Mathc initiation/Fichiers h : c72a3
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c01c.c |
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/* --------------------------------- */
/* save as c01c.c */
/* --------------------------------- */
#include "x_hfile.h"
#include "fc.h"
/* --------------------------------- */
int main(void)
{
CTRL_splot p;
p.xmin = -1, p.xmax = 1;
p.ymin = -1, p.ymax = 1;
p.zmin = -1, p.zmax = 1;
p.rot_x = 56, p.rot_z = 16;
p.scale = 1, p.scale_z = 1;
pt2d Q = i_pt2d(0.,0.);
clrscrn();
printf(" Let f be a function of two variables \n\n");
printf(" that has continuous second partial derivatives\n");
printf(" throughout an open disk R containing (a,b). \n\n");
printf(" If f_x(a,b) = f_y(a,b) = 0 and \n\n");
printf(" Hessian(a,b) < 0, \n\n");
printf(" Then p(a,b,f(a,b)) is a saddle point on the \n");
printf(" graph of f \n\n\n");
stop();
clrscrn();
printf(" Verify if f_x(a,b) = f_y(a,b) = 0.\n\n\n");
printf(" f : x,y-> %s\n\n\n", feq );
printf(" f_x(%0.2f,%0.2f) = %0.9f \n\n",Q.x,Q.y, fxy_x(f,H,Q));
printf(" f_y(%0.2f,%0.2f) = %0.9f \n\n\n",Q.x,Q.y, fxy_y(f,H,Q));
stop();
clrscrn();
printf(" Verify if Hessian(a,b) < 0\n\n\n");
printf(" f : x,y-> %s\n\n\n",feq);
printf(" Hessian(%0.2f,%0.2f) = %0.9f \n\n",Q.x,Q.y,Hessian(f,f_xy,Q) );
printf(" Then p(%0.2f,%0.2f,%0.2f,) is a saddle point on the\n",
Q.x,Q.y, f(Q.x,Q.y));
printf(" graph of f\n\n\n");
stop();
clrscrn();
printf(" f : (x,y)-> %s\n\n\n", feq);
G_3d_p( p,
feq,f,
Q);
printf(" ... load \"a_main.plt\" ... with gnuplot. \n\n");
stop();
return 0;
}
/* --------------------------------- */
/* --------------------------------- */
Exemple de sortie écran :
Let f be a function of two variables
that has continuous second partial derivatives
throughout an open disk R containing (a,b).
If f_x(a,b) = f_y(a,b) = 0 and
Hessian(a,b) < 0,
Then p(a,b,f(a,b)) is a saddle point on the
graph of f
Press return to continue.
Exemple de sortie écran :
Verify if f_x(a,b) = f_y(a,b) = 0.
f : x,y-> x**3 + 3*x*y - y**3
f_x(0.00,0.00) = 0.000000010
f_y(0.00,0.00) = -0.000000010
Press return to continue.
Exemple de sortie écran :
Verify if Hessian(a,b) < 0
f : x,y-> x**3 + 3*x*y - y**3
D(0.00,0.00) = -9.000000000
Then p(0.00,0.00,0.00,) is a saddle point on the
graph of f
Press return to continue.
Exemple de sortie écran :
f : (x,y)-> x**3 + 3*x*y - y**3
Open the file ... load "a_main.plt" ... with gnuplot.
Press return to continue.