Mathc initiation/Fichiers h : c26a4

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	x_fxyz.h utilitaire

/* --------------------------------- */
/* save as x_fxyz.h                  */
/* --------------------------------- */
double fxyz_x(
double (*P_f)(double x, double y, double z),
double   h,
pt3d  p
)
{
double tplsh;
double tmnsh;

 tplsh = ((*P_f)(p.x+h,p.y,p.z));
 tmnsh = ((*P_f)(p.x-h,p.y,p.z));

 return(( tplsh-tmnsh)/(2.*h) );
}
/* --------------------------------- */
double fxyz_y(
double (*P_f)(double x, double y, double z),
double   h,
pt3d  p
)
{
double tplsh;
double tmnsh;

 tplsh = ((*P_f)(p.x,p.y+h,p.z));
 tmnsh = ((*P_f)(p.x,p.y-h,p.z));

 return(( tplsh-tmnsh)/(2.*h) );
}/* --------------------------------- */
double fxyz_z(
double (*P_f)(double x, double y, double z),
double   h,
pt3d  p
)
{
double tplsh;
double tmnsh;

 tplsh = ((*P_f)(p.x,p.y,p.z+h));
 tmnsh = ((*P_f)(p.x,p.y,p.z-h));

 return(( tplsh-tmnsh)/(2.*h) );
}
/* --------------------------------- */
double fxyz_xx(
double (*P_f)(double x, double y, double z),
double   h,
pt3d  p
)
{
double t;
double tplsh;
double tmnsh;

 t     = ((*P_f)(p.x  , p.y,p.z));
 tplsh = ((*P_f)(p.x+h, p.y,p.z));
 tmnsh = ((*P_f)(p.x-h, p.y,p.z));

 return( (tplsh-2*t+tmnsh)/(h*h) );
}
/* --------------------------------- */
double fxyz_yy(
double (*P_f)(double x, double y, double z),
double   h,
pt3d  p
)
{
double t;
double tplsh;
double tmnsh;

 t     = ((*P_f)(p.x, p.y  ,p.z));
 tplsh = ((*P_f)(p.x, p.y+h,p.z));
 tmnsh = ((*P_f)(p.x, p.y-h,p.z));

 return( (tplsh-2*t+tmnsh)/(h*h) );
}
/* --------------------------------- */
double fxyz_zz(
double (*P_f)(double x, double y, double z),
double   h,
pt3d  p
)
{
double t;
double tplsh;
double tmnsh;

 t     = ((*P_f)(p.x,p.y,p.z  ));
 tplsh = ((*P_f)(p.x,p.y,p.z+h));
 tmnsh = ((*P_f)(p.x,p.y,p.z-h));

 return( (tplsh-2*t+tmnsh)/(h*h) );
}
/* --------------------------------- */
/* --------------------------------- */

Dans ce fichier il y a les fonctions pour calculer les dérivées partielles.

Les méthodes de calculs :

        First partial derivatives.

f_x  =  [f(x+h,y,z)-f(x-h,y,z)]/2h

f_y  =  [f(x,y+h,z)-f(x,y-h,z)]/2h

f_z  =  [f(x,y,z+h)-f(x,y,z-h)]/2h

         Second partial derivatives.

f_xx =  [f(x+h,y,z)-2f(x,y,z)+f(x-h,y,z)]/h**2

f_yy =  [f(x,y+h,z)-2f(x,y,z)+f(x,y-h),z]/h**2

f_zz =  [f(x,y,z+h)-2f(x,y,z)+f(x,y,z-h)]/h**2

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