85 lines
2.6 KiB
Mathematica
85 lines
2.6 KiB
Mathematica
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%%**********************************************************
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%% cheby0:
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%%
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%% minimize || p(d) ||_infty
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%% p = polynomial of degree <= m such that p(0) = 1.
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%%
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%% Here d = n-vector
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%%----------------------------------------------------------
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%% [blk,Avec,C,b,X0,y0,Z0,objval,p] = cheby0(d,m,solve);
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%%
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%% d = a vector.
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%% m = degree of polynomial.
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%% feas = 1 if want feasible starting point
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%% = 0 if otherwise.
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%% solve = 0 if just want initialization
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%% = 1 if want to solve the problem
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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,Avec,C,b,X0,y0,Z0,objval,p] = cheby0(d,m,solve);
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if nargin <= 2; solve = 0; end;
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if (size(d,1) < size(d,2)); d = d.'; end;
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cmp = 1-isreal(d);
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tstart=cputime;
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n = length(d);
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e = ones(n,1);
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V(1:n,1) = e/norm(e); R(1,1) = 1/norm(e);
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for i =1:m
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v = d.*V(:,i);
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for j = 1:i %% Arnoldi iterations:
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H(j,i) = (V(:,j))'*v; %% constructing upper-Hessenberg matrix.
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v = v - H(j,i)*V(:,j); %% orthonormaliztion of Krylov basis.
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end;
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H(i+1,i) = norm(v);
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V(:,i+1) = v/H(i+1,i);
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R(1:i+1,i+1) = (1/H(i+1,i))*([0; R(1:i,i)] - [R(1:i,1:i)*H(1:i,i); 0]);
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end
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if (cmp)
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blk{1,1} = 'q'; blk{1,2} = 3*ones(1,n);
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C = zeros(3*n,1); C(2:3:3*n) = ones(n,1);
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b = [zeros(2*m,1); -1];
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Atmp = [];
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II = [0:3:3*n-3]'; ee = ones(n,1);
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for k=1:m
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dVk = d.*V(:,k);
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Atmp = [Atmp; [2+II, k*ee, real(dVk)]; [3+II, k*ee, imag(dVk)]];
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Atmp = [Atmp; [2+II, (m+k)*ee, -imag(dVk)]; [3+II, (m+k)*ee, real(dVk)]];
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end
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Atmp = [Atmp; [1+II, (2*m+1)*ee, -ones(n,1)]];
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else
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blk{1,1} = 'l'; blk{1,2} = 2*ones(1,n);
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b = [zeros(m,1); -1];
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C = [ones(n,1); -ones(n,1)];
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Atmp = [];
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II = [1:n]'; ee = ones(n,1);
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for k=1:m
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dVk = d.*V(:,k);
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Atmp = [Atmp; [II, k*ee, dVk]; [n+II, k*ee, -dVk]];
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end
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Atmp = [Atmp; [II, (m+1)*ee, -ee]; [n+II, (m+1)*ee, -ee]];
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end
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Avec = spconvert(Atmp);
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[X0,y0,Z0] = infeaspt(blk,Avec,C,b);
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%%
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if (solve)
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[obj,X,y,Z] = sqlp(blk,Avec,C,b,[],X0,y0,Z0);
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if (cmp)
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y = y(1:m) + sqrt(-1)*y(m+1:2*m);
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else
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y = y(1:m);
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end
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x1 = R(1:m,1:m)*y(1:m);
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p = [-x1(m:-1:1); 1];
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objval = -mean(obj);
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else
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objval = []; p = [];
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end
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%%**********************************************************
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