Mathc complexes/a249
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c03d.c |
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/* ------------------------------------ */
/* Save as : c03d.c */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
#define RB R3
#define CB C1
/* ------------------------------------ */
/* ------------------------------------ */
int main(void)
{
double b[RB*(CB*C2)]={
+0.072961373391,-0.506437768240,
-1.373390557940,-0.231759656652,
+1.0,+0.0
};
double x[RB*(CB*C2)]={
-1,-3,
2,-4,
-3,-5,
};
nb_Z a;
double **B = ca_A_mZ(b, i_mZ(RB,CB));
double **BT = i_mZ(CB,RB);
double **BTB = i_mZ(CB,CB); // BT*B
double **invBTB = i_mZ(CB,CB); // inv(BT*B)
double **invBTB_BT = i_mZ(CB,RB); // inv(BT*B)*BT
double **B_invBTB_BT = i_mZ(RB,RB); // B_inv(BT*B)*BT
double **Id = eye_mZ( i_mZ(RB,RB));
double **V = i_mZ(RB,RB); // V = Id - (B_inv(BT*B)*BT)
double **X = ca_A_mZ(x, i_mZ(RB,C1));
double **VX = i_mZ(RB,C1);
clrscrn();
printf(" B is a basis for the orthogonal complement of A : \n\n"
" Find a transformation matrix for \n"
" a projection onto R%d : \n\n"
" Proj(x) = [Id-(B*inv(BT*B)*BT)] * x \n\n",RB);
printf(" B :");
p_mZ(B,S5,P4,S5,P4,C7);
stop();
clrscrn();
printf(" BT :");
p_mZ(ctranspose_mZ(B,BT),S5,P4,S5,P4,C7);
printf(" BTB :");
p_mZ(mul_mZ(BT,B,BTB),S5,P4,S5,P4,C7);
printf(" inv(BT*B) :");
a = i_Z(BTB[R1][C1],BTB[R1][C2]);
invBTB[R1][C1] = inv_Z(a).r;
invBTB[R1][C2] = inv_Z(a).i;
p_mZ(invBTB,S5,P4,S5,P4,C7);
printf(" inv(BT*B)*BT :");
p_mZ(mul_mZ(invBTB,BT,invBTB_BT),S5,P4,S5,P4,C7);
printf(" B*inv(BT*B)*BT :");
p_mZ(mul_mZ(B,invBTB_BT,B_invBTB_BT),S5,P4,S5,P4,C7);
printf(" V = Id - (B*inv(BT*B)*BT) :");
p_mZ(sub_mZ(Id,B_invBTB_BT,V),S5,P4,S5,P4,C7);
stop();
clrscrn();
printf(" V is transformation matrix for \n"
" a projection onto a subspace R%d :\n\n",RB);
p_mZ(V,S5,P4,S5,P4,C7);
printf(" X :");
p_mZ(X,S5,P1,S5,P1,C7);
printf(" Proj(x) = [Id-(B*inv(BT*B)*BT)] * x \n\n");
printf(" Proj(x) = V * x :");
p_mZ(mul_mZ(V,X,VX),S5,P4,S5,P4,C7);
stop();
f_mZ(B);
f_mZ(BT);
f_mZ(BTB); // BT*B
f_mZ(invBTB); // inv(BT*B)
f_mZ(invBTB_BT); // inv(BT*B)*BT
f_mZ(V); // B*inv(BT*B)*BT
f_mZ(X);
f_mZ(VX);
return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */
Trouver une projection sur un sous-espace vectoriel par une application linéaire :
- B est une base pour le complément orthogonal de A. Trouver une matrice V qui projette un vecteur x sur R3.
Proj(x) = V * x
V = Id - (B * inv(BT*B) * BT) .
Exemple de sortie écran :
------------------------------------
B is a basis for the orthogonal complement of A :
Find a transformation matrix for
a projection onto R3 :
Proj(x) = [Id-(B*inv(BT*B)*BT)] * x
B :
+0.0730-0.5064i
-1.3734-0.2318i
+1.0000+0.0000i
Press return to continue.
------------------------------------
BT :
+0.0730+0.5064i -1.3734+0.2318i +1.0000-0.0000i
BTB :
+3.2017+0.0000i
inv(BT*B) :
+0.3123-0.0000i
inv(BT*B)*BT :
+0.0228+0.1582i -0.4290+0.0724i +0.3123+0.0000i
B*inv(BT*B)*BT :
+0.0818+0.0000i +0.0054+0.2225i +0.0228-0.1582i
+0.0054-0.2225i +0.6059+0.0000i -0.4290-0.0724i
+0.0228+0.1582i -0.4290+0.0724i +0.3123+0.0000i
V = Id - (B*inv(BT*B)*BT) :
+0.9182+0.0000i -0.0054-0.2225i -0.0228+0.1582i
-0.0054+0.2225i +0.3941+0.0000i +0.4290+0.0724i
-0.0228-0.1582i +0.4290-0.0724i +0.6877+0.0000i
Press return to continue.
------------------------------------
V is transformation matrix for
a projection onto a subspace R3 :
+0.9182+0.0000i -0.0054-0.2225i -0.0228+0.1582i
-0.0054+0.2225i +0.3941+0.0000i +0.4290+0.0724i
-0.0228-0.1582i +0.4290-0.0724i +0.6877+0.0000i
X :
-1.0 -3.0i
+2.0 -4.0i
-3.0 -5.0i
Proj(x) = [Id-(B*inv(BT*B)*BT)] * x
Proj(x) = V * x :
-0.9598-3.5389i
+0.5362-4.1448i
-1.9464-5.0724i
Press return to continue.