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tt_qcirc

PURPOSE ^

returns the multilevel circulant matrix tt generated by the multi-dimensional input vector x

SYNOPSIS ^

function [tt]=tt_qcirc(x,d)

DESCRIPTION ^

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

 The size of the input vector is 2^d(1) x ... x 2^d(D),
 The output matrix is square of order 2^d(1) x ... x 2^d(D).

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

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