78 lines
2.7 KiB
Mathematica
78 lines
2.7 KiB
Mathematica
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function varargout = max_internal(varargin)
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switch class(varargin{1})
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case 'double'
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varargout{1} = max(varargin{:});
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case 'char'
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extstruct.var = varargin{2};
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extstruct.arg = {varargin{3:end}};
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[F,properties,arguments]=max_model([],varargin{1},[],extstruct);
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varargout{1} = F;
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varargout{2} = properties;
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varargout{3} = arguments;
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otherwise
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end
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function [F,properties,arguments]=max_model(X,method,options,extstruct)
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switch method
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case 'graph'
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t = extstruct.var;
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X = extstruct.arg{1};
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basis = getbase(X);
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inf_row = find(basis(:,1) == -inf);
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if length(inf_row)>0
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X(inf_row) = [];
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end
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F = t-X>= 0;
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arguments = X(:);
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any_constant = find(~any(basis(:,2:end),2));
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if ~isempty(any_constant)
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k = basis(any_constant,1);
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if any(k>=0)
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% This is something like max(x,0), so it is guaranteed to be
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% non-negative
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properties = struct('convexity','convex','monotonicity','increasing','definiteness','positive');
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else
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properties = struct('convexity','convex','monotonicity','increasing','definiteness','none');
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end
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else
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properties = struct('convexity','convex','monotonicity','increasing','definiteness','none');
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end
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case 'exact'
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arguments = [];
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F = ([]);
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t = extstruct.var;
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X = extstruct.arg{1};
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basis = getbase(X);
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inf_row = find(basis(:,1) == -inf);
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if length(inf_row)>0
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X(inf_row) = [];
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end
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X = reshape(X,length(X),1);
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if prod(size(X)) == 1
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F = F + (X == t);
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elseif (prod(size(X)) == 2) & ((nnz(basis(1,:))==0) | (nnz(basis(2,:))==0))
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% Special case to test a particular problem max(0,y), so we
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% keep it since it is optimized
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if (nnz(basis(2,:))==0)
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X = [0 1;1 0]*X;
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end
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[M,m] = derivebounds(X);
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d = binvar(1,1);
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F = [F, 0 <= t <= M(2)*d, X(2)<=M(2)*d];
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F = [F, -(1-d)*M(2) <= t-X(2) <= (-m(2))*(1-d),X(2)>=m(2)*(1-d)];
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elseif all(ismember(getvariables(X),yalmip('binvariables'))) & (is(X,'lpcone') | is(X,'sdpcone'))
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% Special case max(x) where x is simple binary
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F = [F, X <= t, sum(X) >= t];
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else
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F = max_integer_model(X,t);
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end
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arguments = [arguments;X(:)];
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properties = struct('convexity','convex','monotonicity','increasing','definiteness','none','model','integer');
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otherwise
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F = [];
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return
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end
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