Mathc complexes/a92
Application
Installer et compiler ces fichiers dans votre répertoire de travail.
/* ------------------------------------ */
/* Save as : c00d.c */
/* ------------------------------------ */
/* ------------------------------------ */
double f(
double x)
 return(1.0/(x));
char feq[] = "1.0/(x)";
/* ------------------------------------ */
void fun(void)
double a[RC4*(RC4*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 **invEValue = i_mZ(RCA,RCA);
double **EigsValue = i_mZ(RCA,RCA);
double **InvA = i_mZ(RCA,RCA);
 clrscrn();
 printf(" A :");
 p_mZ(A, S8,P0, S7,P0, C4);
/* V and cV_T*/ 
 eigs_V_uv_mZ(A,V,FACTOR_E);
 ctranspose_mZ(V,cV_T);
/* EigsValue : cV_T * A * V */ 
 mul_mZ(cV_T,A,T);
 mul_mZ(T,V,EigsValue); 
 f_eigs_uv_mZ(f,EigsValue,invEValue); 
/* inv : V * inv(EigsValue) * cV_T*/ 
 mul_mZ(V,invEValue,T);
 mul_mZ(T,cV_T,InvA); 
 printf(" invA = V * inv(EigsValue) * cV_T");
 pE_mZ(InvA, S12,P4, S12,P4, C3); 
 printf(" Ide = InvA * A"); 
 mul_mZ(InvA,A,T);
 p_mZ(T, S8,P4, S8,P4, C4); 
 stop(); 
 f_mZ(A);
 f_mZ(V);
 f_mZ(cV_T);
 f_mZ(T); 
 f_mZ(invEValue);
 f_mZ(EigsValue);
 f_mZ(InvA);
/* ------------------------------------ */
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 :
 invA = V * inv(EigsValue) * cV_T
 Exemple de sortie écran :
 A :
 +25072 +0i +21293 -4811i +5386 -6531i +11975 -5847i 
 +21293 +4811i +30848 +0i -1526 -1774i +13478 -6658i 
 +5386 +6531i -1526 +1774i +20007 +0i +7542 -1322i 
 +11975 +5847i +13478 +6658i +7542 +1322i +21250 +0i 
 invA = V * inv(EigsValue) * cV_T
 +2.4401e-04 -4.2021e-22i -1.6775e-04 +9.5627e-05i -7.7699e-05 +1.0843e-04i 
 -1.6775e-04 -9.5627e-05i +2.0965e-04 -1.3553e-20i +1.1807e-04 -4.3268e-05i 
 -7.7699e-05 -1.0843e-04i +1.1807e-04 +4.3268e-05i +1.3955e-04 +8.4703e-21i 
 -4.0241e-05 +8.9388e-05i -5.1345e-05 -9.6122e-05i -6.4355e-05 -5.7956e-05i 
 -4.0241e-05 -8.9388e-05i 
 -5.1345e-05 +9.6122e-05i 
 -6.4355e-05 +5.7956e-05i 
 +1.3427e-04 -2.3510e-38i 
 Ide = InvA * A
 +1.0000 -0.0000i +0.0000 -0.0000i -0.0000 +0.0000i +0.0000 -0.0000i 
 +0.0000 +0.0000i +1.0000 -0.0000i +0.0000 +0.0000i +0.0000 +0.0000i 
 -0.0000 -0.0000i -0.0000 -0.0000i +1.0000 +0.0000i -0.0000 -0.0000i 
 -0.0000 -0.0000i -0.0000 +0.0000i -0.0000 -0.0000i +1.0000 +0.0000i 
 Press return to continue.

Mathc complexes/a93
Application
Installer et compiler ces fichiers dans votre répertoire de travail.
/* ------------------------------------ */
/* Save as : c00a.c */
/* ------------------------------------ */
/* ------------------------------------ */
double f(
double x)
 return(sin(x)*sin(x));
char feq[] = "sin(x)*sin(x)";
double g(
double x)
 return(cos(x)*cos(x));
char geq[] = "cos(x)*cos(x)";
void fun(void)
double a[RC4*(RC4*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 **EigsValue = i_mZ(RCA,RCA);
double **sin_EValue = i_mZ(RCA,RCA);
double **cos_EValue = i_mZ(RCA,RCA);
double **sin_A = i_mZ(RCA,RCA);
double **cos_A = i_mZ(RCA,RCA);
 clrscrn();
 printf(" A :");
 p_mZ(A, S7,P0, S7,P0, C6);
 stop();
 clrscrn();
 eigs_V_uv_mZ(A,V,FACTOR_E);
 ctranspose_mZ(V,cV_T);
/* EigsValue = cV_T * A * V */ 
 mul_mZ(cV_T,A,T);
 mul_mZ(T,V,EigsValue); 
 f_eigs_uv_mZ(f,EigsValue,sin_EValue); 
 f_eigs_uv_mZ(g,EigsValue,cos_EValue); 
/* sin**2 = V * sin_EValue * cV_T*/ 
 mul_mZ(V,sin_EValue,T);
 mul_mZ(T,cV_T,sin_A); 
 printf(" sin(A)**2");
 p_mZ(sin_A, S7,P3, S7,P3, C6);
/* cos**2 = V * cos_EValue * cV_T*/ 
 mul_mZ(V,cos_EValue,T);
 mul_mZ(T,cV_T,cos_A);
 printf(" cos(A)**2");
 p_mZ(cos_A, S7,P3, S7,P3, C6); 
 add_mZ(sin_A,cos_A,A);
 printf(" sin(A)**2 + cos(A)**2 = 1");
 p_mZ(A, S7,P3, S7,P3, C6);
 stop();
 f_mZ(A);
 f_mZ(V);
 f_mZ(cV_T);
 f_mZ(T);
 f_mZ(EigsValue);
 f_mZ(sin_EValue);
 f_mZ(cos_EValue);
 f_mZ(sin_A);
 f_mZ(cos_A);
/* ------------------------------------ */
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 :
 sin(A)**2 + cos(A)**2 = 1
 Exemple de sortie écran :
A :
 +25072 +0i +21293 -4811i +5386 -6531i +11975 -5847i 
 +21293 +4811i +30848 +0i -1526 -1774i +13478 -6658i 
 +5386 +6531i -1526 +1774i +20007 +0i +7542 -1322i 
 +11975 +5847i +13478 +6658i +7542 +1322i +21250 +0i 
 Press return to continue. 
 sin(A)**2
 +0.693 -0.000i +0.125 -0.108i +0.055 -0.098i -0.014 +0.162i 
 +0.125 +0.108i +0.535 +0.000i +0.167 -0.042i +0.057 -0.180i 
 +0.055 +0.098i +0.167 +0.042i +0.203 +0.000i -0.119 +0.046i 
 -0.014 -0.162i +0.057 +0.180i -0.119 -0.046i +0.802 +0.000i 
 cos(A)**2
 +0.307 -0.000i -0.125 +0.108i -0.055 +0.098i +0.014 -0.162i 
 -0.125 -0.108i +0.465 +0.000i -0.167 +0.042i -0.057 +0.180i 
 -0.055 -0.098i -0.167 -0.042i +0.797 -0.000i +0.119 -0.046i 
 +0.014 +0.162i -0.057 -0.180i +0.119 +0.046i +0.198 -0.000i 
 sin(A)**2 + cos(A)**2 = 1
 +1.000 -0.000i +0.000 -0.000i -0.000 +0.000i -0.000 +0.000i 
 +0.000 +0.000i +1.000 +0.000i +0.000 +0.000i +0.000 -0.000i 
 -0.000 -0.000i +0.000 -0.000i +1.000 -0.000i -0.000 +0.000i 
 -0.000 -0.000i +0.000 +0.000i -0.000 -0.000i +1.000 -0.000i 
 Press return to continue.

Mathc complexes/a94
Application
Installer et compiler ces fichiers dans votre répertoire de travail.
/* Save as : inv_z.c */
/* ------------------------------------ */
/* ------------------------------------ */
void fun(void)
int r = RCA; 
double a[RCA*(RCA*C2)] ={ +81, +82, -14, -66, -71, +1, 
 +69, +85, +11, +72, +9, -93, 
 -54, -93, -30, +10, -78, -7 };
double **A = ca_A_mZ(a, i_mZ(r,r));
double **Inv = i_mZ(r,r);
 clrscrn();
 printf(" A\n");
 p_mZ(r_mZ(A,99.), S5,P0, S4,P0, C6);
 stop();
 clrscrn();
 printf(" invgj_mZ(A,invA);");
 pE_mZ(invgj_mZ(A,Inv), S1,P4, S1,P4, C3);
 printf(" inv_mZ(A,Inv); :");
 pE_mZ(inv_mZ(A,Inv), S1,P4, S1,P4, C3);
 stop();
 clrscrn();
 printf(" Copy/Past into the octave window.\n\n");
 p_Octave_mZ(A,"A",P0, P0);
 printf(" inv(A)\n");
 pE_mZ(Inv, S1,P4, S1,P4, C3);
 stop();
 f_mZ(Inv);
 f_mZ(A);
/* ------------------------------------ */
int main(void)
 fun();
 return 0;
/* ------------------------------------ */
 Vérifier le résultat avec octave.