www.gusucode.com > 矩阵计算工具箱 - mctoolbox源码程序 > matrixcomp\matsignt.m
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. % Called by SIGNM. if ~isequal(T,triu(T)), error('Matrix must be upper triangular.'), end n = length(T); S = diag( sign( diag(real(T)) ) ); 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; S(i,j) = -S(i,k)*S(k,j) / (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