Mercurial > matrix-functions
diff toolbox/matsignt.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 |
line wrap: on
line diff
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/toolbox/matsignt.m Thu May 07 18:36:24 2015 +0200 @@ -0,0 +1,41 @@ +function S = matsignt(T) +%MATSIGNT Matrix sign function of a triangular matrix. +% S = MATSIGN(T) computes the matrix sign function S of the +% upper triangular matrix T using a recurrence. + +% Adapted from FUNM. Called by SIGNM. + +if norm(tril(T,-1),1), error('Matrix must be upper triangular.'), end + +n = max(size(T)); + +S = diag( sign( diag(real(T)) ) ); +tol = 0; +for p = 1:n-1 + for i = 1:n-p + + j = i+p; + d = T(j,j) - T(i,i); + + if S(i,i) ~= -S(j,j) % Solve via S^2 = I if we can. + + % Get S(i,j) from S^2 = I. + k = i+1:j-1; + RHS = 0; + if k, RHS = RHS - S(i,k)*S(k,j); end + S(i,j) = RHS / (S(i,i)+S(j,j)); + + else + + % Get S(i,j) from S*T = T*S. + s = T(i,j)*(S(j,j)-S(i,i)); + if p > 1 + k = i+1:j-1; + s = s + T(i,k)*S(k,j) - S(i,k)*T(k,j); + end + S(i,j) = s/d; + + end + + end +end