Mathc complexes/a89
Installer et compiler ces fichiers dans votre répertoire de travail.
|
c03c.c |
|---|
/* ------------------------------------ */
/* Xave as : c03c.c */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
#define RA R3
#define CA C2
#define FACTOR_E +1.E-2
/* ------------------------------------ */
/* ------------------------------------ */
int main(void)
{
int r = RA;
int c = CA;
double a[RA*(CA*C2)] ={ 1,2, 3,4,
5,4, 1,3,
7,2, 5,1};
double **A = ca_A_mZ(a, i_mZ(r,c));
double **A_T = ctranspose_mZ(A,i_mZ(c,r));
double **V = i_mZ(r,c);
double **V_T = i_mZ(c,r);
double **U = i_mZ(r,c);
double **U_T = i_mZ(c,r); // :c,r
double **U_TA = i_mZ(c,c); // c,r r,c :c,c
double **U_TAr = i_mZ(c,r); // c,r :c,r
double **X = i_mZ(c,c); // c,r r,c :c,c U_TArV
double **invX = i_mZ(c,c); // c,r r,c :c,c invX
double **VinvX = i_mZ(r,c);
double **Pinv = i_mZ(r,r);
double **PinvA = i_mZ(r,c); // r,c | r,r
clrscrn();
printf(" A :");
p_mZ(A, S10,P2, S8,P2, C3);
printf(" U :");
X_U_mZ(A_T,U,FACTOR_E);
p_mZ(U, S10,P4, S8,P4, C3);
printf(" V :");
X_V_mZ(A_T,V,FACTOR_E);
p_mZ(V, S10,P4, S8,P4, C3);
ctranspose_mZ(U,U_T);
ctranspose_mZ(V,V_T);
stop();
clrscrn();
printf(" X = U_T * A * V :");
mul_mZ(U_T, A, U_TA); // U_TA : c,c
c_mZ(U_TA, U_TAr); // U_TAr : c,r
mul_mZ(U_TAr, V, X); // V : r,c
p_mZ(X, S11,P4, S9,P4, C3);
printf(" invX :");
X_inv_mZ(X, invX);
pE_mZ(invX, S10,P4, S8,P4, C3);
stop();
clrscrn();
printf(" Copy/Past into the octave window.\n\n");
p_Octave_mZ(A,"A",P0, P0);
printf(" format short e\n");
printf(" pinv(A)\n\n");
stop();
clrscrn();
printf(" Pinv = V * invX * U_T:");
mul_mZ(V,invX,VinvX);
mul_mZ(VinvX,U_T,Pinv);
pE_mZ(Pinv, S10,P4, S8,P4, C2);
stop();
clrscrn();
printf(" Ide = Pinv * A ");
mul_mZ(Pinv,A,PinvA);
p_mZ(PinvA, S10,P4, S8,P4, C3);
stop();
f_mZ(A);
f_mZ(A_T);
f_mZ(V);
f_mZ(V_T);
f_mZ(U);
f_mZ(U_T);
f_mZ(U_TA);
f_mZ(U_TAr);
f_mZ(X);
f_mZ(invX);
f_mZ(VinvX);
f_mZ(Pinv);
f_mZ(PinvA);
return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */
Diagonaliser une matrice avec un nombre de lignes supérieur ou égal aux nombres de colonnes Exemple de sortie écran :
A :
+1.00 +2.00i +3.00 +4.00i
+5.00 +4.00i +1.00 +3.00i
+7.00 +2.00i +5.00 +1.00i
U :
+0.2940 +0.2567i -0.6119 +0.4960i
+0.4702 +0.3112i +0.1304 -0.5579i
+0.7278 +0.0000i +0.2265 -0.0000i
V :
+0.7964 +0.0735i -0.5977 -0.0552i
+0.6002 -0.0000i +0.7998 +0.0000i
+0.0000 +0.0000i +0.0000 +0.0000i
Press return to continue.
X = U_T * A * V :
+11.5820 +3.7205i +0.0000 -0.0000i
-0.0000 +0.0000i -0.3277 -3.4507i
invX :
+7.8265e-02-2.5141e-02i +0.0000e+00+0.0000e+00i
+0.0000e+00+0.0000e+00i -2.7275e-02+2.8721e-01i
Press return to continue.
Copy/Past into the octave window.
A=[
+1+2*i,+3+4*i;
+5+4*i,+1+3*i;
+7+2*i,+5+1*i]
format short e
pinv(A)
Press return to continue.
Pinv = V * invX * U_T:
-8.8864e-02+6.7492e-02i +1.2486e-01-3.0934e-02i
+1.3723e-01-1.4623e-01i -1.1361e-01-3.9370e-03i
+0.0000e+00+0.0000e+00i +0.0000e+00+0.0000e+00i
+5.3993e-02-4.8931e-02i
+2.9246e-02+4.1057e-02i
+0.0000e+00+0.0000e+00i
Press return to continue.
Ide = Pinv * A
+1.0000 +0.0000i -0.0000 +0.0000i
-0.0000 -0.0000i +1.0000 -0.0000i
+0.0000 +0.0000i +0.0000 +0.0000i
Press return to continue.