Mathc matrices/c29a3
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c00d.c |
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/* ------------------------------------ */
/* Save as: c00d.c */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
#define ARRAY A3
/* ------------------------------------ */
#define RC RC3
/* ------------------------------------ */
void fun(void)
{
double **A = rsymmetric_mR( i_mR(RC,RC),999);
double **AEVect = eigs_V_mR(A, i_mR(RC,RC));
double **InvAEVect = transpose_mR(AEVect, i_mR(RC,RC));
double **T = i_mR(RC,RC);
double **b [ARRAY];
double **r [ARRAY];
double **br[ARRAY];
int i;
for(i=A0; i<ARRAY; i++)
{
b[i] = c_c_mR( AEVect,i+C1, i_mR(RC,C1),C1);
r[i] = c_r_mR(InvAEVect,i+R1, i_mR(R1,RC),R1);
br[i] = mul_mR(b[i],r[i], i_mR(RC,RC));
}
clrscrn();
printf(" A:");
p_mR(A, S10,P4,C6);
printf(" AEVect: Eingvectors of A");
p_mR(AEVect, S10,P4,C6);
transpose_mR(AEVect,InvAEVect);
printf(" Inverse of AEVect = InvAEVect");
p_mR(InvAEVect, S10,P4,C6);
stop();
clrscrn();
printf(" The bnrn are projectors. \n"
" Several consecutive projections\n\n"
" bnrn**p \n\n"
" give the same result \n\n\n"
" b1r1:");
p_mR(br[0], S10,P4,C6);
pow_mR(2, br[0], T);
printf(" b1r1**2 = b1r1");
p_mR(T, S10,P4,C6);
pow_mR(6, br[0], T);
printf(" b1r1**6 = b1r1");
p_mR(T, S10,P4,C6);
stop();
clrscrn();
printf(" The bnrn are projectors. \n"
" Several consecutive projections\n\n"
" bnrn**p \n\n"
" give the same result \n\n\n"
" b2r2:");
p_mR(br[1], S10,P4,C6);
pow_mR(2, br[1], T);
printf(" b2r2**2 = b2r2");
p_mR(T, S10,P4,C6);
pow_mR(6, br[1], T);
printf(" b2r2**6 = b2r2");
p_mR(T, S10,P4,C6);
stop();
clrscrn();
printf(" The bnrn are projectors. \n"
" Several consecutive projections\n\n"
" bnrn**p \n\n"
" give the same result \n\n\n"
" b3r3:");
p_mR(br[2], S10,P4,C6);
pow_mR(2, br[2], T);
printf(" b3r3**2 = b3r3");
p_mR(T, S10,P4,C6);
pow_mR(6, br[2], T);
printf(" b3r3**6 = b3r3");
p_mR(T, S10,P4,C6);
f_mR(A);
f_mR(AEVect);
f_mR(InvAEVect);
f_mR(T);
for(i=A0; i<ARRAY; i++)
{
f_mR (b[i]);
f_mR( r[i]);
f_mR(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**2 = b1r1 * b1r1**4 = b1r1 * b1r1**6 = b1r1 Les b*r* sont des projecteurs. Si par exemple je projette le point P sur l'axe des x. P est sur l'axe des x. Une fois que P est sur l'axe de x, je peut le projeter une infinité de fois sur l'axe des x il ne bougera plus. Cela ce matérialise dans notre cas par le faite b1r1**2 = b1r1, b1r1**3 = b1r1, ... b1r1**n = b1r1
Exemple de sortie écran :
A:
-871.0000 -392.0000 -378.0000
-392.0000 -457.0000 +455.0000
-378.0000 +455.0000 +377.0000
AEVect: Eingvectors of A
+0.8795 -0.3038 -0.3664
+0.4692 +0.4244 +0.7744
+0.0798 +0.8530 -0.5158
Inverse of AEVect = InvAEVect
+0.8795 +0.4692 +0.0798
-0.3038 +0.4244 +0.8530
-0.3664 +0.7744 -0.5158
Press return to continue.
The bnrn are projectors.
Several consecutive projections
bnrn**p
give the same result
b1r1:
+0.7735 +0.4127 +0.0701
+0.4127 +0.2202 +0.0374
+0.0701 +0.0374 +0.0064
b1r1**2 = b1r1
+0.7735 +0.4127 +0.0701
+0.4127 +0.2202 +0.0374
+0.0701 +0.0374 +0.0064
b1r1**6 = b1r1
+0.7735 +0.4127 +0.0701
+0.4127 +0.2202 +0.0374
+0.0701 +0.0374 +0.0064
Press return to continue.
The bnrn are projectors.
Several consecutive projections
bnrn**p
give the same result
b2r2:
+0.0923 -0.1289 -0.2591
-0.1289 +0.1801 +0.3620
-0.2591 +0.3620 +0.7276
b2r2**2 = b2r2
+0.0923 -0.1289 -0.2591
-0.1289 +0.1801 +0.3620
-0.2591 +0.3620 +0.7276
b2r2**6 = b2r2
+0.0923 -0.1289 -0.2591
-0.1289 +0.1801 +0.3620
-0.2591 +0.3620 +0.7276
Press return to continue.
The bnrn are projectors.
Several consecutive projections
bnrn**p
give the same result
b3r3:
+0.1342 -0.2837 +0.1890
-0.2837 +0.5997 -0.3994
+0.1890 -0.3994 +0.2661
b3r3**2 = b3r3
+0.1342 -0.2837 +0.1890
-0.2837 +0.5997 -0.3994
+0.1890 -0.3994 +0.2661
b3r3**6 = b3r3
+0.1342 -0.2837 +0.1890
-0.2837 +0.5997 -0.3994
+0.1890 -0.3994 +0.2661
Press return to continue
Press X return to stop