Description of innerprod

DESCRIPTION

INNERPROD Inner product between two TT/MPS tensors.
   innerprod(X,Y) computes the inner product between the TT/MPS tensors X and Y.
   Assumes that the first rank of both tensors, X.rank(1) and Y.rank(1), is 1. 
   The last rank may be different from 1, resulting in a matrix of size 
   [X.rank(end), Y.rank(end)].

   See also NORM

CROSS-REFERENCE INFORMATION

tensorprod_ttemps TENSORPROD_TTEMPS Tensor-times-Matrix product.

unfold UNFOLD Left/right-unfold a 3D array.

fixedranktensorembeddedfactory Manifold of tensors with fixed multilinear rank in Tucker format

TTeMPS

contract CONTRACT Contraction of two TT/MPS tensors.

norm NORM Norm of a TT/MPS tensor.

TTeMPS_block

contract CONTRACT Contraction of two TT/MPS tensors with inner TT/MPS operator.

constr_precond_inner TTeMPS Toolbox.

contract CONTRACT Contraction of two TT/MPS tensors with inner TT/MPS Laplace operator.

TTeMPS_tangent

TTeMPS_tangent_orth

completion Completion for Tensor train but without individual orthogonalization

completion_orth RTTC: Riemannian Tensor Train Completion

completion_orth_lambda RTTC: Riemannian Tensor Train Completion

amen_eigenvalue AMEN_EIGENVALUE Calculate p smallest eigenvalues of a TTeMPS operator

block_eigenvalue BLOCK_EIGENVALUE Calculate p smallest eigenvalues of a TTeMPS operator

RiemannLinsolve Riemannian approx. Newton for linear systems. For more information, we refer to the report

RiemannPrecondSteep TTeMPS Toolbox.

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.

precond_laplace_noorth TTeMPS Toolbox.

precond_laplace_overlapGS TTeMPS Toolbox.

precond_laplace_overlapJacobi TTeMPS Toolbox.

precond_rankOne TTeMPS Toolbox.

example TTeMPS Toolbox.

linearsystem_compare Example code for the algorithms described in

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

SOURCE CODE

0001 function res = innerprod( x, y, dir, upto )
0002     %INNERPROD Inner product between two TT/MPS tensors.
0003     %   innerprod(X,Y) computes the inner product between the TT/MPS tensors X and Y.
0004     %   Assumes that the first rank of both tensors, X.rank(1) and Y.rank(1), is 1.
0005     %   The last rank may be different from 1, resulting in a matrix of size
0006     %   [X.rank(end), Y.rank(end)].
0007     %
0008     %   See also NORM
0009 
0010     %   TTeMPS Toolbox.
0011     %   Michael Steinlechner, 2013-2016
0012     %   Questions and contact: michael.steinlechner@epfl.ch
0013     %   BSD 2-clause license, see LICENSE.txt
0014 
0015     if ~exist( 'dir', 'var' )
0016         dir = 'LR';
0017     end
0018     if ~exist( 'upto', 'var' )
0019         if strcmpi( dir, 'LR')
0020             upto = x.order;
0021         else
0022             upto = 1;
0023         end
0024     end
0025 
0026     % Left-to-Right procedure
0027     if strcmpi( dir, 'LR')
0028         
0029         res = unfold( x.U{1}, 'left')' * unfold( y.U{1}, 'left');
0030 
0031         for i = 2:upto
0032             tmp = tensorprod_ttemps( x.U{i}, res', 1);
0033             res = unfold( tmp, 'left')' * unfold( y.U{i}, 'left');
0034         end
0035 
0036     % Right-to-Left procedure
0037     elseif strcmpi( dir, 'RL')
0038         d = x.order;
0039         res = conj(unfold( x.U{d}, 'right')) * unfold( y.U{d}, 'right').';
0040         
0041         for i = d-1:-1:upto
0042             tmp = tensorprod_ttemps( x.U{i}, res', 3);
0043             res = conj(unfold( tmp, 'right')) * unfold( y.U{i}, 'right').';
0044         end
0045 
0046     else
0047         error('Unknown direction specified. Choose either LR (default) or RL')
0048     end
0049 
0050 end
0051

innerprod

PURPOSE

SYNOPSIS

DESCRIPTION

CROSS-REFERENCE INFORMATION

SOURCE CODE