// 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: Harpreet Singh
// Organization: FOSSEE, IIT Bombay
// Email: toolbox@scilab.in

function [xopt,fopt,status,iter] = symphonymat (varargin)
	// Solves a mixed integer linear programming constrained optimization problem in intlinprog format.
	//
	//   Calling Sequence
	//   xopt = symphonymat(c,intcon,A,b)
	//   xopt = symphonymat(c,intcon,A,b,Aeq,beq)
	//   xopt = symphonymat(c,intcon,A,b,Aeq,beq,lb,ub)
	//   xopt = symphonymat(c,intcon,A,b,Aeq,beq,lb,ub,options)
	//   [xopt,fopt,status,output] = symphonymat( ... )
	//   
	//   Parameters
	//   c : a vector of double, contains coefficients of the variables in the objective 
	//   intcon : Vector of integer constraints, specified as a vector of positive integers. The values in intcon indicate the components of the decision variable x that are integer-valued. intcon has values from 1 through number of variable.
	//   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.
	//   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.
	//   
	//   Description
	//   Search the minimum or maximum of a constrained mixed integer linear programming optimization 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 \\
	//	& & x_i \in \!\, \mathbb{Z}, i \in \!\, I
	//    \end{eqnarray}
	//   </latex>
	//   
	//   The routine calls SYMPHONY written in C by gateway files for the actual computation.
	//
	// The status allows to know the status of the optimization which is given back by Ipopt.
	// <itemizedlist>
	//   <listitem>status=227 : Optimal Solution Found </listitem>
	//   <listitem>status=228 : Maximum CPU Time exceeded.</listitem>
	//   <listitem>status=229 : Maximum Number of Node Limit Exceeded.</listitem>
	//   <listitem>status=230 : Maximum Number of Iterations Limit Exceeded.</listitem>
	// </itemizedlist>
	//
	// For more details on status see the symphony documentation, go to http://www.coin-or.org/SYMPHONY/man-5.6/
	//
	// 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>
	// </itemizedlist>
	//
	// Examples
	//    // Objective function
	// 	  // Reference: Westerberg, Carl-Henrik, Bengt Bjorklund, and Eskil Hultman. "An application of mixed integer programming in a Swedish steel mill." Interfaces 7, no. 2 (1977): 39-43.
	//    c = [350*5,330*3,310*4,280*6,500,450,400,100]';
	//    // Lower Bound of variable
	//    lb = repmat(0,1,8);
	//    // Upper Bound of variables
	//    ub = [repmat(1,1,4) repmat(%inf,1,4)];
	//    // Constraint Matrix
	//    Aeq = [5,3,4,6,1,1,1,1;
	//           5*0.05,3*0.04,4*0.05,6*0.03,0.08,0.07,0.06,0.03;
	//           5*0.03,3*0.03,4*0.04,6*0.04,0.06,0.07,0.08,0.09;]
	//    beq = [ 25, 1.25, 1.25]
	//    intcon = [1 2 3 4];
	//    // Calling Symphony
	//    [x,f,status,output] = symphonymat(c,intcon,[],[],Aeq,beq,lb,ub)
	//	// Press ENTER to continue 
	//
	// Examples 
	//    // An advanced case where we set some options in symphony
	//    // This problem is taken from 
	//    // P.C.Chu and J.E.Beasley 
	//    // "A genetic algorithm for the multidimensional knapsack problem",
	//    // Journal of Heuristics, vol. 4, 1998, pp63-86.
	//    // The problem to be solved is:
	//    // Max  sum{j=1,...,n} p(j)x(j)
	//    // st   sum{j=1,...,n} r(i,j)x(j) <= b(i)       i=1,...,m
	//    //                     x(j)=0 or 1
	//    // The function to be maximize i.e. P(j)
	//    c = -1*[   504 803 667 1103 834 585 811 856 690 832 846 813 868 793 ..
	//            825 1002 860 615 540 797 616 660 707 866 647 746 1006 608 ..
	//            877 900 573 788 484 853 942 630 591 630 640 1169 932 1034 ..
	//            957 798 669 625 467 1051 552 717 654 388 559 555 1104 783 ..
	//            959 668 507 855 986 831 821 825 868 852 832 828 799 686 ..
	//            510 671 575 740 510 675 996 636 826 1022 1140 654 909 799 ..
	//            1162 653 814 625 599 476 767 954 906 904 649 873 565 853 1008 632]';
	//    //Constraint Matrix
	//    A = [   //Constraint 1
	//            42 41 523 215 819 551 69 193 582 375 367 478 162 898 ..
	//            550 553 298 577 493 183 260 224 852 394 958 282 402 604 ..
	//            164 308 218 61 273 772 191 117 276 877 415 873 902 465 ..
	//            320 870 244 781 86 622 665 155 680 101 665 227 597 354 ..
	//            597 79 162 998 849 136 112 751 735 884 71 449 266 420 ..
	//            797 945 746 46 44 545 882 72 383 714 987 183 731 301 ..
	//            718 91 109 567 708 507 983 808 766 615 554 282 995 946 651 298;
	//            //Constraint 2
	//            509 883 229 569 706 639 114 727 491 481 681 948 687 941 ..
	//            350 253 573 40 124 384 660 951 739 329 146 593 658 816 ..
	//            638 717 779 289 430 851 937 289 159 260 930 248 656 833 ..
	//            892 60 278 741 297 967 86 249 354 614 836 290 893 857 ..
	//            158 869 206 504 799 758 431 580 780 788 583 641 32 653 ..
	//            252 709 129 368 440 314 287 854 460 594 512 239 719 751 ..
	//            708 670 269 832 137 356 960 651 398 893 407 477 552 805 881 850;
	//            //Constraint 3
	//            806 361 199 781 596 669 957 358 259 888 319 751 275 177 ..
	//            883 749 229 265 282 694 819 77 190 551 140 442 867 283 ..
	//            137 359 445 58 440 192 485 744 844 969 50 833 57 877 ..
	//            482 732 968 113 486 710 439 747 174 260 877 474 841 422 ..
	//            280 684 330 910 791 322 404 403 519 148 948 414 894 147 ..
	//            73 297 97 651 380 67 582 973 143 732 624 518 847 113 ..
	//            382 97 905 398 859 4 142 110 11 213 398 173 106 331 254 447 ;
	//            //Constraint 4
	//            404 197 817 1000 44 307 39 659 46 334 448 599 931 776 ..
	//            263 980 807 378 278 841 700 210 542 636 388 129 203 110 ..
	//            817 502 657 804 662 989 585 645 113 436 610 948 919 115 ..
	//            967 13 445 449 740 592 327 167 368 335 179 909 825 614 ..
	//            987 350 179 415 821 525 774 283 427 275 659 392 73 896 ..
	//            68 982 697 421 246 672 649 731 191 514 983 886 95 846 ..
	//            689 206 417 14 735 267 822 977 302 687 118 990 323 993 525 322;
	//            //Constrain 5
	//            475 36 287 577 45 700 803 654 196 844 657 387 518 143 ..
	//            515 335 942 701 332 803 265 922 908 139 995 845 487 100 ..
	//            447 653 649 738 424 475 425 926 795 47 136 801 904 740 ..
	//            768 460 76 660 500 915 897 25 716 557 72 696 653 933 ..
	//            420 582 810 861 758 647 237 631 271 91 75 756 409 440 ..
	//            483 336 765 637 981 980 202 35 594 689 602 76 767 693 ..
	//            893 160 785 311 417 748 375 362 617 553 474 915 457 261 350 635 ;
	//     ];
	//    nbVar = size(c,1)
	//    b=[11927 13727 11551 13056 13460 ];
	//    // Lower Bound of variables
	//    lb = repmat(0,1,nbVar)
	//    // Upper Bound of variables
	//    ub = repmat(1,1,nbVar)
	//    // Lower Bound of constrains
	//    intcon = [];
	//    for i = 1:nbVar
	//        intcon = [intcon i];
	//    end
	//    options = list("time_limit", 25);
	//    // The expected solution :
	//    // Output variables
	//    xopt = [0 1 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 ..
	//            0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 ..
	//            0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0]
	//    // Optimal value
	//    fopt = [ 24381 ]
	//    // Calling Symphony
	//    [x,f,status,output] = symphonymat(c,intcon,A,b,[],[],lb,ub,options);
	// Authors
	// Keyur Joshi, Saikiran, Iswarya, Harpreet Singh
    
    
	//To check the number of input and output argument
   	[lhs , rhs] = argn();
	
	//To check the number of argument given by user
	if ( rhs < 4 | rhs == 5 | rhs == 7 | rhs > 9 ) then
		errmsg = msprintf(gettext("%s: Unexpected number of input arguments : %d provided while should be in the set [4 6 8 9]"), "Symphony", rhs);
		error(errmsg);
	end
   
	c = [];
	intcon = [];
	A = [];
	b = [];
	Aeq = [];
	beq = [];
	lb = [];
	ub = [];
	options = list();
	
	c = varargin(1)
	intcon = varargin(2)
	A = varargin(3)
	b = varargin(4)

	if(size(c,2) == 0) then
		errmsg = msprintf(gettext("%s: Cannot determine the number of variables because input objective coefficients is empty"),"Symphonymat");
		error(errmsg);
	end

   if (size(c,2)~=1) then
	errmsg = msprintf(gettext("%s: Objective Coefficients should be a column matrix"), "Symphonymat");
	error(errmsg);
   end

   nbVar = size(c,1);

   if ( rhs<5 ) then
      Aeq = []
      beq = []
   else
      Aeq = varargin(5);
      beq = varargin(6);
   end
   
   if ( rhs<7 ) then
      lb = repmat(-%inf,1,nbVar);
      ub = repmat(%inf,1,nbVar);
   else
      lb = varargin(7);
      ub = varargin(8);
   end
   
   if (rhs<9|size(varargin(9))==0) then
      options = list();
   else
      options = varargin(9);
   end

// Check if the user gives empty matrix
    if (size(lb,2)==0) then
        lb = repmat(-%inf,nbVar,1);
    end
    
    if (size(intcon,2)==0) then
        intcon = [];
    end
    
    if (size(ub,2)==0) then
        ub = repmat(%inf,nbVar,1);
    end

// Calculating the size of equality and inequality constraints
   nbConInEq = size(A,1);
   nbConEq = size(Aeq,1);

// Check if the user gives row vector 
// and Changing it to a column matrix

	if (size(lb,2)== [nbVar]) then
		lb = lb';
	end

	if (size(ub,2)== [nbVar]) then
		ub = ub';
	end

	if (size(b,2)== [nbConInEq]) then
		b = b';
	end

	if (size(beq,2)== [nbConEq]) then
		beq = beq';
	end

    for i=1:size(intcon,2)
		if(intcon(i)>nbVar) then
			errmsg = msprintf(gettext("%s: The values inside intcon should be less than the number of variables"), "Symphonymat");
			error(errmsg);
		end

		if (intcon(i)<0) then
			errmsg = msprintf(gettext("%s: The values inside intcon should be greater than 0 "), "Symphonymat");
			error(errmsg);
		end

		if(modulo(intcon(i),1)) then
			errmsg = msprintf(gettext("%s: The values inside intcon should be an integer "), "Symphonymat");
			error(errmsg);
		end
    end

   //Check the size of inequality constraint which should equal to the number of inequality constraints
	if ( size(A,2) ~= nbVar & size(A,2) ~= 0) then
		errmsg = msprintf(gettext("%s: The size of inequality constraint is not equal to the number of variables"), "Symphonymat");
		error(errmsg);
	end


   //Check the size of lower bound of inequality constraint which should equal to the number of constraints
	if ( size(b,1) ~= size(A,1)) then
		errmsg = msprintf(gettext("%s: The Lower Bound of inequality constraint is not equal to the number of constraint"), "Symphonymat");
		error(errmsg);
	end

   //Check the size of equality constraint which should equal to the number of inequality constraints
	if ( size(Aeq,2) ~= nbVar & size(Aeq,2) ~= 0) then
		errmsg = msprintf(gettext("%s: The size of equality constraint is not equal to the number of variables"), "Symphonymat");
		error(errmsg);
	end

   //Check the size of upper bound of equality constraint which should equal to the number of constraints
	if ( size(beq,1) ~= size(Aeq,1)) then
		errmsg = msprintf(gettext("%s: The equality constraint upper bound is not equal to the number of equality constraint"), "Symphonymat");
		error(errmsg);
	end

   //Check the size of Lower Bound which should 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"), "Symphonymat");
      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"), "Symphonymat");
      error(errmsg);
   end
   
   if (type(options) ~= 15) then
      errmsg = msprintf(gettext("%s: Options should be a list "), "Symphonymat");
      error(errmsg);
   end
   

   if (modulo(size(options),2)) then
	errmsg = msprintf(gettext("%s: Size of parameters should be even"), "Symphonymat");
	error(errmsg);
   end

   //Check if the user gives a matrix instead of a vector
   
   if (((size(intcon,1)~=1)& (size(intcon,2)~=1))&(size(intcon,2)~=0)) then
      errmsg = msprintf(gettext("%s: intcon should be a vector"), "symphonymat");
      error(errmsg); 
   end
   
   if (size(lb,1)~=1)& (size(lb,2)~=1) then
      errmsg = msprintf(gettext("%s: Lower Bound should be a vector"), "symphonymat");
      error(errmsg); 
   end
   
   if (size(ub,1)~=1)& (size(ub,2)~=1) then
      errmsg = msprintf(gettext("%s: Upper Bound should be a vector"), "symphonymat");
      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"), "symphonymat");
            error(errmsg); 
        end
    end
    
    if (nbConEq) then
        if (size(beq,1)~=1)& (size(beq,2)~=1) then
            errmsg = msprintf(gettext("%s: Constraint Upper Bound should be a vector"), "symphonymat");
            error(errmsg); 
        end
   end
  

    //Changing the inputs in symphony's format 
    conMatrix = [A;Aeq]
    nbCon = size(conMatrix,1);
    conLB = [repmat(-%inf,size(A,1),1); beq];
    conUB = [b;beq] ;
    
    isInt = repmat(%f,1,nbVar);
    // Changing intcon into column vector
    intcon = intcon(:);
    for i=1:size(intcon,1)
        isInt(intcon(i)) = %t
    end
    
    objSense = 1;

    //Changing into row vector
    lb = lb';
    ub = ub';
    c = c';
    

   [xopt,fopt,status,iter] = symphony_call(nbVar,nbCon,c,isInt,lb,ub,conMatrix,conLB,conUB,objSense,options);

endfunction