Mathc complexes/a91
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c00c.c |
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/* ------------------------------------ */
/* Save as : c00c.c */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
#define FACTOR_E +1.E-2
#define RCA RC4
/* ------------------------------------ */
/* ------------------------------------ */
int main(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 **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,%d) \n\n\n",RCA);
printf(" A :");
p_mZ(A, S8,P0, S6,P0, C4);
stop();
clrscrn();
/* V and cV_T*/
eigs_V_mZ(A,V,FACTOR_E);
printf(" V :");
p_mZ(V, S8,P2, S6,P2, C4);
printf(" cV_T :");
p_mZ(ctranspose_mZ(V,cV_T), S8,P2, S6,P2, C4);
stop();
clrscrn();
/* EigsValue : cV_T * A * V */
mul_mZ(cV_T,A,T);
mul_mZ(T,V,EigsValue);
printf(" EigsValue :");
p_mZ(EigsValue, S8,P2, S6,P2, C4);
printf(" A :");
p_mZ(A, S8,P0, S6,P0, C4);
/* A = V * EigsValue * cV_T*/
mul_mZ(V,EigsValue,T);
mul_mZ(T,cV_T,A);
printf(" A = V * EigsValue * cV_T");
p_mZ(A, S8,P0, S6,P0, C4);
stop();
f_mZ(A);
f_mZ(V);
f_mZ(cV_T);
f_mZ(T);
f_mZ(EigsValue);
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 :
- FACTOR_E ..... +1.E-1 ......... -9 < x < 9
- FACTOR_E ..... +1.E-2 ....... -99 < x < 99
- FACTOR_E ..... +1.E-3 ..... -999 < x < 999
Nous allons étudier une des propriétés des valeurs propres et des vecteurs propres :
A = V * EigsValue * cV_T
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,4)
Press return to continue.
------------------------------------
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
V :
+0.49 -0.32i +0.01 -0.03i -0.24 +0.48i -0.13 -0.59i
+0.58 -0.26i -0.26 +0.36i -0.17 -0.22i -0.20 +0.54i
+0.19 +0.05i +0.70 -0.50i -0.22 -0.01i -0.28 +0.31i
+0.46 +0.00i +0.26 -0.00i +0.77 +0.00i +0.36 +0.00i
cV_T :
+0.49 +0.32i +0.58 +0.26i +0.19 -0.05i +0.46 -0.00i
+0.01 +0.03i -0.26 -0.36i +0.70 +0.50i +0.26 +0.00i
-0.24 -0.48i -0.17 +0.22i -0.22 +0.01i +0.77 -0.00i
-0.13 +0.59i -0.20 -0.54i -0.28 -0.31i +0.36 -0.00i
Press return to continue.
------------------------------------
EigsValue :
+61819.15 -0.00i -0.00 +0.00i -0.00 -0.00i -0.00 -0.00i
-0.00 -0.00i +22896.22 -0.00i -0.00 -0.00i -0.00 +0.00i
-0.00 +0.00i -0.00 +0.00i +10720.54 +0.00i +0.00 -0.00i
+0.00 +0.00i -0.00 -0.00i +0.00 +0.00i +1741.10 +0.00i
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
A = V * EigsValue * cV_T
+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.