Mathc complexes/c083b

Application

Installer et compiler ces fichiers dans votre répertoire de travail.

	c01b.c

/* ------------------------------------ */
/*  Save as :   c01b.c                 */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
void fun(int r)
{
double **A =      i_mZ(r,r);
double **Inv =    i_mZ(r,r);
double **B = r_mZ(i_mZ(r,C5),99.);
double **X =      i_mZ(r,C5);
double **T =      i_mZ(r,C5);

 do
  {
   r_mZ(A,99.);
   printf(".");
  }while(!det_Z(A).r);

  clrscrn();

  printf("                                                 \n");
  printf(" Linear systems with common coefficient matrix.\n\n");
  printf("                Ax1=b1                           \n");
  printf("                Ax2=b2                           \n");
  printf("                ...                              \n");
  printf("                Axn=bn                         \n\n");
  printf(" We can write these equalities in this maner.  \n\n");
  printf("    A|x1|x2|...|xn| = b1|b2|...|bn|            \n\n");
  printf("  or simply :                                  \n\n");
  printf("              AX = B                           \n\n");
  printf("  where B = b1|b2|...|bn                       \n\n");
  printf("  and   X = x1|x2|...|xn                       \n\n");
  getchar();

  clrscrn();
  printf(" We want to find X such as,   \n\n");
  printf("         AX = B               \n\n");
  printf(" If A is a square matrix and, \n\n");
  printf(" If A has an inverse matrix,  \n\n");
  printf(" you can find X by this method\n\n");
  printf("         X = inv(A) B       \n\n\n");
  printf(" To verify the result you can \n\n");
  printf(" multiply the matrix A by X.  \n\n");
  printf(" You must refind B.  \n\n");
  getchar();

  clrscrn();
  printf(" A :\n");
  p_mZ(A, S5,P0, S4,P0, C6);
  printf("       b1             b2         ...          bn");
  p_mZ(B, S8,P0, S4,P0, C6);
  getchar();

  clrscrn();
  printf(" inv(A) :");
  inv_mZ(A,Inv);
  pE_mZ(Inv, S1,P4, S1,P4, C3);
  printf(" X = inv(A) * B :\n");
  printf("      x1              x2         ...          xn");
  mul_mZ(Inv,B,X);
  p_mZ(X, S6,P4, S5,P4, C4);
  getchar();

  clrscrn();
  printf("       b1             b2          ...          bn");
  p_mZ(B, S8,P0, S4,P0, C6);
  printf("      Ax1            Ax2          ...          Axn");
  mul_mZ(A,X,T);
  p_mZ(T, S8,P0, S4,P0, C6);

  f_mZ(T);
  f_mZ(X);
  f_mZ(B);
  f_mZ(Inv);
  f_mZ(A);
}
/* ------------------------------------ */
int main(void)
{
time_t t;

  srand(time(&t));
do
{
  fun(rp_I(RC3)+RC1);

} while(stop_w());

  return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */

Nous résolvons un système d'équations, et nous vérifions les calculs.



Exemple de sortie écran :

--------------------------------------                                              
 Linear systems with common coefficient matrix.

                Ax1=b1                           
                Ax2=b2                           
                ...                              
                Axn=bn                         

 We can write these equalities in this maner.  

    A|x1|x2|...|xn| = b1|b2|...|bn|            

  or simply :                                  

              AX = B                           

  where B = b1|b2|...|bn                       

  and   X = x1|x2|...|xn                       

-------------------------------------- 
 We want to find X such as,   

         AX = B               

 If A is a square matrix and, 

 If A has an inverse matrix,  

 you can find X by this method

         X = inv(A) B       


 To verify the result you can 

 multiply the matrix A by X.  

 You must refind B.  


-------------------------------------- 
 A :

  +2  -1i   +8  -7i   +4  +4i 
  +2  -5i   -5  -5i   -3  +2i 
  +6  -9i   +4  -3i   -5  +8i 

       b1             b2         ...          bn
      +8  +4i       +6  +6i       +8  +4i       +2  -1i       +6  -1i 
      -9  -3i       -9  -3i       -7  -5i       +6  +6i       +2  -5i 
      -7  -9i       -3  +6i       -9  -1i       -3  +6i       -3  -7i 

-------------------------------------- 
 inv(A) :
+1.3599e-01-1.8737e-01i -1.0924e-01-2.6287e-01i +8.7837e-02+2.1346e-01i 
-8.0369e-02+3.9115e-02i -1.1129e-01+1.7666e-01i +5.4537e-02-9.6259e-02i 
+1.1497e-01-2.0616e-01i -2.0510e-01-2.3886e-01i +8.2640e-02+1.2054e-01i 

 X = inv(A) * B :
      x1              x2         ...          xn
+3.3383-0.5462i +0.5904+2.2719i +0.7107-0.5777i -0.5379-2.8567i 
-0.5159-1.0817i +1.2287-0.8876i +0.2759+0.1231i -1.4354+1.1668i 
+3.3802-0.0119i +2.0849+2.3521i +1.3626+0.3406i -0.7449-3.0569i 

+0.3265-2.4950i 
-0.6198+1.1319i 
-0.5250-1.7443i 

-------------------------------------- Ax = B ?
       b1             b2          ...          bn
      +8  +4i       +6  +6i       +8  +4i       +2  -1i       +6  -1i 
      -9  -3i       -9  -3i       -7  -5i       +6  +6i       +2  -5i 
      -7  -9i       -3  +6i       -9  -1i       -3  +6i       -3  -7i 

      Ax1            Ax2          ...          Axn
      +8  +4i       +6  +6i       +8  +4i       +2  -1i       +6  -1i 
      -9  -3i       -9  -3i       -7  -5i       +6  +6i       +2  -5i 
      -7  -9i       -3  +6i       -9  -1i       -3  +6i       -3  -7i 


 Press return to continue
 Press X      to stop