Mathc complexes/a230
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c00a.c |
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/* ------------------------------------ */
/* Save as : c00a.c */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
#define RA R3
#define CA C4
#define Cb C1
/* ------------------------------------ */
#define CB C3 /* B : a basis for the column space of A */
/* ------------------------------------ */
void fun(void)
{
double ab[RA*((CA+Cb)*C2)] ={
1*1,2*1, 3*1,4*1, 5*1,6*1, 5*1,2*1, 0,0,
1*3,2*3, 3*3,4*3, 5*3,6*3, 1*3,3*3, 0,0,
1*4,2*4, 3*4,4*4, 1*4,1*4, 4*4,2*4, 0,0};
double **Ab = ca_A_mZ(ab, i_Abr_Ac_bc_mZ(RA,CA,Cb));
double **A = c_Ab_A_mZ(Ab, i_mZ(RA,CA));
double **b = c_Ab_b_mZ(Ab, i_mZ(RA,Cb));
double **B = i_mZ(RA,CB);
double **BT = i_mZ(CB,RA);
double **BTb = i_Abr_Ac_bc_mZ(CB,RA,Cb);
clrscrn();
printf("Basis for a Column Space by Row Reduction :\n\n");
printf(" A :");
p_mZ(A, S3,P0, S3,P0, C8);
printf(" b :");
p_mZ(b, S3,P0, S3,P0, C8);
printf(" Ab :");
p_mZ(Ab, S3,P0, S3,P0, C8);
stop();
clrscrn();
printf(" The leading 1’s of Ab give the position \n"
" of the columns of A which form a basis \n"
" for the column space of A \n\n"
" A :");
p_mZ(A, S8,P4, S8,P4, C4);
printf(" gj_PP_mZ(Ab) :");
p_mZ(gj_PP_mZ(Ab), S8,P4, S8,P4, C4);
c_c_mZ(A,C1,B,C1);
c_c_mZ(A,C3,B,C2);
c_c_mZ(A,C4,B,C3);
printf(" B :");
p_mZ(B, S8,P4, S8,P4, C4);
stop();
clrscrn();
printf(" Check if the columns of B are linearly independent\n\n"
" BT :");
p_mZ(transpose_mZ(B,BT), S4,P0, S3,P0, C4);
printf(" BTb :");
p_mZ(c_mZ(BT,BTb), S4,P0, S3,P0, C4);
printf(" gj_PP_mZ(BTb) :");
p_mZ(gj_PP_mZ(BTb), S8,P4, S8,P4, C4);
stop();
f_mZ(Ab);
f_mZ(A);
f_mZ(b);
f_mZ(B);
f_mZ(BT);
f_mZ(BTb);
}
/* ------------------------------------ */
int main(void)
{
fun();
return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */
La position des pivots de Ab donne la position des colonnes de A qui forment une base pour l'espace colonnes de A.
Exemple de sortie écran :
Basis for a Column Space by Row Reduction :
A :
+1 +2i +3 +4i +5 +6i +5 +2i
+3 +6i +9+12i +15+18i +3 +9i
+4 +8i +12+16i +4 +4i +16 +8i
b :
+0 +0i
+0 +0i
+0 +0i
Ab :
+1 +2i +3 +4i +5 +6i +5 +2i +0 +0i
+3 +6i +9+12i +15+18i +3 +9i +0 +0i
+4 +8i +12+16i +4 +4i +16 +8i +0 +0i
Press return to continue.
The leading 1’s of Ab give the position
of the columns of A which form a basis
for the column space of A
A :
+1.0000 +2.0000i +3.0000 +4.0000i +5.0000 +6.0000i +5.0000 +2.0000i
+3.0000 +6.0000i +9.0000+12.0000i +15.0000+18.0000i +3.0000 +9.0000i
+4.0000 +8.0000i +12.0000+16.0000i +4.0000 +4.0000i +16.0000 +8.0000i
gj_PP_mZ(Ab) :
+1.0000 +0.0000i +2.2000 -0.4000i +0.6000 -0.2000i +1.6000 -1.2000i
+0.0000 +0.0000i -0.0000 +0.0000i +1.0000 -0.0000i -0.1707 +0.4634i
+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
B :
+1.0000 +2.0000i +5.0000 +6.0000i +5.0000 +2.0000i
+3.0000 +6.0000i +15.0000+18.0000i +3.0000 +9.0000i
+4.0000 +8.0000i +4.0000 +4.0000i +16.0000 +8.0000i
Press return to continue.
Check if the columns of B are linearly independent
BT :
+1 +2i +3 +6i +4 +8i
+5 +6i +15+18i +4 +4i
+5 +2i +3 +9i +16 +8i
BTb :
+1 +2i +3 +6i +4 +8i +0 +0i
+5 +6i +15+18i +4 +4i +0 +0i
+5 +2i +3 +9i +16 +8i +0 +0i
gj_PP_mZ(BTb) :
+1.0000 +0.0000i +3.0000 +0.0000i +0.7213 -0.0656i +0.0000 +0.0000i
-0.0000 +0.0000i +1.0000 +0.0000i -0.8267 -0.7805i +0.0000 -0.0000i
+0.0000 -0.0000i -0.0000 -0.0000i +1.0000 +0.0000i +0.0000 +0.0000i
Press return to continue.