wpinv

 WPINV - Compute weighted pseudoinverse.
 
  [G,F] = wpinv(A,W)
 
 Computes the optimal solution x = Gy + Fx0 to the least squares
 problem
 
  min ||W(x-x0)||  subj. to  Ax = y
   x

 See also PINV.

0001 function [G,F] = wpinv(A,W)
0002   
0003 % WPINV - Compute weighted pseudoinverse.
0004 %
0005 %  [G,F] = wpinv(A,W)
0006 %
0007 % Computes the optimal solution x = Gy + Fx0 to the least squares
0008 % problem
0009 %
0010 %  min ||W(x-x0)||  subj. to  Ax = y
0011 %   x
0012 %
0013 % See also PINV.
0014   
0015   [m,n] = size(A);
0016   if nargin < 2
0017     W = eye(n);
0018   end
0019   
0020   % Thesis, Lemma B.1
0021   G = inv(W)*pinv(A*inv(W));
0022   F = eye(n) - G*A;