Mathc matrices/c22z
Application ou QR décomposition
Installer et compiler ces fichiers dans votre répertoire de travail.
|
c00i.c |
|---|
/* ------------------------------------ */
/* Save as : c00i.c */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
#define RA R4
#define CA C4
#define Cb C1
/* ------------------------------------ */
/* ------------------------------------ */
void fun(void)
{
double ab[RA*(CA+Cb)]={
/* x**0 x**1 x**2 x**3 y */
1, -5., +25., -125., -3.00,
1, -2., +4., -8., +0.00,
1, +2., +4., +8., +3.00,
1, +3., +9., +27., -2.00,
};
double **Ab = ca_A_mR(ab,i_Abr_Ac_bc_mR(RA,CA,Cb));
double **A = c_Ab_A_mR(Ab,i_mR(RA,CA));
double **b = c_Ab_b_mR(Ab,i_mR(RA,Cb));
double **Q = i_mR(RA,CA);
double **R = i_mR(CA,CA);
double **invR = i_mR(CA,CA);
double **Q_T = i_mR(CA,RA);
double **invR_Q_T = i_mR(CA,RA);
double **x = i_mR(CA,Cb); // x invR * Q_T * b
clrscrn();
printf(" Fitting a Cubic equation Curve to Data :\n\n");
printf(" A :");
p_mR(A,S7,P2,C7);
printf(" b :");
p_mR(b,S7,P2,C7);
printf(" Ab :");
p_mR(Ab,S7,P2,C7);
stop();
clrscrn();
QR_mR(A,Q,R);
printf(" Q :");
p_mR(Q,S10,P4,C6);
printf(" R :");
p_mR(R,S10,P4,C6);
stop();
clrscrn();
transpose_mR(Q,Q_T);
printf(" Q_T :");
pE_mR(Q_T,S7,P4,C6);
inv_mR(R,invR);
printf(" invR :");
pE_mR(invR,S7,P4,C6);
stop();
clrscrn();
printf(" Solving this system yields a unique\n"
" least squares solution, namely \n\n");
mul_mR(invR,Q_T,invR_Q_T);
mul_mR(invR_Q_T,b,x);
printf(" x = invR * Q_T * b :");
p_mR(x,S10,P2,C6);
printf(" The Cubic equation Curve to Data : \n\n"
" s = %+.3f %+.3f*t %+.3f*t**2 %+.3f*t**2\n\n"
,x[R1][C1],x[R2][C1],x[R3][C1],x[R4][C1]);
stop();
f_mR(A);
f_mR(b);
f_mR(Ab);
f_mR(Q);
f_mR(Q_T);
f_mR(R);
f_mR(invR);
f_mR(invR_Q_T);
f_mR(x);
}
/* ------------------------------------ */
int main(void)
{
fun();
return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */
Trouver la meilleur équation cubique qui s'ajuste au mieux aux points donnés.
On utilise la QR décomposition. Dans l'exemple suivant on utilise un autre algorithme sur le même exemple. Exemple de sortie écran :
-----------------------------------
Fitting a Cubic equation Curve to Data :
A :
+1.00 -5.00 +25.00 -125.00
+1.00 -2.00 +4.00 -8.00
+1.00 +2.00 +4.00 +8.00
+1.00 +3.00 +9.00 +27.00
b :
-3.00
+0.00
+3.00
-2.00
Ab :
+1.00 -5.00 +25.00 -125.00 -3.00
+1.00 -2.00 +4.00 -8.00 +0.00
+1.00 +2.00 +4.00 +8.00 +3.00
+1.00 +3.00 +9.00 +27.00 -2.00
Press return to continue.
-----------------------------------
Q :
+0.5000 -0.7028 +0.4900 -0.1265
+0.5000 -0.2343 -0.7547 +0.3542
+0.5000 +0.3904 -0.1462 -0.7591
+0.5000 +0.5466 +0.4110 +0.5313
R :
+2.0000 -1.0000 +21.0000 -49.0000
+0.0000 +6.4031 -12.0254 +107.6037
+0.0000 -0.0000 +12.3446 -45.2848
-0.0000 -0.0000 +0.0000 +21.2539
Press return to continue.
-----------------------------------
Q_T :
+5.0000e-01 +5.0000e-01 +5.0000e-01 +5.0000e-01
-7.0278e-01 -2.3426e-01 +3.9043e-01 +5.4661e-01
+4.8999e-01 -7.5475e-01 -1.4621e-01 +4.1096e-01
-1.2651e-01 +3.5423e-01 -7.5907e-01 +5.3135e-01
invR :
+5.0000e-01 +7.8087e-02 -7.7450e-01 -8.9281e-01
+0.0000e+00 +1.5617e-01 +1.5213e-01 -4.6653e-01
-0.0000e+00 -0.0000e+00 +8.1007e-02 +1.7260e-01
-0.0000e+00 -0.0000e+00 +0.0000e+00 +4.7050e-02
Press return to continue.
-----------------------------------
Solving this system yields a unique
least squares solution, namely
x = invR * Q_T * b :
+4.43
+1.31
-0.73
-0.14
The Cubic equation Curve to Data :
s = +4.429 +1.307*t -0.732*t**2 -0.139*t**2
Press return to continue.