Mathc complexes/a46
Application
Installer et compiler ces fichiers dans votre répertoire de travail.
/* ------------------------------------ */
/* Save as : c00b.c */
/* ------------------------------------ */
/* ------------------------------------ */
void fun(void)
double a[RCA*(RCA*C2)] ={ 
 +25072, +0, +21293, -4811, +5386, -6531, +11975, -5847, 
 +21293, +4811, +30848, +0, -1526, -1774, +13478, -6658, 
 +5386, +6531, -1526, +1774, +20007, +0, +7542, -1322, 
 +11975, +5847, +13478, +6658, +7542, +1322, +21250, +0 };
double **A = ca_A_mZ(a, i_mZ(RCA,RCA));
double **V = i_mZ(RCA,RCA);
double **cV_T = i_mZ(RCA,RCA);
double **T = i_mZ(RCA,RCA);
double **EValue = i_mZ(RCA,C1);
double **EigsValue = i_mZ(RCA,RCA);
 clrscrn();
 printf(" Copy/Past into the octave windows \n\n\n");
 p_Octave_mZ(A,"a",P0,P0); 
 printf(" [V, E] = eigs (a,10) \n\n\n");
 stop();
 clrscrn();
/* V and cV_T*/ 
 eigs_V_uv_mZ(A,V,FACTOR_E);
 printf(" V :");
 pE_mZ(V, S12,P4, S12,P4, C3);
 printf(" cV_T :");
 pE_mZ(ctranspose_mZ(V,cV_T), S12,P4, S12,P4, C3);
 stop();
 clrscrn(); 
 eigsuv_mZ(A,EValue);
 printf(" EigsValue :"); 
 p_mZ(EValue, S12,P4, S8,P4, C3); 
/* EigsValue = cV_T * A * V */ 
 mul_mZ(cV_T,A,T);
 mul_mZ(T,V,EigsValue); 
 printf(" EigsValue = cV_T * A * V");
 p_mZ(EigsValue, S12,P4, S8,P4, C3);
 stop(); 
 f_mZ(A);
 f_mZ(V);
 f_mZ(cV_T);
 f_mZ(EigsValue);
 f_mZ(EValue);
 f_mZ(T); 
/* ------------------------------------ */
int main(void)
 fun();
 return 0;
/* ------------------------------------ */
Avec les matrices réelles nous avons calculer les vecteurs et valeurs propres des matrices symétriques. Avec les matrices complexes nous allons calculer les vecteurs et valeurs propres des matrices symétriques conjuguées.
Contrôle du facteur : 
Nous allons étudier une des propriétés des valeurs propres et des vecteurs propres :
 EigsValue = cV_T * A * V
 Exemple de sortie écran :
 Copy/Past into the octave windows 
 a=[
+25072+0*i,+21293-4811*i,+5386-6531*i,+11975-5847*i;
+21293+4811*i,+30848+0*i,-1526-1774*i,+13478-6658*i;
+5386+6531*i,-1526+1774*i,+20007+0*i,+7542-1322*i;
+11975+5847*i,+13478+6658*i,+7542+1322*i,+21250+0*i]
 [V, E] = eigs (a,10) 
 Press return to continue. 
 ------------------------------------
 V :
 +4.8972e-01 -3.2491e-01i +1.2352e-02 -3.1358e-02i -2.3564e-01 +4.7870e-01i 
 +5.8126e-01 -2.5956e-01i -2.5508e-01 +3.5827e-01i -1.6780e-01 -2.1539e-01i 
 +1.8661e-01 +5.4231e-02i +6.9872e-01 -4.9734e-01i -2.2037e-01 -5.7021e-03i 
 +4.6001e-01 +1.5960e-17i +2.6435e-01 -2.3604e-17i +7.6953e-01 +0.0000e+00i 
 -1.3282e-01 -5.9258e-01i 
 -1.9928e-01 +5.3580e-01i 
 -2.8408e-01 +3.1206e-01i 
 +3.5543e-01 +3.7510e-18i 
 cV_T :
 +4.8972e-01 +3.2491e-01i +5.8126e-01 +2.5956e-01i +1.8661e-01 -5.4231e-02i 
 +1.2352e-02 +3.1358e-02i -2.5508e-01 -3.5827e-01i +6.9872e-01 +4.9734e-01i 
 -2.3564e-01 -4.7870e-01i -1.6780e-01 +2.1539e-01i -2.2037e-01 +5.7021e-03i 
 -1.3282e-01 +5.9258e-01i -1.9928e-01 -5.3580e-01i -2.8408e-01 -3.1206e-01i 
 +4.6001e-01 -1.5960e-17i 
 +2.6435e-01 +2.3604e-17i 
 +7.6953e-01 -0.0000e+00i 
 +3.5543e-01 -3.7510e-18i 
 Press return to continue. 
 ------------------------------------
 EigsValue :
 +61819.1491 +0.0000i 
 +22896.2153 +0.0000i 
 +10720.5399 +0.0000i 
 +1741.0958 +0.0000i 
 EigsValue = cV_T * A * V
 +61819.1491 -0.0000i -0.0000 +0.0000i -0.0000 -0.0000i 
 -0.0000 -0.0000i +22896.2153 -0.0000i -0.0000 -0.0000i 
 -0.0000 +0.0000i -0.0000 +0.0000i +10720.5399 +0.0000i 
 +0.0000 +0.0000i -0.0000 -0.0000i +0.0000 +0.0000i 
 -0.0000 -0.0000i 
 -0.0000 +0.0000i 
 +0.0000 -0.0000i 
 +1741.0958 +0.0000i 
 Press return to continue
 Press X to stop

Mathc complexes/a47
Application
Installer et compiler ces fichiers dans votre répertoire de travail.
/* ------------------------------------ */
/* Save as : c00b.c */
/* ------------------------------------ */
void fun(int r)
double **A = rcsymmetric_mZ(i_mZ(RCA,RCA),99);
double **V = i_mZ(RCA,RCA);
double **cV_T = i_mZ(RCA,RCA);
double **T = i_mZ(RCA,RCA);
double **EValue = i_mZ(RCA,C1);
double **EigsValue = i_mZ(RCA,RCA);
 clrscrn();
 printf(" Copy/Past into the octave windows \n\n\n");
 p_Octave_mZ(A,"a",P0,P0); 
 printf(" [V, E] = eigs (a,10) \n\n\n");
 printf(" A :");
 p_mZ(A, S8,P0, S6,P0, C3); 
 stop();
 clrscrn();
/* V and cV_T*/ 
 eigs_V_uv_mZ(A,V,FACTOR_E);
 printf(" V :");
 pE_mZ(V, S12,P4, S12,P4, C3);
 printf(" cV_T :");
 pE_mZ(ctranspose_mZ(V,cV_T), S12,P4, S12,P4, C3);
 stop();
 clrscrn(); 
 eigsuv_mZ(A,EValue);
 printf(" EigsValue :"); 
 p_mZ(EValue, S12,P4, S8,P4, C3); 
/* EigsValue = cV_T * A * V */ 
 mul_mZ(cV_T,A,T);
 mul_mZ(T,V,EigsValue); 
 printf(" EigsValue = cV_T * A * V");
 p_mZ(EigsValue, S12,P4, S8,P4, C3); 
 f_mZ(A);
 f_mZ(V);
 f_mZ(cV_T);
 f_mZ(EigsValue);
 f_mZ(EValue);
 f_mZ(T); 
/* ------------------------------------ */
int main(void)
time_t t;
 srand(time(&t));
do
 fun(R3);
} while(stop_w());
 return 0;
/* ------------------------------------ */
Avec les matrices réelles nous avons calculer les vecteurs et valeurs propres des matrices symétriques. Avec les matrices complexes nous allons calculer les vecteurs et valeurs propres des matrices symétriques conjuguées.
Contrôle du facteur : 
Nous allons étudier une des propriétés des valeurs propres et des vecteurs propres :
 EigsValue = cV_T * A * V
 Exemple de sortie écran :
 Copy/Past into the octave windows 
 a=[
+26723+0*i,+6300+372*i,-5754-11448*i;
+6300-372*i,+14814+0*i,-4606-1775*i;
-5754+11448*i,-4606+1775*i,+7052+0*i]
 [V, E] = eigs (a,10) 
 A :
 +26723 +0i +6300 +372i -5754-11448i 
 +6300 -372i +14814 +0i -4606 -1775i 
 -5754+11448i -4606 +1775i +7052 +0i 
 Press return to continue. 
 ------------------------------------
 V :
 -4.2555e-01 -7.2220e-01i +2.9361e-01 -1.9581e-01i +1.4145e-01 +3.9087e-01i 
 -2.3471e-01 -2.4594e-01i -4.2882e-01 +8.0912e-01i +2.0638e-01 -5.7180e-02i 
 +4.2634e-01 -2.6625e-17i +1.9205e-01 +0.0000e+00i +8.8394e-01 +0.0000e+00i 
 cV_T :
 -4.2555e-01 +7.2220e-01i -2.3471e-01 +2.4594e-01i +4.2634e-01 +2.6625e-17i 
 +2.9361e-01 +1.9581e-01i -4.2882e-01 -8.0912e-01i +1.9205e-01 -0.0000e+00i 
 +1.4145e-01 -3.9087e-01i +2.0638e-01 +5.7180e-02i +8.8394e-01 -0.0000e+00i 
 Press return to continue. 
 ------------------------------------
 EigsValue :
 +35747.4376 -0.0000i 
 +12733.1027 -0.0000i 
 +108.4598 +0.0000i 
 EigsValue = cV_T * A * V
 +35747.4376 +0.0000i -0.0000 -0.0000i +0.0000 +0.0000i 
 -0.0000 +0.0000i +12733.1027 +0.0000i +0.0000 -0.0000i 
 +0.0000 -0.0000i +0.0000 +0.0000i +108.4598 +0.0000i 
 Press return to continue
 Press X to stop