Mathc complexes/a250
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c04a.c |
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/* ------------------------------------ */
/* Save as : c04a.c */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
#define RA R4
#define CA C2
/* ------------------------------------ */
/* ------------------------------------ */
int main(void)
{
double a[RA*(CA*C2)]={
-2,-3, -4,-2,
1, 0, -3,-5,
0, 1, -6,-4,
3, 5, -1,-0,
};
double x[RA*(C1*C2)]={
-1,-3,
2,-4,
-3,-5,
-1,-2,
};
double **A = ca_A_mZ(a,i_mZ(RA,CA));
double **AT = i_mZ(CA,RA);
double **ATA = i_mZ(CA,CA); // AT*A
double **invATA = i_mZ(CA,CA); // inv(AT*A)
double **invATA_AT = i_mZ(CA,RA); // inv(AT*A)*AT
double **V = i_mZ(RA,RA); // inv(AT*A)*AT
double **X = ca_A_mZ(x,i_mZ(RA,C1));
double **VX = i_mZ(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_mZ(A,S5,P1,S5,P1,C7);
stop();
clrscrn();
printf(" AT :");
p_mZ(ctranspose_mZ(A,AT),S5,P1,S5,P1,C7);
printf(" ATA :");
p_mZ(mul_mZ(AT,A,ATA),S5,P1,S5,P1,C7);
printf(" inv(AT*A) :");
p_mZ(invgj_mZ(ATA,invATA),S5,P4,S5,P4,C7);
printf(" inv(AT*A)*AT :");
p_mZ(mul_mZ(invATA,AT,invATA_AT),S5,P4,S5,P4,C7);
printf(" V = A*inv(AT*A)*AT :");
p_mZ(mul_mZ(A,invATA_AT,V),S5,P4,S5,P4,C7);
stop();
clrscrn();
printf(" V is transformation matrix for \n"
" a projection onto a subspace R%d :\n\n",RA);
p_mZ(V,S5,P4,S5,P4,C7);
printf(" X :");
p_mZ(X,S5,P1,S5,P1,C7);
printf(" Proj(x) = A * inv(AT*A) * AT * x \n\n");
printf(" Proj(x) = V * x :");
p_mZ(mul_mZ(V,X,VX),S5,P4,S5,P4,C7);
stop();
f_mZ(A);
f_mZ(AT);
f_mZ(ATA); // AT*A
f_mZ(invATA); // inv(AT*A)
f_mZ(invATA_AT); // inv(AT*A)*AT
f_mZ(V); // A*inv(AT*A)*AT
f_mZ(X);
f_mZ(VX);
return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */
Trouver une projection sur un sous-espace vectoriel par une application linéaire :
- A est un sous espace de R4. Trouver une matrice V qui projette un vecteur x sur R4.
Proj(x) = V * x
V = A * inv(AT*A) * AT
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 :
-2.0 -3.0i -4.0 -2.0i
+1.0 +0.0i -3.0 -5.0i
+0.0 +1.0i -6.0 -4.0i
+3.0 +5.0i -1.0 +0.0i
Press return to continue.
------------------------------------
AT :
-2.0 +3.0i +1.0 -0.0i +0.0 -1.0i +3.0 -5.0i
-4.0 +2.0i -3.0 +5.0i -6.0 +4.0i -1.0 -0.0i
ATA :
+49.0 +0.0i +4.0 -2.0i
+4.0 +2.0i +107.0 +0.0i
inv(AT*A) :
+0.0205+0.0000i -0.0008+0.0004i
-0.0008-0.0004i +0.0094+0.0000i
inv(AT*A)*AT :
-0.0387+0.0584i +0.0209-0.0050i +0.0031-0.0258i +0.0622-0.1028i
-0.0348+0.0172i -0.0289+0.0465i -0.0567+0.0383i -0.0136+0.0027i
V = A*inv(AT*A)*AT :
+0.4264+0.0000i +0.1520-0.1809i +0.2196+0.0027i -0.3732+0.0354i
+0.1520+0.1809i +0.3402+0.0000i +0.3645+0.1426i +0.1164-0.0429i
+0.2196-0.0027i +0.3645-0.1426i +0.5191-0.0000i +0.1951+0.1005i
-0.3732-0.0354i +0.1164+0.0429i +0.1951-0.1005i +0.7143+0.0000i
Press return to continue.
------------------------------------
V is transformation matrix for
a projection onto a subspace R4 :
+0.4264+0.0000i +0.1520-0.1809i +0.2196+0.0027i -0.3732+0.0354i
+0.1520+0.1809i +0.3402+0.0000i +0.3645+0.1426i +0.1164-0.0429i
+0.2196-0.0027i +0.3645-0.1426i +0.5191-0.0000i +0.1951+0.1005i
-0.3732-0.0354i +0.1164+0.0429i +0.1951-0.1005i +0.7143+0.0000i
X :
-1.0 -3.0i
+2.0 -4.0i
-3.0 -5.0i
-1.0 -2.0i
Proj(x) = A * inv(AT*A) * AT * x
Proj(x) = V * x :
-1.0475-2.6443i
+0.4886-4.4384i
-1.6203-5.4855i
-1.1310-1.3276i
Press return to continue.