Mathc matrices/c23k
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c00l.c |
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/* ------------------------------------ */
/* Save as : c00l.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 **A_T = i_mR(CA,RA);
double **A_TA = i_mR(CA,CA); // A_T*A
double **invA_TA = i_mR(CA,CA); // inv(A_T*A)
double **invA_TAA_T = i_mR(CA,RA); // inv(A_T*A)*A_T
double **x = i_mR(CA,Cb); // x = inv(A_T*A)*A_T*b
clrscrn();
printf(" Fitting a Quartic equation Curve to Data :\n\n");
printf(" A :");
p_mR(A,S10,P2,C7);
printf(" b :");
p_mR(b,S10,P2,C7);
printf(" Ab :");
p_mR(Ab,S10,P2,C7);
stop();
clrscrn();
printf(" A_T :");
p_mR(transpose_mR(A,A_T),S10,P2,C7);
printf(" A_TA :");
p_mR(mul_mR(A_T,A,A_TA),S10,P2,C7);
printf(" inv(A_TA) :");
p_mR(inv_mR(A_TA,invA_TA),S10,P4,C7);
stop();
clrscrn();
printf(" inv(A_TA)*A_T :");
p_mR(mul_mR(invA_TA,A_T,invA_TAA_T),S10,P4,C7);
printf("\n x = inv(A_TA)*A_T*b :");
p_mR(mul_mR(invA_TAA_T,b,x),S10,P4,C7);
stop();
clrscrn();
printf("\n x = inv(A_TA)*A_T*b :");
p_mR(x,S10,P2,C7);
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(A_T);
f_mR(A_TA); // A_T*A
f_mR(invA_TA); // inv(A_T*A)
f_mR(invA_TAA_T); // inv(A_T*A)*A_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.
-----------------------------------
A_T :
+1.00 +1.00 +1.00 +1.00 +1.00
+1.00 +2.00 +3.00 +4.00 +5.00
+1.00 +4.00 +9.00 +16.00 +25.00
+1.00 +8.00 +27.00 +64.00 +125.00
+1.00 +16.00 +81.00 +256.00 +625.00
A_TA :
+5.00 +15.00 +55.00 +225.00 +979.00
+15.00 +55.00 +225.00 +979.00 +4425.00
+55.00 +225.00 +979.00 +4425.00 +20515.00
+225.00 +979.00 +4425.00 +20515.00 +96825.00
+979.00 +4425.00 +20515.00 +96825.00 +462979.00
inv(A_TA) :
+251.0000 -458.3333 +271.2500 -64.1667 +5.2500
-458.3333 +847.1528 -505.7292 +120.3889 -9.8958
+271.2500 -505.7292 +304.3299 -72.9167 +6.0243
-64.1667 +120.3889 -72.9167 +17.5694 -1.4583
+5.2500 -9.8958 +6.0243 -1.4583 +0.1215
Press return to continue.
-----------------------------------
inv(A_TA)*A_T :
+5.0000 -10.0000 +10.0000 -5.0000 +1.0000
-6.4167 +17.8333 -19.5000 +10.1667 -2.0833
+2.9583 -9.8333 +12.2500 -6.8333 +1.4583
-0.5833 +2.1667 -3.0000 +1.8333 -0.4167
+0.0417 -0.1667 +0.2500 -0.1667 +0.0417
x = inv(A_TA)*A_T*b :
-184.0000
+329.7500
-191.8750
+44.7500
-3.6250
Press return to continue.
-----------------------------------
x = inv(A_TA)*A_T*b :
-184.00
+329.75
-191.88
+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