Linear Algebra and the C Language/a0ih

Install and compile this file in your working directory.

/* ------------------------------------ */
/*  Save as :  c00b.c                   */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
void fun(int r)
{
double **A      = rdefinite_negative_mR( i_mR(r,r), 99);
double **TA     =                        i_mR(r,r);

double **V      =                        i_mR(r,r);
double **VT     =                        i_mR(r,r);
double **EValue =                        i_mR(r,r);

double **T1     =                        i_mR(r,r);

  clrscrn();
  printf(" A: Definite negative");
  p_mR(A,S10,P2,C6);  

/* Eigenvector */ 
  eigs_V_mR(A,V); 
  transpose_mR(V,VT); 
    
/* Eigenvalue = VT A V */ 
  mul_mR(VT,A,T1);
  mul_mR(T1,V,EValue);   
 
  printf(" TA = V EValue VT");
  mul_mR(V,EValue,T1);
  mul_mR(T1,VT,TA);    
  p_mR(TA,S10,P2,C6);  
  
  printf(" A - TA = 0"); 
  sub_mR(A,TA,T1); 
  p_mR(T1,S10,P2,C6);  
   
  f_mR(A);
  f_mR(TA);
    
  f_mR(V);
  f_mR(VT);
  
  f_mR(EValue);  
     
  f_mR(T1);
}
/* ------------------------------------ */
int main(void)
{
time_t t;

  srand(time(&t));

do
{
  fun(RC4);

} while(stop_w());

  return 0;
}

/* ------------------------------------ */
/* ------------------------------------ */

Let's check that A = V * EValue * VT.

Screen output example:

                                                                                       
 A: Definite negative
    -48.38     -22.55     +17.54     +15.82 
    -22.55     -71.78      -0.14      +2.78 
    +17.54      -0.14     -20.28      -9.50 
    +15.82      +2.78      -9.50     -64.56 

 TA = V EValue VT
    -48.38     -22.55     +17.54     +15.82 
    -22.55     -71.78      -0.14      +2.78 
    +17.54      -0.14     -20.28      -9.50 
    +15.82      +2.78      -9.50     -64.56 

 A - TA = 0
     +0.00      +0.00      +0.00      +0.00 
     +0.00      -0.00      -0.00      +0.00 
     +0.00      -0.00      -0.00      -0.00 
     +0.00      +0.00      -0.00      +0.00 


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