Mathc initiation/Fichiers h : c73a3
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c01b.c |
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/* --------------------------------- */
/* save as c01b.c */
/* --------------------------------- */
#include "x_hfile.h"
#include "fb.h"
/* --------------------------------- */
int main(void)
{
CTRL_splot p;
p.xmin = -3, p.xmax = 3;
p.ymin = -2, p.ymax = 2;
p.zmin = -1, p.zmax = 5;
p.rot_x = 90, p.rot_z = 36;
p.scale = 1, p.scale_z = 1;
pt2d Q = i_pt2d(1./2.,-1./4.);
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 f(a,b) is \n\n\n");
printf(" (I) a local maximum of f if f_xx(a,b) < 0\n\n");
printf(" (II) a local minimum of f if f_xx(a,b) > 0\n\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) );
stop();
clrscrn();
printf(" if f_xx(a,b) < 0 then it is a local maximum.\n\n");
printf(" if f_xx(a,b) > 0 then it is a local minimum\n\n\n\n");
printf(" f : x,y-> %s\n\n\n", feq );
printf(" f_xx(%0.2f,%0.2f) = %0.9f\n\n\n\n",Q.x,Q.y, fxy_xx(f,H,Q));
printf(" You can use f_yy instead of f_xx.\n\n");
printf(" f_yy(%0.2f,%0.2f) = %0.9f \n\n",Q.x,Q.y, fxy_yy(f,H,Q));
stop();
clrscrn();
printf(" f : (x,y)-> %s\n\n\n", feq);
G_3d_p( p,
feq,f,
Q);
printf(" Open the file ... 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 f(a,b) is
(I) a local maximum of f if f_xx(a,b) < 0
(II) a local minimum of f if f_xx(a,b) > 0
Press return to continue.
Exemple de sortie écran :
Verify if f_x(a,b) = f_y(a,b) = 0.
f : x,y-> x**2 + 4*y**2 - x + 2*y
f_x(0.50,-0.25) = -0.000000000
f_y(0.50,-0.25) = 0.000000000
Press return to continue.
Exemple de sortie écran :
Verify if D(a,b) > 0
f : x,y-> x**2 + 4*y**2 - x + 2*y
Hessian(0.50,-0.25) = 15.999999939
Press return to continue.
Exemple de sortie écran :
if f_xx(a,b) < 0 then it is a local maximum.
if f_xx(a,b) > 0 then it is a local minimum
f : x,y-> x**2 + 4*y**2 - x + 2*y
f_xx(0.50,-0.25) = 1.999999993
You can use f_yy instead of f_xx.
f_yy(0.50,-0.25) = 7.999999996
Press return to continue.
.
Exemple de sortie écran :
f : (x,y)-> x**2 + 4*y**2 - x + 2*y
Open the file ... load "a_main.plt" ... with gnuplot.
Press return to continue.