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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,resnorm,residual,exitflag,output,lambda] = lsqnonneg (varargin)
// Solves nonnegative least-squares curve fitting problems.
//
// Calling Sequence
// x = lsqnonneg(C,d)
// x = lsqnonneg(C,d,param)
// [xopt,resnorm,residual,exitflag,output,lambda] = lsqnonneg( ... )
//
// Parameters
// C : a matrix of doubles, represents the multiplier of the solution x in the expression C*x - d. C is M-by-N, where M is the number of equations, and N is the number of elements of x.
// d : a vector of doubles, represents the additive constant term in the expression C*x - d. d is M-by-1, where M is the number of equations.
// xopt : a vector of doubles, the computed solution of the optimization problem.
// resnorm : a double, objective value returned as the scalar value norm(C*x-d)^2.
// residual : a vector of doubles, solution residuals returned as the vector C*x-d.
// 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
// Solves nonnegative least-squares curve fitting problems specified by :
//
// <latex>
// \begin{eqnarray}
// &\mbox{min}_{x}
// & 1/2||C*x - d||_2^2 \\
// & & x \geq 0 \\
// \end{eqnarray}
// </latex>
//
// We are calling IPOpt for solving the nonnegative least-squares curve fitting problems, IPOpt is a library written in C++. The code has been written by Andreas Wächter and Carl Laird.
//
// Examples
// A basic lsqnonneg problem
// C = [
// 0.0372 0.2869
// 0.6861 0.7071
// 0.6233 0.6245
// 0.6344 0.6170];
// d = [
// 0.8587
// 0.1781
// 0.0747
// 0.8405];
// [xopt,resnorm,residual,exitflag,output,lambda] = lsqnonneg(C,d)
//
// Authors
// 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 ) then
errmsg = msprintf(gettext("%s: Unexpected number of input arguments : %d provided while should be in the set of [2 3]"), "lsqlin", rhs);
error(errmsg)
end
C = varargin(1);
d = varargin(2);
nbVar = size(C,2);
if ( rhs<3 | size(varargin(3)) ==0 ) then
param = list();
else
param =varargin(10);
end
if (type(param) ~= 15) then
errmsg = msprintf(gettext("%s: param should be a list "), "lsqlin");
error(errmsg);
end
if (modulo(size(param),2)) then
errmsg = msprintf(gettext("%s: Size of parameters should be even"), "lsqlin");
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) = param(2*i);
case "CpuTime" then
options(2*i) = param(2*i);
else
errmsg = msprintf(gettext("%s: Unrecognized parameter name ''%s''."), "lsqlin", param(2*i-1));
error(errmsg)
end
end
// Check if the user gives row vector
// and Changing it to a column matrix
if (size(d,2)== [nbVar]) then
d=d';
end
//Check the size of f which should equal to the number of variable
if ( size(d,1) ~= size(C,1)) then
errmsg = msprintf(gettext("%s: The number of rows in C must be equal the number of elements of d"), "lsqlin");
error(errmsg);
end
//Converting it into Quadratic Programming Problem
Q = C'*C;
p = [-C'*d]';
op_add = d'*d;
LB = repmat(0,1,nbVar);
UB = repmat(%inf,1,nbVar);
x0 = repmat(0,1,nbVar);;
conMatrix = [];
nbCon = size(conMatrix,1);
conLB = [];
conUB = [] ;
[xopt,fopt,status,iter,Zl,Zu,lmbda] = solveqp(nbVar,nbCon,Q,p,conMatrix,conLB,conUB,LB,UB,x0,options);
xopt = xopt';
residual = -1*(C*xopt-d);
resnorm = residual'*residual;
exitflag = status;
output = struct("Iterations" , []);
output.Iterations = iter;
lambda = struct("lower" , [], ..
"upper" , []);
lambda.lower = Zl;
lambda.upper = Zu;
select status
case 0 then
printf("\nOptimal Solution Found.\n");
case 1 then
printf("\nMaximum Number of Iterations Exceeded. Output may not be optimal.\n");
case 2 then
printf("\nMaximum CPU Time exceeded. Output may not be optimal.\n");
case 3 then
printf("\nStop at Tiny Step\n");
case 4 then
printf("\nSolved To Acceptable Level\n");
case 5 then
printf("\nConverged to a point of local infeasibility.\n");
case 6 then
printf("\nStopping optimization at current point as requested by user.\n");
case 7 then
printf("\nFeasible point for square problem found.\n");
case 8 then
printf("\nIterates diverging; problem might be unbounded.\n");
case 9 then
printf("\nRestoration Failed!\n");
case 10 then
printf("\nError in step computation (regularization becomes too large?)!\n");
case 12 then
printf("\nProblem has too few degrees of freedom.\n");
case 13 then
printf("\nInvalid option thrown back by IPOpt\n");
case 14 then
printf("\nNot enough memory.\n");
case 15 then
printf("\nINTERNAL ERROR: Unknown SolverReturn value - Notify IPOPT Authors.\n");
else
printf("\nInvalid status returned. Notify the Toolbox authors\n");
break;
end
endfunction
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