411 REFERENCE · Wikibooks
Linear Algebra and the C Language/a0jv
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__NOTOC__
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/* ------------------------------------ */
/* Save as : c00b.c */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
#define RA R3
#define CA C3
#define CXY C2
/* ------------------------------------ */
int main(void)
{
double tA[RA*CA]={
/* x**0 x**1 x**2 */
+1, +1, +1,
+4, +2, +1,
+9, +3, +1,
};
double tb[RA*C1]={
/* y */
-9,
+8,
-8
};
double xy[RA*CXY] ={1, -9,
2, 8,
3, -8, };
double **XY = ca_A_mR(xy,i_mR(RA,CXY));
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(" Fitting a linear Curve to Data :\n\n");
printf(" x y \n");
p_mR(XY,S5,P0,C6);
printf(" A :\n x**2 x**1 x**0");
p_mR(A,S6,P2,C7);
printf(" b :\n y ");
p_mR(b,S6,P2,C7);
stop();
clrscrn();
printf(" Inv : ");
invgj_mR(A,Inv);
pE_mR(Inv,S12,P4,C10);
printf(" x = Inv * b ");
mul_mR(Inv,b,Invb);
p_mR(Invb,S10,P4,C10);
printf("\n The coefficients a, b, c of the curve are : \n\n"
" y = %+.2fx**2 %+.2fx %+.2f\n\n"
,Invb[R1][C1],Invb[R2][C1],Invb[R3][C1]);
stop();
f_mR(XY);
f_mR(b);
f_mR(A);
f_mR(Inv);
f_mR(Invb);
return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */
Presentation :
Let's calculate the coefficients of a polynomial.
y = ax**2 + bx + c
Which passes through these three points.
x[1], y[1]
x[2], y[2]
x[3], y[3]
Using the points we obtain the matrix:
x**2 x**1 x**0 y
x[1]**2 x[1]**1 x[1]**0 y[1]
x[2]**2 x[2]**1 x[2]**0 y[2]
x[3]**2 x[3]**1 x[3]**0 y[3]
That we can write:
x**2 x 1 y
x[1]**2 x[1] 1 y[1]
x[2]**2 x[2] 1 y[2]
x[3]**2 x[3] 1 y[3]
Let's use the invgj_mR() function to solve
the system that will give us the coefficients a, b, c
Screen output example:
Fitting a linear Curve to Data :
x y
+1 -9
+2 +8
+3 -8
A :
x**2 x**1 x**0
+1.00 +1.00 +1.00
+4.00 +2.00 +1.00
+9.00 +3.00 +1.00
b :
y
-9.00
+8.00
-8.00
Press return to continue.
Inv :
+5.0000e-01 -1.0000e+00 +5.0000e-01
-2.5000e+00 +4.0000e+00 -1.5000e+00
+3.0000e+00 -3.0000e+00 +1.0000e+00
x = Inv * b
-16.5000
+66.5000
-59.0000
The coefficients a, b, c of the curve are :
y = -16.50x**2 +66.50x -59.00
Press return to continue.
Copy and paste in Octave:
function y = f (x)
y = -16.50*x^2 +66.50*x -59.00;
endfunction
f (+1)
f (+2)
f (+3)