Mathc matrices/c25f
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c03a.c |
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/* ------------------------------------ */
/* Save as : c03a.c */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
#define RA R4
#define CA C2
/* ------------------------------------ */
/* ------------------------------------ */
void fun(void)
{
double **A = r_Q_mR(i_mR(RA,CA), 9);
double **AT = i_mR(CA,RA);
double **ATA = i_mR(CA,CA); // AT*A
double **invATA = i_mR(CA,CA); // inv(AT*A)
double **invATA_AT = i_mR(CA,RA); // inv(AT*A)*AT
double **V = i_mR(RA,RA); // inv(AT*A)*AT
double **AAT = i_mR(RA,RA);
double **x = r_mR(i_mR(RA,C1),9.);
double **Vx = i_mR(RA,C1);
clrscrn();
printf(" A is subspace of R%d \n\n"
" Find a transformation matrix for \n"
" a projection onto R%d : \n\n"
" Proj(x) = A * inv(AT*A) * AT * x \n\n",RA,RA);
printf(" A :");
p_mR(A,S5,P4,C7);
printf(" Compute Proj(x) with : \n\n"
" x :");
p_mR(x,S5,P4,C7);
stop();
clrscrn();
printf(" AT :");
p_mR(transpose_mR(A,AT),S5,P4,C7);
printf(" ATA :");
p_mR(mul_mR(AT,A,ATA),S5,P4,C7);
printf(" inv(AT*A) :");
p_mR(inv_mR(ATA,invATA),S5,P4,C7);
printf(" inv(AT*A)*AT :");
p_mR(mul_mR(invATA,AT,invATA_AT),S5,P4,C7);
printf(" V = A*inv(AT*A)*AT :");
p_mR(mul_mR(A,invATA_AT,V),S5,P4,C7);
stop();
clrscrn();
printf(" V is transformation matrix for \n"
" a projection onto a subspace R%d :\n\n",RA);
p_mR(V,S5,P4,C7);
printf(" Proj(x) = A * inv(AT*A) * AT * x \n\n");
printf(" Proj(x) = V * x :");
p_mR(mul_mR(V,x,Vx),S5,P4,C7);
stop();
clrscrn();
printf(" Proj(x) = A * inv(AT*A) * AT * x :");
p_mR(Vx,S5,P4,C7);
printf(" A * AT :");
p_mR(mul_mR(A,AT,AAT),S5,P4,C7);
printf(" Proj(x) = A * AT * x :");
p_mR(mul_mR(AAT,x,Vx),S5,P4,C7);
f_mR(A);
f_mR(AT);
f_mR(ATA); // AT*A
f_mR(invATA); // inv(AT*A)
f_mR(invATA_AT); // inv(AT*A)*AT
f_mR(V); // A*inv(AT*A)*AT
f_mR(AAT);
f_mR(x);
f_mR(Vx);
}
/* ------------------------------------ */
int main(void)
{
time_t t;
srand(time(&t));
do
{
fun();
} while(stop_w());
return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */
Présentation deux deux algorithmes pour calculer la matrice de projection de x sur Rn quand la matrice A est un sous espace orthonormale de Rn.
(Id)
Proj(x) = A * inv(AT*A) * AT * x :
Proj(x) = A * AT * x :
Exemple de sortie écran :
--------------------------------
A is subspace of R4
Find a transformation matrix for
a projection onto R4 :
Proj(x) = A * inv(AT*A) * AT * x
A :
+0.5644 +0.2555
-0.5644 -0.2555
+0.4704 -0.8737
-0.3763 -0.3256
Compute Proj(x) with :
x :
-1.0000
+3.0000
+8.0000
-5.0000
Press return to continue.
--------------------------------
AT :
+0.5644 -0.5644 +0.4704 -0.3763
+0.2555 -0.2555 -0.8737 -0.3256
ATA :
+1.0000 -0.0000
-0.0000 +1.0000
inv(AT*A) :
+1.0000 -0.0000
-0.0000 +1.0000
inv(AT*A)*AT :
+0.5644 -0.5644 +0.4704 -0.3763
+0.2555 -0.2555 -0.8737 -0.3256
V = A*inv(AT*A)*AT :
+0.3839 -0.3839 +0.0422 -0.2956
-0.3839 +0.3839 -0.0422 +0.2956
+0.0422 -0.0422 +0.9846 +0.1075
-0.2956 +0.2956 +0.1075 +0.2476
Press return to continue.
--------------------------------
V is transformation matrix for
a projection onto a subspace R4 :
+0.3839 -0.3839 +0.0422 -0.2956
-0.3839 +0.3839 -0.0422 +0.2956
+0.0422 -0.0422 +0.9846 +0.1075
-0.2956 +0.2956 +0.1075 +0.2476
Proj(x) = A * inv(AT*A) * AT * x
Proj(x) = V * x :
+0.2802
-0.2802
+7.1708
+0.8042
Press return to continue.
--------------------------------
Proj(x) = A * inv(AT*A) * AT * x :
+0.2802
-0.2802
+7.1708
+0.8042
A * AT :
+0.3839 -0.3839 +0.0422 -0.2956
-0.3839 +0.3839 -0.0422 +0.2956
+0.0422 -0.0422 +0.9846 +0.1075
-0.2956 +0.2956 +0.1075 +0.2476
Proj(x) = A * AT * x :
+0.2802
-0.2802
+7.1708
+0.8042