MATLAB_nonlinear_regression.zip_regression_supercontinuum

function y = apm_quadprog(H,f,A,b,Aeq,beq,lb,ub,x0) %apm_quadprog Quadratic programming. % y = apm_quadprog(H,f,A,b,Aeq,beq,LB,UB,X0) writes a quadratic % programming model in APMonitor Modeling Language and attempts % to solve the quadratic programming problem: % % min 0.5*x'*H*x + f'*x subject to: A*x <= b, Aeq*x = beq % x % % lb and ub are a set of lower and upper bounds on the design variables, % x, so that the solution is in the range lb <= x <= ub. Use empty % matrices for any of the arguments. Set lb(i) = -1e20 if x(i) has no % lower limit and set ub(i) = 1e20 if x(i) has no upper limit. x0 is % the initial guess and starting point to x. This is similar to the % Matlab quadprog solver but uses different solvers such as IPOPT, % APOPT, and BPOPT to solve the QP. Additional nonlinear constraints % can be added to the qp.apm model for nonlinear programming solution % with support for possible mixed-integer variables. % % The solution is returned in the structure y with y.names (variable % names), y.values (variable values), y.nvar (number of variables), % and y.x (a structure containing each variable and value). % % Example usage is below: % % clear all; close all; clc % disp('APM MATLAB available for download at http://apmonitor.com') % addpath('apm') % % %% example Quadratic program % H = [1 -1; -1 2]; % f = [-2; -6]; % A = [1 1; -1 2; 2 1]; % b = [2; 2; 3]; % Aeq = []; % beq = []; % lb = zeros(2,1); % ub = []; % x0 = []; % % %% generate APMonitor QP model % y1 = apm_quadprog(H,f,A,b,Aeq,beq,lb,ub,x0); % % %% compare solution to quadprog (MATLAB) % y2 = quadprog(H,f,A,b,Aeq,beq,lb,ub,x0) % % disp('Validate Results with MATLAB linprog') % for i = 1:nx, % disp(['x[' int2str(i) ']: ' num2str(y1.values(i)) ' = ' num2str(y2(i))]) % end % filename to write filename = ['qp.apm']; % extract H and f in sparse form if ~isempty(H), [mH,nH] = size(H); if (mH~=nH), error('H must be a square matrix'); end if isempty(f), f = zeros(mH,1); mf = mH; else if size(f,1)==1, f = f'; end [mf,nf] = size(f); end if (mH~=mf), error('Rows of H and f must agree'); end % convert to sparse form [hi,hj,hv] = find(sparse(H)); h = [hi,hj,hv]'; [fi,fj,fv] = find(sparse(f)); f = [fi,fj,fv]'; if(size(f,2)==0), f = [1,1,0]'; end fr = [f(1,:); f(3,:)]; end % extract A and b in sparse form if ~isempty(A), [mA,nA] = size(A); if isempty(b), b = zeros(mA,1); mB = mA; else if size(b,1)==1, b = b'; end [mB,nB] = size(b); end if (mA~=mB), error('Rows of A and b must agree'); end % convert to sparse form [ai,aj,av] = find(sparse(A)); if (mA==1), a = [ai;aj;av]; else a = [ai,aj,av]'; end [bi,bj,bv] = find(sparse(b)); b = [bi,bj,bv]'; if(size(b,2)==0), b = [1,1,0]'; end br = [b(1,:); b(3,:)]; end % extract Aeq and beq in sparse form if ~isempty(Aeq), [mAeq,nAeq] = size(Aeq); if isempty(beq), beq = zeros(mAeq,1); mBeq = mAeq; else if size(beq,1)==1, beq = beq'; end [mBeq,nBeq] = size(beq); end if (mAeq~=mBeq), error('Rows of Aeq and beq must agree'); end % convert to sparse form [aeqi,aeqj,aeqv] = find(sparse(Aeq)); if (mAeq==1), aeq = [aeqi;aeqj;aeqv]; else aeq = [aeqi,aeqj,aeqv]'; end [beqi,beqj,beqv] = find(sparse(beq)); beq = [beqi,beqj,beqv]'; if(size(beq,2)==0), beq = [1,1,0]'; end beqr = [beq(1,:); beq(3,:)]; end disp('Creating Quadratic Programming Model qp.apm'); fid = fopen(filename,'w'); fprintf( fid,'\n'); fprintf( fid,'Objects \n'); if ~isempty(H), fprintf( fid,[' h = qobj\n']); end if ~isempty(A), fprintf( fid,[' a = axb\n']); end if ~isempty(Aeq), fprintf( fid,[' aeq = axb\n']); end fprintf( fid,'End Objects \n'); fprintf( fid,'\n'); fprintf( fid,'Connections\n'); sz = -1; if ~isempty(H), fprintf( fid,[' x[1:%d] = h.x[1:%d]\n'],nH,nH); sz = nH; end if ~isempty(A), fprintf( fid,[' x[1:%d] = a.x[1:%d]\n'],nA,nA); if (sz>=0), if (nA~=sz), error('Variables in Ax < b model must be consistent'); end end end if ~isempty(Aeq), fprintf( fid,[' x[1:%d] = aeq.x[1:%d]\n'],nAeq,nAeq); if (sz>=0), if (nAeq~=sz), error('Variables in Ax = b model must be consistent'); end end end fprintf( fid,'End Connections\n'); fprintf( fid,'\n'); fprintf( fid,'Model \n'); fprintf( fid,' Variables \n'); if (isempty(x0)&&isempty(lb)&&isempty(ub)), % default initial conditions fprintf( fid,' x[1:%d] = 0\n',nH); else % create default values if (isempty(x0)), x0 = zeros(nH,1); end if (isempty(lb)), lb = -1e10 * ones(nH,1); end if (isempty(ub)), ub = 1e10 * ones(nH,1); end % generate initial conditions and bounds for i = 1:nH, fprintf( fid,' x[%i] > %d = %d < %d\n',i,lb(i),x0(i),ub(i)); end end fprintf( fid,' End Variables \n'); fprintf( fid,'\n'); fprintf( fid,' Equations \n'); fprintf( fid,' ! add any additional equations here \n'); fprintf( fid,' End Equations \n'); fprintf( fid,'End Model \n'); fprintf( fid,'\n'); if ~isempty(H), fprintf( fid,'\n'); fprintf( fid,['File h.txt\n']); fprintf( fid,[' sparse, minimize ! dense or sparse, minimize or maximize\n']); fprintf( fid,' %d ! n=number of variables \n',mH); fprintf( fid,'End File\n'); fprintf( fid,'\n'); fprintf( fid,['File h.a.txt \n']); fprintf( fid,' %d %d %f\n', h ); fprintf( fid,'End File \n'); fprintf( fid,'\n'); fprintf( fid,['File h.b.txt \n']); fprintf( fid,' %d %f\n', fr ); fprintf( fid,'End File \n'); end if ~isempty(A), fprintf( fid,'\n'); fprintf( fid,['File a.txt\n']); fprintf( fid,[' sparse, Ax<b \n']); fprintf( fid,' %d ! m=number of rows in A and b \n',mA); fprintf( fid,' %d ! n=number of columns in A or variables x\n',nA); fprintf( fid,'End File\n'); fprintf( fid,'\n'); fprintf( fid,['File a.a.txt \n']); fprintf( fid,' %d %d %f\n', a ); fprintf( fid,'End File \n'); fprintf( fid,'\n'); fprintf( fid,['File a.b.txt \n']); fprintf( fid,' %d %f\n', br ); fprintf( fid,'End File \n'); end if ~isempty(Aeq), fprintf( fid,'\n'); fprintf( fid,['File aeq.txt\n']); fprintf( fid,[' sparse, Ax=b \n']); fprintf( fid,' %d ! m=number of rows in A and b \n',mAeq); fprintf( fid,' %d ! n=number of columns in A or variables x\n',nAeq); fprintf( fid,'End File\n'); fprintf( fid,'\n'); fprintf( fid,['File aeq.a.txt \n']); fprintf( fid,' %d %d %f\n', aeq ); fprintf( fid,'End File \n'); fprintf( fid,'\n'); fprintf( fid,['File aeq.b.txt \n']); fprintf( fid,' %d %f\n', beqr ); fprintf( fid,'End File \n'); end fclose(fid); disp('Solving Quadratic Programming Model qp.apm'); s = 'http://xps.apmonitor.com'; a = 'qp'; apm(s,a,'clear all'); apm_load(s,a,'qp.apm'); % select solver (1=APOPT,2=BPOPT,3=IPOPT) apm_option(s,a,'nlc.solver',1); output = apm(s,a,'solve'); disp(output); % return solution y = apm_sol(s,a); end