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Risk and Asset Allocation

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Risk and Asset Allocation

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16 Nov 2005 (Updated )

Software for quantitative portfolio and risk management

posttransfo(x,y,prep,K,pars)
function [xp,yp,K] = posttransfo(x,y,prep,K,pars)
%                                       [xp,yp] = posttransfo(x,y,prep,K)
% POSTTRANSFO  Transforms (x,y) from internal SeDuMi format into original
%   user format.
%
% **********  INTERNAL FUNCTION OF SEDUMI **********
%
% See also sedumi

%
% This file is part of SeDuMi 1.1 by Imre Polik and Oleksandr Romanko
% Copyright (C) 2005 McMaster University, Hamilton, CANADA  (since 1.1)
%
% Copyright (C) 2001 Jos F. Sturm (up to 1.05R5)
%   Dept. Econometrics & O.R., Tilburg University, the Netherlands.
%   Supported by the Netherlands Organization for Scientific Research (NWO).
%
% Affiliation SeDuMi 1.03 and 1.04Beta (2000):
%   Dept. Quantitative Economics, Maastricht University, the Netherlands.
%
% Affiliations up to SeDuMi 1.02 (AUG1998):
%   CRL, McMaster University, Canada.
%   Supported by the Netherlands Organization for Scientific Research (NWO).
%
% This program is free software; you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation; either version 2 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program; if not, write to the Free Software
% Foundation, Inc.,  51 Franklin Street, Fifth Floor, Boston, MA
% 02110-1301, USA
%

K.l = K.l - 1;       % remove artificial var of self-dual embedding
xp=x(2:end);
% ------------------------------------------------------------
% If there are Lorentz cones then reorder the variables
% ------------------------------------------------------------
if ~isempty(K.q)
    xp = qreshape(xp,1,K);
end
% ------------------------------------------------------------
% Transform LQ-vars into F-vars (free)
% ------------------------------------------------------------
K.f = prep.Kf;
if K.f>0
    switch pars.free
        case 0
            K.l = K.l - 2 * K.f;
            xp = [xp(K.f+1 : 2*K.f) - xp(1:K.f); xp(2*K.f+1:end)];
        otherwise
            K.q=K.q(2:end);
            xp=[xp(K.l+2:K.l+K.f+1);xp(1:K.l);xp(K.l+K.f+2:end)];
    end
end

% -----------------------------------------------------
% Reenter the split free variables (if any)
% -----------------------------------------------------
if isfield(prep,'freeblock1')
    numvars=length(prep.freeblock1);
    block1=false(1,K.l+2*numvars);
    block2=block1;
    block1(prep.freeblock1)=true;
    block2(prep.freeblock2)=true;
    xkl=zeros(K.l+2*numvars,1);
    xkl(~(block1+block2))=xp(K.f+1:K.f+K.l);
    xkl(prep.freeblock1)=max(xp(1:numvars),0);
    xkl(prep.freeblock2)=-min(xp(1:numvars),0);
    xp=[xp(numvars+1:K.f);xkl;xp(K.f+K.l+1:end)];
    K.f=K.f-numvars;
    K.l=K.l+2*numvars;
end

% ----------------------------------------
% Postprocess the SDP part
% ----------------------------------------
if pars.sdp==1 & isfield(prep,'sdp')
    xpf(1:K.f,1)=xp(1:K.f);
    xp=xp(K.f+1:end);
    Kf=K.f;
    K.f=0;
    [xp,yp,K]=postprocessSDP(xp,y,prep.sdp,K);
    xp=[xpf;xp];
    K.f=Kf;
    clear Kf xpf
end

% ----------------------------------------
% transform q-variables into r-variables (Lorentz) (if any)
% ----------------------------------------
if prep.rq==1
    K.r = K.q(prep.lenKq + 1 : end);
    K.q = K.q(1:prep.lenKq);
    xp(K.f+1:end) = rotlorentz(xp(K.f+1:end),K);
else
    K.r=[];
end

% ----------------------------------------
% Bring x into the complex format of original (At,c),
% ----------------------------------------
xp = veccomplex(xp,prep.cpx,K);
% ----------------------------------------
% bring y into complex format, indicated by K.ycomplex.
% ----------------------------------------
ylen = length(y) - length(K.ycomplex);
yp = y(1:ylen) ...
    + sqrt(-1) * sparse(K.ycomplex,1,y(ylen+1:length(y)),ylen,1);
% ---------------------------
% Make x sparse if necessary
% ---------------------------
if nnz(xp)/length(xp)<2/3
    xp=sparse(xp);
end

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