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-I1 +I4 +I6 = 0
b) -I2 R2 -I6 R6 = -90
c) +I2 R2 -I3 R3 -I5 R5 = 0
d) -I4 R4 +I5 R5 +I6 R6 = 0
e) -I3 R3 -I4 R4 = -90
Avec R2 = 50, R3 = 20, R4 = 50,
R5 = 10, R6 = 20
a) +I1 -I2 -I3 = 0
+I3 -I4 -I5 = 0
+I2 +I5 -I6 = 0
-I1 +I4 +I6 = 0
b) -I2 50 -I6 20 = -90
c) +I2 50 -I3 20 -I5 10 = 0
d) -I4 50 +I5 10 +I6 20 = 0
e) -I3 20 -I4 50 = -90
Arrangeons le système
I1 I2 I3 I4 I5 I6
+1 -1 -1 +0 +0 +0 0 0 0
+0 +0 +1 -1 -1 +0 0 0 0
+0 +1 +0 +0 +1 -1 0 0 0
-1 +0 +0 +1 +0 +1 0 0 0
+0 -50 +0 +0 +0 -20 0 0 -90
+0 +50 -20 +0 -10 +0 0 0 0
+0 +0 +0 -50 +10 +20 0 0 0
+0 +0 -20 -50 +0 +0 0 0 -90
Le code en langage C :
double ab[RA*(CA+Cb)]={
// I1 I2 I3 I4 I5 I6
+1, -1, -1, +0, +0, +0, 0, 0, 0,
+0, +0, +1, -1, -1, +0, 0, 0, 0,
+0, +1, +0, +0, +1, -1, 0, 0, 0,
-1, +0, +0, +1, +0, +1, 0, 0, 0,
+0, -50, +0, +0, +0, -20, 0, 0, -90,
+0, +50, -20, +0, -10, +0, 0, 0, 0,
+0, +0, +0, -50, +10, +20, 0, 0, 0,
+0, +0, -20, -50, +0, +0, 0, 0, -90,
La solution est donné par la résolution du système :
I1 I2 I3 I4 I5 I6
+1.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +3.00
+0.00 +1.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +1.00
+0.00 +0.00 +1.00 +0.00 +0.00 +0.00 +0.00 +0.00 +2.00
+0.00 +0.00 +0.00 +1.00 +0.00 +0.00 +0.00 +0.00 +1.00
+0.00 +0.00 +0.00 +0.00 +1.00 +0.00 +0.00 +0.00 +1.00
+0.00 +0.00 +0.00 +0.00 +0.00 +1.00 +0.00 +0.00 +2.00
+0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00
+0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00
I1 = 3, I2 = 1, I3 = 2, I4 = 1, I5 = 1, I6 = 2,
Mathc matrices/a220
Application
Installer et compiler ces fichiers dans votre répertoire de travail.
/* Save as : c00a.c */
int main(void)
double ab[RA*(CA+Cb)]={
// I1 I2 I3 I4 I5 I6
+1, -1, -1, +0, +0, +0, 0, 0, 0,
+0, +0, +1, -1, -1, +0, 0, 0, 0,
+0, +1, +0, +0, +1, -1, 0, 0, 0,
-1, +0, +0, +1, +0, +1, 0, 0, 0,
+0, -50, +0, +0, +0, -20, 0, 0, -90,
+0, +50, -20, +0, -10, +0, 0, 0, 0,
+0, +0, +0, -50, +10, +20, 0, 0, 0,
+0, +0, -20, -50, +0, +0, 0, 0, -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(" Ab :\n"
" I1 I2 I3 I4 I5 I6 ");
p_mR(Ab,S6,P2,C9);
getchar();
clrscrn();
printf(" Copy/Past into the octave window.\n\n");
p_Octave_mR(Ab,"Ab",P0);
printf("\n rref(Ab.00000000001)\n\n");
getchar();
clrscrn();
printf(" gj_TP_mR(Ab) :\n\n"
" I1 I2 I3 I4 I5 I6 ");
gj_TP_mR(Ab);
p_mR(Ab,S6,P2,C9);
stop();
f_mR(Ab);
f_mR(b);
f_mR(A);
return 0;
/* ------------------------------------ */
Exemple de sortie écran :
Ab :
I1 I2 I3 I4 I5 I6
+1.00 -1.00 -1.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00
+0.00 +0.00 +1.00 -1.00 -1.00 +0.00 +0.00 +0.00 +0.00
+0.00 +1.00 +0.00 +0.00 +1.00 -1.00 +0.00 +0.00 +0.00
-1.00 +0.00 +0.00 +1.00 +0.00 +1.00 +0.00 +0.00 +0.00