Linear Algebra and the C Language/a0n3

Install and compile this file in your working directory.

/* ------------------------------------ */
/*  Save as:  c00c.c                    */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
#define ARRAY   A3
/* ------------------------------------ */
#define RC     RC3
/* ------------------------------------ */
void fun(void)
{
double **A         = rsymmetric_mR(        i_mR(RC,RC),999);
double **AEVect    =     eigs_V_mR(A,      i_mR(RC,RC));
double **InvAEVect =  transpose_mR(AEVect, i_mR(RC,RC));
double **AEValue   =       eigs_mR(A,      i_mR(RC,C1)); 

double **T         =                       i_mR(RC,RC);
double **a         =                       i_mR(RC,RC);

double **b    [ARRAY];
double **r    [ARRAY];
double **br   [ARRAY];
double **EVabr[ARRAY];

int i;

  for(i=A0; i<ARRAY; i++)
     {
      b[i]     =  c_c_mR(   AEVect,i+C1,           i_mR(RC,C1),C1);
      r[i]     =  c_r_mR(InvAEVect,i+R1,           i_mR(R1,RC),R1);
      
      br[i]    =  mul_mR(b[i],r[i],                i_mR(RC,RC));
      
      EVabr[i] = smul_mR(AEValue[i+R1][C1], br[i], i_mR(RC,RC));  
      }
      
  clrscrn();
  printf(" A:");
  p_mR(A, S10,P4,C6);

  printf(" AEVect:        Eingvectors of A");
  p_mR(AEVect, S10,P4,C6);
   
  printf(" AEValue:      Eignvalues of A");
  p_mR(AEValue, S10,P4,C6);
  stop();

  clrscrn(); 
  printf(" A:");
  p_mR(A, S10,P4,C6);
  
  add_mR(EVabr[0], EVabr[1], T); 
  add_mR(       T, EVabr[2], a);  
  printf(" E1*b1r1 + E2*b2r2 + E3*b3r3 = A");
  p_mR(a, S10,P4,C6);
   
  f_mR(A);
  f_mR(AEVect);
  f_mR(InvAEVect);
  f_mR(AEValue);
      
  f_mR(T);
  
  for(i=A0; i<ARRAY; i++)
     {
       f_mR(    b[i]);
       f_mR(    r[i]);
       f_mR(   br[i]); 
       f_mR(EVabr[i]);                   
     }   
}
/* ------------------------------------ */
int main(void)
{
time_t t;

  srand(time(&t));

do
{
 fun();

} while(stop_w());

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

A property of spectral decomposition:

        E1 b1r1 + E2 b2r2 + E3 b3r3 = A
        
 b: The columns of the eigenvectors of A
 r: The rows of eigenvectors of the inverse of A
 E: The eignvalues of A.
 
 b1r1 is obtained by multiplying the first column of the eigenvector of A by the first row of the eigenvector of the inverse of A

Screen output example:

                                                                                       
 A:
 +333.0000  -413.0000  +924.0000 
 -413.0000  -118.0000  +712.0000 
 +924.0000  +712.0000  +870.0000 

 AEVect:        Eingvectors of A
   +0.5196    +0.5509    -0.6531 
   +0.2137    +0.6564    +0.7236 
   +0.8273    -0.5155    +0.2233 

 AEValue:      Eignvalues of A
+1634.2674 
-1023.8379 
 +474.5705 

 Press return to continue. 


 A:
 +333.0000  -413.0000  +924.0000 
 -413.0000  -118.0000  +712.0000 
 +924.0000  +712.0000  +870.0000 

 E1*b1r1 + E2*b2r2 + E3*b3r3 = A
 +333.0000  -413.0000  +924.0000 
 -413.0000  -118.0000  +712.0000 
 +924.0000  +712.0000  +870.0000 


 Press   return to continue
 Press X return to stop