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# Untitled

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1. %% gram_schmidt: function description
2. function outputs = gram_schmidt(arg)
3.   c1 = arg([1 : rows(arg)],1);
4.   c2 = arg([1 : rows(arg)],2);
5.
6.   res1 = c1 / sqrt(dot(c1, c1));
7.
8.   res2 = c2 - dot(c2, c1) / dot(c1, c1) * c1;
9.   res2 = res2 /sqrt(dot(res2,res2));
10.
11.   outputs =transpose([transpose(res1); transpose(res2)]);
12. end
13.
14. function [Z,B]=dwaww (mat,max_iter_count =1000,TOL=0.001)
15.     if(norm(mat-transpose(mat))!=0)
16.       error("not a symmetric matrix")
17.     endif
18.
19.     iter_count = 0;
20.     columns_count = columns(mat);
21.     Z = eye(columns_count,2);
22.
23.     while(true)
24.       if(iter_count > max_iter_count)
25.         error('exceeded the maximal iteration limit')
26.       endif
27.       iter_count = iter_count+1;
28.
29.       W = mat*Z;
30.       B = transpose(Z) * mat * Z;
31.       if (abs(B(2, 1)) < TOL)
32.         return
33.       endif
34.       Z = gram_schmidt(W);
35.       endwhile
36. end
37.
38.
39. %% test1: function description
40. function [] = test1(i)
41.   % for i=2:arg
42.     sim_matrix=randi(20,i,i);
43.     sim_matrix=sim_matrix-tril(sim_matrix,-1)+triu(sim_matrix,1)';
44.     [z,b]=dwaww(sim_matrix)
45.
46.     all_eigenvalues= eig(sim_matrix)
47.     eigenvalues=-sort(-abs(eig(sim_matrix)))([1:2])
48.     my_eigenvalues= -sort(abs([b(1,1),b(2,2)]))
49.     if(norm(eigenvalues-my_eigenvalues)>0.1)
50.       error('eigenvalues are not equal');
51.     endif
52.   % endfor
53.  end
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