Mercurial > repos > public > sbplib
comparison minorsSym.m @ 127:967152d7d58b
Added function for printing the minors of a matrix.
| author | Jonatan Werpers <jonatan@werpers.com> |
|---|---|
| date | Wed, 03 Feb 2016 16:56:05 +0100 |
| parents | |
| children |
comparison
equal
deleted
inserted
replaced
| 126:54055b32d516 | 127:967152d7d58b |
|---|---|
| 1 function ineq = minorsSym(B) | |
| 2 B | |
| 3 | |
| 4 [n, m] = size(B); | |
| 5 | |
| 6 if n ~= m | |
| 7 error('B must be square'); | |
| 8 end | |
| 9 | |
| 10 subB = {}; | |
| 11 ks = {}; | |
| 12 | |
| 13 ind = 1:n; | |
| 14 for k = 1:n | |
| 15 C = nchoosek(ind,k); | |
| 16 for i = 1:size(C,1) | |
| 17 ks{end + 1} = k; | |
| 18 subB{end + 1} = B(C(i,:),C(i,:)); | |
| 19 end | |
| 20 end | |
| 21 | |
| 22 | |
| 23 | |
| 24 for i = 1:length(subB) | |
| 25 fprintf('%d:\n', ks{i}); | |
| 26 disp(subB{i}) | |
| 27 | |
| 28 minor{i} = det(subB{i}); | |
| 29 end | |
| 30 | |
| 31 for i = 1:length(subB) | |
| 32 fprintf('%d:\n', ks{i}); | |
| 33 disp(minor{i}); | |
| 34 | |
| 35 if mod(ks{i},2) == 0 | |
| 36 ineq{i} = minor{i} >= 0; | |
| 37 else | |
| 38 ineq{i} = minor{i} <= 0; | |
| 39 end | |
| 40 end | |
| 41 | |
| 42 ineqsys = true; | |
| 43 for i = 1:length(ineq) | |
| 44 ineqsys = ineqsys & ineq{i}; | |
| 45 end | |
| 46 | |
| 47 ineq = simplify(ineqsys) | |
| 48 end | |
| 49 | |
| 50 | |
| 51 % B is positive semidefinite if all minors are non-negative | |
| 52 % B is negative semidefinite if all odd minors are non-positive and all even minors are non-negative | |
| 53 |