67 lines
1.7 KiB
Mathematica
67 lines
1.7 KiB
Mathematica
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%%*****************************************************************
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%% Doptdesign: D-optimal experiment design.
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%%
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%% max log(det(sum_{i=1}^p lambda_i v_i v_i^T)) + const
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%%
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%% s.t. lambda_i >= 0, sum_{i=1}^p lambda_i = 1.
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%%
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%% Note: const = n.
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%% V: nxp matrix with n <= p.
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%% lambda: lambda_i is the fraction of the experiments
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%% allocated to test vector v_i.
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%% S: = V*diag(lambda)*V'.
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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,OPTIONS,lambda,bblk,AAt] = Doptdesign(V,solve);
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if (nargin == 1); solve = 0; end
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[n,p] = size(V);
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if (n > p);
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error(' size(V,1) > size(V,2)');
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end
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%%
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%% form blk, At, C, b
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%%
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b = zeros(p,1);
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blk{1,1} = 's'; blk{1,2} = n;
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F = cell(1,p);
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for k = 1:p
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F{1,k} = -V(:,k)*V(:,k)';
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end
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At(1) = svec(blk(1,:),F,1);
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C{1,1} = sparse(n,n);
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blk{2,1} = 'l'; blk{2,2} = p;
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At{2,1} = -speye(p,p);
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C{2,1} = zeros(p,1);
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blk{3,1} = 'u'; blk{3,2} = 1;
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At{3,1} = ones(1,p);
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C{3,1} = 1;
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OPTIONS.parbarrier{1,1} = 1;
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OPTIONS.parbarrier{2,1} = 0;
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OPTIONS.parbarrier{3,1} = 0;
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%%
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%% form bblk, AAt to take into account of
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%% low-rank constraint matrices of the form: -vk*vk'.
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%%
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bblk = blk; AAt = At;
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bblk{1,1} = 's'; bblk{1,2} = n; bblk{1,3} = ones(1,p);
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AAt{1,1} = []; AAt{1,2} = V; AAt{1,3} = -ones(p,1);
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%%
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if (solve)
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[obj,X,y,Z] = sqlp(blk,At,C,b,OPTIONS);
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lambda = -y;
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else
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lambda = [];
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end
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%%*******************************************************
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