Linear Algebra and the C Language/a04a
Install and compile this file in your working directory.
/* ------------------------------------ */
/* Save as: c00d.c */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
#define RA R5
#define CA C5
/* ------------------------------------ */
#define FACTOR_E +1.E-2
/* ------------------------------------ */
int main(void)
{
double txy[6] ={
10, 10,
-5, 1,
7, -10 };
double tA[RA*CA]={
/* x**2 y**2 x y e */
+1, +0, +0, +0, +0,
+0, +1, +0, +0, +0,
+100, +100, +10, +10, +1,
+25, +1, -5, +1, +1,
+49, +100, +7, -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(" 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
+10 +10
-5 +1
+7 -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
+100.00 +100.00 +10.00 +10.00 +1.00
+25.00 +1.00 -5.00 +1.00 +1.00
+49.00 +100.00 +7.00 -10.00 +1.00
b :
+1.00
+1.00
+0.00
+0.00
+0.00
Pinv = V * invS_T * U_T
+1.0000e+00 -2.0747e-10 +8.7796e-13 +3.3409e-12 +1.1642e-12
+2.4431e-10 +1.0000e+00 -9.3712e-13 -3.4447e-12 -1.3169e-12
-3.8132e+00 -7.2527e+00 +4.0293e-02 -7.3260e-02 +3.2967e-02
-1.9780e+00 +1.0879e+00 +4.3956e-02 +1.0989e-02 -5.4945e-02
-4.2088e+01 -3.8352e+01 +1.5751e-01 +6.2271e-01 +2.1978e-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
-3.8132 -7.2527 +0.0403 -0.0733 +0.0330
-1.9780 +1.0879 +0.0440 +0.0110 -0.0549
-42.0879 -38.3516 +0.1575 +0.6227 +0.2198
Pinv * b
+1.0000
+1.0000
-11.0659
-0.8901
-80.4396
The coefficients a, b, c, d, e, of the curve are :
+1.000000000*x^2 +1.000000000*y^2 -11.065934068*x -0.890109889*y -80.439560439 = 0
Press return to continue.
Copy and paste in Octave:
function xy = f (x,y)
xy = +1.000000000*x^2 +1.000000000*y^2 -11.065934068*x -0.890109889*y -80.439560439;
endfunction
f (+10,+10)
f (-5,+1)
f (+7,-10)