************************/
/********************************************************************
********************* Other Routine Prototypes *********************
********************************************************************/
/********************************************************************
********************* Local Data *****************************
********************************************************************/
/********************************************************************
********************* External Routines **********************
********************************************************************/
/*@@
@routine ADMAnalysis_CartToSphere
@date Thu Apr 25 16:17:58 2002
@author Tom Goodale
@desc
Calculates the spherical components (r,q,p) corresponding to
the cartesian components (xyz) of a symmetric spatial tensor.
q corresponds to theta, and p to phi.
@enddesc
@calls
@calledby
@history
@hdate Thu Apr 25 16:20:07 2002 @hauthor Tom Goodale
@hdesc Took old metric_ and curv_cartosphere routines and
made this generic one.
@endhistory
@var lsh
@vdesc the local shape of the grid
@vtype const int *
@vio in
@var project_rdtheta_rdphi
@vdesc If set project angular components onto r*dtheta and
r*sin(theta)*dphi instead of dtheta and dphi
@vtype int
@vio in
@var x
@vdesc the x coordinate
@vtype const CCTK_REAL *
@vio in
@var y
@vdesc the y coordinate
@vtype const CCTK_REAL *
@vio in
@var z
@vdesc the z coordinate
@vtype const CCTK_REAL *
@vio in
@var r
@vdesc the r coordinate
@vtype const CCTK_REAL *
@vio in
@var cart_xx
@vdesc the xx component of the tensor
@vtype const CCTK_REAL *
@vio in
@var cart_xy
@vdesc the xy component of the tensor
@vtype const CCTK_REAL *
@vio in
@var cart_xz
@vdesc the xz component of the tensor
@vtype const CCTK_REAL *
@vio in
@var cart_yy
@vdesc the yy component of the tensor
@vtype const CCTK_REAL *
@vio in
@var cart_yz
@vdesc the yz component of the tensor
@vtype const CCTK_REAL *
@vio in
@var cart_zz
@vdesc the zz component of the tensor
@vtype const CCTK_REAL *
@vio in
@var sphere_rr
@vdesc the rr component of the tensor
@vtype const CCTK_REAL *
@vio in
@var sphere_rq
@vdesc the rq component of the tensor
@vtype const CCTK_REAL *
@vio in
@var sphere_rp
@vdesc the rp component of the tensor
@vtype const CCTK_REAL *
@vio in
@var sphere_qq
@vdesc the qq component of the tensor
@vtype const CCTK_REAL *
@vio in
@var sphere_qp
@vdesc the qp component of the tensor
@vtype const CCTK_REAL *
@vio in
@var sphere_pp
@vdesc the pp component of the tensor
@vtype const CCTK_REAL *
@vio in
@@*/
void ADMAnalysis_CartToSphere(const CCTK_INT *lsh,
CCTK_INT project_rdtheta_rdphi,
const CCTK_REAL *x,
const CCTK_REAL *y,
const CCTK_REAL *z,
const CCTK_REAL *r,
const CCTK_REAL *cart_xx,
const CCTK_REAL *cart_xy,
const CCTK_REAL *cart_xz,
const CCTK_REAL *cart_yy,
const CCTK_REAL *cart_yz,
const CCTK_REAL *cart_zz,
CCTK_REAL *sphere_rr,
CCTK_REAL *sphere_rq,
CCTK_REAL *sphere_rp,
CCTK_REAL *sphere_qq,
CCTK_REAL *sphere_qp,
CCTK_REAL *sphere_pp)
{
int i;
CCTK_REAL cost;
CCTK_REAL sint;
CCTK_REAL sinp;
CCTK_REAL cosp;
CCTK_REAL rvalue;
CCTK_REAL sxy;
CCTK_REAL txx,txy,txz,tyy,tyz,tzz;
/* loop over all the grid */
for(i = 0; i < lsh[0]*lsh[1]*lsh[2]; i++)
{
txx = cart_xx[i];
txy = cart_xy[i];
txz = cart_xz[i];
tyy = cart_yy[i];
tyz = cart_yz[i];
tzz = cart_zz[i];
rvalue = r[i];
sxy = sqrt( SQR(x[i]) + SQR(y[i]));
/* be careful with r=0 and xy plane */
if (rvalue==0.0)
{
cost = 1.0;
sint = 0.0;
sinp = 0.0;
cosp = 1.0;
}
else if (sxy==0)
{
cost = 1.0;
sint = 0.0;
sinp = 0.0;
cosp = 1.0;
}
else
{
cost = z[i]/rvalue;
sint = sxy/rvalue;
sinp = y[i]/sxy;
cosp = x[i]/sxy;
}
sphere_rr[i]=
tyy*SQR(sinp)*SQR(sint)+
2*cosp*txy*sinp*SQR(sint)+
SQR(cosp)*txx*SQR(sint)+
2*cost*tyz*sinp*sint+
2*cosp*cost*txz*sint+
SQR(cost)*tzz;
sphere_qq[i] =
(tzz*SQR(sint)+
(-2*cost*tyz*sinp-
2*cosp*cost*txz)*sint+
SQR(cost)*tyy*SQR(sinp)+
2*cosp*SQR(cost)*txy*sinp
+SQR(cosp)*SQR(cost)*txx);
if (!project_rdtheta_rdphi)
{
sphere_qq[i] *= SQR(r[i]);
}
sphere_pp[i] =
(txx*SQR(sinp)-
2*cosp*txy*sinp+
SQR(cosp)*tyy);
if (!project_rdtheta_rdphi)
{
sphere_pp[i] *= SQR(r[i]) * SQR(sint);
}
sphere_rq[i] =
(cost*tyy*SQR(sinp)*sint+
2*cosp*cost*txy*sinp*sint-
cost*tzz*sint+
SQR(cosp)*cost*txx*sint+
2*SQR(cost)*tyz*sinp-
tyz*sinp+
2*cosp*SQR(cost)*txz-
cosp*txz);
if (!project_rdtheta_rdphi)
{
sphere_rq[i] *= r[i];
}
sphere_rp[i] =
((-txy*SQR(sinp)+
(cosp*tyy-cosp*txx)*sinp+
SQR(cosp)*txy)*sint-
cost*txz*sinp+cosp*cost*tyz);
if (!project_rdtheta_rdphi)
{
sphere_rp[i] *= r[i] * sint;
}
sphere_qp[i] =
((txz*sinp-cosp*tyz)*sint+
cost*(-txy*SQR(sinp)+
cosp*(tyy-txx)*sinp+SQR(cosp)*txy));
if (!project_rdtheta_rdphi)
{
sphere_qp[i] *= SQR(r[i]) * sint;
}
}
}
/********************************************************************
********************* Local Routines *************************
********************************************************************/
|
