left_orth_with_gauge

 LEFT_ORTH_WITH_GAUGE Left orthogonalization with storage of gauge matrices

 Given a right orthogonal X, compute a left orthogonalization and keep 
 the gauge matrices that relates them.

  The i-th core of xR
       unfold(xR.U{i},'left')
  is equal to the transformed i-th core of xL
       kron(eye(n(i)),inv(G{i-1}))*unfold(xL.U{i},'left')*G{i}
  (where fore i=1 and i=d, G{i} = 1).

  Or, equivalently
       tensorprod_ttemps( tensorprod_ttemps( xL.U{i}, G{i}', 3), inv(G{i-1}), 1)
  equals
       xR.U{i}.

   See also GAUGE_MATRICES

0001 function [xL, G] = left_orth_with_gauge( xR )
0002 % LEFT_ORTH_WITH_GAUGE Left orthogonalization with storage of gauge matrices
0003 %
0004 % Given a right orthogonal X, compute a left orthogonalization and keep
0005 % the gauge matrices that relates them.
0006 %
0007 %  The i-th core of xR
0008 %       unfold(xR.U{i},'left')
0009 %  is equal to the transformed i-th core of xL
0010 %       kron(eye(n(i)),inv(G{i-1}))*unfold(xL.U{i},'left')*G{i}
0011 %  (where fore i=1 and i=d, G{i} = 1).
0012 %
0013 %  Or, equivalently
0014 %       tensorprod_ttemps( tensorprod_ttemps( xL.U{i}, G{i}', 3), inv(G{i-1}), 1)
0015 %  equals
0016 %       xR.U{i}.
0017 %
0018 %   See also GAUGE_MATRICES
0019 
0020 %   TTeMPS Toolbox.
0021 %   Michael Steinlechner, 2013-2016
0022 %   Questions and contact: michael.steinlechner@epfl.ch
0023 %   BSD 2-clause license, see LICENSE.txt
0024     
0025     xL = xR;
0026     G = cell(xR.order-1, 1);
0027     % left orthogonalization till pos (from left)
0028     for i = 1:xR.order-1
0029         [xL, G{i}] = orth_at( xL, i, 'left' );
0030     end
0031     
0032 end