Mathc complexes/a221
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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 RAFree R4
#define CbFree C2
/* ------------------------------------ */
void fun(void)
{
double ab[RA*((CA+Cb)*C2)] ={
1,2, 3,4, 5,6, 5,2, 0,0,
1,2, 3,4, 5,6, 1,3, 0,0,
1,2, 3,4, 1,1, 4,2, 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 **Ab_New = i_Abr_Ac_bc_mZ(RAFree,CA,CbFree) ;
double **b_Free = i_mZ(RAFree,CbFree);
double **A_bFree = i_mZ(RA,CbFree);
clrscrn();
printf("Find a basis for the orthogonal complement of A :\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(" gj_PP_mZ(Ab) :");
p_mZ(gj_PP_mZ(Ab), S8,P4, S8,P4, C4);
put_zeroR_mZ(Ab,Ab_New);
put_freeV_mZ(Ab_New);
printf(" put_zero_row_mZ(Ab,Ab_New);\n"
" put_freeV_mZ(Ab_New);\n\n"
" Ab_New :");
p_mZ(Ab_New, S8,P4, S8,P4, C4);
stop();
clrscrn();
printf(" gj_mZ(Ab) :");
p_mZ(gj_mZ(Ab_New), S8,P4, S8,P4, C4);
printf(" b_Free : Free variables");
p_mZ(c_Ab_b_mZ(Ab_New,b_Free), S8,P4, S8,P4, C4);
stop();
clrscrn();
printf(" A :");
p_mZ(A, S8,P4, S8,P4, C4);
printf(" b_Free :");
p_mZ(b_Free, S8,P4, S8,P4, C4);
printf(" A * b_Free :");
p_mZ(mul_mZ(A,b_Free,A_bFree), S8,P4, S8,P4, C4);
stop();
f_mZ(Ab);
f_mZ(A);
f_mZ(b);
f_mZ(Ab_New);
f_mZ(b_Free);
f_mZ(A_bFree);
}
/* ------------------------------------ */
int main(void)
{
fun();
return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */
On commence par calculer les variables libres.
Les colonnes de b_free sont une base pour le complément orthogonal de A.
A * b_free = 0
Cela prouve que les vecteurs lignes de A sont orthogonaux aux vecteurs colonnes de b_free.
Exemple de sortie écran :
------------------------------------
Find a basis for the orthogonal complement of A :
A :
+1 +2i +3 +4i +5 +6i +5 +2i
+1 +2i +3 +4i +5 +6i +1 +3i
+1 +2i +3 +4i +1 +1i +4 +2i
b :
+0 +0i
+0 +0i
+0 +0i
Ab :
+1 +2i +3 +4i +5 +6i +5 +2i +0 +0i
+1 +2i +3 +4i +5 +6i +1 +3i +0 +0i
+1 +2i +3 +4i +1 +1i +4 +2i +0 +0i
Press return to continue.
------------------------------------
gj_PP_mZ(Ab) :
+1.0000 +0.0000i +2.2000 -0.4000i +3.4000 -0.8000i +1.8000 -1.6000i
-0.0000 +0.0000i +0.0000 -0.0000i +1.0000 +0.0000i +0.0976 -0.1220i
+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
put_zero_row_mZ(Ab,Ab_New);
put_freeV_mZ(Ab_New);
Ab_New :
+1.0000 +0.0000i +2.2000 -0.4000i +3.4000 -0.8000i +1.8000 -1.6000i
+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 +0.0976 -0.1220i
+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
-0.0000 +0.0000i +0.0000 +0.0000i
+0.0000 -0.0000i +0.0000 +0.0000i
Press return to continue.
------------------------------------
gj_mZ(Ab) :
+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
-0.0000 +0.0000i -2.2000 +0.4000i
+0.0000 +0.0000i +1.0000 +0.0000i
+0.0000 +0.0000i +0.0000 +0.0000i
+0.0000 +0.0000i -0.0000 -0.0000i
new_b : Free variables
-0.0000 +0.0000i -2.2000 +0.4000i
+0.0000 +0.0000i +1.0000 +0.0000i
+0.0000 +0.0000i +0.0000 +0.0000i
+0.0000 +0.0000i -0.0000 -0.0000i
Press return to continue.
------------------------------------
A :
+1.0000 +2.0000i +3.0000 +4.0000i +5.0000 +6.0000i +5.0000 +2.0000i
+1.0000 +2.0000i +3.0000 +4.0000i +5.0000 +6.0000i +1.0000 +3.0000i
+1.0000 +2.0000i +3.0000 +4.0000i +1.0000 +1.0000i +4.0000 +2.0000i
b_Free :
-0.0000 +0.0000i -2.2000 +0.4000i
+0.0000 +0.0000i +1.0000 +0.0000i
+0.0000 +0.0000i +0.0000 +0.0000i
+0.0000 +0.0000i -0.0000 -0.0000i
A * b_Free :
+0.0000 +0.0000i -0.0000 +0.0000i
+0.0000 +0.0000i +0.0000 +0.0000i
+0.0000 +0.0000i -0.0000 -0.0000i
Press return to continue.