37 lines
1.1 KiB
Mathematica
37 lines
1.1 KiB
Mathematica
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%%****************************************************
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%% corrmat: find the nearest correlation matrix
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%% to a given symmetric matrix.
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%%
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%% [blk,At,C,b] = corrmat(H);
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%%
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%% min || X - H ||_F
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%% s.t. diag(X) = e, X psd.
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%%
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%% min t
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%% s.t. diag(X) = e
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%% svec(X) + y = svec(H),
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%% X psd, ||y||_2 <= t.
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%%*****************************************************************
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%% SDPT3: version 4.0
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%% Copyright (c) 1997 by
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%% Kim-Chuan Toh, Michael J. Todd, Reha H. Tutuncu
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%% Last Modified: 16 Sep 2004
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%%*****************************************************************
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function [blk,At,C,b] = corrmat(H);
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if size(H,1) ~= size(H,2); error('corrmat: matrix must be square'); end;
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n = length(H);
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n2 = n*(n+1)/2;
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blk{1,1} = 's'; blk{1,2} = n;
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for k=1:n; AA{1,k} = spconvert([k,k,1; n,n,0]); end;
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matrepdiag = svec(blk(1,:),AA);
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At{1,1} = [matrepdiag{1}, speye(n2)];
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blk{2,1} = 'q'; blk{2,2} = n2+1;
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At{2,1} = [sparse(n,n2+1); sparse(n2,1), speye(n2)];
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b = [ones(n,1); svec(blk(1,:),H)];
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C{1,1} = sparse(n,n); C{2,1} = [1; zeros(n2,1)];
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%%****************************************************
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