411 REFERENCE · Wikibooks
Linear Algebra and the C Language/a05x
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__NOTOC__
Install and compile this file in your working directory.
/* ------------------------------------ */
/* Save as : c00b.c */
/* ------------------------------------ */
#include "v_a.h"
#include "dline.h"
/* --------------------------------- */
int main(void)
{
double p[R2*C2] ={ 0, 1,
1, -1};
double **Ap = ca_A_mR(p, i_mR(R2,C2));
double **A = m_line_A_mR(Ap, i_mR(R3,C3));
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 line: \n\n");
printf(" c1 x + c2 y + c3 = 0\n\n");
printf(" The same equation with the values of the two points:\n\n");
printf(" c1 x1 + c2 y1 + c3 = 0\n");
printf(" c1 x2 + c2 y2 + c3 = 0\n\n");
printf(" The three equation:\n\n");
printf(" c1 x + c2 y + c3 = 0\n");
printf(" c1 x1 + c2 y1 + c3 = 0\n");
printf(" c1 x2 + c2 y2 + c3 = 0\n\n");
stop();
clrscrn();
printf(" The two points:\n\n");
printf(" P1(%+.0f,%+.0f) ", Ap[R1][C1],Ap[R1][C2]);
printf(" P2(%+.0f,%+.0f)\n\n",Ap[R2][C1],Ap[R2][C2]);
printf("\n\nCofactor expansion along the first row\n\n");
printf(" x y 1");
p_Det_mR(A,6,0);
printf(" The equation of the line : \n\n");
printf(" eq = %+.0f x %+.0f y %+.0f = 0\n\n",
cofactor_R(A,R1,C1),
cofactor_R(A,R1,C2),
cofactor_R(A,R1,C3));
printf(" Verify the result : \n\n");
for(r=R1;r<Ap[R_SIZE][C0];r++)
verify_eq_line_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 line:
c1 x + c2 y + c3 = 0
The same equation with the values of the two points:
c1 x1 + c2 y1 + c3 = 0
c1 x2 + c2 y2 + c3 = 0
The three equation:
c1 x + c2 y + c3 = 0
c1 x1 + c2 y1 + c3 = 0
c1 x2 + c2 y2 + c3 = 0
Press return to continue.
The two points:
P1(+0,+1) P2(+1,-1)
Cofactor expansion along the first row
x y 1
+0 +1 +1
+1 -1 +1
The equation of the line :
eq = +2 x +1 y -1 = 0
Verify the result :
With x= +0.0 y= +1.0 eq=+0.00000
With x= +1.0 y= -1.0 eq=+0.00000
Press return to continue.