411 REFERENCE · Wikibooks
Linear Algebra and the C Language/a060
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__NOTOC__
Install and compile this file in your working directory.
/* ------------------------------------ */
/* Save as : c00a.c */
/* ------------------------------------ */
#include "v_a.h"
#include "dplan.h"
/* --------------------------------- */
int main(void)
{
double p[R3*C3] ={ 1, 1, 0,
2, 0, -1,
2, 9, 2};
double **Ap = ca_A_mR(p, i_mR(R3,C3));
double **A = m_plan_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 plane: \n\n");
printf(" c1 x + c2 y + c3 z + 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 + c2 y%d + c3 z%d + c4 = 0\n",r,r,r);
printf("\n The four equation:\n\n");
printf(" c1 x + c2 y + c3 z + c4 = 0\n");
for(r=R1;r<Ap[R_SIZE][C0];r++)
printf(" c1 x%d + c2 y%d + c3 z%d + c4 = 0\n",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,%+.0f)",
r,Ap[r][C1],Ap[r][C2],Ap[r][C3]);
printf("\n\nCofactor expansion along the first row\n\n");
printf(" x y z 1");
p_Det_mR(A,6,0);
printf(" The equation of the plane : \n\n");
printf(" %+.0f x %+.0f y %+.0f z %+.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_plan_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.
Equation of a plane:
c1 x + c2 y + c3 z + c4 = 0
The same equation with the values of the three points:
c1 x1 + c2 y1 + c3 z1 + c4 = 0
c1 x2 + c2 y2 + c3 z2 + c4 = 0
c1 x3 + c2 y3 + c3 z3 + c4 = 0
The four equation:
c1 x + c2 y + c3 z + c4 = 0
c1 x1 + c2 y1 + c3 z1 + c4 = 0
c1 x2 + c2 y2 + c3 z2 + c4 = 0
c1 x3 + c2 y3 + c3 z3 + c4 = 0
Press return to continue.
The three points:
P1(+1,+1,+0) P2(+2,+0,-1) P3(+2,+9,+2)
Cofactor expansion along the first row
x y z 1
+1 +1 +0 +1
+2 +0 -1 +1
+2 +9 +2 +1
The equation of the plane :
+6 x -3 y +9 z -3 = 0
Verify the result :
With x=+1 y=+1 z=+0 eq=-0.00000
With x=+2 y=+0 z=-1 eq=+0.00000
With x=+2 y=+9 z=+2 eq=-0.00000
Press return to continue.