203 lines
8.1 KiB
Mathematica
203 lines
8.1 KiB
Mathematica
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function varargout = pwq_yalmip(varargin)
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%PWQ_YALMIP Defines a piecewise quadratic 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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% Currently only a container for PWQ functions. Can not be
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% used in actual optmization problem.
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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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for k = 1:length(jj)
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Q = pwastruct{i}.Ai{jj(k)};
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if index>1 | min(size(pwastruct{i}.Bi{jj(k)}))>1
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% FIX: Why?? Where is this feature used
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val = min(val,x'*Q*x + reshape(pwastruct{i}.Bi{jj(k)}(index,:),1,[])*x+pwastruct{i}.Ci{jj(k)}(index));
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else
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val = min(val,x'*Q*x + reshape(pwastruct{i}.Bi{jj(k)},1,[])*x+pwastruct{i}.Ci{jj(k)});
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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} = min(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 PWQ (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}{1}.Ai = cell(1, varargin{1}{i}.Fi);
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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 PWQ (requires field Pn)');
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end
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% This will be a container for binary variables in the furture
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varargin{end+1} = binvar(length(varargin{1}{1}.Pn),1);
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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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varargout{1} = [];
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varargout{2} = struct('convexity','none','monotoncity','none','definiteness','none');
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varargout{3} = [];
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case {'integer','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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pwq_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 length(d)==1
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% Don't introduce any binary variables when
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% there is only one quadratic cost
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F = ([]);
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cost = x'*pwq_struct{1}.Ai{1}*x+pwq_struct{1}.Bi{1}*x+pwq_struct{1}.Ci{1};
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else
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n = length(x);
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m = length(d);
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z = sdpvar(n,m,'full');
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F = (sum(d) == 1);
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cost = 0;
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[Mm,mm] = derivebounds(x);
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try
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[aux,mx,Mx] = bounding_box(pwq_struct{1}.Pfinal);
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catch
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Mx = 10000*ones(length(x),1);
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mx = -10000*ones(length(x),1);
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end
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Mx = min([Mx Mm],[],2);
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mx = max([mx mm],[],2);
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for i = 1:m
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% bounds(z(:,i),mx,Mx);
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F = F + (-(Mx-mx)*(1-d(i)) <= z(:,i)-x <= (Mx-mx)*(1-d(i)));
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F = F + (mx*d(i) <= z(:,i) <= Mx*d(i));
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[H,K] = double(pwq_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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cost = cost + z(:,i)'*pwq_struct{1}.Ai{i}*z(:,i)+pwq_struct{1}.Bi{i}(:)'*z(:,i)+d(i)*pwq_struct{1}.Ci{i};
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end
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end
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varargout{1} = F;
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varargout{2} = struct('convexity','none','monotoncity','none','definiteness','none','model','integer');
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varargout{2}.replacer = cost;
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varargout{3} = x;
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case {'convexoverlapping'}
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n = length(x);
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cost = 0;
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r = binvar(length(pwq_struct),1);
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d = {};
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% Derive bounds from polytopes
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[aux,mx,Mx] = bounding_box(pwq_struct{1}.Pfinal);
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for i = 2:length(pwq_struct)
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[aux,L,U] = bounding_box(pwq_struct{i}.Pfinal);
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Mx = max([Mx U],[],2);
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mx = min([mx L],[],2);
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end
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bounds(x,mx,Mx);
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% Some overlapping function is active
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% (it will automatically be the smallest one)
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F = (sum(r) == 1);
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for j = 1:length(pwq_struct)
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if length(pwq_struct{j}.Pn) == 1
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d{j} = r(j);
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else
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d{j} = binvar(length(pwq_struct{j}.Pn),1);
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F = F + (sum(d{j}) == r(j));
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end
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m = length(d{j});
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z = sdpvar(n,m,'full');
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for i = 1:m
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bounds(z(:,i),mx,Mx);
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F = F + (-(Mx-mx)*(1-d{j}(i)) <= z(:,i)-x <= (Mx-mx)*(1-d{j}(i)));
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F = F + (mx*d{j}(i) <= z(:,i) <= Mx*d{j}(i));
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[H,K] = double(pwq_struct{j}.Pn(i));
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[M,m] = derivebounds(H*x-K);
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F = F + (H*x-K <= M*(1-d{j}(i)));
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cost = cost + z(:,i)'*pwq_struct{j}.Ai{i}*z(:,i)+pwq_struct{j}.Bi{i}*z(:,i)+d{j}(i)*pwq_struct{j}.Ci{i};
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end
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end
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varargout{1} = F;
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varargout{2} = struct('convexity','none','monotoncity','none','definiteness','none','model','integer');
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varargout{2}.replacer = cost;
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varargout{3} = x;
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otherwise
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varargout{1} = [];
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varargout{2} = struct('convexity','convex','monotoncity','none','definiteness','none');
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varargout{3} = [];
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return
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end
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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 PWQ_YALMIP');
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end
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