Linear Algebra and the C Language/a048
Install and compile this file in your working directory.
/* ------------------------------------ */
/* Save as: c00b.c */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
#define RA R5
#define CA C5
/* ------------------------------------ */
#define FACTOR_E +1.E-2
/* ------------------------------------ */
int main(void)
{
double txy[6] ={
1, -1,
2, -9,
3, -8 };
double tA[RA*CA]={
/* x**2 y**2 x y e */
+1, +0, +0, +0, +0,
+0, +1, +0, +0, +0,
+1, +1, +1, -1, +1,
+4, +81, +2, -9, +1,
+9, +64, +3, -8, +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(" Pinv b ");
p_mR(Pinvb, S10,P4,C10);
printf(" The coefficients a, b, c, d, e, of the curve are: \n\n"
" %+.9f*x^2 %+.9f*y^2 %+.9f*x %+.9f*y %+.9f = 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 -1
+2 -9
+3 -8
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 +1.00 +1.00 -1.00 +1.00
+4.00 +81.00 +2.00 -9.00 +1.00
+9.00 +64.00 +3.00 -8.00 +1.00
b :
+1.00
+1.00
+0.00
+0.00
+0.00
Pinv = V * invS_T * U_T
+1.0000e+00 +9.7165e-09 -4.4193e-09 -3.6790e-09 +4.5744e-09
+1.8872e-07 +1.0000e+00 +3.1730e-08 +2.7938e-08 -3.6322e-08
-4.7778e+00 +6.2222e+00 -1.1111e-01 -7.7778e-01 +8.8889e-01
-2.2222e-01 +1.0778e+01 +1.1111e-01 -2.2222e-01 +1.1111e-01
+3.5556e+00 +3.5556e+00 +1.2222e+00 +5.5556e-01 -7.7778e-01
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
-4.7778 +6.2222 -0.1111 -0.7778 +0.8889
-0.2222 +10.7778 +0.1111 -0.2222 +0.1111
+3.5556 +3.5556 +1.2222 +0.5556 -0.7778
Pinv * b
+1.0000
+1.0000
+1.4444
+10.5556
+7.1111
The coefficients a, b, c, d, e, of the curve are :
+0.999999988*x^2 +1.000000219*y^2 +1.444445879*x +10.555557922*y +7.111111809 = 0
Press return to continue.
Copy and paste in Octave:
function xy = f (x,y)
xy = +0.999999988*x^2 +1.000000219*y^2 +1.444445879*x +10.555557922*y +7.111111809;
endfunction
f (+1,-1)
f (+2,-9)
f (+3,-8)