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Create local repository for matrix toolboxes. Step #0 done.
author Antonio Pino Robles <data.script93@gmail.com>
date Wed, 06 May 2015 14:56:53 +0200
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8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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1 function A = makejcf(n, e, m, X)
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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2 %MAKEJCF A matrix with given Jordan canonical form.
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3 % MAKEJCF(N, E, M) is a matrix having the Jordan canonical form
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4 % whose i'th Jordan block is of dimension M(i) with eigenvalue E(i),
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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5 % and where N = SUM(M).
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6 % Defaults: E = 1:N, M = ONES(SIZE(E)) with M(1) so that SUM(M) = N.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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7 % The matrix is constructed by applying a random similarity
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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8 % transformation to the Jordan form.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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9 % Alternatively, the matrix used in the similarity transformation
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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10 % can be specified as a fifth parameter.
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11 % In particular, MAKEJCF(N, E, M, EYE(N)) returns the Jordan form
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12 % itself.
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13 % NB: The JCF is very sensitive to rounding errors.
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15 if nargin < 2, e = 1:n; end
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16 if nargin < 3, m = ones(size(e)); m(1) = m(1) + n - sum(m); end
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17
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18 if any( size(e(:)) ~= size(m(:)) )
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19 error('Parameters E and M must be of same dimension.')
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20 end
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21
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22 if sum(m) ~= n, error('Block dimensions must add up to N.'), end
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23
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24 A = zeros(n);
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25 j = 1;
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26 for i=1:max(size(m))
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27 if m(i) > 1
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28 Jb = jordbloc(m(i),e(i));
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29 else
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30 Jb = e(i); % JORDBLOC fails in n = 1 case.
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31 end
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32 A(j:j+m(i)-1,j:j+m(i)-1) = Jb;
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33 j = j + m(i);
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34 end
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35
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36 if nargin < 4
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37 X = randn(n);
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38 end
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39 A = X\A*X;