Linear Algebra and the C Language/a0d8

Code study: eigs_V_mR();

You must use the algorithm of free variables .
GJ_PP_FreeV_mR(); displays a zero row, introduces the free variable, solves the system, and returns a free vector.
The for loop allows you to calculate all vectors.

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double **eigs_V_mR(
double **A,
double **V
)
{
int i;	
int r = rsize_R(A);
	
double **EValue =              i_mR(r,C1);

double **Ab        = i_Abr_Ac_bc_mR(r,r,C1);
double **b         =           i_mR(r,C1);
double **b_free    =           i_mR(r,r);

double **Ide       =  eye_mR(  i_mR(r,r));
double **sIde      =           i_mR(r,r);
double **AmnssIde  =           i_mR(r,r);

  eigs_mR(A,EValue);                         // Compute the eigenvalues
  
  for(i = R1; i <= rsize_R(EValue); i++)
  {  
          smul_mR(EValue[i][C1],Ide,sIde);   //  A - λ Id
           sub_mR(A,sIde,AmnssIde);
                                             //         A|b 
      c_A_b_Ab_mR(AmnssIde,b,Ab);            //  A - λ Id|0       
   
   GJ_PP_FreeV_mR(Ab,b_free);                // b_free = an eigenvector 
   
           c_c_mR(b_free,C2,V,i);            // copy an eigenvector into V
  }    
   
  Normalize_mR(V);  

  f_mR(EValue);

  f_mR(Ab);
  f_mR(b);
  f_mR(b_free); 
   
  f_mR(Ide);
  f_mR(sIde);
  f_mR(AmnssIde);
  
  return(V);
}
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