Linear Algebra and the C Language/a0i9

Install and compile this file in your working directory.

/* ------------------------------------ */
/*  Save as :  c00b.c                   */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
void fun(int r)
{
double **A      =  rdefinite_positive_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:");
  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,P6,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(rp_I(R3)+R2);

} while(stop_w());

  return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */

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

Screen output example:

                                                                                       
 A:
    +57.64     +12.78      +7.50      +0.39      -0.77 
    +12.78     +80.50     +10.24      -9.83      +4.40 
     +7.50     +10.24     +60.46      +2.97     -15.95 
     +0.39      -9.83      +2.97     +61.19      +2.31 
     -0.77      +4.40     -15.95      +2.31     +48.21 

 TA = V EValue VT
    +57.64     +12.78      +7.50      +0.39      -0.77 
    +12.78     +80.50     +10.24      -9.83      +4.40 
     +7.50     +10.24     +60.46      +2.97     -15.95 
     +0.39      -9.83      +2.97     +61.19      +2.31 
     -0.77      +4.40     -15.95      +2.31     +48.21 

 A - TA = 0
 -0.000000  +0.000000  -0.000000  -0.000000  +0.000000 
 +0.000000  -0.000000  -0.000000  -0.000000  +0.000000 
 -0.000000  -0.000000  +0.000000  +0.000000  +0.000000 
 -0.000000  -0.000000  +0.000000  +0.000000  +0.000000 
 +0.000000  +0.000000  +0.000000  +0.000000  -0.000000 


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