function x = lsolve(L,y,W,T) 
%LSOLVE Utility routine for "preconditioned" iterative methods. 
% 
% x = lsolve(L,y,W,T) 
% 
% Computes the vector 
%    x = L_p*y 
% where L_p is the A-weighted generalized inverse of L. 
% 
% Here, L is a p-by-n matrix, W holds a basis for the null space of L, 
% and T is a utility matrix which should be computed by routine pinit. 
% 
% Alternatively, L is square, and W and T are not needed. 
% 
% Notice that x and y may be matrices, in which case 
%    x(:,i) = L_p*y(:,i) . 
 
% Reference: P. C. Hansen, "Rank-Deficient and Discrete Ill-Posed Problems. 
% Numerical Aspects of Linear Inversion", SIAM, Philadelphia, 1997. 
 
% Per Christian Hansen, IMM, 07/29/97. 
 
% Initialization. 
[p,n] = size(L); nu = n-p; ly = size(y,2); 
 
% Special treatment of square L. 
if (nu==0), x = L\y; return; end 
  
% The general case. 
x = L(:,1:p)\y; 
x = [x;zeros(nu,ly)] - W*(T(:,1:p)*x); 
