Mathc complexes/a254
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c05a.c |
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/* ------------------------------------ */
/* Save as : c05a.c */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
#define RA R5
#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,
5, 4, -3,-2
};
double x[RA*(C1*C2)]={
-1,-3,
2,-4,
-3,-5,
-1,-2,
-2,-3
};
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 R5
Find a transformation matrix for
a projection onto R5 :
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
+5.0 +4.0i -3.0 -2.0i
Press return to continue.
------------------------------------
AT :
-2.0 +3.0i +1.0 -0.0i +0.0 -1.0i +3.0 -5.0i +5.0 -4.0i
-4.0 +2.0i -3.0 +5.0i -6.0 +4.0i -1.0 -0.0i -3.0 +2.0i
ATA :
+90.0 +0.0i -19.0 +0.0i
-19.0 +0.0i +120.0 +0.0i
inv(AT*A) :
+0.0115+0.0000i +0.0018+0.0000i
+0.0018+0.0000i +0.0086+0.0000i
inv(AT*A)*AT :
-0.0303+0.0381i +0.0060+0.0091i -0.0109-0.0042i +0.0327-0.0575i +0.0520-0.0423i
-0.0381+0.0227i -0.0240+0.0431i -0.0517+0.0327i -0.0032-0.0091i -0.0168+0.0100i
V = A*inv(AT*A)*AT :
+0.3728+0.0000i +0.1976-0.1606i +0.2814+0.0140i -0.2433+0.0597i -0.1441-0.0777i
+0.1976+0.1606i +0.2937+0.0000i +0.3076+0.1564i -0.0034-0.0144i +0.1521+0.0116i
+0.2814-0.0140i +0.3076-0.1564i +0.4453+0.0000i +0.0400+0.0999i +0.1828+0.0593i
-0.2433-0.0597i -0.0034+0.0144i +0.0400-0.0999i +0.3885-0.0000i +0.3845+0.1231i
-0.1441+0.0777i +0.1521-0.0116i +0.1828-0.0593i +0.3845-0.1231i +0.4997-0.0000i
Press return to continue.
------------------------------------
V is transformation matrix for
a projection onto a subspace R5 :
+0.3728+0.0000i +0.1976-0.1606i +0.2814+0.0140i -0.2433+0.0597i -0.1441-0.0777i
+0.1976+0.1606i +0.2937+0.0000i +0.3076+0.1564i -0.0034-0.0144i +0.1521+0.0116i
+0.2814-0.0140i +0.3076-0.1564i +0.4453+0.0000i +0.0400+0.0999i +0.1828+0.0593i
-0.2433-0.0597i -0.0034+0.0144i +0.0400-0.0999i +0.3885-0.0000i +0.3845+0.1231i
-0.1441+0.0777i +0.1521-0.0116i +0.1828-0.0593i +0.3845-0.1231i +0.4997-0.0000i
X :
-1.0 -3.0i
+2.0 -4.0i
-3.0 -5.0i
-1.0 -2.0i
-2.0 -3.0i
Proj(x) = A * inv(AT*A) * AT * x
Proj(x) = V * x :
-0.9768-2.6649i
+0.4362-4.3941i
-1.6976-5.4468i
-1.2929-1.2455i
-1.8398-3.1581i
Press return to continue.