Mathc matrices/c21w
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c00a.c |
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/* ------------------------------------ */
/* Save as : c00a.c */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
#define RA R4
#define CA C6
#define Cb C1
/* ------------------------------------ */
#define CbFREE Cb+C2
/* ------------------------------------ */
int main(void)
{
double ab[RA*(CA+Cb)]={
+34, -85, +51, -136, +34, +34, +0,
+55, -99, +66, -99, +66, +22, +0,
+35, -63, +42, -63, +42, +49, +0,
-70, +126, -42, +112, -28, -28, +0
};
double **Ab = ca_A_mR(ab, i_Abr_Ac_bc_mR(RA,CA,Cb));
double **A = c_Ab_A_mR(Ab, i_mR(RA,CA));
double **b = c_Ab_b_mR(Ab, i_mR(RA,Cb));
double **Ab_free = i_Abr_Ac_bc_mR(CA,CA,CbFREE);
double **b_free = i_mR(CA,CbFREE);
double **A_bfree = i_mR(RA,CbFREE);
int r;
clrscrn();
printf("Find a basis for the orthogonal complement of A :\n\n");
printf(" A :");
p_mR(A,S6,P1,C10);
printf(" b :");
p_mR(b,S6,P1,C10);
printf(" Ab :");
p_mR(Ab,S6,P1,C10);
stop();
clrscrn();
printf(" Ab : gj_PP_mR(Ab,NO) :");
gj_PP_mR(Ab,NO);
p_mR(Ab,S7,P3,C10);
put_zeroR_mR(Ab,Ab_free);
printf(" Ab_free : put_zeroR_mR(Ab,Ab_free);");
p_mR(Ab_free,S7,P3,C10);
put_freeV_mR(Ab_free);
printf(" Ab_free : put_freeV_mR(Ab_free);");
p_mR(Ab_free,S7,P3,C10);
stop();
clrscrn();
r = rsize_R(Ab_free);
while(r>R1)
zero_below_pivot_gj1Ab_mR(Ab_free,r--);
printf(" Ab_free : zero_below_pivot_gj1Ab_mR(Ab_free,r--);");
p_mR(Ab_free,S7,P3,C10);
c_Ab_b_mR(Ab_free,b_free);
printf(" b_free :");
p_mR(b_free,S10,P3,C7);
stop();
clrscrn();
printf(" A :");
p_mR(A,S10,P3,C10);
printf(" b_free :");
p_mR(b_free,S10,P3,C7);
printf(" A * bfree :");
p_mR(mul_mR(A,b_free,A_bfree),S10,P3,C7);
stop();
f_mR(Ab);
f_mR(A);
f_mR(b);
f_mR(Ab_free);
f_mR(b_free);
f_mR(A_bfree);
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 :
+34.0 -85.0 +51.0 -136.0 +34.0 +34.0
+55.0 -99.0 +66.0 -99.0 +66.0 +22.0
+35.0 -63.0 +42.0 -63.0 +42.0 +49.0
-70.0 +126.0 -42.0 +112.0 -28.0 -28.0
b :
+0.0
+0.0
+0.0
+0.0
Ab :
+34.0 -85.0 +51.0 -136.0 +34.0 +34.0 +0.0
+55.0 -99.0 +66.0 -99.0 +66.0 +22.0 +0.0
+35.0 -63.0 +42.0 -63.0 +42.0 +49.0 +0.0
-70.0 +126.0 -42.0 +112.0 -28.0 -28.0 +0.0
Press return to continue.
Ab : gj_PP_mR(Ab,NO) :
+1.000 -1.800 +0.600 -1.600 +0.400 +0.400 -0.000
-0.000 +1.000 -1.286 +3.429 -0.857 -0.857 -0.000
+0.000 +0.000 +1.000 -0.333 +1.333 +0.000 +0.000
+0.000 +0.000 +0.000 +0.000 -0.000 +1.000 +0.000
Ab_free : put_zeroR_mR(Ab,Ab_free);
+1.000 -1.800 +0.600 -1.600 +0.400 +0.400 -0.000 +0.000 +0.000
-0.000 +1.000 -1.286 +3.429 -0.857 -0.857 -0.000 +0.000 +0.000
+0.000 +0.000 +1.000 -0.333 +1.333 +0.000 +0.000 +0.000 +0.000
+0.000 +0.000 +0.000 +0.000 +0.000 +0.000 +0.000 +0.000 +0.000
+0.000 +0.000 +0.000 +0.000 +0.000 +0.000 +0.000 +0.000 +0.000
+0.000 +0.000 +0.000 +0.000 -0.000 +1.000 +0.000 +0.000 +0.000
Ab_free : put_freeV_mR(Ab_free);
+1.000 -1.800 +0.600 -1.600 +0.400 +0.400 -0.000 +0.000 +0.000
-0.000 +1.000 -1.286 +3.429 -0.857 -0.857 -0.000 +0.000 +0.000
+0.000 +0.000 +1.000 -0.333 +1.333 +0.000 +0.000 +0.000 +0.000
+0.000 +0.000 +0.000 +1.000 +0.000 +0.000 +0.000 +1.000 +0.000
+0.000 +0.000 +0.000 +0.000 +1.000 +0.000 +0.000 +0.000 +1.000
+0.000 +0.000 +0.000 +0.000 -0.000 +1.000 +0.000 +0.000 +0.000
Press return to continue.
Ab_free : zero_below_pivot_gj1Ab_mR(Ab_free,r--);
+1.000 +0.000 +0.000 +0.000 +0.000 +0.000 +0.000 -4.000 -1.143
+0.000 +1.000 +0.000 +0.000 +0.000 +0.000 +0.000 -3.000 -0.857
+0.000 +0.000 +1.000 +0.000 +0.000 +0.000 +0.000 +0.333 -1.333
+0.000 +0.000 +0.000 +1.000 +0.000 +0.000 +0.000 +1.000 +0.000
+0.000 +0.000 +0.000 +0.000 +1.000 +0.000 +0.000 +0.000 +1.000
+0.000 +0.000 +0.000 +0.000 -0.000 +1.000 +0.000 +0.000 +0.000
b_free :
+0.000 -4.000 -1.143
+0.000 -3.000 -0.857
+0.000 +0.333 -1.333
+0.000 +1.000 +0.000
+0.000 +0.000 +1.000
+0.000 +0.000 +0.000
Press return to continue.
A :
+34.000 -85.000 +51.000 -136.000 +34.000 +34.000
+55.000 -99.000 +66.000 -99.000 +66.000 +22.000
+35.000 -63.000 +42.000 -63.000 +42.000 +49.000
-70.000 +126.000 -42.000 +112.000 -28.000 -28.000
b_free :
+0.000 -4.000 -1.143
+0.000 -3.000 -0.857
+0.000 +0.333 -1.333
+0.000 +1.000 +0.000
+0.000 +0.000 +1.000
+0.000 +0.000 +0.000
A * bfree :
+0.000 +0.000 -0.000
+0.000 -0.000 -0.000
+0.000 -0.000 -0.000
+0.000 +0.000 +0.000
Press return to continue.