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annotate minorsSym.m @ 127:967152d7d58b

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Added function for printing the minors of a matrix.
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 03 Feb 2016 16:56:05 +0100
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127
967152d7d58b Added function for printing the minors of a matrix.
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1 function ineq = minorsSym(B)
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2 B
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3
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4 [n, m] = size(B);
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5
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6 if n ~= m
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7 error('B must be square');
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8 end
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9
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10 subB = {};
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11 ks = {};
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12
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13 ind = 1:n;
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14 for k = 1:n
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15 C = nchoosek(ind,k);
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16 for i = 1:size(C,1)
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17 ks{end + 1} = k;
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18 subB{end + 1} = B(C(i,:),C(i,:));
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19 end
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20 end
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21
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22
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23
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24 for i = 1:length(subB)
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25 fprintf('%d:\n', ks{i});
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26 disp(subB{i})
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27
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28 minor{i} = det(subB{i});
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29 end
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30
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31 for i = 1:length(subB)
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32 fprintf('%d:\n', ks{i});
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33 disp(minor{i});
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34
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35 if mod(ks{i},2) == 0
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36 ineq{i} = minor{i} >= 0;
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37 else
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38 ineq{i} = minor{i} <= 0;
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39 end
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40 end
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41
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42 ineqsys = true;
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43 for i = 1:length(ineq)
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44 ineqsys = ineqsys & ineq{i};
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45 end
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46
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47 ineq = simplify(ineqsys)
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48 end
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49
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50
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51 % B is positive semidefinite if all minors are non-negative
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52 % B is negative semidefinite if all odd minors are non-positive and all even minors are non-negative
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53