function [B1] = Bfull(S,Y,gamma_inv)
%
% Computes the full SR1 matrix for debugging purposes
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% "On efficiently computing the eigenvalues of limited-memory
% quasi-Newton matrices"
% by Jennifer Erway and Roummel Marcia
%
% Copyright (2015): Jennifer Erway and Roummel Marcia
%
% The technical report and software are available at 
% www.wfu.edu/~erwayjb/publications.html
% www.wfu.edu/~erwayjb/software.html
%
% 
% This code is distributed under the terms of the GNU General Public
% License
% 2.0.
%
% Permission to use, copy, modify, and distribute this software for
% any purpose without fee is hereby granted, provided that this entire 
% notice is included in all copies of any software which is or includes
% a copy or modification of this software and in all copies of the
% supporting documentation for such software.
% This software is being provided "as is", without any express or
% implied warranty.  In particular, the authors do not make any
% representation or warranty of any kind concerning the merchantability
% of this software or its fitness for any particular purpose.
%---------------------------------------------------------------------------    
% Inputs: S,Y: the quasi-Newton pairs that define the SR1 matrix
%         gamma_inv: the initial SR1 matrix (B_0 = gamma_inv*I)%
%
% Output: B1 is the full SR1 matrix
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[n,K]=size(S);

B1 = gamma_inv*eye(n);
for i=1:K
  p2 = Y(:,i)-B1*S(:,i);
  B1 = B1 + (1/(p2'*S(:,i)))*p2*p2';
end
