Mercurial > matrix-functions
diff toolbox/signm.m @ 0:8f23314345f4 draft
Create local repository for matrix toolboxes. Step #0 done.
author | Antonio Pino Robles <data.script93@gmail.com> |
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date | Wed, 06 May 2015 14:56:53 +0200 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/toolbox/signm.m Wed May 06 14:56:53 2015 +0200 @@ -0,0 +1,21 @@ +function [S, N] = signm(A) +%SIGNM Matrix sign decomposition. +% [S, N] = SIGNM(A) is the matrix sign decomposition A = S*N, +% computed via the Schur decomposition. +% S is the matrix sign function, sign(A). + +% Reference: +% N.J. Higham, The matrix sign decomposition and its relation to the +% polar decomposition, Linear Algebra and Appl., 212/213:3-20, 1994. + +[Q, T] = schur(A); +[Q, T] = rsf2csf(Q, T); +S = Q * matsignt(T) * Q'; + +% Only problem with Schur method is possible nonzero imaginary part when +% A is real. Next line takes care of that. +if ~norm(imag(A),1), S = real(S); end + +if nargout == 2 + N = S*A; +end