Bugs by Prof fixed 1

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-// Copyright (C) 2015 - IIT Bombay - FOSSEE
-//
-// Author: Harpreet Singh
-// Organization: FOSSEE, IIT Bombay
-// Email: harpreet.mertia@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] = qpipoptmat (varargin)
-  // Solves a linear quadratic problem.
-  //
-  //   Calling Sequence
-  //   x = qpipoptmat(H,f)
-  //   x = qpipoptmat(H,f,A,b)
-  //   x = qpipoptmat(H,f,A,b,Aeq,beq)
-  //   x = qpipoptmat(H,f,A,b,Aeq,beq,lb,ub)
-  //   x = qpipoptmat(H,f,A,b,Aeq,beq,lb,ub,x0)
-  //   x = qpipoptmat(H,f,A,b,Aeq,beq,lb,ub,x0,param)
-  //   [xopt,fopt,exitflag,output,lamda] = qpipoptmat( ... )
-  //   
-  //   Parameters
-  //   H : a n x n matrix of doubles, where n is number of variables, represents coefficients of quadratic in the quadratic problem.
-  //   f : a n x 1 matrix of doubles, where n is number of variables, represents coefficients of linear in the quadratic problem
-  //   A : a m x n matrix of doubles, represents the linear coefficients in the inequality constraints
-  //   b : a column vector of doubles, represents the linear coefficients in the inequality constraints
-  //   Aeq : a meq x n matrix of doubles, represents the linear coefficients in the equality constraints
-  //   beq : a vector of doubles, represents the linear coefficients in the equality constraints
-  //   LB : a n x 1 matrix of doubles, where n is number of variables, contains lower bounds of the variables.
-  //   UB : a n x 1 matrix of doubles, where n is number of variables, contains upper bounds of the variables.
-  //   x0 : a m x 1 matrix of doubles, where m is number of constraints, contains initial guess of variables.
-  //   param : a list containing the the parameters to be set.
-  //   xopt : a nx1 matrix of doubles, the computed solution of the optimization problem.
-  //   fopt : a 1x1 matrix of doubles, the function value at x.
-  //   exitflag : Integer identifying the reason the algorithm terminated.
-  //   output : Structure containing information about the optimization.
-  //   lambda : Structure containing the Lagrange multipliers at the solution x (separated by constraint type).
-  //   
-  //   Description
-  //   Search the minimum of a constrained linear quadratic optimization problem specified by :
-  //   find the minimum of f(x) such that 
-  //
-  //   <latex>
-  //    \begin{eqnarray}
-  //    &\mbox{min}_{x}
-  //    & 1/2*x'*H*x + f'*x  \\
-  //    & \text{subject to} & A.x \leq b \\
-  //    & & Aeq.x \leq beq \\
-  //    & & lb \leq x \leq ub \\
-  //    \end{eqnarray}
-  //   </latex>
-  //   
-  //   We are calling IPOpt for solving the quadratic problem, IPOpt is a library written in C++. The code has been written by ​Andreas Wächter and ​Carl Laird.
-  //
-  // Examples
-  //      //Find x in R^6 such that:
-  //      
-  //      Aeq= [1,-1,1,0,3,1;
-  //           -1,0,-3,-4,5,6;
-  //           2,5,3,0,1,0];
-  //      beq=[1; 2; 3];
-  //      A= [0,1,0,1,2,-1;
-  //          -1,0,2,1,1,0];
-  //      b = [-1; 2.5];
-  //      lb=[-1000; -10000; 0; -1000; -1000; -1000];
-  //      ub=[10000; 100; 1.5; 100; 100; 1000];
-  //      x0 = repmat(0,6,1);
-  //	  param = list("MaxIter", 300, "CpuTime", 100);
-  //      //and minimize 0.5*x'*Q*x + p'*x with
-  //      f=[1; 2; 3; 4; 5; 6]; H=eye(6,6);
-  //      [xopt,fopt,exitflag,output,lambda]=qpipoptmat(H,f,A,b,Aeq,beq,lb,ub,[],param)
-  //      clear H f A b Aeq beq lb ub;
-  //    
-  // Examples 
-  //    //Find the value of x that minimize following function
-  //    // f(x) = 0.5*x1^2 + x2^2 - x1*x2 - 2*x1 - 6*x2
-  //    // Subject to:
-  //    // x1 + x2 ≤ 2
-  //    // –x1 + 2x2 ≤ 2
-  //    // 2x1 + x2 ≤ 3
-  //    // 0 ≤ x1, 0 ≤ x2.
-  //	H = [1 -1; -1 2]; 
-  //	f = [-2; -6];
-  //    A = [1 1; -1 2; 2 1];
-  //	b = [2; 2; 3];
-  //	lb = [0; 0];
-  //	ub = [%inf; %inf];
-  //	[xopt,fopt,exitflag,output,lambda] = qpipoptmat(H,f,A,b,[],[],lb,ub)
-  //
-  // 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 < 2 | rhs == 3 | rhs == 5 | rhs == 7 | rhs > 10 ) then
-    errmsg = msprintf(gettext("%s: Unexpected number of input arguments : %d provided while should be in the set of [2 4 6 8 9 10]"), "qpipoptmat", rhs);
-    error(errmsg)
-   end
-   
-   H = varargin(1);
-   f = varargin(2);
-   nbVar = size(H,1);
-
-   
-   if ( rhs<2 ) then
-      A = []
-      b = []
-   else
-      A = varargin(3);
-      b = varargin(4);
-  end
-      
-   if ( rhs<4 ) then
-      Aeq = []
-      beq = []
-   else
-      Aeq = varargin(5);
-      beq = varargin(6);
-  end
-  
-  if ( rhs<6 ) then
-      LB = repmat(-%inf,nbVar,1);
-      UB = repmat(%inf,nbVar,1);
-   else
-      LB = varargin(7);
-      UB = varargin(8);
-  end
-
-
-  if ( rhs<10 | size(varargin(9)) ==0 ) then
-      x0 = repmat(0,nbVar,1)
-  else
-      x0 = varargin(9);
-  end
-
-   if ( rhs<11 ) then
-      param = list();
-   else
-      param =varargin(10);
-   end
-   
-
-   if (modulo(size(param),2)) then
-	errmsg = msprintf(gettext("%s: Size of parameters should be even"), "qpipoptmat");
-	error(errmsg);
-   end
-
-
-   options = list(..
-      "MaxIter"     , [3000], ...
-      "CpuTime"   , [600] ...
-      );
-
-   for i = 1:(size(param))/2
-        
-       	select param(2*i-1)
-    	case "MaxIter" then
-          		options(2*i-1) = param(2*i);
-       	case "CpuTime" then
-          		options(2*i-1) = param(2*i);
-    	else
-    	      errmsg = msprintf(gettext("%s: Unrecognized parameter name ''%s''."), "qpipoptmat", param(2*i-1));
-    	      error(errmsg)
-    	end
-   end
-
-   nbConInEq = size(A,1);
-   nbConEq = size(Aeq,1);
-
-   //Checking the H matrix which needs to be a symmetric matrix
-   if ( H~=H') then
-      errmsg = msprintf(gettext("%s: H is not a symmetric matrix"), "qpipoptmat");
-      error(errmsg);
-   end
-
-   //Check the size of H which should equal to the number of variable
-   if ( size(H) ~= [nbVar nbVar]) then
-      errmsg = msprintf(gettext("%s: The Size of H is not equal to the number of variables"), "qpipoptmat");
-      error(errmsg);
-   end
-   
-   //Check the size of f which should equal to the number of variable
-   if ( size(f,1) ~= [nbVar]) then
-      errmsg = msprintf(gettext("%s: The Size of f is not equal to the number of variables"), "qpipoptmat");
-      error(errmsg);
-   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 size of inequality constraints is not equal to the number of variables"), "qpipoptmat");
-      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 size of equality constraints is not equal to the number of variables"), "qpipoptmat");
-      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"), "qpipoptmat");
-      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"), "qpipoptmat");
-      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,1) ~= 0) then
-      errmsg = msprintf(gettext("%s: The Lower Bound of inequality constraints is not equal to the number of constraints"), "qpipoptmat");
-      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,1) ~= 0) then
-      errmsg = msprintf(gettext("%s: The Upper Bound of equality constraints is not equal to the number of constraints"), "qpipoptmat");
-      error(errmsg);
-   end
-
-   //Check the size of initial of variables which should equal to the number of variables
-   if ( size(x0,1) ~= nbVar) then
-      errmsg = msprintf(gettext("%s: The initial guess of variables is not equal to the number of variables"), "qpipoptmat");
-      error(errmsg);
-   end
-
-   
-   //Converting it into ipopt format
-   f = f';
-   LB = LB';
-   UB = UB';
-   x0 = x0';
-   conMatrix = [Aeq;A];
-   nbCon = size(conMatrix,1);
-   conLB = [beq; repmat(-%inf,nbConInEq,1)]';
-   conUB = [beq;b]' ; 
-   [xopt,fopt,status,iter,Zl,Zu,lmbda] = solveqp(nbVar,nbCon,H,f,conMatrix,conLB,conUB,LB,UB,x0,options);
-   
-   xopt = xopt';
-   exitflag = status;
-   output = struct("Iterations"      , []);
-   output.Iterations = iter;
-   lambda = struct("lower"           , [], ..
-                   "upper"           , [], ..
-                   "ineqlin"         , [], ..
-                   "eqlin"           , []);
-   
-   lambda.lower = Zl;
-   lambda.upper = Zu;
-   lambda.eqlin = lmbda(1:nbConEq);
-   lambda.ineqlin = lmbda(nbConEq+1:nbCon);
-    
-
-endfunction