Mathc matrices/c24s

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Application


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c03d.c
/* ------------------------------------ */
/*  Save as :  c03d.c                   */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
#define   RA R3
#define   CA C3

#define   RX R3
#define   CX C1
/* ------------------------------------ */
/* ------------------------------------ */
int main(void)
{
double a[RA*CA]={
    +3, -4, -2,  
    +5, -3, -1,
    +4, -3, -1   
};

double x_B[RX*CX]={
   +1,
   +2, 
   +3 
};

double b[RA*CA]={
    +1, +2, +6,   
    +3, +4, +1,
    +5, +5, +2 
};

double **A   = ca_A_mR(a, i_mR(RA,CA));
double **B   = ca_A_mR(b, i_mR(RA,CA));
double **D     =          i_mR(RA,CA) ;

double **X_B = ca_A_mR(x_B,  i_mR(RX,CX));
double **X   = mul_mR(B,X_B, i_mR(RX,CX));
double **T   =               i_mR(RA,CX) ;

double **invB  =  inv_mR(B, i_mR(RA,CA));
double **invBA =            i_mR(RA,CA) ;

double **DX_B  =            i_mR(RA,CX) ;

/* D = invB*A*B        */
  mul_mR(invB,A,invBA);       
  mul_mR(invBA,B,D);
/* [T(x)]_B = D*x_B    */ 
  mul_mR(D,X_B,DX_B);  
  
  clrscrn();  
  printf(" In the Standard basis\n\n"
         " T(x) = A*x");
  p_mR(mul_mR(A,X,T),S8,P2,C7);
  printf(" In the the B basis  with  D = invB*A*B\n\n"
         " [T(x)]_B = D*x_B");
  p_mR(DX_B,S8,P2,C7);      
  printf(" Verify the result if it is the same in the two basis :\n\n"
         " With B*[x_B] = [x]  then B*[D*x_B] = [A*x]\n\n"
         " B*[D*x_B]");
  p_mR(mul_mR(B,DX_B,T),S8,P2,C7);  
  stop();
  
  f_mR(A);
  f_mR(B);
  f_mR(D);  
  
  f_mR(X_B);
  f_mR(X);
  f_mR(T);  
  
  f_mR(invB);  
  f_mR(invBA);  

  f_mR(DX_B);
    
  return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */


 Vérifions si les résultats sont compatibles


Exemple de sortie écran :
 ------------------------------------ 
 In the Standard basis

 T(x) = A*x
  -29.00 
  +52.00 
  +29.00 

 In the the B basis  with  D = invB*A*B

 [T(x)]_B = D*x_B
  -21.62 
  +32.21 
  -11.97 

 Verify the result if it is the same in the two basis :

 With B*[x_B] = [x]  then B*[D*x_B] = [A*x]

 B*[D*x_B]
  -29.00 
  +52.00 
  +29.00 

 Press return to continue.