Description of orthogonalize

DESCRIPTION

ORTHOGONALIZE Orthogonalize tensor.
   X = ORTHOGONALIZE( X, POS ) orthogonalizes all cores of the TTeMPS tensor X
   except the core at position POS. Cores 1...POS-1 are left-, cores POS+1...end
   are right-orthogonalized. Therefore,

   X = ORTHOGONALIZE( X, 1 ) right-orthogonalizes the full tensor,

   X = ORTHOGONALIZE( X, X.order ) left-orthogonalizes the full tensor.

   See also ORTH_AT.

CROSS-REFERENCE INFORMATION

orth_at ORTH_AT Orthogonalize single core.

low_rank_tensor_completion_TT Example file for the manifold encoded in fixedTTrankfactory.

TTeMPS

gauge_matrices GAUGE_MATRICES Right and left orthogonalization with storage of gauge matrices

norm NORM Norm of a TT/MPS tensor.

norm NORM Norm of a TT/MPS block-mu tensor.

orthogonalize ORTHOGONALIZE Orthogonalize TT/MPS Block-mu tensor.

TTeMPS_tangent_orth

completion Completion for Tensor train but without individual orthogonalization

completion_als ALS Completion

completion_orth RTTC: Riemannian Tensor Train Completion

completion_orth_lambda RTTC: Riemannian Tensor Train Completion

completion_rankincrease

amen_eigenvalue AMEN_EIGENVALUE Calculate p smallest eigenvalues of a TTeMPS operator

block_eigenvalue BLOCK_EIGENVALUE Calculate p smallest eigenvalues of a TTeMPS operator

increaseRank_mod Rank-1 gradient approximation to increase the rank.

alsLinsolve TTeMPS Toolbox.

alsLinsolve_fast TTeMPS Toolbox.

alsLinsolve_rankOne TTeMPS Toolbox.

amen TTeMPS Toolbox.

amen_fast TTeMPS Toolbox.

construct_initial_guess TTeMPS Toolbox.

construct_initial_guess_rankOne TTeMPS Toolbox.

ex_completion_compare_als_riemann This example shows a simple comparison of two different algorithm for tensor completion:

ex_completion_rankadaptive Example script for RANK-ADAPTIVE TENSOR COMPLETION, see Algorithm RTTC described in

example TTeMPS Toolbox.

fixedTTrankfactory Manifold of tensors of fixed Tensor Train (TT) rank, embedded geometry

orthogonalizetwice Orthonormalizes a basis of tangent vectors twice for increased accuracy.

tangentorthobasis Returns an orthonormal basis of tangent vectors in the Manopt framework.

SOURCE CODE

0001 function x = orthogonalize( x, pos )
0002     %ORTHOGONALIZE Orthogonalize tensor.
0003     %   X = ORTHOGONALIZE( X, POS ) orthogonalizes all cores of the TTeMPS tensor X
0004     %   except the core at position POS. Cores 1...POS-1 are left-, cores POS+1...end
0005     %   are right-orthogonalized. Therefore,
0006     %
0007     %   X = ORTHOGONALIZE( X, 1 ) right-orthogonalizes the full tensor,
0008     %
0009     %   X = ORTHOGONALIZE( X, X.order ) left-orthogonalizes the full tensor.
0010     %
0011     %   See also ORTH_AT.
0012     
0013     %   TTeMPS Toolbox.
0014     %   Michael Steinlechner, 2013-2014
0015     %   Questions and contact: michael.steinlechner@epfl.ch
0016     %   BSD 2-clause license, see LICENSE.txt
0017 
0018     % left orthogonalization till pos (from left)
0019     for i = 1:pos-1
0020         x = orth_at( x, i, 'left' );
0021     end
0022 
0023     % right orthogonalization till pos (from right)
0024     for i = x.order:-1:pos+1
0025         x = orth_at( x, i, 'right' );
0026     end
0027 end

orthogonalize

PURPOSE

SYNOPSIS

DESCRIPTION

CROSS-REFERENCE INFORMATION

SOURCE CODE