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Application
En regardant le réseau nous pouvons écrire :
Entrées = Sorties
A = x1 = x2 + x3
B = x2 + x4 = x5
C = x5 + x6 = x7
D = x3 + x7 = x8
E = x8 = x1 + x4 + x6
posons x1 = 50; x3 = 20; x5 = 60; x8 = 90;
A = 50 = x2 + 20
B = x2 + x4 = 60
C = 60 + x6 = x7
D = 20 + x7 = 90
E = 90 = 50 + x4 + x6
arrangeons le système
-x2 = +20 -50
+x2 +x4 = +60
+x6 -x7 = -60
+x7 = +90 -20
-x4 -x6 = +50 -90
Soit
// x2 x4 x6 x7
-x2 +0 +0 +0 +0 = +20 -50
+x2 +x4 +0 +0 +0 = +60
+0 +0 +x6 -x7 +0 = -60
+0 +0 +0 +x7 +0 = +90 -20
+0 -x4 -x6 +0 +0 = +50 -90
Le code en langage C :
double ab[RA*(CA+Cb)]={
// x2 x4 x6 x7
-1, +0, +0, +0, +0, +20 -50,
+1, +1, +0, +0, +0, +60,
+0, +0, +1, -1, +0, -60,
+0, +0, +0, +1, +0, +90 -20,
+0, -1, -1, +0, +0, +50 -90
La solution est donné par la résolution du système :
x2 x4 x6 x7
+1 +0 +0 +0 +0 +30
+0 +1 +0 +0 +0 +30
+0 +0 +1 +0 +0 +10
+0 +0 +0 +1 +0 +70
+0 +0 +0 +0 +0 +0
x2 = +30; x4 = +20; x6 = +10; x7 = +70;
et x1 = 50; x3 = 20; x5 = 60; x8 = 90;
Mathc matrices/a215
Application
Installer et compiler ces fichiers dans votre répertoire de travail.
/* Save as : c00a.c */
int main(void)
double ab[RA*(CA+Cb)]={
// x2 x4 x6 x7
-1, +0, +0, +0, +0, +20 -50,
+1, +1, +0, +0, +0, +60,
+0, +0, +1, -1, +0, -60,
+0, +0, +0, +1, +0, +90 -20,
+0, -1, -1, +0, +0, +50 -90
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));
clrscrn();
printf(" A :");
p_mR(A,S5,P0,C7);
printf(" b :");
p_mR(b,S5,P0,C7);
printf(" Ab :");
p_mR(Ab,S5,P0,C7);
getchar();
clrscrn();
printf(" Copy/Past into the octave window.\n\n");
p_Octave_mR(Ab,"Ab",P0);
printf("\n rref(Ab.00000000001)\n\n");
printf(" gj_TP_mR(Ab) :\n\n"
" x2 x4 x6 x7 ");
gj_TP_mR(Ab);
p_mR(Ab,S5,P0,C7);
stop();
f_mR(Ab);
f_mR(b);
f_mR(A);
return 0;
/* ------------------------------------ */
Exemple de sortie écran :
A :
-1 +0 +0 +0 +0
+1 +1 +0 +0 +0
+0 +0 +1 -1 +0
+0 +0 +0 +1 +0
+0 -1 -1 +0 +0
b :
-30
+60
-60
+70