Linear Algebra and the C Language/a0mr

/* ------------------------------------ */
/*  Save as :  c00d.c                   */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
#define   RA R4
#define   CA C4

#define   RX R4
#define   CX C1
/* ------------------------------------ */
/* ------------------------------------ */
int main(void)
{
double a[RA*CA]={
    +3, -4, -2, -1,
    +5, -3, -0, -2,      
    +6, -0, -3, -2,
    +3, -3, -1, -3   
};

double x_B[RX*CX]={
   +1,
   +2, 
   +3, 
   +4 
};

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

double **A     = ca_A_mR(a,       i_mR(RA,CA));
double **B     = ca_A_mR(b,       i_mR(RA,CA));
double **x_b   = ca_A_mR(x_B,     i_mR(RX,CX));
double **x_s   =  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 =  mul_mR(invB,A,  i_mR(RA,CA));
double **D     =  mul_mR(invBA,B, i_mR(RA,CA));
double **Dx_b  =  mul_mR(D,x_b,   i_mR(RA,CX));
  
  clrscrn();
  printf(" In the Standard basis the linear application is:\n\n" 
         " With A :");
  p_mR(A,S6,P2,C7);
  
  printf(" And x_s:");
  p_mR(x_s,S6,P2,C7);
  
  printf(" T(x_s) = A x_s");
  p_mR(mul_mR(A,x_s,T),S8,P2,C7);

  stop();
  
  clrscrn();
   printf(" In the \"B\" basis the linear application is: \n\n"
         " With D:     (InvB A B)");
  p_mR(D,S7,P2,C7); 
  
  printf(" And x_b:");
  p_mR(x_b,S7,P2,C7);
  
  printf(" [T(x_b)]_b = D x_b");
  p_mR(mul_mR(D,x_b,Dx_b),S8,P2,C7);
  stop();   
    
  clrscrn(); 
  
  printf("               A                    \n"
         "       x_s -----------> T(x_s)      \n" 
         "        ^                 ^         \n"
         "        |                 |         \n"
         "     B  |                 |   B     \n"
         "        |       D         |         \n"
         "       x_b -----------> [T(x_b)]_b\n\n"
         
         " Verify if:           B [T(x_b)]_b = T(x_s)\n\n");         
         
  printf(" B [T(x_b)]_b:");
  p_mR(mul_mR(B,Dx_b,T),S8,P2,C7);
  
  printf(" T(x_s):");
  p_mR(mul_mR(A,x_s,T),S8,P2,C7);       
  stop();
  
  f_mR(A);
  f_mR(B);
  f_mR(D);  
  
  f_mR(x_b);
  f_mR(x_s);
  f_mR(T);  
  
  f_mR(invB);  
  f_mR(invBA);  

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

                                                                                       
 In the Standard basis the linear application is:

 With A :
 +3.00  -4.00  -2.00  -1.00 
 +5.00  -3.00  +0.00  -2.00 
 +6.00  +0.00  -3.00  -2.00 
 +3.00  -3.00  -1.00  -3.00 

 And x_s:
+47.00 
+34.00 
+48.00 
+37.00 

 T(x_s) = A x_s
 -128.00 
  +59.00 
  +64.00 
 -120.00 

 Press return to continue. 


 In the "B" basis the linear application is: 

 With D:     (InvB A B)
-115.00  -89.00 -118.00 -304.00 
+107.00  +82.20 +112.40 +289.20 
 -48.00  -37.80  -50.60 -126.80 
 +27.50  +22.40  +33.80  +77.40 

 And x_b:
  +1.00 
  +2.00 
  +3.00 
  +4.00 

 [T(x_b)]_b = D x_b
-1863.00 
+1765.40 
 -782.60 
 +483.30 

 Press return to continue. 


               A                    
       x_s -----------> T(x_s)      
        ^                 ^         
        |                 |         
     B  |                 |   B     
        |       D         |         
       x_b -----------> [T(x_b)]_b

 Verify if:           B [T(x_b)]_b = T(x_s)

 B [T(x_b)]_b:
 -128.00 
  +59.00 
  +64.00 
 -120.00 

 T(x_s):
 -128.00 
  +59.00 
  +64.00 
 -120.00 

 Press return to continue.