Mercurial > matrix-functions
view 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> |
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date | Thu, 07 May 2015 18:36:24 +0200 |
parents | 8f23314345f4 |
children |
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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