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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

pretransfo(At,b,c,K,pars)
%                                      [At,b,c,K,prep] = pretransfo(At,b,c,K)
% PRETRANSFO  Checks data and then transforms into internal SeDuMi format.
%
% **********  INTERNAL FUNCTION OF SEDUMI **********
%
% See also sedumi

function [At,b,c,K,prep,origcoeff] = pretransfo(At,b,c,K,pars)

% 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

% ----------------------------------------
% Make sure that all fields exist in K-structure
% ----------------------------------------
if ~isfield(K,'f')                       % K.f
    K.f = 0;
elseif isempty(K.f)
    K.f = 0;
elseif (K.f~= floor(K.f)) | (K.f < 0)
    error('K.f should be nonnegative integer')
end
if ~isfield(K,'l')                        % K.l
    K.l = 0;
elseif isempty(K.l)
    K.l = 0;
elseif (K.l~= floor(K.l)) | (K.l < 0)
    error('K.l should be nonnegative integer')
end
if ~isfield(K,'q')                       % K.q
    K.q = [];
elseif sum(K.q) == 0
    K.q = [];
elseif ~isempty(K.q)
    if (min(K.q) < 2) | any(K.q~= floor(K.q))
        error('K.q should contain only integers bigger than 1')
    end
    if size(K.q,1) > 1
        K.q = K.q';
    end
end
if ~isfield(K,'r')                       % K.r
    K.r = [];
elseif sum(K.r) == 0
    K.r = [];
elseif ~isempty(K.r)
    if (min(K.r) < 3) | any(K.r~= floor(K.r))
        error('K.r should contain only integers bigger than 2')
    end
    if size(K.r,1) > 1
        K.r = K.r';
    end
end
if ~isfield(K,'s')                       % K.s
    K.s = [];
elseif sum(K.s) == 0
    K.s = [];
elseif ~isempty(K.s)
    if min(K.s < 1) | any(K.s~= floor(K.s))
        error('K.s should contain only positive integers')
    end
    if size(K.s,1) > 1
        K.s = K.s';
    end
end
% ------------------------------------------------------------
% Validity check: Info on complex interpretation of variables
% ------------------------------------------------------------
if ~isfield(K,'ycomplex')                        % K.ycomplex
    K.ycomplex = [];
elseif ~isempty(K.ycomplex)
    if  (min(K.ycomplex) < 1) | (min(size(K.ycomplex)) > 1) | ...
            any(K.ycomplex~= floor(K.ycomplex))
        error('K.ycomplex should be a list containing only positive integers')
    end
    if size(K.ycomplex,1) > 1
        K.ycomplex = K.ycomplex';
    end
    if max(K.ycomplex) > length(b)
        error('K.ycomplex out of range')
    end
end
if ~isfield(K,'xcomplex')                        % K.xcomplex
    K.xcomplex = [];
elseif ~isempty(K.xcomplex)
    if  (min(K.xcomplex) < 1) | (min(size(K.xcomplex))) > 1 | ...
            any(K.xcomplex~= floor(K.xcomplex))
        error('K.xcomplex should be a list containing only positive integers')
    end
    if size(K.xcomplex,1) > 1
        K.xcomplex = K.xcomplex';
    end
    if max(K.xcomplex) > K.f+K.l+sum(K.q)+sum(K.r)
        error('K.xcomplex out of range')
    end
end
if ~isfield(K,'scomplex')                        % K.scomplex
    K.scomplex = [];
elseif ~isempty(K.scomplex)
    if  min(K.scomplex) < 1 |  min(size(K.scomplex)) > 1 | ...
            any(K.scomplex~= floor(K.scomplex))
        error('K.scomplex should be a list containing only positive integers')
    end
    if size(K.scomplex,1) > 1
        K.scomplex = K.scomplex';
    end
    if max(K.scomplex) > length(K.s)
        error('K.scomplex out of range')
    end
end
% ----------------------------------------
% Check size of At,b,c (w.r.t. K)
% Let m = #eq-constraints, N = #variables (before transformations)
% ----------------------------------------
if (min(size(b)) > 1) | (min(size(c)) > 1)
    error('Parameters b and c must be vectors')
end
m = min(size(At));
N = K.f + K.l + sum(K.q) + sum(K.r) + sum((K.s).^2);
if nnz(b) == 0
    b = sparse(m,1);
elseif length(b) ~= m
    error('Size b mismatch')
end
if m ~= size(b,1)                    % make b an m x 1 vector
    b = b';
end
if nnz(c) == 0
    c = sparse(N,1);
elseif length(c) ~= N
    error('Size c mismatch')
end
if N ~= size(c,1)                     % make c an N x 1 vector
    c = c';
end
if N <= m
    error('Should have length(c) > length(b) in any sensible model')
end
if size(At,2) ~= m
    if m == size(At,1)
        At = At';        %user gave A instead of At.
    else
        error('Size At mismatches b.')
    end
end
if size(At,1) ~= N;
    error('Size At mismatches cone K.')
end
% ------------------------------------------------------------
% Check for NaN and Inf
% ------------------------------------------------------------
if any(any(isnan(At))) | any(isnan(b)) | any(isnan(c))
    error('A,b,c data contains NaN values')
end
if any(any(isinf(At))) | any(isinf(b)) | any(isinf(c))
    error('A,b,c data contains Inf values')
end
% ------------------------------------------------------------
% Save the standardized data for further use if needed
% ------------------------------------------------------------
if isfield(pars,'errors') & pars.errors==1
    origcoeff.At=At;
    origcoeff.c=c;
    origcoeff.b=b;
    origcoeff.K=K;
else
    origcoeff=[];
end
% ----------------------------------------
% First add constraints IM(Ax)=IM(b) where i in K.ycomplex, i.e.
% Make "imag(Ax) = imag(b)" and "imag(y)" explicit.
% ----------------------------------------
if ~isempty(K.ycomplex)
    b = [real(b);...
        imag(b(K.ycomplex))];      % RE b'*y = [RE b; IM b]'*[RE y; IM y].
    At = [At, sqrt(-1) * At(:,K.ycomplex)];
else
    b = real(b);
end
m = length(b);
% ----------------------------------------
% Transform any complex data into internal format,
% which uses only MATLAB's real representation.
% ----------------------------------------
cpx = whichcpx(K);
cpx.s = K.scomplex;
cpx.dim = length(K.xcomplex) + sum(K.s(K.scomplex).^2);
At = makereal(sparse(At),K,cpx);
c = makereal(sparse(c),K,cpx);
K.f = K.f + length(cpx.f);          % Update cone K structure wrt complex
K.q = vec(K.q) + vec(cpx.q);
K.r = vec(K.r) + vec(cpx.r);
sperm = ones(length(K.s),1);
sperm(cpx.s) = 0;
sperm = find(sperm);
K.rsdpN = length(sperm);          % #real sym PSD blocks
K.s = K.s([vec(sperm); vec(cpx.s)]);
prep.cpx = cpx;
% ----------------------------------------
% Transform R-cones (rotated Lorentz) into Q-cones (standard Lorentz).
% ----------------------------------------
prep.lenKq = length(K.q);
if ~isempty(K.r)
    c(K.f+1:end) = rotlorentz(c(K.f+1:end),K);
    At(K.f+1:end,:) = rotlorentz(At(K.f+1:end,:),K);
    K.q = [K.q; K.r];
    K.r = [];
    prep.rq=1;
else
    prep.rq=0;
end
% ----------------------------------------
% Now that complex Lorentz cones are transformed to real,
% we need K.q(k) >= 3 for all k.
% ----------------------------------------
% if min(K.q) < 3
%     error('The real dimension of each Lorentz cone should be at least 3.')
% end
% ---------------------------------------------------
% Remove diagonal SDP blocks
% ---------------------------------------------------
if ~isfield(pars,'sdp')
    pars.sdp=1;    % Enable/disable SDP preprocessing
end
if cpx.dim>0
    pars.sdp=0;    % No SDP preprocessing for complex problems
end
if pars.sdp==1
    Atf=At(1:K.f,:);
    cf=c(1:K.f);
    Kf=K.f;
    K.f=0;
    [At,b,c,K,prep.sdp]=preprocessSDP(At(Kf+1:end,:),b,c(Kf+1:end),K);
    At=[Atf;At];
    c=[cf;c];
    K.f=Kf;
    clear Atf cf Kf
    
    %[At,b,c,K,prep.sdp]=preprocessSDP(At,b,c,K);
end
% ------------------------------------------------------------
% Search for hidden free variables in split form and convert them into free
% variables if pars.free=1 (they stay split if pars.free=0)
% ------------------------------------------------------------
if ~isfield(pars,'free')
    pars.free=1;
end
if pars.free & K.l>0
    stest=c(K.f+1:K.f+K.l)-At(K.f+1:K.f+K.l,:)*rand(m,1);
    %Now we detect if stest contains the same vector twice, or opposite
    %vectors.
    [sabssorted,sindex]=sort(abs(stest));
    sabsdiff=diff(sabssorted);
    zeroindex=find(sabsdiff==0);
    if length(zeroindex)>=2
        %Allocate storage for the indices
        block1ind=zeros(1,length(zeroindex));
        block2ind=block1ind;
        blockind=1;
        for i=zeroindex'
            if stest(sindex(i))==-stest(sindex(i+1))
                block1ind(blockind)=sindex(i);
                block2ind(blockind)=sindex(i+1);
                blockind=blockind+1;
            end
        end
        %Get rid of the tails
        block1ind=block1ind(1:blockind-1);
        block2ind=block2ind(1:blockind-1);
        block1=false(1,K.l);
        block2=block1;
        block1(block1ind)=true;
        block2(block2ind)=true;
        %block1ind and block2ind contain the corresponding indices of the split
        %variables, while block1 and block2 the logical vectors that are used
        %for indexing
        At=[At(K.f+block1ind,:);At(1:K.f,:);At([false(1,K.f),~(block1+block2)],:);At(K.f+K.l+1:end,:)];
        c=[c(K.f+block1ind);c(1:K.f);c([false(1,K.f),~(block1+block2)]);c(K.f+K.l+1:end)];
        K.f=K.f+length(block1ind);
        K.l=K.l-2*length(block1ind);
        prep.freeblock1=block1ind;
        prep.freeblock2=block2ind;
    end
end

% ------------------------------------------------------------
% Transform F-cone into L-cone or Q-cone
% Split if pars.free=0, put in Q-cone otherwise
% ------------------------------------------------------------
prep.Kf = K.f;
if K.f>0
    switch pars.free
        case 0
            At = [-At(1:K.f,:);At];
            c = [-c(1:K.f);c];
            K.l = K.l + 2 * K.f;
            K.f = 0;
        case 1
            c=[c(K.f+1:K.f+K.l);0;c(1:K.f);c(K.f+K.l+1:end)];
            At=[At(K.f+1:K.f+K.l,:);zeros(1,m);At(1:K.f,:);At(K.f+K.l+1:end,:)];
            K.q=[K.f+1;K.q];
            K.f=0;
    end
end
% --------------------------------------------------
% Split Lorentz blocks in trace-block + norm-bound-blocks
% --------------------------------------------------
if ~isempty(K.q)
    At = qreshape(At,0,K);
    c = qreshape(c,0,K);
end
% ----------------------------------------
% Correct A s.t. At has tril-blocks (for PSD),
% ----------------------------------------
At = vectril(At,K);
c = vectril(c,K);
% ----------------------------------------
% Create artificial (x0,z0) variable for
% self-dual model
% ----------------------------------------
c = [0;c];            %does not affect sparse/dense status of c.
At = [zeros(1,m); At];
K.l = K.l + 1;    % add (x0,z0)
% ----------------------------------------
% Now K has field K.{l,q,s}
% Make more detailed description of cone K:
% Let K.blkstart(i):K.blkstart(i+1)-1 give the index range of block i.
% Compute maxN=max(order), len=sum(order) for LORENTZ, real PSD and herm PSD.
% yields: K.{l,q,s, rsdpN,blkstart,    rLen,hLen, qMaxn,rMaxn,hMaxn}
% ----------------------------------------
K.rsdpN = length(K.s) - length(prep.cpx.s);    % # real symmetric PSD vars
K = statsK(K);
K.mainblks = K.blkstart(cumsum([1 1 length(K.q)]));
K.qblkstart = K.blkstart(2:2+length(K.q));  % Also include blkend
K.sblkstart = K.blkstart(2+length(K.q):end);
K.lq = K.mainblks(end)-1;
K.N = length(c);

%Correct the sparsity structure of the variables, this can save a lot of
%memory.
[i j s]=find(At);
At=sparse(i,j,s,K.N,m);
if spars(c)<2/3
    [i j s]=find(c);
    c=sparse(i,j,s,K.N,1);
else
    c=full(c);
end
if spars(b)<2/3
    [i j s]=find(b);
    b=sparse(i,j,s,m,1);
else
    b=full(b);
end

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