Mathc complexes/03t
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c00a.c |
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/* ------------------------------------ */
/* Save as : c00a.c */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
#define RCA RC3
#define CX C1
/* ------------------------------------ */
/* ------------------------------------ */
int main(void)
{
double a[RCA*(RCA*C2)]={
+3,1, -4,1, -2,1,
+5,2, -3,2, -0,2,
+6,3, -0,3, -3,3
};
double x_B[RCA*(CX*C2)]={
+1,+1,
+2,+2,
+3,+3
};
double b[RCA*(RCA*C2)]={
+1,+2, +2,+5, +6,+2,
+3,+3, +2,+4, +1,+3,
+5,+4, +5,+3, +3,+4,
};
double **A = ca_A_mZ(a, i_mZ(RCA,RCA));
double **B = ca_A_mZ(b, i_mZ(RCA,RCA));
double **D = i_mZ(RCA,RCA) ;
double **X_B = ca_A_mZ(x_B, i_mZ(RCA,CX));
double **X_S = mul_mZ(B,X_B, i_mZ(RCA,CX));
double **T = i_mZ(RCA,CX) ;
double **invB = inv_mZ(B, i_mZ(RCA,RCA));
double **invBA = i_mZ(RCA,RCA) ;
double **DX_B = i_mZ(RCA,CX) ;
/* D = invB*A*B */
mul_mZ(invB,A,invBA);
mul_mZ(invBA,B,D);
/* [T(x)]_B = D*x_B */
mul_mZ(D,X_B,DX_B);
clrscrn();
printf(" In the Standard basis the linear application is :\n\n");
printf(" T(x_S) = A x_S");
p_mZ(mul_mZ(A,X_S,T), S10,P2, S8,P2, C4);
printf("with\n\n"
"x_S");
p_mZ(X_S, S10,P2, S8,P2, C4);
printf("A");
p_mZ(A, S10,P2, S8,P2, C4);
stop();
clrscrn();
printf(" In the B basis the linear application is :\n\n"
" [T(x_B)]_B = D*x_B with D = (invB A B)");
p_mZ(DX_B, S10,P2, S8,P2, C4);
printf("with\n\n"
"x_B");
p_mZ(X_B, S10,P2, S8,P2, C4);
printf("D = (invB A B)");
p_mZ(D, S10,P2, S8,P2, C4);
stop();
clrscrn();
printf(" [T(x_B)]_B = D*x_B with D = (invB A B)");
p_mZ(DX_B, S10,P2, S8,P2, C4);
printf(" Remark : x_S = B x_B\n\n"
" [D*x_B]\n"
" B [D*x_B] = B [(InvB A B) x_B] = (A B)*x_B = A (B x_B) = A x_S \n\n"
" B*[D*x_B] = A x_S");
p_mZ(mul_mZ(B,DX_B,T), S10,P2, S8,P2, C4);
printf(" T(x_S) = A x_S");
p_mZ(mul_mZ(A,X_S,T), S10,P2, S8,P2, C4);
stop();
f_mZ(A);
f_mZ(B);
f_mZ(D);
f_mZ(X_B);
f_mZ(X_S);
f_mZ(T);
f_mZ(invB);
f_mZ(invBA);
f_mZ(DX_B);
return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */
Vérifions si les résultats sont compatibles
Exemple de sortie écran :
In the Standard basis the linear application is :
T(x_S) = A x_S
-66.00 -92.00i
-179.00 +109.00i
-327.00 +99.00i
with
x_S
+5.00 +41.00i
-10.00 +30.00i
+2.00 +46.00i
A
+3.00 +1.00i -4.00 +1.00i -2.00 +1.00i
+5.00 +2.00i -3.00 +2.00i +0.00 +2.00i
+6.00 +3.00i +0.00 +3.00i -3.00 +3.00i
Press return to continue.
In the B basis the linear application is :
[T(x_B)]_B = D*x_B with D = (invB A B)
-35.06 +88.21i
+15.37 -29.92i
-11.59 -17.32i
with
x_B
+1.00 +1.00i
+2.00 +2.00i
+3.00 +3.00i
D = (invB A B)
-0.35 +10.10i +3.36 +13.60i +6.74 +8.11i
+1.03 -1.38i -0.87 -3.77i -2.19 -4.57i
-3.30 -1.70i -2.91 -0.10i -1.78 -0.33i
Press return to continue.
[T(x_B)]_B = D*x_B with D = (invB A B)
-35.06 +88.21i
+15.37 -29.92i
-11.59 -17.32i
Remark : x_S = B x_B
[D*x_B]
B [D*x_B] = B [(InvB A B) x_B] = (A B)*x_B = A (B x_B) = A x_S
B*[D*x_B] = A x_S
-66.00 -92.00i
-179.00 +109.00i
-327.00 +99.00i
T(x_S) = A x_S
-66.00 -92.00i
-179.00 +109.00i
-327.00 +99.00i
Press return to continue.