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// Copyright (C) 2015 - IIT Bombay - FOSSEE
//
// Author: Guru Pradeep Reddy, Bhanu Priya Sayal
// Organization: FOSSEE, IIT Bombay
// Email: gurupradeept@gmail.com, bhanupriyasayal@gmail.com
// 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
function [xopt,fopt,exitflag,output,lambda] = matrix_linprog (varargin)
//To check the number of input and output argument
[lhs , rhs] = argn();
c = [];
A = [];
b = [];
Aeq = [];
beq = [];
lb = [];
ub = [];
options = list();
//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);
if(size(c,2) == 0) then
errmsg = msprintf(gettext("%s: Cannot determine the number of variables because input objective coefficients is empty"), "linprog");
error(errmsg);
end
if (size(c,2)~=1) then
errmsg = msprintf(gettext("%s: Objective Coefficients should be a column matrix"), "linprog");
error(errmsg);
end
nbVar = size(c,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
//Check type of variables
Checktype("linprog", c, "c", 1, "constant")
Checktype("linprog", A, "A", 2, "constant")
Checktype("linprog", b, "b", 3, "constant")
Checktype("linprog", Aeq, "Aeq", 4, "constant")
Checktype("linprog", beq, "beq", 5, "constant")
Checktype("linprog", lb, "lb", 6, "constant")
Checktype("linprog", ub, "ub", 7, "constant")
nbConInEq = size(A,1);
nbConEq = size(Aeq,1);
lb = lb(:);
ub = ub(:)
b = b(:);
beq = beq(:);
if (size(lb,2)==0) then
lb = repmat(-%inf,nbVar,1);
end
if (size(ub,2)==0) then
ub = repmat(%inf,nbVar,1);
end
if (type(param) ~= 15) then
errmsg = msprintf(gettext("%s: options should be a list "), "linprog");
error(errmsg);
end
if (modulo(size(param),2)) then
errmsg = msprintf(gettext("%s: Size of parameters should be even"), "linprog");
error(errmsg);
end
options = list("MaxIter", [3000]);
for i = 1:(size(param))/2
select convstr(param(2*i-1),'l')
case "maxiter" then
options(2*i) = param(2*i);
else
errmsg = msprintf(gettext("%s: Unrecognized parameter name ''%s''."), "linprog", param(2*i-1));
error(errmsg)
end
end
//Check the size of inequality constraint which should be equal to the number of variables
if ( size(A,2) ~= nbVar & size(A,2) ~= 0) then
errmsg = msprintf(gettext("%s: The number of columns in A must be the same as the number of elements of c"), "linprog");
error(errmsg);
end
//Check the size of equality constraint which should be equal to the number of variables
if ( size(Aeq,2) ~= nbVar & size(Aeq,2) ~= 0 ) then
errmsg = msprintf(gettext("%s: The number of columns in Aeq must be the same as the number of elements of c"), "linprog");
error(errmsg);
end
//Check the size of Lower Bound which should be equal to the number of variables
if ( size(lb,1) ~= nbVar) then
errmsg = msprintf(gettext("%s: The Lower Bound is not equal to the number of variables"), "linprog");
error(errmsg);
end
//Check the size of Upper Bound which should equal to the number of variables
if ( size(ub,1) ~= nbVar) then
errmsg = msprintf(gettext("%s: The Upper Bound is not equal to the number of variables"), "linprog");
error(errmsg);
end
//Check the size of constraints of Lower Bound which should equal to the number of constraints
if ( size(b,1) ~= nbConInEq & size(b,2) ~= 0) then
errmsg = msprintf(gettext("%s: The number of rows in A must be the same as the number of elements of b"), "linprog");
error(errmsg);
end
//Check the size of constraints of Upper Bound which should equal to the number of constraints
if ( size(beq,1) ~= nbConEq & size(beq,2) ~= 0) then
errmsg = msprintf(gettext("%s: The number of rows in Aeq must be the same as the number of elements of beq"), "linprog");
error(errmsg);
end
//Check if the user gives a matrix instead of a vector
if (size(lb,1)~=1)& (size(lb,2)~=1) then
errmsg = msprintf(gettext("%s: Lower Bound should be a vector"), "linprog");
error(errmsg);
end
if (size(ub,1)~=1)& (size(ub,2)~=1) then
errmsg = msprintf(gettext("%s: Upper Bound should be a vector"), "linprog");
error(errmsg);
end
if (nbConInEq) then
if ((size(b,1)~=1)& (size(b,2)~=1)) then
errmsg = msprintf(gettext("%s: Constraint Lower Bound should be a vector"), "linprog");
error(errmsg);
end
end
if (nbConEq) then
if (size(beq,1)~=1)& (size(beq,2)~=1) then
errmsg = msprintf(gettext("%s: Constraint should be a vector"), "linprog");
error(errmsg);
end
end
for i = 1:nbConInEq
if (b(i) == -%inf)
errmsg = msprintf(gettext("%s: Value of b can not be negative infinity"), "linprog");
error(errmsg);
end
end
for i = 1:nbConEq
if (beq(i) == -%inf)
errmsg = msprintf(gettext("%s: Value of beq can not be negative infinity"), "linprog");
error(errmsg);
end
end
nbVar = size(c,1);
c = c';
conMatrix = [Aeq;A];
nbCon = size(conMatrix,1);
conlb = [beq; repmat(-%inf,nbConInEq,1)];
conub = [beq;b];
[xopt,fopt,status,iter,Zl,dual] = linearprog(nbVar,nbCon,c,conMatrix,conlb,conub,lb',ub',options);
xopt = xopt';
exitflag = status;
output = struct("Iterations" , [],..
"constrviolation" , []);
output.Iterations = iter;
output.constrviolation = max([0;norm(Aeq*xopt-beq, 'inf');(lb-xopt);(xopt-ub);(A*xopt-b)]);
lambda = struct("reduced_cost" , [], ..
"ineqlin" , [], ..
"eqlin" , []);
lambda.reduced_cost = Zl;
lambda.eqlin = dual(1:nbConEq);
lambda.ineqlin = dual(nbConEq+1:nbCon);
select status
case 0 then
printf("\nOptimal Solution.\n");
case 1 then
printf("\nPrimal Infeasible.\n");
case 2 then
printf("\nDual Infeasible.\n");
case 3 then
printf("\nIteration limit reached.\n");
case 4 then
printf("\nNumerical Difficulties.\n");
case 5 then
printf("\nPrimal Objective limit reached.\n");
case 6 then
printf("\nDual Objective limit reached.\n");
else
printf("\nInvalid status returned. Notify the Toolbox authors\n");
break;
end
endfunction
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