Mathc complexes/a344
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c00b.c |
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/* ------------------------------------ */
/* Save as: c00b.c */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
#define FACTOR_E +1.E-1
#define ARRAY A3
/* ------------------------------------ */
#define RC RC3
/* ------------------------------------ */
void fun(void)
{
double **A = rcsymmetric_mZ( i_mZ(RC,RC),99);
double **AEVect = eigs_V_mZ(A, i_mZ(RC,RC),FACTOR_E);
double **InvAEVect = ctranspose_mZ(AEVect, i_mZ(RC,RC));
double **T = i_mZ(RC,RC);
double **Ide = i_mZ(RC,RC);
double **b [ARRAY];
double **r [ARRAY];
double **br[ARRAY];
int i;
for(i=A0; i<ARRAY; i++)
{
b[i] = c_c_mZ( AEVect,i+C1, i_mZ(RC,C1),C1);
r[i] = c_r_mZ(InvAEVect,i+R1, i_mZ(R1,RC),R1);
br[i] = mul_mZ(b[i],r[i], i_mZ(RC,RC));
}
clrscrn();
printf(" A:");
p_mZ(A, S7,P0,S6,P0,C7);
printf(" eigenvectors of A");
p_mZ(AEVect, S5,P4,S5,P4,C7);
printf(" Conjugate transpose of Eigenvector of A");
p_mZ(InvAEVect, S5,P4,S5,P4,C7);
stop();
clrscrn();
printf(" eigenvectors of A");
p_mZ(AEVect, S5,P4,S5,P4,C7);
for(i=A0; i<ARRAY; i++)
{
printf(" b%d:",i+C1);
p_mZ(b[i], S5,P4,S5,P4,C7);
}
stop();
clrscrn();
printf(" Conjugate transpose of Eigenvector of A");
p_mZ(InvAEVect, S5,P4,S5,P4,C7);
for(i=A0; i<ARRAY; i++)
{
printf(" r%d:",i+R1);
p_mZ(r[i], S5,P4,S5,P4,C7);
}
stop();
clrscrn();
for(i=A0; i<ARRAY; i++)
{
printf(" b%dr%d:",i+C1,i+R1);
p_mZ(br[i], S5,P4,S5,P4,C7);
}
stop();
clrscrn();
add_mZ(br[0], br[1], T);
add_mZ( T, br[2], Ide);
printf(" b1r1 + b2r2 + b3r3 = Ide");
p_mZ(Ide, S5,P4,S5,P4,C7);
f_mZ(A);
f_mZ(AEVect);
f_mZ(InvAEVect);
f_mZ(T);
f_mZ(Ide);
for(i=A0; i<ARRAY; i++)
{
f_mZ( b[i]);
f_mZ( r[i]);
f_mZ(br[i]);
}
}
/* ------------------------------------ */
int main(void)
{
time_t t;
srand(time(&t));
do
{
fun();
} while(stop_w());
return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */
Nous voyons une des propriètés de la décomposition spectral:
b1r1 + b2r2 + b3r3 = Ide
b1r1 est obtenue en multipliant la première colonne de la matrice des vecteurs propres par la première ligne de la matrice inverse des vecteurs propres.
Vp invVp
r1
b1 b2 b3 r2 -> b1*r1; b2*r2; b3*r3; Cela nous donne trois matrices [3x3]
r3
Exemple de sortie écran :
A:
+17880 +0i -11431 +8119i +2451 -6543i
-11431 -8119i +19115 +0i -8993 +2402i
+2451 +6543i -8993 -2402i +8894 +0i
eigenvectors of A
+0.3169-0.5431i -0.6182+0.2145i +0.4078+0.1003i
-0.6325+0.2515i -0.2452-0.3258i +0.5850+0.1678i
+0.3758+0.0000i +0.6368+0.0000i +0.6732+0.0000i
Conjugate transpose of Eigenvector of A
+0.3169+0.5431i -0.6325-0.2515i +0.3758-0.0000i
-0.6182-0.2145i -0.2452+0.3258i +0.6368-0.0000i
+0.4078-0.1003i +0.5850-0.1678i +0.6732-0.0000i
Press return to continue.
eigenvectors of A
+0.3169-0.5431i -0.6182+0.2145i +0.4078+0.1003i
-0.6325+0.2515i -0.2452-0.3258i +0.5850+0.1678i
+0.3758+0.0000i +0.6368+0.0000i +0.6732+0.0000i
b1:
+0.3169-0.5431i
-0.6325+0.2515i
+0.3758+0.0000i
b2:
-0.6182+0.2145i
-0.2452-0.3258i
+0.6368+0.0000i
b3:
+0.4078+0.1003i
+0.5850+0.1678i
+0.6732+0.0000i
Press return to continue.
Conjugate transpose of Eigenvector of A
+0.3169+0.5431i -0.6325-0.2515i +0.3758-0.0000i
-0.6182-0.2145i -0.2452+0.3258i +0.6368-0.0000i
+0.4078-0.1003i +0.5850-0.1678i +0.6732-0.0000i
r1:
+0.3169+0.5431i -0.6325-0.2515i +0.3758-0.0000i
r2:
-0.6182-0.2145i -0.2452+0.3258i +0.6368-0.0000i
r3:
+0.4078-0.1003i +0.5850-0.1678i +0.6732-0.0000i
Press return to continue.
b1r1:
+0.3954+0.0000i -0.3371+0.2638i +0.1191-0.2041i
-0.3371-0.2638i +0.4633+0.0000i -0.2377+0.0945i
+0.1191+0.2041i -0.2377-0.0945i +0.1413+0.0000i
b2r2:
+0.4282+0.0000i +0.0817-0.2540i -0.3937+0.1366i
+0.0817+0.2540i +0.1663+0.0000i -0.1561-0.2075i
-0.3937-0.1366i -0.1561+0.2075i +0.4055+0.0000i
b3r3:
+0.1764+0.0000i +0.2554-0.0098i +0.2746+0.0675i
+0.2554+0.0098i +0.3704+0.0000i +0.3938+0.1130i
+0.2746-0.0675i +0.3938-0.1130i +0.4532+0.0000i
Press return to continue.
b1r1 + b2r2 + b3r3 = Ide
+1.0000+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 +1.0000+0.0000i
Press return to continue
Press X return to stop