I would like to organize these results and trace them somehow. I don't know how to keep going until a size 2 matrix is reached. Also there may be a better way of doing what I want, it would make me very happy.
Edit: I would like to be able to see the results from more levels of recursing. The problem is I don't know how to send results from level 10 to the first level so that it can be used for the entire program. Also I am not sure I can trace them to know all the values for all the i's for each result, meaning which lines/columns were deleted.
clc
close all
clear all
fclose('all');
d2=[0 -1.165 -3.5493 -2.3828 -1.1464
1.165 0 -2.3843 -1.2178 0.0186
3.5493 2.3843 0 1.1665 2.4029
2.3828 1.2178 -1.1665 0 1.2364
1.1464 -0.0186 -2.4029 -1.2364 0];
[a,f] = smaller(d2, 0);
function [e,next] = smaller(d, level)
[Rows,~] = size(d);
level = level + 1;
for i = 1 : Rows
d_s = d;
d_s(i,:) = [];
d_s(:,i) = [];
e(i,1) = s2a(eig(d_s));
if nnz(d_s) > 11
[next(:,i)] = smaller(d_s, level);
end
end
end
function f = s2a(u)
Rows = size(u);
f = 0;
for i = 1 : Rows
f = f + u(i)*u(i);
end
end
The results for all smaller 5x5 matrices are:a
-31.6632098200000
-56.5056698200000
-22.7225231200000
-53.4562986200000
-56.3222738200000
for all smaller 4x4:f
-17.3266712400000 -17.3266712400000 -6.02413552000000 -22.9183217200000 -17.0572911600000
-6.02413552000000 -17.0413075200000 -17.0413075200000 -39.3713837200000 -39.2719771600000
-22.9183217200000 -39.3713837200000 -5.34360784000000 -5.34360784000000 -17.0359953600000
-17.0572911600000 -39.2719771600000 -17.0359953600000 -39.2792839600000 -39.2792839600000
I would like all results for all smaller matrices, and a way to organize them.
I came upon this other much faster way of doing it:
S=dec2bin(1:2^size(d1,1)-1)=='1';
b=cell(size(S,1),1);
for ix=1:size(S,1)
b{ix}=d1(find(S(ix,:)),find(S(ix,:)));
if isempty(b{ix})<1
e(ix,1)=s2a(eig(b{ix}));
end
end