Mercurial > matrix-functions
comparison toolbox/makejcf.m @ 2:c124219d7bfa draft
Re-add the 1995 toolbox after noticing the statement in the ~higham/mctoolbox/ webpage.
| author | Antonio Pino Robles <data.script93@gmail.com> |
|---|---|
| date | Thu, 07 May 2015 18:36:24 +0200 |
| parents | 8f23314345f4 |
| children |
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| 1:e471a92d17be | 2:c124219d7bfa |
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| 1 function A = makejcf(n, e, m, X) | |
| 2 %MAKEJCF A matrix with given Jordan canonical form. | |
| 3 % MAKEJCF(N, E, M) is a matrix having the Jordan canonical form | |
| 4 % whose i'th Jordan block is of dimension M(i) with eigenvalue E(i), | |
| 5 % and where N = SUM(M). | |
| 6 % Defaults: E = 1:N, M = ONES(SIZE(E)) with M(1) so that SUM(M) = N. | |
| 7 % The matrix is constructed by applying a random similarity | |
| 8 % transformation to the Jordan form. | |
| 9 % Alternatively, the matrix used in the similarity transformation | |
| 10 % can be specified as a fifth parameter. | |
| 11 % In particular, MAKEJCF(N, E, M, EYE(N)) returns the Jordan form | |
| 12 % itself. | |
| 13 % NB: The JCF is very sensitive to rounding errors. | |
| 14 | |
| 15 if nargin < 2, e = 1:n; end | |
| 16 if nargin < 3, m = ones(size(e)); m(1) = m(1) + n - sum(m); end | |
| 17 | |
| 18 if any( size(e(:)) ~= size(m(:)) ) | |
| 19 error('Parameters E and M must be of same dimension.') | |
| 20 end | |
| 21 | |
| 22 if sum(m) ~= n, error('Block dimensions must add up to N.'), end | |
| 23 | |
| 24 A = zeros(n); | |
| 25 j = 1; | |
| 26 for i=1:max(size(m)) | |
| 27 if m(i) > 1 | |
| 28 Jb = jordbloc(m(i),e(i)); | |
| 29 else | |
| 30 Jb = e(i); % JORDBLOC fails in n = 1 case. | |
| 31 end | |
| 32 A(j:j+m(i)-1,j:j+m(i)-1) = Jb; | |
| 33 j = j + m(i); | |
| 34 end | |
| 35 | |
| 36 if nargin < 4 | |
| 37 X = randn(n); | |
| 38 end | |
| 39 A = X\A*X; |