Mercurial > matrix-functions
view 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> |
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date | Thu, 07 May 2015 18:36:24 +0200 |
parents | 8f23314345f4 |
children |
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function A = makejcf(n, e, m, X) %MAKEJCF A matrix with given Jordan canonical form. % MAKEJCF(N, E, M) is a matrix having the Jordan canonical form % whose i'th Jordan block is of dimension M(i) with eigenvalue E(i), % and where N = SUM(M). % Defaults: E = 1:N, M = ONES(SIZE(E)) with M(1) so that SUM(M) = N. % The matrix is constructed by applying a random similarity % transformation to the Jordan form. % Alternatively, the matrix used in the similarity transformation % can be specified as a fifth parameter. % In particular, MAKEJCF(N, E, M, EYE(N)) returns the Jordan form % itself. % NB: The JCF is very sensitive to rounding errors. if nargin < 2, e = 1:n; end if nargin < 3, m = ones(size(e)); m(1) = m(1) + n - sum(m); end if any( size(e(:)) ~= size(m(:)) ) error('Parameters E and M must be of same dimension.') end if sum(m) ~= n, error('Block dimensions must add up to N.'), end A = zeros(n); j = 1; for i=1:max(size(m)) if m(i) > 1 Jb = jordbloc(m(i),e(i)); else Jb = e(i); % JORDBLOC fails in n = 1 case. end A(j:j+m(i)-1,j:j+m(i)-1) = Jb; j = j + m(i); end if nargin < 4 X = randn(n); end A = X\A*X;