Linear Algebra and the C Language/a0k0

/* ------------------------------------ */
/*  Save as :   c00a.c                  */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
#define   RA R3
#define   CA C3
#define   Cb C1
/* ------------------------------------ */
int main(void)
{
double ab[RA*(CA+Cb)]={
    +0.4790, -0.1540, -0.5010, -0.1760, 
    +0.9920, -0.7630, -0.5910, -0.3620, 
    -0.8430, +0.7080, +0.0880, -0.0470  
};

double **Ab =   ca_A_mR(ab, i_Abr_Ac_bc_mR(RA,CA,Cb));
double **A  = c_Ab_A_mR(Ab,           i_mR(RA,CA));
double **b  = c_Ab_b_mR(Ab,           i_mR(RA,Cb));

  clrscrn();
  printf(" You have this nonlinear system of equations :\n\n");
  printf("               (x, y, z  [0..2pi])\n");
  printf("\n"); 
  printf(" a sin(x) + b cos(y) + c sin(z) = d\n");
  printf(" e sin(x) + f cos(y) + g sin(z) = h\n");
  printf(" i sin(x) + j cos(y) + k sin(z) = l\n\n\n");
  printf(" We write X = sin(x)  Y = cos(y)  Z = sin(z)\n\n"); 
  printf(" a X + b Y + c Z = d\n");
  printf(" e X + f Y + g Z = h\n");
  printf(" i X + j Y + k Z = l\n\n");  
  printf(" Ab :\n");  
  printf(" a  b  c  d\n");
  printf(" e  f  g  h\n");
  printf(" i  j  k  l\n\n\n"); 
  stop();  
  
  clrscrn();
  printf(" With  A:");
  p_mR(A, S8,P4,C7);
  printf("   And b:");
  p_mR(b, S8,P4,C7);
  printf("      Ab:");
  p_mR(Ab, S8,P4,C7);
  stop();

  clrscrn();
  printf(" Copy/Paste into the octave window.\n\n");
  p_Octave_mR(Ab,"Ab",P4);
  printf("\n rref(Ab,.00000000001)\n\n");

  printf("  gj_TP_mR(Ab):");
  p_mR(gj_TP_mR(Ab), S10,P4,C7);
  printf(" Then X = sin(x) = 1;  Y = cos(y) = 1;  Z = sin(z) = 1\n\n");
  stop();

  f_mR(Ab);
  f_mR(b);
  f_mR(A);
  
  return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */

                                                                                       
 You have this nonlinear system of equations :

               (x, y, z  [0..2pi])

 a sin(x) + b cos(y) + c sin(z) = d
 e sin(x) + f cos(y) + g sin(z) = h
 i sin(x) + j cos(y) + k sin(z) = l


 We write X = sin(x)  Y = cos(y)  Z = sin(z)

 a X + b Y + c Z = d
 e X + f Y + g Z = h
 i X + j Y + k Z = l

 Ab :
 a  b  c  d
 e  f  g  h
 i  j  k  l


 Press return to continue. 


 With  A:
 +0.4790  -0.1540  -0.5010 
 +0.9920  -0.7630  -0.5910 
 -0.8430  +0.7080  +0.0880 

   And b:
 -0.1760 
 -0.3620 
 -0.0470 

      Ab:
 +0.4790  -0.1540  -0.5010  -0.1760 
 +0.9920  -0.7630  -0.5910  -0.3620 
 -0.8430  +0.7080  +0.0880  -0.0470 

 Press return to continue. 


 Copy/Paste into the octave window.

 Ab=[
+0.4790,-0.1540,-0.5010,-0.1760;
+0.9920,-0.7630,-0.5910,-0.3620;
-0.8430,+0.7080,+0.0880,-0.0470]


 rref(Ab,.00000000001)

  gj_TP_mR(Ab):
   +1.0000    +0.0000    +0.0000    +1.0000 
   +0.0000    +1.0000    +0.0000    +1.0000 
   +0.0000    +0.0000    +1.0000    +1.0000 

 Then X = sin(x) = 1;  Y = cos(y) = 1;  Z = sin(z) = 1

 Press return to continue.