Description of round

ROUND Approximate TTeMPS tensor within a prescribed tolerance.
   X = ROUND( X, tol ) truncates the given TTeMPS tensor X to a
   lower rank such that the error is in order of tol.

CROSS-REFERENCE INFORMATION

tensorprod_ttemps TENSORPROD_TTEMPS Tensor-times-Matrix product.

trunc_singular REL_TRUNC_SINGULAR Helper routine to truncate singular values

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

elliptope_SDP Solver for semidefinite programs (SDP's) with unit diagonal constraints.

elliptope_SDP_complex Solver for complex semidefinite programs (SDP's) with unit diagonal.

low_rank_tensor_completion Given partial observation of a low rank tensor, attempts to complete it.

low_rank_tensor_completion_TT Example file for the manifold encoded in fixedTTrankfactory.

low_rank_tensor_completion_embedded Given partial observation of a low rank tensor (possibly including noise),

realphasefactory Returns a manifold struct to optimize over phases of fft's of real signals

essentialfactory Manifold structure to optimize over the space of essential matrices.

TTeMPS_block

round ROUND Approximate TTeMPS tensor within a prescribed tolerance.

TTeMPS_op

round ROUND Approximate TTeMPS operator within a prescribed tolerance.

example TTeMPS Toolbox.

trs_gep Solves trust-region subproblem with TRSgep in a subspace of tangent space.

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

SOURCE CODE

0001 function x = round( x, tol )
0002     %ROUND Approximate TTeMPS tensor within a prescribed tolerance.
0003     %   X = ROUND( X, tol ) truncates the given TTeMPS tensor X to a
0004     %   lower rank such that the error is in order of tol.
0005 
0006     %   TTeMPS Toolbox.
0007     %   Michael Steinlechner, 2013-2016
0008     %   Questions and contact: michael.steinlechner@epfl.ch
0009     %   BSD 2-clause license, see LICENSE.txt
0010     
0011     sz = x.size;
0012     d = x.order;
0013     
0014     % Left-right procedure
0015     x = x.orthogonalize( d );
0016 
0017     right_rank = 1;
0018     for i = d:-1:2
0019         [U,S,V] = svd( unfold( x.U{i}, 'right'), 'econ' );
0020         r = trunc_singular( diag(S), tol, true );
0021         U = U(:,1:r);
0022         V = V(:,1:r);
0023         S = S(1:r,1:r);
0024         x.U{i} = reshape( V', [r, sz(i), right_rank] );
0025         x.U{i-1} = tensorprod_ttemps( x.U{i-1}, (U*S).', 3 );
0026         right_rank = r;
0027     end
0028 
0029 end

round

PURPOSE

SYNOPSIS

DESCRIPTION

CROSS-REFERENCE INFORMATION

SOURCE CODE