pwf.m

optimization toolbox

function varargout = pwf(varargin)
%PWF Defines a piecewise function
%
% t = PWF(h1,F1,h2,F2,...,hn,Fn)
%
% The variable t can only be used in convexity/concavity preserving
% operations, depending on the convexity of hi

% Author Johan L鰂berg
% $Id: pwf.m,v 1.9 2006/07/11 13:48:05 joloef Exp $

switch class(varargin{1})
        
    case {'cell','struct'}
        % This should be an internal call to 
        % setup a pwa function defined fromk MPT
                
        if nargin<3
            pwaclass = 'general'
        end

        if isa(varargin{1},'struct')
            varargin{1} = {varargin{1}};
        end

        % Put in standard format
        if ~isfield(varargin{1}{1},'Bi')
            if ~isfield(varargin{1}{1},'Fi')
                error('Wrong format on input to PWA (requires Bi or Fi)');
            else
                for i = 1:length(varargin{1})
                    varargin{1}{1}.Ai = cell(1, varargin{1}{i}.Fi);
                    varargin{1}{i}.Bi = varargin{1}{i}.Fi
                    varargin{1}{i}.Ci = varargin{1}{i}.Gi
                end
            end
        end
        
        if isempty(varargin{1}{1}.Ai{1})
            varargout{1} = pwa_yalmip(varargin{:});
        else
            if  nnz([varargin{1}{1}.Ai{:}]) == 0
                varargout{1} = pwa_yalmip(varargin{:});
            else
                varargout{1} = pwq_yalmip(varargin{:});
            end
        end
        
    case {'sdpvar','double'} % Overloaded operator for SDPVAR objects. Pass on args and save them.
        if length(varargin{1}) == 1
            varargout{1} = yalmip('addextendedvariable',mfilename,varargin{:});
        else
            y = [];
            VV = varargin;
            for i = 1:length(varargin{1})
                VV = varargin;
                for j = 1:(length(varargin)/2)
                    VV{2*j-1} = VV{2*j-1}(i);
                end
                y = [y;yalmip('addextendedvariable',mfilename,VV{:})];
            end
            varargout{1} = y;
        end

    case 'char' % YALMIP sends 'model' when it wants the epigraph or hypograph
        if isequal(varargin{1},'graph')
            varargout{1} = [];
            varargout{2} =  struct('convexity','failure','monotoncity','failure','definiteness','failure');;
            varargout{3} = [];
        elseif isequal(varargin{1},'milp')
            % pwf represented by t
            t = varargin{2};
            % Get functions and guards
            for i = 3:2:nargin
                f{(i-1)/2} = varargin{i};
                Guard{(i+1)/2-1} = varargin{i+1};
            end

            % Indicator for where we are
            indicators = binvar(length(f),1);
            % We are in some of the regions
            F = set(sum(indicators) == 1);

            % Control where we are using the indicators and big-M
            X = [];
            for i = 1:length(Guard)
                Xi = sdpvar(Guard{i});
                if is(Xi,'linear')
                    [M,m] = derivebounds(Xi);
                else
                    m = -1e4;
                end
                F = F + set(Xi >= m*(1-indicators(i)));
                X = [X;recover(depends(Guard{i}))];
            end
            % cost = sum(delta_i*cost_i(x)) = sum(cost_i(delta_i*x))
            X = recover(getvariables(X));

            if 0
                cost = 0;
                for i = 1:length(f)
                    [Q{i},c{i},g{i},xi,info] = quaddecomp(f{i},X);
                    if info
                        error('Only convex quadratic functions allowed in PWF');
                    end
                    [M,m] = derivebounds(xi);
                    z{i} = sdpvar(length(xi),1);
                    cost = cost + z{i}'*Q{i}*z{i}+c{i}'*z{i} + g{i}*indicators(i);
                    F = F + set(xi+(1-indicators(i))*m<z{i}<xi+(1-indicators(i)).*M);
                    F = F + set(m*indicators(i) < z{i} < M*indicators(i));
                end
                F = F + set(cost < t);
            else
                fmax_max = -inf;
                fmin_min = inf;
                for i = 1:length(f)
                    [Q{i},c{i},g{i},xi,info] = quaddecomp(f{i},X);
                    if info
                        error('Only convex quadratic functions allowed in PWF');
                    end                    
                    [fmax,fmin] = derivebounds(c{i}'*xi+g{i});                                        
                    fmax_max = max(fmax,fmax_max);
                    fmin_min = min(fmin,fmin_min);
                    F = F + set(c{i}'*xi +g{i} < t + fmax*(1-indicators(i)));
                end
            end
            % To help variable strenghtening, constraint removal etc in
            % other functions, let us update the internal bound info
            bounds(t,fmin_min,fmax_max);

            % This function is convex when we relax the binary variables
            varargout{1} = F;
            varargout{2} = struct('convexity','milp','monotoncity','milp','definiteness','none');
            varargout{3} = X;
        else
            error('SDPVAR/NORM called with CHAR argument?');
        end
    otherwise
        error('Strange type on first argument in SDPVAR/NORM');
end