Linear Algebra and the C Language/a049
Install and compile this file in your working directory.
/* ------------------------------------ */
/* Save as: c00c.c */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
#define RA R5
#define CA C5
/* ------------------------------------ */
#define FACTOR_E +1.E-2
/* ------------------------------------ */
int main(void)
{
double txy[6] ={
1, 10,
2, 1,
3, -10 };
double tA[RA*CA]={
/* x**2 y**2 x y e */
+1, +0, +0, +0, +0,
+0, +1, +0, +0, +0,
+1, +100, +1, +10, +1,
+4, +1, +2, +1, +1,
+9, +100, +3, -10, +1,
};
double tb[RA*C1]={
/* = 0 */
+1,
+1,
+0,
+0,
+0,
};
double **xy = ca_A_mR(txy, i_mR(R3,C2));
double **A = ca_A_mR(tA, i_mR(RA,CA));
double **b = ca_A_mR(tb, i_mR(RA,C1));
double **Pinv = Pinv_Rn_mR(A, i_mR(CA,RA),FACTOR_E);
double **Pinvb = mul_mR(Pinv,b, i_mR(CA,C1));
clrscrn();
printf("\n");
printf(" Find the coefficients a, b, c, d, of a circle \n\n");
printf(" ax**2 + ay**2 + bx + cy + d = 0 \n\n");
printf(" that passes through these three xy. \n\n");
printf(" x y");
p_mR(xy, S5,P0,C6);
stop();
clrscrn();
printf(" Using the given xy, we obtain this matrix.\n");
printf(" (a = 1. This is my choice)\n\n");
printf(" A:");
p_mR(A, S10,P2,C7);
printf(" b:");
p_mR(b, S10,P2,C7);
printf(" Pinv = V invS_T U_T ");
pE_mR(Pinv, S12,P4,C10);
stop();
clrscrn();
printf(" Pinv = V invS_T U_T ");
p_mR(Pinv, S10,P4,C10);
printf(" x = Pinv b ");
p_mR(Pinvb, S10,P4,C10);
printf(" The coefficients a, b, c, d, e, of the curve are: \n\n"
" %+.2f*x^2 %+.2f*y^2 %+.2f*x %+.2f*y %+.2f = 0\n\n"
,Pinvb[R1][C1],Pinvb[R2][C1],Pinvb[R3][C1],
Pinvb[R4][C1],Pinvb[R5][C1]);
stop();
f_mR(xy);
f_mR(A);
f_mR(b);
f_mR(Pinv);
f_mR(Pinvb);
return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */
Screen output example:
Find the coefficients a, b, c, d, of a circle
ax**2 + ay**2 + bx + cy + d = 0
that passes through these three XY.
x y
+1 +10
+2 +1
+3 -10
Press return to continue.
Using the given XY, we obtain this matrix.
(a = 1. This is my choice)
A :
+1.00 +0.00 +0.00 +0.00 +0.00
+0.00 +1.00 +0.00 +0.00 +0.00
+1.00 +100.00 +1.00 +10.00 +1.00
+4.00 +1.00 +2.00 +1.00 +1.00
+9.00 +100.00 +3.00 -10.00 +1.00
b :
+1.00
+1.00
+0.00
+0.00
+0.00
Pinv = V * invS_T * U_T
+1.0000e+00 +1.7254e-09 +3.6743e-12 -6.3020e-10 -1.3827e-11
-2.1077e-10 +1.0000e+00 -2.4611e-12 +3.9388e-11 +2.1562e-12
+6.0000e+00 +9.9000e+02 -5.5000e+00 +1.0000e+01 -4.5000e+00
+1.0000e+00 +9.9000e+01 -5.0000e-01 +1.0000e+00 -5.0000e-01
-1.7000e+01 -2.0800e+03 +1.1500e+01 -2.0000e+01 +9.5000e+00
Press return to continue.
Pinv = V * invS_T * U_T
+1.0000 +0.0000 +0.0000 -0.0000 -0.0000
-0.0000 +1.0000 -0.0000 +0.0000 +0.0000
+6.0000 +990.0000 -5.5000 +10.0000 -4.5000
+1.0000 +99.0000 -0.5000 +1.0000 -0.5000
-17.0000 -2080.0000 +11.5000 -20.0000 +9.5000
x = Pinv * b
+1.0000
+1.0000
+996.0000
+100.0000
-2097.0000
The coefficients a, b, c, d, e, of the curve are :
+1.00*x^2 +1.00*y^2 +996.00*x +100.00*y -2097.00 = 0
Press return to continue.
Copy and paste in Octave:
function xy = f (x,y)
xy = +1.00*x^2 +1.00*y^2 +996.00*x +100.00*y -2097.00;
endfunction
f (+1,+10)
f (+2,+1)
f (+3,-10)