411 REFERENCE · Wikibooks
Linear Algebra and the C Language/a068
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__NOTOC__
Install and compile this file in your working directory.
/* ------------------------------------ */
/* Save as : c00a.c */
/* ------------------------------------ */
#include "v_a.h"
#include "dcircle.h"
/* ------------------------------------ */
int main(void)
{
double p[R3*C3] ={ 6, 2,
0, 2,
3, 5};
double **Ap = ca_A_mR( p, i_mR(R3,C2));
double **A = m_circle_A_mR(Ap, i_mR(R4,C4));
int r;
clrscrn();
printf(" A homogeneous linear system with as many equations\n");
printf(" as unknowns has a nontrivial solution if and only\n");
printf(" if the determinant of the matrix is zero. \n\n");
printf(" Equation of a circle: \n\n");
printf(" c1(x^2 +y^2) + c2 x + c3 y + c4 = 0\n\n");
printf(" The same equation with the values of the three points:\n\n");
for(r=R1;r<Ap[R_SIZE][C0];r++)
printf(" c1(x%d^2+y%d^2)"
" + c2 x%d + c3 y%d + c4 = 0\n",r,r,r,r);
printf(" The four equation:\n\n");
printf(" c1(x^2 + y^2) + c2 x + c3 y + c4 = 0\n");
for(r=R1;r<Ap[R_SIZE][C0];r++)
printf(" c1(x%d^2+y%d^2)"
" + c2 x%d + c3 y%d + c4 = 0\n",r,r,r,r);
stop();
clrscrn();
printf(" The three points:\n\n");
for(r=R1;r<Ap[R_SIZE][C0];r++)
printf(" P%d(%+.0f,%+.0f)",r,Ap[r][C1],Ap[r][C2]);
printf("\n\nCofactor expansion along the first row\n\n");
printf(" x^2+y^2 x y 1");
p_Det_mR(A,6,0);
printf(" The equation of the circle : \n\n");
printf(" %+.0f(x^2+y^2) %+.0f x %+.0f y %+.0f = 0\n\n",
cofactor_R(A,R1,C1),
cofactor_R(A,R1,C2),
cofactor_R(A,R1,C3),
cofactor_R(A,R1,C4));
printf(" Verify the result : \n\n");
for(r=R1;r<Ap[R_SIZE][C0];r++)
verify_eq_circle_mR(A, Ap[r][C1],
Ap[r][C2]);
stop();
f_mR(A);
f_mR(Ap);
return 0;
}
/* --------------------------------- */
/* --------------------------------- */
Screen output example:
A homogeneous linear system with as many equations
as unknowns has a nontrivial solution if and only
if the determinant of the matrix is zero.
Equation of a circle:
c1(x^2 +y^2) + c2 x + c3 y + c4 = 0
The same equation with the values of the three points:
c1(x1^2+y1^2) + c2 x1 + c3 y1 + c4 = 0
c1(x2^2+y2^2) + c2 x2 + c3 y2 + c4 = 0
c1(x3^2+y3^2) + c2 x3 + c3 y3 + c4 = 0
The four equation:
c1(x^2 + y^2) + c2 x + c3 y + c4 = 0
c1(x1^2+y1^2) + c2 x1 + c3 y1 + c4 = 0
c1(x2^2+y2^2) + c2 x2 + c3 y2 + c4 = 0
c1(x3^2+y3^2) + c2 x3 + c3 y3 + c4 = 0
Press return to continue.
The three points:
P1(+6,+2) P2(+0,+2) P3(+3,+5)
Cofactor expansion along the first row
x^2+y^2 x y 1
+40 +6 +2 +1
+4 +0 +2 +1
+34 +3 +5 +1
The equation of the circle :
-18(x^2+y^2) +108 x +72 y -72 = 0
Verify the result :
With x= +6.0 y= +2.0 eq=+0.00000
With x= +0.0 y= +2.0 eq=+0.00000
With x= +3.0 y= +5.0 eq=+0.00000
Press return to continue.