function [x,status,lambda,nu] = gpposy(A,b,szs,varargin)% [x,status,lambda,nu] = gpposy(A,b,szs,G,h,l,u,quiet)%% solves the geometric program in posynomial form%%  minimize    sum_k b0_k*x1^A0_{k1}*...*xn^A0_{kn}%  subject to  sum_k bi_k*x1^Ai_{k1}*...*xn^Ai_{kn} <= 1, i=1,...,m,%              hi*x1^G_{i1}*...*xn^G_{in} = 1,            i=1,...,p,%              li <= xi <= ui,                            i=1,...,n,%% where variables are x1,...,xn and the problem data are bi_k, Ai_{kj},% for i = 1,...,m, hi, G_{ij} for i = 1,...,p.%% Calling sequences:%%  [x,status,lambda,nu] = gpposy(A,b,szs)%  [x,status,lambda,nu] = gpposy(A,b,szs,G,h)%  [x,status,lambda,nu] = gpposy(A,b,szs,G,h,l,u)%  [x,status,lambda,nu] = gpposy(A,b,szs,G,h,l,u,quiet)%% Examples:%%  [x,status,lambda,nu] = gpposy(A,b,szs,G,h)%  [x,status,lambda,nu] = gpposy(A,b,szs,[],[],[],[],quiet)%% Input arguments:%% - A:         (sum_i n_i) x n matrix;  A   = [A0' A1' ... Am' ]'% - b:         (sum_i n_i) vector;      b   = [b0' b1' ... bm' ]'% - szs:       dimensions of Ai and bi; szs = [n0 n1 ... nm]'%              where Ai is (ni x n) and bi is (ni x 1)% - G:         p x n matrix% - h:         p-vector% - l:         n-vector; lower bound for x% - u:         n-vector; upper bound for x% - quiet:     boolean variable; suppress all the print messages if true%% Output arguments:%% - x:         n-vector; primal optimal point% - nu:        (sum_i n_i) vector;  nu = [nu0' nu1' ... num']'%              optimal sensitivity for constraints Ai*x + bi = yi% - mu:        (sum_i l_i) vector;  mu = [mu0' mu1' ... mul']'%              optimal sensitivity for constraints G*x + h = 0% - lambda:    m-vector, optimal sensitivity for inequality constraints% - status:    string; 'INFEASIBLE', 'SOLVED', or 'FAILED'%              % gpposy changes the problem data into posynomial form and calls the the% sovler, gpcvx.m.%----------------------------------------------------------------------%       INITIALIZATION%----------------------------------------------------------------------% PARAMETERSLOWER_BOUND = 1e-100;UPPER_BOUND = 1e+100;n   = size(A,2);     % # of variables (x1,..,xn)% VARIABLE ARGUMENT HANDLINGdefaults  = {[],[],LOWER_BOUND*ones(n,1),UPPER_BOUND*ones(n,1),false};givenArgs = ~cellfun('isempty',varargin);defaults(givenArgs) = varargin(givenArgs);[G,h,l,u,quiet]  = deal(defaults{:});% CONVERT PROBLEM DATA INTO CONVEX FORMb = log(b); h = log(h); l = log(l); u = log(u);if ( ~(all(isfinite(b)) && all(isfinite(h))) )    disp('ERROR: Too small value of b or h');    x = []; status = 'FAILED'; lambda = []; nu = [];    return;end%----------------------------------------------------------------------%       Call gpcvx%----------------------------------------------------------------------[x,status,lambda,empty,nu] = gpcvx(A,b,szs,G,h,l,u,quiet);% CONVERT SOLUTION TO POSYNOMIAL FORMx = exp(x);