411 REFERENCE · Wikibooks
Linear Algebra and the C Language/a0jt
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__NOTOC__
Install and compile this file in your working directory.
/* ------------------------------------ */
/* Save as : c00d.c */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
#define RA R5
#define CA C5
/* ------------------------------------ */
int main(void)
{
double xy[8] ={
1, 2,
2, -8,
3, -8,
4, -3 };
double tA[RA*CA]={
/* x**2 y**2 x y e */
+1, +0, +0, +0, +0,
+1, +4, +1, +2, +1,
+4, +64, +2, -8, +1,
+9, +64, +3, -8, +1,
+16, +9, +4, -3, +1,
};
double tb[RA*C1]={
/* = 0 */
+1,
+0,
+0,
+0,
+0
};
double **XY = ca_A_mR(xy,i_mR(R4,C2));
double **A = ca_A_mR(tA,i_mR(RA,CA));
double **b = ca_A_mR(tb,i_mR(RA,C1));
double **Inv = i_mR(CA,RA);
double **Invb = i_mR(CA,C1);
clrscrn();
printf("\n");
printf(" Find the coefficients a, b, c, d, e, of the curve \n\n");
printf(" ax**2 + by**2 + cx + dy + e = 0 \n\n");
printf(" that passes through these four points.\n\n");
printf(" x y");
p_mR(XY,S10,P0,C6);
stop();
clrscrn();
printf(" Using the given points, 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(" Inv ");
invgj_mR(A,Inv);
pE_mR(Inv,S12,P4,C10);
stop();
clrscrn();
printf(" x = Inv * b ");
mul_mR(Inv,b,Invb);
p_mR(Invb,S10,P4,C10);
printf(" The coefficients a, b, c, d, e, of the curve are : \n\n"
" %+.2fx**2 %+.2fy**2 %+.2fx %+.2fy %+.2f = 0\n\n"
,Invb[R1][C1],Invb[R2][C1],Invb[R3][C1],
Invb[R4][C1],Invb[R5][C1]);
stop();
f_mR(XY);
f_mR(b);
f_mR(A);
f_mR(Inv);
f_mR(Invb);
return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */
Screen output example:
Find the coefficients a, b, c, d, e, of the curve
ax**2 + by**2 + cx + dy + e = 0
that passes through these four points.
x y
+1 +2
+2 -8
+3 -8
+4 -3
Press return to continue.
Using the given points, we obtain this matrix.
(a = 1. This is my choice)
A :
+1.00 +0.00 +0.00 +0.00 +0.00
+1.00 +4.00 +1.00 +2.00 +1.00
+4.00 +64.00 +2.00 -8.00 +1.00
+9.00 +64.00 +3.00 -8.00 +1.00
+16.00 +9.00 +4.00 -3.00 +1.00
b :
+1.00
+0.00
+0.00
+0.00
+0.00
Inv
+1.0000e+00 -3.4694e-18 -1.3878e-17 -2.7756e-17 +3.4694e-18
+4.0000e-02 +2.0000e-02 -8.0000e-02 +1.0000e-01 -4.0000e-02
-5.0000e+00 -3.4694e-17 -1.0000e+00 +1.0000e+00 -0.0000e+00
+4.0000e-02 +2.2000e-01 -6.8000e-01 +7.0000e-01 -2.4000e-01
+3.7600e+00 +4.8000e-01 +2.6800e+00 -2.8000e+00 +6.4000e-01
Press return to continue.
x = Inv * b
+1.0000
+0.0400
-5.0000
+0.0400
+3.7600
The coefficients a, b, c, d, e, of the curve are :
+1.00x**2 +0.04y**2 -5.00x +0.04y +3.76 = 0
Press return to continue.
Copy and paste in Octave:
function xy = f (x,y)
xy = +1.00*x^2 +0.04*y^2 -5.00*x +0.04*y +3.76;
endfunction
f (+1,+2)
f (+2,-8)
f (+3,-8)
f (+4,-3)