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/*@@
@header DXZDG_guts.h
@date Jun 98
@author Gabrielle Allen
@desc
Macro to calculate the (first and) second derivatives of the
physical metric with respect to x,z
The macro is defined in terms of standard variables in
@seefile DXZDG_declare.h
The macro uses @seefile DXDG_guts.h , @seefile DZDG_guts.h and
@seefile DXDG_declare.h , @seefile DZDG_declare.h
@enddesc
@@*/
#ifndef DXZDG_GUTS
#define DXZDG_GUTS
#include "DXDG_guts.h"
#include "DZDG_guts.h"
#ifdef FCODE
DXZDG_OO4DXDZ = 1D0/(4D0*dx*dz)
/* Factor involving 2nd derivative of conformal factor */
IF (conformal_state .eq. 0) THEN
DXZDG_FAC = 0
ELSE
DXZDG_FAC = DXDG_PSI4*(4*DXZDG_DXZDPSI_O_PSI + 12*DXDG_DXDPSI_O_PSI*DZDG_DZDPSI_O_PSI)
ENDIF
/* Now calculate the second deriatives */
DXZDG_DXZDGXX = DZDCG_DZDCGXX*DXDG_FAC+DXDCG_DXDCGXX*DZDG_FAC+DXZDG_FAC*DXDG_GXX+ \
DXDG_PSI4*DXZDG_OO4DXDZ*(DXZDG_GXX_IPKP-DXZDG_GXX_IPKM-DXZDG_GXX_IMKP+ \
DXZDG_GXX_IMKM)
DXZDG_DXZDGXY = DZDCG_DZDCGXY*DXDG_FAC+DXDCG_DXDCGXY*DZDG_FAC+DXZDG_FAC*DXDG_GXY+ \
DXDG_PSI4*DXZDG_OO4DXDZ*(DXZDG_GXY_IPKP-DXZDG_GXY_IPKM-DXZDG_GXY_IMKP+ \
DXZDG_GXY_IMKM)
DXZDG_DXZDGXZ = DZDCG_DZDCGXZ*DXDG_FAC+DXDCG_DXDCGXZ*DZDG_FAC+DXZDG_FAC*DXDG_GXZ+ \
DXDG_PSI4*DXZDG_OO4DXDZ*(DXZDG_GXZ_IPKP-DXZDG_GXZ_IPKM-DXZDG_GXZ_IMKP+ \
DXZDG_GXZ_IMKM)
DXZDG_DXZDGYY = DZDCG_DZDCGYY*DXDG_FAC+DXDCG_DXDCGYY*DZDG_FAC+DXZDG_FAC*DXDG_GYY+ \
DXDG_PSI4*DXZDG_OO4DXDZ*(DXZDG_GYY_IPKP-DXZDG_GYY_IPKM-DXZDG_GYY_IMKP+ \
DXZDG_GYY_IMKM)
DXZDG_DXZDGYZ = DZDCG_DZDCGYZ*DXDG_FAC+DXDCG_DXDCGYZ*DZDG_FAC+DXZDG_FAC*DXDG_GYZ+ \
DXDG_PSI4*DXZDG_OO4DXDZ*(DXZDG_GYZ_IPKP-DXZDG_GYZ_IPKM-DXZDG_GYZ_IMKP+ \
DXZDG_GYZ_IMKM)
DXZDG_DXZDGZZ = DZDCG_DZDCGZZ*DXDG_FAC+DXDCG_DXDCGZZ*DZDG_FAC+DXZDG_FAC*DXDG_GZZ+ \
DXDG_PSI4*DXZDG_OO4DXDZ*(DXZDG_GZZ_IPKP-DXZDG_GZZ_IPKM-DXZDG_GZZ_IMKP+ \
DXZDG_GZZ_IMKM)
#endif
#ifdef CCODE
/* Factor involving 2nd derivative of conformal factor */
DXZDG_FAC = ((*conformal_state == 0)?0:
DXDG_PSI4*(4*DXZDG_DXZDPSI_O_PSI + 12*DXDG_DXDPSI_O_PSI*DZDG_DZDPSI_O_PSI));
/* Now calculate the second deriatives */
DXZDG_DXZDGXX = DZDCG_DZDCGXX*DXDG_FAC+DXDCG_DXDCGXX*DZDG_FAC+DXZDG_FAC*DXDG_GXX+
DXDG_PSI4*DXZDG_OO4DXDZ*(DXZDG_GXX_IPKP-DXZDG_GXX_IPKM-DXZDG_GXX_IMKP+
DXZDG_GXX_IMKM);
DXZDG_DXZDGXY = DZDCG_DZDCGXY*DXDG_FAC+DXDCG_DXDCGXY*DZDG_FAC+DXZDG_FAC*DXDG_GXY+
DXDG_PSI4*DXZDG_OO4DXDZ*(DXZDG_GXY_IPKP-DXZDG_GXY_IPKM-DXZDG_GXY_IMKP+
DXZDG_GXY_IMKM);
DXZDG_DXZDGXZ = DZDCG_DZDCGXZ*DXDG_FAC+DXDCG_DXDCGXZ*DZDG_FAC+DXZDG_FAC*DXDG_GXZ+
DXDG_PSI4*DXZDG_OO4DXDZ*(DXZDG_GXZ_IPKP-DXZDG_GXZ_IPKM-DXZDG_GXZ_IMKP+
DXZDG_GXZ_IMKM);
DXZDG_DXZDGYY = DZDCG_DZDCGYY*DXDG_FAC+DXDCG_DXDCGYY*DZDG_FAC+DXZDG_FAC*DXDG_GYY+
DXDG_PSI4*DXZDG_OO4DXDZ*(DXZDG_GYY_IPKP-DXZDG_GYY_IPKM-DXZDG_GYY_IMKP+
DXZDG_GYY_IMKM);
DXZDG_DXZDGYZ = DZDCG_DZDCGYZ*DXDG_FAC+DXDCG_DXDCGYZ*DZDG_FAC+DXZDG_FAC*DXDG_GYZ+
DXDG_PSI4*DXZDG_OO4DXDZ*(DXZDG_GYZ_IPKP-DXZDG_GYZ_IPKM-DXZDG_GYZ_IMKP+
DXZDG_GYZ_IMKM);
DXZDG_DXZDGZZ = DZDCG_DZDCGZZ*DXDG_FAC+DXDCG_DXDCGZZ*DZDG_FAC+DXZDG_FAC*DXDG_GZZ+
DXDG_PSI4*DXZDG_OO4DXDZ*(DXZDG_GZZ_IPKP-DXZDG_GZZ_IPKM-DXZDG_GZZ_IMKP+
DXZDG_GZZ_IMKM);
#endif
#endif
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