Home > tt2 > core > qtt_tucker_m.m

qtt_tucker_m

PURPOSE ^

Compute the QTT-Tucker representation of TT

SYNOPSIS ^

function [fc,core]=qtt_tucker_m(tt, sz, tol)

DESCRIPTION ^

Compute the QTT-Tucker representation of TT
   [FC,CORE]=QTT_TUCKER_M(TT, SZ, TOL) Computes the QTT-Tucker 
   representation of TT-tensor. This is a technical function: use 
   corresponding constructors of the QTT-Tucker class


 TT-Toolbox 2.2, 2009-2012

This is TT Toolbox, written by Ivan Oseledets et al.
Institute of Numerical Mathematics, Moscow, Russia
webpage: http://spring.inm.ras.ru/osel

For all questions, bugs and suggestions please mail
ivan.oseledets@gmail.com
---------------------------

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 function [fc,core]=qtt_tucker_m(tt, sz, tol)
0002 %Compute the QTT-Tucker representation of TT
0003 %   [FC,CORE]=QTT_TUCKER_M(TT, SZ, TOL) Computes the QTT-Tucker
0004 %   representation of TT-tensor. This is a technical function: use
0005 %   corresponding constructors of the QTT-Tucker class
0006 %
0007 %
0008 % TT-Toolbox 2.2, 2009-2012
0009 %
0010 %This is TT Toolbox, written by Ivan Oseledets et al.
0011 %Institute of Numerical Mathematics, Moscow, Russia
0012 %webpage: http://spring.inm.ras.ru/osel
0013 %
0014 %For all questions, bugs and suggestions please mail
0015 %ivan.oseledets@gmail.com
0016 %---------------------------
0017 
0018 
0019 d = tt.d;
0020 n = tt.n;
0021 rcr = tt.r;
0022 
0023 fc = cell(d,1);
0024 
0025 % Initial orthogonalization - 1->d
0026 for i=1:d-1
0027     cr = tt{i};
0028     cr = reshape(cr, rcr(i)*n(i), rcr(i+1));
0029     [cr, rv]=qr(cr, 0);
0030     cr2 = tt{i+1};
0031     cr2 = rv*reshape(cr2, rcr(i+1), n(i+1)*rcr(i+2));
0032     rcr(i+1) = size(cr,2);
0033     tt{i} = reshape(cr, rcr(i), n(i), rcr(i+1));
0034     tt{i+1} = reshape(cr2, rcr(i+1), n(i+1), rcr(i+2));
0035 end;
0036 
0037 % Split tucker factors from d->1
0038 core = tt;
0039 nextcr = core{d};
0040 rtuck = zeros(d,1);
0041 for i=d:-1:1
0042     cr = nextcr;
0043     cr = permute(cr, [2, 1, 3]);
0044     cr = reshape(cr, n(i), rcr(i)*rcr(i+1));
0045     [u,s,v]=svd(cr, 'econ');
0046     s = diag(s);
0047     nrm = norm(s);
0048     r = my_chop2(s, tol*nrm); % !!!!!!
0049     rtuck(i) = r;
0050     if (i>1)
0051         fc{i} = u(:,1:r);
0052         cr = diag(s(1:r))*v(:,1:r)';
0053         cr = reshape(cr, r, rcr(i), rcr(i+1));
0054         cr = permute(cr, [1, 3, 2]);
0055         cr = reshape(cr, r*rcr(i+1), rcr(i));
0056         [cr,rv] = qr(cr, 0);
0057         cr2 = core{i-1};
0058         cr2 = reshape(cr2, rcr(i-1)*n(i-1), rcr(i));
0059         cr2 = cr2*(rv.');
0060         rcr(i) = size(cr, 2);
0061         nextcr = reshape(cr2, rcr(i-1), n(i-1), rcr(i));
0062         cr = reshape(cr, r, rcr(i+1), rcr(i));
0063         core{i} = permute(cr, [3, 1, 2]);
0064     else
0065         cr = v(:,1:r)';
0066         cr = reshape(cr, r, rcr(i), rcr(i+1));
0067         core{i} = permute(cr, [2, 1, 3]);
0068         fc{i} = u(:,1:r)*diag(s(1:r));
0069     end;    
0070 end;
0071 
0072 % Quantics approximation
0073 for i=1:d
0074     %d0 = log2(n(i));
0075     fc{i} = tt_tensor(fc{i});
0076     szc=sz{i}; d0=numel(szc); m0=szc(end); szc=szc(:);
0077     %fc{i} = tt_reshape(fc{i}, [2*ones(1,d0-1), 2*rtuck(i)], tol);
0078     fc{i}=tt_reshape(fc{i},[szc(1:end-1); m0*rtuck(i)],tol);
0079     nocore = fc{i}{d0}; % rqtt, 2*rtuck, 1
0080     rqtt = size(nocore, 1);
0081     if (i<d)
0082         % Play with QRs: fc{i}->cr{i}->cr{i+1}->fc{i+1}
0083         nocore = reshape(nocore, rqtt*m0, rtuck(i));
0084         [ocore, nocore]=qr(nocore, 0);               
0085         cr1 = core{i};
0086         cr1 = permute(cr1, [2, 1, 3]);
0087         cr1 = reshape(cr1, rtuck(i), rcr(i)*rcr(i+1));
0088         cr1 = nocore*cr1;
0089         rtuck(i) = size(cr1, 1);
0090         fc{i}{d0} = reshape(ocore, rqtt, m0, rtuck(i));
0091         
0092         cr1 = reshape(cr1, rtuck(i)*rcr(i), rcr(i+1));
0093         [cr1, rv]=qr(cr1, 0);
0094         cr2 = core{i+1};
0095         cr2 = reshape(cr2, rcr(i+1), rtuck(i+1)*rcr(i+2));
0096         cr2 = rv*cr2;
0097         rcr(i+1) = size(cr1, 2);
0098         cr1 = reshape(cr1, rtuck(i), rcr(i), rcr(i+1));
0099         core{i} = permute(cr1, [2,1,3]);
0100         cr2 = reshape(cr2, rcr(i+1), rtuck(i+1), rcr(i+2));
0101         cr2 = permute(cr2, [1, 3, 2]);
0102         cr2 = reshape(cr2, rcr(i+1)*rcr(i+2), rtuck(i+1));
0103         [cr2, rv]=qr(cr2, 0);
0104         fc{i+1} = fc{i+1}*(rv.');
0105         rtuck(i+1) = size(cr2, 2);
0106         cr2 = reshape(cr2, rcr(i+1), rcr(i+2), rtuck(i+1));
0107         core{i+1} = permute(cr2, [1, 3, 2]); 
0108     else
0109         fc{i}{d0} = reshape(nocore, rqtt, m0, rtuck(i));
0110     end;
0111 end;
0112 
0113 end

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