Mathc matrices/c26b1
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c01.c |
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/* ------------------------------------ */
/* Save as : c01.c */
/* ------------------------------------ */
#include "v_a.h"
#include "d.h"
/* --------------------------------- */
int main(void)
{
double xy[8] ={
1, 0,
2, 3,
3, 4,
4, 0 };
double **XY = ca_A_mR(xy,i_mR(R4,C2));
double **A = i_mR(R5,C5);
double **b = i_mR(R5,C1);
double **Ab = i_Abr_Ac_bc_mR(R5,C5,C1);
clrscrn();
printf("\n");
printf(" Find the coefficients a, b, c, d, e, of the curve \n\n");
printf(" ax**2 + by**2 + cx + dy + e = 0 \n\n");
printf(" that passes through these four points. \n\n");
printf(" x y");
p_mR(XY,S5,P0,C6);
printf("\n");
printf(" Using the given points, we obtain this matrix.\n");
printf(" (a = 1. This is my choice)\n\n");
printf(" x**2 y**2 x y ");
i_A_b_with_XY_mR(XY,A,b);
c_A_b_Ab_mR(A,b,Ab);
p_mR(Ab,S7,P2,C6);
stop();
clrscrn();
printf(" The Gauss Jordan process will reduce this matrix to : \n");
gj_TP_mR(Ab);
p_mR(Ab,S7,P2,C6);
printf(" The coefficients a, b, c, d, e, of the curve are : \n\n");
p_eq_conica_mR(Ab);
stop();
clrscrn();
printf(" x y \n");
p_mR(XY,S5,P0,C6);
printf("\n");
printf(" Verify the result : \n\n");
verify_XY_mR(Ab,XY[R1][C1],XY[R1][C2]);
verify_XY_mR(Ab,XY[R2][C1],XY[R2][C2]);
verify_XY_mR(Ab,XY[R3][C1],XY[R3][C2]);
verify_XY_mR(Ab,XY[R4][C1],XY[R4][C2]);
printf("\n\n\n");
stop();
f_mR(XY);
f_mR(A);
f_mR(b);
f_mR(Ab);
return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */
Exemple de sortie écran :
------------------------------------
Find the coefficients a, b, c, d, e, of the curve
ax**2 + by**2 + cx + dy + e = 0
that passes through these four points.
x y
+1 +0
+2 +3
+3 +4
+4 +0
Using the given points, we obtain this matrix.
(a = 1. This is my choice)
x**2 y**2 x y
+1.00 +0.00 +0.00 +0.00 +0.00 +1.00
+1.00 +0.00 +1.00 +0.00 +1.00 +0.00
+4.00 +9.00 +2.00 +3.00 +1.00 +0.00
+9.00 +16.00 +3.00 +4.00 +1.00 +0.00
+16.00 +0.00 +4.00 +0.00 +1.00 +0.00
Press return to continue.
The Gauss Jordan process will reduce this matrix to :
+1.00 +0.00 +0.00 +0.00 +0.00 +1.00
+0.00 +1.00 +0.00 +0.00 +0.00 -0.17
-0.00 -0.00 +1.00 -0.00 -0.00 -5.00
+0.00 +0.00 +0.00 +1.00 +0.00 +1.17
+0.00 +0.00 +0.00 +0.00 +1.00 +4.00
The coefficients a, b, c, d, e, of the curve are :
+1.00x**2 -0.17y**2 -5.00x +1.17y +4.00 = 0
Press return to continue.
x y
+1 +0
+2 +3
+3 +4
+4 +0
Verify the result :
With x = +1.0 and y = +0.0 ax**2 + by**2 + cx+ dy + e = +0.00000
With x = +2.0 and y = +3.0 ax**2 + by**2 + cx+ dy + e = +0.00000
With x = +3.0 and y = +4.0 ax**2 + by**2 + cx+ dy + e = +0.00000
With x = +4.0 and y = +0.0 ax**2 + by**2 + cx+ dy + e = +0.00000
Press return to continue.