Mathc matrices/c23j
Application ou QR décomposition
Installer et compiler ces fichiers dans votre répertoire de travail.
|
c00k.c |
|---|
/* ------------------------------------ */
/* Save as : c00k.c */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
#define RA R5
#define CA C5
#define Cb C1
/* ------------------------------------ */
/* ------------------------------------ */
void fun(void)
{
double ab[RA*(CA+Cb)]={
/* x**0 x**1 x**2 x**3 x**4 y */
1, 1., 1., 1., 1., -5.,
1, 2., 4., 8., 16., 8.,
1, 3., 9., 27., 81., -7.,
1, 4., 16., 64., 256., 1.,
1, 5., 25., 125., 625., -4.,
};
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 quartic 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 Quartic equation Curve to Data : \n\n"
" s = %+.3f %+.3f*t %+.3f*t**2 %+.3f*t**3 %+.3f*t**4\n\n"
,x[R1][C1],x[R2][C1],x[R3][C1],x[R4][C1],x[R5][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 quartique 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 quartic equation Curve to Data :
A :
+1.00 +1.00 +1.00 +1.00 +1.00
+1.00 +2.00 +4.00 +8.00 +16.00
+1.00 +3.00 +9.00 +27.00 +81.00
+1.00 +4.00 +16.00 +64.00 +256.00
+1.00 +5.00 +25.00 +125.00 +625.00
b :
-5.00
+8.00
-7.00
+1.00
-4.00
Ab :
+1.00 +1.00 +1.00 +1.00 +1.00 -5.00
+1.00 +2.00 +4.00 +8.00 +16.00 +8.00
+1.00 +3.00 +9.00 +27.00 +81.00 -7.00
+1.00 +4.00 +16.00 +64.00 +256.00 +1.00
+1.00 +5.00 +25.00 +125.00 +625.00 -4.00
Press return to continue.
-----------------------------------
Q :
+0.4472 -0.6325 +0.5345 -0.3162 +0.1195
+0.4472 -0.3162 -0.2673 +0.6325 -0.4781
+0.4472 +0.0000 -0.5345 +0.0000 +0.7171
+0.4472 +0.3162 -0.2673 -0.6325 -0.4781
+0.4472 +0.6325 +0.5345 +0.3162 +0.1195
R :
+2.2361 +6.7082 +24.5967 +100.6231 +437.8221
+0.0000 +3.1623 +18.9737 +96.1332 +470.5469
+0.0000 +0.0000 +3.7417 +33.6749 +218.6197
+0.0000 +0.0000 +0.0000 +3.7947 +45.5368
-0.0000 -0.0000 -0.0000 -0.0000 +2.8685
Press return to continue.
-----------------------------------
Q_T :
+4.4721e-01 +4.4721e-01 +4.4721e-01 +4.4721e-01 +4.4721e-01
-6.3246e-01 -3.1623e-01 +0.0000e+00 +3.1623e-01 +6.3246e-01
+5.3452e-01 -2.6726e-01 -5.3452e-01 -2.6726e-01 +5.3452e-01
-3.1623e-01 +6.3246e-01 +0.0000e+00 -6.3246e-01 +3.1623e-01
+1.1952e-01 -4.7809e-01 +7.1714e-01 -4.7809e-01 +1.1952e-01
invR :
+4.4721e-01 -9.4868e-01 +1.8708e+00 -4.4272e+00 +1.5060e+01
+0.0000e+00 +3.1623e-01 -1.6036e+00 +6.2191e+00 -2.8387e+01
-0.0000e+00 +0.0000e+00 +2.6726e-01 -2.3717e+00 +1.7281e+01
+0.0000e+00 -0.0000e+00 +0.0000e+00 +2.6352e-01 -4.1833e+00
-0.0000e+00 +0.0000e+00 -0.0000e+00 -0.0000e+00 +3.4861e-01
Press return to continue.
-----------------------------------
Solving this system yields a unique
least squares solution, namely
x = invR * Q_T * b :
-184.00
+329.75
-191.87
+44.75
-3.63
The Quartic equation Curve to Data :
s = -184.000 +329.750*t -191.875*t**2 +44.750*t**3 -3.625*t**4
Press return to continue.