411 REFERENCE · Wikibooks
Linear Algebra and the C Language/a07r
Reference material by Wikibooks contributors. This retains its source identity and is not 411 news reporting.
__NOTOC__
Install and compile this file in your working directory.
/* ------------------------------------ */
/* Save as : c00c.c */
/* ------------------------------------ */
#include "v_a.h"
#include "dconic.h"
/* ------------------------------------ */
int main(void)
{
double xy[8] ={
1, 4,
2, 5,
3, -7,
4, 5 };
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;
}
/* ------------------------------------ */
/* ------------------------------------ */
Screen output example:
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 +4
+2 +5
+3 -7
+4 +5
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 +16.00 +1.00 +4.00 +1.00 +0.00
+4.00 +25.00 +2.00 +5.00 +1.00 +0.00
+9.00 +49.00 +3.00 -7.00 +1.00 +0.00
+16.00 +25.00 +4.00 +5.00 +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 +0.28
-0.00 -0.00 +1.00 -0.00 -0.00 -6.00
+0.00 +0.00 +0.00 +1.00 +0.00 +0.48
+0.00 -0.00 +0.00 +0.00 +1.00 -1.39
The coefficients a, b, c, d, e, of the curve are :
+1.00x**2 +0.28y**2 -6.00x +0.48y -1.39 = 0
Press return to continue.
x y
+1 +4
+2 +5
+3 -7
+4 +5
Verify the result :
With x = +1.0 and y = +4.0 ax**2 + by**2 + cx+ dy + e = -0.00000
With x = +2.0 and y = +5.0 ax**2 + by**2 + cx+ dy + e = +0.00000
With x = +3.0 and y = -7.0 ax**2 + by**2 + cx+ dy + e = -0.00000
With x = +4.0 and y = +5.0 ax**2 + by**2 + cx+ dy + e = +0.00000
Press return to continue.
Copy and paste in Octave:
function xy = f (x,y)
xy = +1.000000000*x^2 +0.280303030*y^2 -6.000000000*x +0.477272727*y -1.393939394;
endfunction
f (+1,+4)
f (+2,+5)
f (+3,-7)
f (+4,+5)