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diff --git a/macros/lsqlin.sci b/macros/lsqlin.sci new file mode 100644 index 0000000..003edc5 --- /dev/null +++ b/macros/lsqlin.sci @@ -0,0 +1,372 @@ +// 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] = lsqlin (varargin) + // Solves a linear quadratic problem. + // + // Calling Sequence + // x = lsqlin(C,d,A,b) + // x = lsqlin(C,d,A,b,Aeq,beq) + // x = lsqlin(C,d,A,b,Aeq,beq,lb,ub) + // x = lsqlin(C,d,A,b,Aeq,beq,lb,ub,x0) + // x = lsqlin(C,d,A,b,Aeq,beq,lb,ub,x0,param) + // [xopt,resnorm,residual,exitflag,output,lambda] = lsqlin( ... ) + // + // 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. + // A : a vector of doubles, represents the linear coefficients in the inequality constraints + // b : a vector of doubles, represents the linear coefficients in the inequality constraints + // Aeq : a 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 vector of doubles, where n is number of variables, contains lower bounds of the variables. + // UB : a vector of doubles, where n is number of variables, contains upper bounds of the variables. + // x0 : a vector of doubles, contains initial guess of variables. + // param : a list containing the the parameters to be set. + // xopt : a vector of doubles, the computed solution of the optimization problem. + // fopt : a double, 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 least square problem specified by : + // find the minimum of f(x) such that + // + // <latex> + // \begin{eqnarray} + // &\mbox{min}_{x} + // & 1/2||C*x - d||_2^2 \\ + // & \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 linear least square problem, IPOpt is a library written in C++. The code has been written by Andreas Wächter and Carl Laird. + // + // Examples + // //A simple linear least square example + // C = [0.9501 0.7620 0.6153 0.4057 + // 0.2311 0.4564 0.7919 0.9354 + // 0.6068 0.0185 0.9218 0.9169 + // 0.4859 0.8214 0.7382 0.4102 + // 0.8912 0.4447 0.1762 0.8936]; + // d = [0.0578 + // 0.3528 + // 0.8131 + // 0.0098 + // 0.1388]; + // A = [0.2027 0.2721 0.7467 0.4659 + // 0.1987 0.1988 0.4450 0.4186 + // 0.6037 0.0152 0.9318 0.8462]; + // b = [0.5251 + // 0.2026 + // 0.6721]; + // [xopt,resnorm,residual,exitflag,output,lambda] = lsqlin(C,d,A,b) + // + // Examples + // C = [0.9501 0.7620 0.6153 0.4057 + // 0.2311 0.4564 0.7919 0.9354 + // 0.6068 0.0185 0.9218 0.9169 + // 0.4859 0.8214 0.7382 0.4102 + // 0.8912 0.4447 0.1762 0.8936]; + // d = [0.0578 + // 0.3528 + // 0.8131 + // 0.0098 + // 0.1388]; + // A =[0.2027 0.2721 0.7467 0.4659 + // 0.1987 0.1988 0.4450 0.4186 + // 0.6037 0.0152 0.9318 0.8462]; + // b =[0.5251 + // 0.2026 + // 0.6721]; + // Aeq = [3 5 7 9]; + // beq = 4; + // lb = -0.1*ones(4,1); + // ub = 2*ones(4,1); + // [xopt,resnorm,residual,exitflag,output,lambda] = lsqlin(C,d,A,b,Aeq,beq,lb,ub) + // + // 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 < 4 | 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 [4 6 8 9 10]"), "lsqlin", rhs); + error(errmsg) + end + + C = varargin(1); + d = varargin(2); + A = varargin(3); + b = varargin(4); + nbVar = size(C,2); + + if ( rhs<5 ) then + Aeq = [] + beq = [] + else + Aeq = varargin(5); + beq = varargin(6); + end + + if ( rhs<7 ) then + LB = repmat(-%inf,nbVar,1); + UB = repmat(%inf,nbVar,1); + else + LB = varargin(7); + UB = varargin(8); + end + + + if ( rhs<9 | size(varargin(9)) ==0 ) then + x0 = repmat(0,nbVar,1) + else + x0 = varargin(9); + end + + if ( rhs<10 | size(varargin(10)) ==0 ) then + param = list(); + else + param =varargin(10); + end + + 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: 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 + + nbConInEq = size(A,1); + nbConEq = size(Aeq,1); + + // Check if the user gives row vector + // and Changing it to a column matrix + + + if (size(d,2)== [nbVar]) then + d=d'; + end + + 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 + + if (size(x0,2)== [nbVar]) then + x0=x0'; + 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 + + //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 d"), "lsqlin"); + 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 d"), "lsqlin"); + 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"), "lsqlin"); + 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"), "lsqlin"); + 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 number of rows in A must be the same as the number of elementsof b"), "lsqlin"); + 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 number of rows in Aeq must be the same as the number of elements of beq"), "lsqlin"); + error(errmsg); + end + + //Check the size of initial of variables which should equal to the number of variables + if ( size(x0,1) ~= nbVar) then + warnmsg = msprintf(gettext("%s: Ignoring initial guess of variables as it is not equal to the number of variables"), "lsqlin"); + warning(warnmsg); + end + + //Check if the user gives a matrix instead of a vector + + if ((size(d,1)~=1)& (size(d,2)~=1)) then + errmsg = msprintf(gettext("%s: d should be a vector"), "lsqlin"); + error(errmsg); + end + + if (size(LB,1)~=1)& (size(LB,2)~=1) then + errmsg = msprintf(gettext("%s: Lower Bound should be a vector"), "lsqlin"); + error(errmsg); + end + + if (size(UB,1)~=1)& (size(UB,2)~=1) then + errmsg = msprintf(gettext("%s: Upper Bound should be a vector"), "lsqlin"); + 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"), "lsqlin"); + 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"), "lsqlin"); + error(errmsg); + end + end + + for i = 1:nbConInEq + if (b(i) == -%inf) + errmsg = msprintf(gettext("%s: Value of b can not be negative infinity"), "qpipoptmat"); + error(errmsg); + end + end + + for i = 1:nbConEq + if (beq(i) == -%inf) + errmsg = msprintf(gettext("%s: Value of beq can not be negative infinity"), "qpipoptmat"); + error(errmsg); + end + end + + //Converting it into Quadratic Programming Problem + + Q = C'*C; + p = [-C'*d]'; + op_add = d'*d; + 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,Q,p,conMatrix,conLB,conUB,LB,UB,x0,options); + + xopt = xopt'; + residual = C*xopt-d; + resnorm = residual'*residual; + exitflag = status; + output = struct("Iterations" , []); + output.Iterations = iter; + lambda = struct("lower" , [], .. + "upper" , [], .. + "constraint" , []); + + lambda.lower = Zl; + lambda.upper = Zu; + lambda.constraint = lmbda; + + 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 |