Home > tt2 > core > tt_qutrtoepl.m

tt_qutrtoepl

PURPOSE ^

returns the multilevel upper-triangular Toeplitz matrix tt generated by the multi-dimensional input vector x

SYNOPSIS ^

function [tt]=tt_qltrtoepl(x)

DESCRIPTION ^

 returns the multilevel upper-triangular Toeplitz matrix tt generated by the multi-dimensional input vector x 
 in the QTT format

 If the size of the input vector is N,
 then the size of the output matrix is N x N.

 April 20, 2011
 Vladimir Kazeev
 vladimir.kazeev@gmail.com
 INM RAS
 Moscow, Russia

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 For details please see the preprint
 http://www.mis.mpg.de/publications/preprints/2011/prepr2011-36.html
 Vladimir A. Kazeev, Boris N. Khoromskij and Eugene E. Tyrtyshnikov
 Multilevel Toeplitz matrices generated by QTT tensor-structured vectors and convolution with logarithmic complexity
 January 12, 2012
 Vladimir Kazeev,
 Seminar for Applied Mathematics, ETH Zurich
 vladimir.kazeev@sam.math.ethz.ch
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 function [tt]=tt_qltrtoepl(x)
0002 
0003 % returns the multilevel upper-triangular Toeplitz matrix tt generated by the multi-dimensional input vector x
0004 % in the QTT format
0005 %
0006 % If the size of the input vector is N,
0007 % then the size of the output matrix is N x N.
0008 %
0009 % April 20, 2011
0010 % Vladimir Kazeev
0011 % vladimir.kazeev@gmail.com
0012 % INM RAS
0013 % Moscow, Russia
0014 %
0015 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0016 % For details please see the preprint
0017 % http://www.mis.mpg.de/publications/preprints/2011/prepr2011-36.html
0018 % Vladimir A. Kazeev, Boris N. Khoromskij and Eugene E. Tyrtyshnikov
0019 % Multilevel Toeplitz matrices generated by QTT tensor-structured vectors and convolution with logarithmic complexity
0020 % January 12, 2012
0021 % Vladimir Kazeev,
0022 % Seminar for Applied Mathematics, ETH Zurich
0023 % vladimir.kazeev@sam.math.ethz.ch
0024 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0025 
0026 d=size(x,1);
0027 tt=tt_qshiftstack_r(d);
0028 tt=tt_qreshape(tt,3,[4*ones(d,1),2*ones(d,1)]);
0029 tt=tt_mv(tt,x);
0030 tt=tt_qreshape(tt,1,2*ones(d,2));
0031 
0032 return
0033 end

Generated on Wed 08-Feb-2012 18:20:24 by m2html © 2005