411 REFERENCE · Wikibooks
Linear Algebra and the C Language/a06d
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__NOTOC__
Install and compile this file in your working directory.
/* ------------------------------------ */
/* Save as : c00b.c */
/* ------------------------------------ */
#include "v_a.h"
#include "dsphere.h"
/* ------------------------------------ */
int main(void)
{
double p[R4*C3] = {0, 1,-2,
1, 3, 1,
2,-1, 0,
3, 1,-1 };
double **Ap = ca_A_mR(p, i_mR(R4,C3));
double **A = m_Sphere_A_mR(Ap, i_mR(R5,C5));
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(" The equation of a sphere,\n");
printf(" With the values of the four points:\n\n");
printf(" c1(x^2 +y^2 +z^2) +c2x +c3y +c4z +c5 = 0\n\n");
for(r=R1;r<Ap[R_SIZE][C0];r++)
printf(" c1(x%d^2+y%d^2+z%d^2)"
" +c2x%d +c3y%d +c4z%d +c5 = 0\n",r,r,r,r,r,r);
stop();
clrscrn();
printf(" The four points:\n\n");
for(r=R1;r<Ap[R_SIZE][C0];r++)
printf(" P%d(%+.0f,%+.0f,%+.0f)",
r,Ap[r][C1],Ap[r][C2],Ap[r][C3]);
printf("\n\nCofactor expansion along the first row\n\n");
printf(" x^2+y^2+z^2 x y z 1");
p_Det_mR(A,8,0);
printf(" The equation of the sphere : \n\n");
printf(" %+.0f(x^2+y^2+Z^2) %+.0fx %+.0fy %+.0fz %+.0f = 0\n\n",
cofactor_R(A,R1,C1),
cofactor_R(A,R1,C2),
cofactor_R(A,R1,C3),
cofactor_R(A,R1,C4),
cofactor_R(A,R1,C5));
printf(" Verify the result : \n\n");
for(r=R1;r<Ap[R_SIZE][C0];r++)
verify_eq_sphere_mR(A, Ap[r][C1],
Ap[r][C2],
Ap[r][C3]);
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.
The equation of a sphere,
With the values of the four points:
c1(x^2 +y^2 +z^2) +c2x +c3y +c4z +c5 = 0
c1(x1^2+y1^2+z1^2) +c2x1 +c3y1 +c4z1 +c5 = 0
c1(x2^2+y2^2+z2^2) +c2x2 +c3y2 +c4z2 +c5 = 0
c1(x3^2+y3^2+z3^2) +c2x3 +c3y3 +c4z3 +c5 = 0
c1(x4^2+y4^2+z4^2) +c2x4 +c3y4 +c4z4 +c5 = 0
Press return to continue.
The four points:
P1(+0,+1,-2) P2(+1,+3,+1) P3(+2,-1,+0) P4(+3,+1,-1)
Cofactor expansion along the first row
x^2+y^2+z^2 x y z 1
+5 +0 +1 -2 +1
+11 +1 +3 +1 +1
+5 +2 -1 +0 +1
+11 +3 +1 -1 +1
The equation of the sphere :
-24(x^2+y^2+Z^2) +48x +48y +0z +72 = 0
Verify the result :
With x= +0.0 y= +1.0 z= -2.0 eq=-0.00000
With x= +1.0 y= +3.0 z= +1.0 eq=-0.00000
With x= +2.0 y= -1.0 z= +0.0 eq=-0.00000
With x= +3.0 y= +1.0 z= -1.0 eq=-0.00000
Press return to continue.