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// Copyright (C) 2015 - IIT Bombay - FOSSEE
//
// This file must be used under the terms of the CeCILL.
// This source file is licensed as described in the file COPYING, which
// you should have received as part of this distribution. The terms
// are also available at
// http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
// Author: Guru Pradeep Reddy, Bhanu Priya Sayal
// Organization: FOSSEE, IIT Bombay
// Email: toolbox@scilab.in
function [xopt,fopt,exitflag,output,lambda] = linprog (varargin)
// Solves a linear programming problem.
//
// Calling Sequence
// xopt = linprog(c,A,b)
// xopt = linprog(c,A,b,Aeq,beq)
// xopt = linprog(c,A,b,Aeq,beq,lb,ub)
// xopt = linprog(c,A,b,Aeq,beq,lb,ub,param)
// [xopt, fopt, exitflag, output, lambda] = linprog(file)
// [xopt,fopt,exitflag,output,lambda] = linprog( ... )
//
// Parameters
// c : a vector of double, contains coefficients of the variables in the objective
// A : a matrix of double, represents the linear coefficients in the inequality constraints A⋅x ≤ b.
// b : a vector of double, represents the linear coefficients in the inequality constraints A⋅x ≤ b.
// Aeq : a matrix of double, represents the linear coefficients in the equality constraints Aeq⋅x = beq.
// beq : a vector of double, represents the linear coefficients in the equality constraints Aeq⋅x = beq.
// lb : Lower bounds, specified as a vector or array of double. lb represents the lower bounds elementwise in lb ≤ x ≤ ub.
// ub : Upper bounds, specified as a vector or array of double. ub represents the upper bounds elementwise in lb ≤ x ≤ ub.
// options : a list containing the parameters to be set.
// file : a string describing the path to the mps file.
// xopt : a vector of double, the computed solution of the optimization problem.
// fopt : a double, the value of the function at x.
// status : status flag returned from symphony. See below for details.
// output : The output data structure contains detailed information about the optimization process. See below for details.
// lambda : The structure consist of the Lagrange multipliers at the solution of problem. See below for details.
//
// Description
// OSI-CLP is used for solving the linear programming problems, OSI-CLP is a library written in C++.
// Search the minimum of a constrained linear programming problem specified by :
//
// <latex>
// \begin{eqnarray}
// &\mbox{min}_{x}
// & c^T⋅x \\
// & \text{subject to} & A⋅x \leq b \\
// & & Aeq⋅x = beq \\
// & & lb \leq x \leq ub \\
// \end{eqnarray}
// </latex>
// The routine calls Clp for solving the linear programming problem, Clp is a library written in C++.
//
// The exitflag allows to know the status of the optimization which is given back by Ipopt.
// <itemizedlist>
// <listitem>exitflag=0 : Optimal Solution Found </listitem>
// <listitem>exitflag=1 : Primal Infeasible </listitem>
// <listitem>exitflag=2 : Dual Infeasible</listitem>
// <listitem>exitflag=3 : Maximum Number of Iterations Exceeded. Output may not be optimal.</listitem>
// <listitem>exitflag=4 : Solution Abandoned</listitem>
// <listitem>exitflag=5 : Primal objective limit reached.</listitem>
// <listitem>exitflag=6 : Dual objective limit reached.</listitem>
// </itemizedlist>
//
// For more details on exitflag see the ipopt documentation, go to http://www.coin-or.org/Ipopt/documentation/
//
// The output data structure contains detailed informations about the optimization process.
// It has type "struct" and contains the following fields.
// <itemizedlist>
// <listitem>output.iterations: The number of iterations performed during the search</listitem>
// <listitem>output.constrviolation: The max-norm of the constraint violation.</listitem>
// </itemizedlist>
//
// The lambda data structure contains the Lagrange multipliers at the end
// of optimization. In the current version the values are returned only when the the solution is optimal.
// It has type "struct" and contains the following fields.
// <itemizedlist>
// <listitem>lambda.lower: The Lagrange multipliers for the lower bound constraints.</listitem>
// <listitem>lambda.upper: The Lagrange multipliers for the upper bound constraints.</listitem>
// <listitem>lambda.eqlin: The Lagrange multipliers for the linear equality constraints.</listitem>
// <listitem>lambda.ineqlin: The Lagrange multipliers for the linear inequality constraints.</listitem>
// </itemizedlist>
//
// Examples
// //Optimal problems
// //Linear program, linear inequality constraints
// c=[-1,-1/3]'
// A=[1,1;1,1/4;1,-1;-1/4,-1;-1,-1;-1,1]
// b=[2,1,2,1,-1,2]
// [xopt,fopt,exitflag,output,lambda]=linprog(c, A, b)
// // Press ENTER to continue
//
// Examples
// //Linear program with Linear Inequalities and Equalities`
// c=[-1,-1/3]'
// A=[1,1;1,1/4;1,-1;-1/4,-1;-1,-1;-1,1]
// b=[2,1,2,1,-1,2]
// Aeq=[1,1/4]
// beq=[1/2]
// [xopt,fopt,exitflag,output,lambda]=linprog(c, A, b, Aeq, beq)
// // Press ENTER to continue
//
// Examples
// //Linear program with all constraint types
// c=[-1,-1/3]'
// A=[1,1;1,1/4;1,-1;-1/4,-1;-1,-1;-1,1]
// b=[2,1,2,1,-1,2]
// Aeq=[1,1/4]
// beq=[1/2]
// lb=[-1,-0.5]
// ub=[1.5,1.25]
// [xopt,fopt,exitflag,output,lambda]=linprog(c, A, b, Aeq, beq, lb, ub)
// // Press ENTER to continue
//
// Examples
// //Primal Infeasible Problem
// c=[-1,-1,-1]'
// A=[1,2,-1]
// b=[-4]
// Aeq=[1,5,3;1,1,0]
// beq=[10,100]
// lb=[0,0,0]
// ub=[%inf,%inf,%inf]
// [xopt,fopt,exitflag,output,lambda]= linprog(c,A,b,Aeq,beq,lb,ub)
// // Press ENTER to continue
//
// Examples
// //Dual Infeasible Problem
// c=[3,5,-7]'
// A=[-1,-1,4;1,1,4]
// b=[-8,5]
// Aeq=[]
// beq=[]
// lb=[-%inf,-%inf,-%inf]
// ub=[%inf,%inf,%inf]
// [xopt,fopt,exitflag,output,lambda]= linprog(c,A,b,Aeq,beq,lb,ub)
// // Press ENTER to continue
//
// Examples
// filepath = get_absolute_file_path('linprog.dem.sce');
// filepath = filepath + "exmip1.mps"
// [xopt,fopt,exitflag,output,lambda] =linprog(filepath)
// Authors
// Bhanu Priya Sayal, Guru Pradeep Reddy
if(type(varargin(1))==1) then
[lhs , rhs] = argn();
//To check the number of argument given by user
if ( rhs < 3 | rhs == 4 | rhs == 6 | rhs >8 ) then
errmsg = msprintf(gettext("%s: Unexpected number of input arguments : %d provided while should be in the set of [3 5 7 8]"), "linprog", rhs);
error(errmsg)
end
c = varargin(1);
A = varargin(2);
b = varargin(3);
if ( rhs<4 ) then
Aeq = []
beq = []
else
Aeq = varargin(4);
beq = varargin(5);
end
if ( rhs<6 ) then
lb = [];
ub = [];
else
lb = varargin(6);
ub = varargin(7);
end
if ( rhs<8 | size(varargin(8)) ==0 ) then
param = list();
else
param =varargin(8);
end
[xopt,fopt,exitflag,output,lambda]=matrix_linprog(c,A,b,Aeq,beq,lb,ub,param);
elseif(type(varargin(1))==10) then
[lhs , rhs] = argn();
//To check the number of argument given by user
if ( rhs < 1 | rhs > 2) then
errmsg = msprintf(gettext("%s: Unexpected number of input arguments : %d provided while should be in the set of [1 2]"),"linprog",rhs);
error(errmsg)
end
mpsFile = varargin(1);
if ( rhs<2 | size(varargin(2)) ==0 ) then
param = list();
else
param =varargin(2);
end
[xopt,fopt,exitflag,output,lambda]=mps_linprog(mpsFile,param);
end
endfunction
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