Mathc matrices/c23j
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c00k.c |
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/* ------------------------------------ */
/* 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.
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.