297 lines
12 KiB
Mathematica
297 lines
12 KiB
Mathematica
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function varargout = pwa_yalmip(varargin)
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%PWA_YALMIP Defines a piecewise function using data from MPT
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%
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%Only intended for internal use in YALMIP
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%
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% Three classes of PWA functions can be generated
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%
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% 1) Convexity aware epigraph version with a
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% convex domain and objective modelled as c'x <t.
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% Note, if used in non-concvex setting, a milp
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% model will be generated as a back-up.
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%
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% This is the function generated to describe value
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% function of a single mpLP problem.
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%
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% 2) Overlapping partitions with convex functions
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% in each partition. Requires one binary per region.
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%
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% This is the function used to describe the value
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% function generated when not removing overlaps in
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% binary mpLP.
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%
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% 3) Non-overlapping general pwa function. Requires
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% one binary per region.
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%
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% This is the function generated for value functions
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% when remove overlaps is done. It is also used to
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% describe the pwa optimizer.
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%
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% The input is a cell with structs. Each struct has
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% the fields Pn, Pfinal, Bi and Ci (or Fi and Gi)
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switch class(varargin{1})
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case {'struct','cell'} % Should only be called internally
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if isa(varargin{2},'double')
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% Called from YALMIP to get double
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pwastruct = varargin{1};
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x = varargin{2};
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index = varargin{5};
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val = inf;
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for i = 1:length(pwastruct)
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[ii,jj] = isinside(pwastruct{i}.Pn,x);
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if ii
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if isfield(pwastruct{1},'valuefunction')
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% Several solutions, pick the one related to the lowest value function
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valfcn = [];
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for k = 1:length(jj)
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valfcn = [valfcn pwastruct{i}.valuefunction.Bi{jj(k)}*x+pwastruct{i}.valuefunction.Ci{jj(k)}];
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end
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[iii,jjj] = min(valfcn);
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val = min(val,pwastruct{i}.Bi{jj(jjj)}(index,:)*x+pwastruct{i}.Ci{jj(jjj)}(index));
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else
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% Several solutions, pick the lowest one
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for k = 1:length(jj)
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val = min(val,pwastruct{i}.Bi{jj(k)}(index,:)*x+pwastruct{i}.Ci{jj(k)}(index));
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end
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end
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end
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end
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if isinf(val)
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val = nan;
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end
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varargout{1} = val;
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return
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end
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if nargin<3
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pwaclass = 'general'
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end
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if isa(varargin{1},'struct')
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varargin{1} = {varargin{1}};
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end
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% Put in standard format
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if ~isfield(varargin{1}{1},'Bi')
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if ~isfield(varargin{1}{1},'Fi')
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error('Wrong format on input to PWA (requires Bi or Fi)');
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else
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for i = 1:length(varargin{1})
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varargin{1}{i}.Bi = varargin{1}{i}.Fi
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varargin{1}{i}.Ci = varargin{1}{i}.Gi
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end
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end
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end
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if ~isfield(varargin{1}{1},'Pfinal')
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error('Wrong format on input to PWA (requires field Pn)');
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end
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% Create binary variables already here to avoid generating
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% binary variables for the same variable several times
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switch varargin{3}
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case 'convex'
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% No binary needed
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varargin{end+1} = [];
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case 'convexoverlapping'
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% One binary per overlap
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varargin{end+1} = binvar(length(varargin{1}),1);
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case 'general'
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% one binary per region
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varargin{end+1} = binvar(length(varargin{1}{1}.Pn),1);
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otherwise
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end
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% Create one variable for each row
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% Inefficient but the only way currently in YALMIP
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varargout{1} = [];
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varargin{end+1} = 1;
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for i = 1:length(varargin{1}{1}.Ci{1})
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varargin{end} = i;
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varargout{1} = [varargout{1};yalmip('define',mfilename,varargin{:})];
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end
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case 'char' % YALMIP sends 'model' when it wants the epigraph or hypograph
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switch varargin{1}
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case 'graph'
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% Can only generate the first class of PWA functions
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t = varargin{2}; % The YALMIP variables modelling this pwa
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pwa_struct = varargin{3};% MPT structure
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x = varargin{4}; % Argument
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flag = varargin{5}; % Type of PWA function
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d = varargin{6}; % Binary for nonconvex cases
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index = varargin{7}; % Which row in Bix+Ci
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switch flag
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case 'convex'
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[H,K] = double(pwa_struct{1}.Pfinal);
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S = unique(([reshape([pwa_struct{1}.Bi{:}]',length(x),[])' reshape([pwa_struct{1}.Ci{:}]',[],1)]),'rows');
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% S = unique(round(S*1e8),'rows')/1e8;
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costs = S*[x;1];
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%costs = reshape([pwa_struct{1}.Bi{:}]',length(x),[])'*x+reshape([pwa_struct{1}.Ci{:}]',[],1);
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F = (H* x <= K) + ((costs<=t):'Epigraph of pwa');
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case 'convexoverlapping'
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% Local costs
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s = sdpvar(length(pwa_struct),1);
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% Some region, one defined as minimizer
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F = (sum(d)==1);
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maxcost = -inf;
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mincost = inf;
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for i = 1:length(pwa_struct)
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% Reduce complexity of max function by
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% removing equal costs
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B = reshape([pwa_struct{i}.Bi{:}]',length(x),[])';
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C = reshape([pwa_struct{i}.Ci{:}]',[],1);
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[ii,jj,kk] = unique(round(1e8*[B C])/1e8,'rows');
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cost = reshape([pwa_struct{i}.Bi{jj}]',length(x),[])'*x+reshape([pwa_struct{i}.Ci{jj}]',[],1);
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[M,m] = derivebounds(cost);
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maxcost = max(maxcost,max(M));
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mincost = min(mincost,min(m));
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[H,K] = double(pwa_struct{i}.Pfinal);
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[M,m] = derivebounds(H*x - K);
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F = F + (H*x-K <= (1+M)*(1-d(i)));
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end
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for i = 1:length(pwa_struct)
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B = reshape([pwa_struct{i}.Bi{:}]',length(x),[])';
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C = reshape([pwa_struct{i}.Ci{:}]',[],1);
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[ii,jj,kk] = unique(round(1e8*[B C])/1e8,'rows');
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cost = reshape([pwa_struct{i}.Bi{jj}]',length(x),[])'*x+reshape([pwa_struct{i}.Ci{jj}]',[],1);
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[M,m] = derivebounds(cost);
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F = F + (cost <= t + 2*(1+maxcost)*(1-d(i)));
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end
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[t_bounds] = yalmip('getbounds',getvariables(t));
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bounds(t,max([t_bounds(1) mincost]),min([t_bounds(2) 3*maxcost]));
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case 'general'
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% In one region
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F = (sum(d) == 1);
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% Extract the wanted row
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for i = 1:length(pwa_struct{1}.Pn)
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pwa_struct{1}.Bi{i} = pwa_struct{1}.Bi{i}(index,:);
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pwa_struct{1}.Ci{i} = pwa_struct{1}.Ci{i}(index);
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end
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% value in different regions
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costs = reshape([pwa_struct{1}.Bi{:}]',length(x),[])'*x+reshape([pwa_struct{1}.Ci{:}]',[],1);
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[M,m] = derivebounds(costs);
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% t equals some of the costs
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% Big-M : |costs-t| < max(costs)-min(t) < M-m
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F = F + ((m-max(M)).*(1-d) <= costs-t <= (M-min(m)).*(1-d));
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for i = 1:length(pwa_struct{1}.Pn)
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[H,K] = double(pwa_struct{1}.Pn(i));
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[M,m] = derivebounds(H*x - K);
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F = F + (H*x - K <= M*(1-d(i)));
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end
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otherwise
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varargout{1} = [];
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varargout{2} = struct('convexity','milp','monotonicity','none','definiteness','none');
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varargout{3} = [];
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return
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end
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varargout{1} = F;
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varargout{2} = struct('convexity','convex','monotonicity','none','definiteness','none','model','graph');
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varargout{3} = x;
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case 'exact'
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% FIX : Should create case for overlapping convex PWAs,
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% used in a nonconvex fashion...
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% Can only generate the first class of PWA functions
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t = varargin{2}; % The YALMIP variables modelling this pwa
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pwa_struct = varargin{3};% MPT structure
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x = varargin{4}; % Argument
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flag = varargin{5}; % Type of PWA function
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d = varargin{6}; % Binary for nonconvex cases
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index = varargin{7}; % Which row in Bix+Ci
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switch flag
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case {'general','convex'}
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if isempty(d)
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d = binvar(length(pwa_struct{1}.Pn),1)
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end
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F = (sum(d) == 1);
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% Extract the wanted row
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for i = 1:length(pwa_struct{1}.Pn)
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pwa_struct{1}.Bi{i} = pwa_struct{1}.Bi{i}(index,:);
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pwa_struct{1}.Ci{i} = pwa_struct{1}.Ci{i}(index);
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end
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[p,lb,ub]=bounding_box(pwa_struct{1}.Pn);
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% Cost in different regions
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H = reshape([pwa_struct{1}.Bi{:}]',length(x),[])';
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K = reshape([pwa_struct{1}.Ci{:}]',[],1);
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costs = H*x+K;
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[M,m] = derivebounds(costs);
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M2 = H.*(H>0)*ub + H.*(H<0)*lb+K;
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m2 = H.*(H>0)*lb + H.*(H<0)*ub+K;
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M = min([M M2],[],2);
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m = max([m m2],[],2);
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% Might be called with a convex function,
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% but wants the complete MILP description
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% Example : Someone tries to maximize value
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% function
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if length(d)~=length(costs)
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d = binvar(length(costs),1);
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F = (sum(d) == 1);
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end
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% t equals some of the costs
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F = F + ((m-max(M)).*(1-d) <= costs-t <= (M-min(m)).*(1-d));
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for i = 1:length(pwa_struct{1}.Pn)
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[H,K] = double(pwa_struct{1}.Pn(i));
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[M,m] = derivebounds(H*x - K);
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M2 = H.*(H>0)*ub + H.*(H<0)*lb-K;
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m2 = H.*(H>0)*lb + H.*(H<0)*ub-K;
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M = min([M M2],[],2);
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m = max([m m2],[],2);
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F = F + (H*x - K <= M*(1-d(i)));
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end
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otherwise
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varargout{1} = [];
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varargout{2} = struct('convexity','convex','monotonicity','none','definiteness','none','model','integer')
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varargout{3} = [];
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return
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end
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varargout{1} = F;
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varargout{2} = struct('convexity','none','monotonicity','none','definiteness','none','model','integer');
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varargout{3} = x;
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otherwise
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error('PWA_YALMIP called with CHAR argument?');
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end
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otherwise
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error('Strange type on first argument in SDPVAR/NORM');
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end
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