44 lines
1.4 KiB
Mathematica
44 lines
1.4 KiB
Mathematica
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%%******************************************************************
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%% geometric_mean: an example with rotated cone variables
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%%
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%% max {prod(d+B*x) : d+B*x > 0, x <= 10}
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%%
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%% where B = 4xn matrix,
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%% d = 4x1 vector
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%%
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%% [blk,At,C,b,xx] = geometric_mean(B,d,solve);
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%%
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%% E.g. p = 6; m = 4; B = [rand(2,p); -rand(2,p)]; d = rand(m,1);
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%%
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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,xx] = geometric_mean(B,d,solve);
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if (nargin == 2); solve = 0; end
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n = size(B,2);
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zz = zeros(1,n);
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r2 = sqrt(2);
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blk{1,1} = 'r'; blk{1,2} = [3,3,3];
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blk{2,1} = 'l'; blk{2,2} = [2];
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At{1,1} = -[B(1,:),0,0,0; B(2,:),0,0,0; zz,r2,0,0; ...
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B(3,:),0,0,0; B(4,:),0,0,0; zz,0,r2,0; ...
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zz, 1,0,0; zz, 0,1,0; zz, 0,0,r2];
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At{2,1} = -[B(1,:),0,0,0; B(3,:),0,0,0];
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C{1,1} = [d(1:2); 0; d(3:4); 0; 0;0;0];
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C{2,1} = [d(1); d(3)];
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b = [zeros(n,1); 0;0;1];
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blk{3,1} = 'l'; blk{3,2} = n;
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At{3,1} = [eye(n), zeros(n,3)]; C{3,1} = 10*ones(n,1);
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if (solve)
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[bblk,AAt,CC,bb,T] = convertRcone(blk,At,C,b);
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[obj,X,y,Z] = sqlp(bblk,AAt,CC,bb);
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xx = y(1:n);
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end
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%%******************************************************************
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