cgsvd.m

求解离散病态问题的正则化方法matlab 工具箱

function [U,sm,X,V] = cgsvds(A,L)
%CGSVD Compact generalized SVD of a matrix pair in regularization problems.
%
% sm = cgsvd(A,L)
% [U,sm,X,V] = cgsvd(A,L) ,  sm = [sigma,mu]
%
% Computes the generalized SVD of the matrix pair (A,L):
%    [ A ] = [ U  0 ]*[ diag(sigma)      0    ]*inv(X)
%    [ L ]   [ 0  V ] [      0       eye(n-p) ]
%                     [  diag(mu)        0    ]
% where
%    U  is  m-by-n ,    sigma  is  p-by-1
%    V  is  p-by-p ,    mu     is  p-by-1
%    X  is  n-by-n .
%
% It is assumed that m >= n >= p, which is true in regularization problems.

% Reference: C. F. Van Loan, "Computing the CS and the generalized
% singular value decomposition", Numer. Math. 46 (1985), 479-491.

% Per Christian Hansen, IMM, 12/19/97.

% Initialization.
[m,n] = size(A); [p,n1] = size(L);
if (n1 ~= n | m < n | n < p)
  error('Incorrect dimensions of A and L')
end

% Call Matlab's GSVD routine.
[U,V,W,C,S] = gsvd(full(A),full(L),0);
sm = [diag(C(1:p,1:p)),diag(S(1:p,1:p))];

% Finalize.
if (nargout < 2)
   U = sm;
else
   % Full decomposition.
   X = inv(W');
end