Mathc matrices/c30d


Sommaire


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Crystal Clear mimetype source c.png c02a.c
'
/* ------------------------------------ */
/*  Save as :   c02a.c               */
/* ------------------------------------ */
#include      "v_a.h"
/* ------------------------------------ */
int main(void)
{
double a[R3*C6]={
 -36,  +21,  -14,    1,0,0,
 -38,  +13,  +27,    0,1,0,
 +41,   -6,  -44,    0,0,1,
};

double inva[R3*C3]={
 -410.00/7165.00,    +1008.00/7165.00,     +749.00/7165.00, 
 -565.00/7165.00,    +2158.00/7165.00,    +1504.00/7165.00, 
  -61.00/1433.00,     +129.00/1433.00,      +66.00/1433.00 
};

double **A    = ca_A_mR(a,   i_mR(R3,C6));
double **invA = ca_A_mR(inva,i_mR(R3,C3));
double **T    =              i_mR(R3,C3);


int i  = 1;

/* 1----------------------------------- 
     -36.00      +21.00      -14.00       +1.00       +0.00       +0.00 
     -38.00      +13.00      +27.00       +0.00       +1.00       +0.00 
     +41.00       -6.00      -44.00       +0.00       +0.00       +1.00 
 ------------------------------------ */
     clrscrn();
     printf(" (%d) \n\n",i++);
     p_mR(A,S11,P2,C6);        
     printf(" R2 = -36*R2   \n");   mulR_mR(A,-36.,R2);
     printf(" R3 = -36*R3 \n\n");   mulR_mR(A,-36.,R3);          
     printf(" R2 =  38*R1 + R2 \n");addR_mR(A, 38.,R1,R2);
     printf(" R3 = -41*R1 + R3 \n");addR_mR(A,-41.,R1,R3);                              
     p_mR(A,S11,P2,C6);
     stop();

/* 2----------------------------------- 
     -36.00      +21.00      -14.00       +1.00       +0.00       +0.00 
      +0.00     +330.00    -1504.00      +38.00      -36.00       +0.00 
      +0.00     -645.00    +2158.00      -41.00       -0.00      -36.00 
   ------------------------------------ */
     clrscrn();
     printf(" (%d) \n\n",i++);
     p_mR(A,S11,P2,C6);    
     printf(" R2 =  1./2.*R2 \n");mulR_mR(A, 1/2., R2);        
     p_mR(A,S11,P2,C6);
     stop();

/* 3----------------------------------- 
     -36.00      +21.00      -14.00       +1.00       +0.00       +0.00 
      +0.00     +165.00     -752.00      +19.00      -18.00       +0.00 
      +0.00     -645.00    +2158.00      -41.00       -0.00      -36.00 
   ------------------------------------ */
     clrscrn();
     printf(" (%d) \n\n",i++);
     p_mR(A,S11,P2,C6);      
     printf(" R3 = 11.*R3  (165/645 = 11/43)\n"); mulR_mR(A,11.,R3);              
     printf(" R3 = 43.*R2 + R3  \n");             addR_mR(A,43.,R2,R3);                                        
     p_mR(A,S11,P2,C6);
     stop();

/* 4----------------------------------- 
     -36.00      +21.00      -14.00       +1.00       +0.00       +0.00 
      +0.00     +165.00     -752.00      +19.00      -18.00       +0.00 
      +0.00       +0.00    -8598.00     +366.00     -774.00     -396.00 
   ------------------------------------ */
     clrscrn();
     printf(" (%d) \n\n",i++);
     p_mR(A,S11,P2,C6);    
     printf(" R3 =  1./6.*R3 \n");mulR_mR(A,1./6.,R3);   
     p_mR(A,S11,P2,C6);
     stop();
     
/* 5----------------------------------- 
     -36.00      +21.00      -14.00       +1.00       +0.00       +0.00 
      +0.00     +165.00     -752.00      +19.00      -18.00       +0.00 
      +0.00       +0.00    -1433.00      +61.00     -129.00      -66.00 
      
   ------------------------------------ */
     clrscrn();
     printf(" (%d) \n\n",i++);
     p_mR(A,S11,P2,C6);    
     printf(" R1 = 1433.*R1  \n");  mulR_mR(A,1433.,R1);     
     printf(" R2 = 1433.*R2  \n");  mulR_mR(A,1433.,R2);     
     printf(" R3 =   -1.*R3\n\n");  mulR_mR(A,-1.,R3);            
     printf(" R1 =  14.*R3 + R1\n");addR_mR(A,14.,R3,R1);     
     printf(" R2 = 752.*R3 + R2\n");addR_mR(A,752.,R3,R2);    
     p_mR(A,S11,P2,C6);
     stop();

/* 6----------------------------------- 
  -51588.00   +30093.00       +0.00     +579.00    +1806.00     +924.00 
      +0.00  +236445.00       +0.00   -18645.00   +71214.00   +49632.00 
      -0.00       -0.00    +1433.00      -61.00     +129.00      +66.00 
   ------------------------------------ */
     clrscrn();
     printf(" (%d) \n\n",i++);
     p_mR(A,S11,P2,C6);                                   
     printf(" R2 =  1./33.*R2 \n");mulR_mR(A,1./33.,R2);                                      
     p_mR(A,S11,P2,C6);
     stop();

/* 7----------------------------------- 
   -51588.000   +30093.000       +0.000   -15777.000
       +0.000    +7165.000       +0.000   -81009.000
       +0.000       +0.000    +1433.000    -5733.000
   ------------------------------------ */
     clrscrn();
     printf(" (%d) \n\n",i++);
     p_mR(A,S11,P2,C6);                               
     printf(" R1 = -5.*R1 (30093/7165 = 21/5)\n");mulR_mR(A,-5.,R1);                                             
     printf(" R1 = 21.*R2 + R1  \n");             addR_mR(A,21.,R2,R1);                                        
     p_mR(A,S11,P2,C6);
     stop();

/* 8----------------------------------- 
 +257940.00       +0.00       +0.00   -14760.00   +36288.00   +26964.00 
      +0.00    +7165.00       +0.00     -565.00    +2158.00    +1504.00 
      -0.00       -0.00    +1433.00      -61.00     +129.00      +66.00 
   ------------------------------------ */
     clrscrn();
     printf(" (%d) \n\n",i++);
     p_mR(A,S11,P2,C6);                                   
     printf(" R1 =  1./36.*R1 \n");mulR_mR(A,1./36.,R1);                                      
     p_mR(A,S11,P2,C6);
     stop();
     
/* 9-----------------------------------      
   +7165.00       +0.00       +0.00     -410.00    +1008.00     +749.00 
      +0.00    +7165.00       +0.00     -565.00    +2158.00    +1504.00 
      -0.00       -0.00    +1433.00      -61.00     +129.00      +66.00 
    ------------------------------------ */    
     clrscrn();
     printf(" A : ");
     ca_A_mR(a, A);
     p_mR(A,S11,P2,C6);
     
     printf(" A : inv_mR(invA, T);        [see : double inva[R3*C3] ]");
     inv_mR(invA, T);
     p_mR(T, S11, P2, C6);
     stop();
   
     
  f_mR(A);
  f_mR(invA);
  f_mR(T);
    
  return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */


Le but de ces exemples est d'inverser une matrice sans faire apparaître de fraction. La matrice double inva[R3*C3] donne le résultat calculé dans le fichier et permet de vérifier que inv(invA) = A.


Exemple de sortie écran :
 ------------------------------------ 
 (1) 


     -36.00      +21.00      -14.00       +1.00       +0.00       +0.00 
     -38.00      +13.00      +27.00       +0.00       +1.00       +0.00 
     +41.00       -6.00      -44.00       +0.00       +0.00       +1.00 

 R2 = -36*R2   
 R3 = -36*R3 

 R2 =  38*R1 + R2 
 R3 = -41*R1 + R3 

     -36.00      +21.00      -14.00       +1.00       +0.00       +0.00 
      +0.00     +330.00    -1504.00      +38.00      -36.00       +0.00 
      +0.00     -645.00    +2158.00      -41.00       -0.00      -36.00 

 Press return to continue. 


 ------------------------------------ 
 (2) 


     -36.00      +21.00      -14.00       +1.00       +0.00       +0.00 
      +0.00     +330.00    -1504.00      +38.00      -36.00       +0.00 
      +0.00     -645.00    +2158.00      -41.00       -0.00      -36.00 

 R2 =  1./2.*R2 

     -36.00      +21.00      -14.00       +1.00       +0.00       +0.00 
      +0.00     +165.00     -752.00      +19.00      -18.00       +0.00 
      +0.00     -645.00    +2158.00      -41.00       -0.00      -36.00 

 Press return to continue. 


 ------------------------------------ 
 (3) 


     -36.00      +21.00      -14.00       +1.00       +0.00       +0.00 
      +0.00     +165.00     -752.00      +19.00      -18.00       +0.00 
      +0.00     -645.00    +2158.00      -41.00       -0.00      -36.00 

 R3 = 11.*R3  (165/645 = 11/43)
 R3 = 43.*R2 + R3  

     -36.00      +21.00      -14.00       +1.00       +0.00       +0.00 
      +0.00     +165.00     -752.00      +19.00      -18.00       +0.00 
      +0.00       +0.00    -8598.00     +366.00     -774.00     -396.00 

 Press return to continue. 



 ------------------------------------ 
 (4) 


     -36.00      +21.00      -14.00       +1.00       +0.00       +0.00 
      +0.00     +165.00     -752.00      +19.00      -18.00       +0.00 
      +0.00       +0.00    -8598.00     +366.00     -774.00     -396.00 

 R3 =  1./6.*R3 

     -36.00      +21.00      -14.00       +1.00       +0.00       +0.00 
      +0.00     +165.00     -752.00      +19.00      -18.00       +0.00 
      +0.00       +0.00    -1433.00      +61.00     -129.00      -66.00 

 Press return to continue. 




 ------------------------------------ 
 (5) 


     -36.00      +21.00      -14.00       +1.00       +0.00       +0.00 
      +0.00     +165.00     -752.00      +19.00      -18.00       +0.00 
      +0.00       +0.00    -1433.00      +61.00     -129.00      -66.00 

 R1 = 1433.*R1  
 R2 = 1433.*R2  
 R3 =   -1.*R3

 R1 =  14.*R3 + R1
 R2 = 752.*R3 + R2

  -51588.00   +30093.00       +0.00     +579.00    +1806.00     +924.00 
      +0.00  +236445.00       +0.00   -18645.00   +71214.00   +49632.00 
      -0.00       -0.00    +1433.00      -61.00     +129.00      +66.00 

 Press return to continue. 



 ------------------------------------ 
 (6) 


  -51588.00   +30093.00       +0.00     +579.00    +1806.00     +924.00 
      +0.00  +236445.00       +0.00   -18645.00   +71214.00   +49632.00 
      -0.00       -0.00    +1433.00      -61.00     +129.00      +66.00 

 R2 =  1./33.*R2 

  -51588.00   +30093.00       +0.00     +579.00    +1806.00     +924.00 
      +0.00    +7165.00       +0.00     -565.00    +2158.00    +1504.00 
      -0.00       -0.00    +1433.00      -61.00     +129.00      +66.00 

 Press return to continue. 



 ------------------------------------ 
 (7) 


  -51588.00   +30093.00       +0.00     +579.00    +1806.00     +924.00 
      +0.00    +7165.00       +0.00     -565.00    +2158.00    +1504.00 
      -0.00       -0.00    +1433.00      -61.00     +129.00      +66.00 

 R1 = -5.*R1 (30093/7165 = 21/5)
 R1 = 21.*R2 + R1  

 +257940.00       +0.00       +0.00   -14760.00   +36288.00   +26964.00 
      +0.00    +7165.00       +0.00     -565.00    +2158.00    +1504.00 
      -0.00       -0.00    +1433.00      -61.00     +129.00      +66.00 

 Press return to continue. 


 ------------------------------------ 
 (8) 


 +257940.00       +0.00       +0.00   -14760.00   +36288.00   +26964.00 
      +0.00    +7165.00       +0.00     -565.00    +2158.00    +1504.00 
      -0.00       -0.00    +1433.00      -61.00     +129.00      +66.00 

 R1 =  1./36.*R1 

   +7165.00       +0.00       +0.00     -410.00    +1008.00     +749.00 
      +0.00    +7165.00       +0.00     -565.00    +2158.00    +1504.00 
      -0.00       -0.00    +1433.00      -61.00     +129.00      +66.00 

 Press return to continue. 


 ------------------------------------ 
 A : 
     -36.00      +21.00      -14.00       +1.00       +0.00       +0.00 
     -38.00      +13.00      +27.00       +0.00       +1.00       +0.00 
     +41.00       -6.00      -44.00       +0.00       +0.00       +1.00 

 A : inv_mR(invA, T);        [see : double inva[R3*C3] ]
     -36.00      +21.00      -14.00 
     -38.00      +13.00      +27.00 
     +41.00       -6.00      -44.00 

 Press return to continue.