85 lines
2.5 KiB
Mathematica
85 lines
2.5 KiB
Mathematica
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function varargout = implies(varargin)
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%IMPLIES Logical implication
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%
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% IMPLIES(X,Y) creates a mixed integer representation of
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% the constraint X --> Y, i.e. Y is true if X is true.
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%
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% Syntax
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% F = implies(X,Y,tol)
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%
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% Input
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% X : binary SDPVAR variable or a constraint
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% Y : binary SDPVAR variable or a constraint
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% tol: Optional threshhold for defining zero (see NOTE)
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%
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% Output
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% F : SET object
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%
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% Examples
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%
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% binvar X Y; F = implies(X,Y);
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% binvar X;sdpvar Y; F = [implies(X,Y>=5), -10 <= Y <= 100];
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% binvar X;Y=sdpvar(3,1); F = [implies(X,[sum(Y);Y(2)]>=[5;0]), -1<= Y <= 10];
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%
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% Note
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%
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% All variables in the expressions have to be explicitly bounded somewhere
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% in the model (implicit constraints are not sufficients such as [Y <= Z,...,Z<= 10]
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%
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% Using implies with X non-binary is highly sensitive numerically.
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% The problem comes from the definition of 0 in a floating-point
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% environment, and precision in the solver. To account for this,
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% the user can supply a third argument to define a dead-zone around
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% zero, i.e Implies(X<=0,Y) will be replaced with IMPLIES(X<=-tol,Y)
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% Note, you typically need to tweak this number for your
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% application/solver. By default, YALMIP uses tol = 0, which means you
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% easily can get garbage... A positive number means YALMIP is cautious in
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% terms of activating the condition, while a negative number means YALMIP
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% will be aggressive in activating the condition.
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%
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% See also @SDPVAR/AND, @SDPVAR/OR, IFF
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% There are some cases to take care of...
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%
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% X --> Y binary/binary : Implemented
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% X --> Y binary/(LP,equality,sdp) Implemented
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% X --> Y (LP,equality,sdp)/binary Not implemented
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% X --> Y (LP,equality,sdp)/(LP,equality,sdp) Not implemented
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X = varargin{1};
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Y = varargin{2};
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if isempty(X)
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varargout{1} = [];
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end
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switch class(X)
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case {'sdpvar','constraint','lmi'}
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varargout{1} = setupMeta(lmi([]), mfilename,varargin{:});
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case 'char'
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varargout{1} = implies_internal(varargin{3:end});
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case 'logical'
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if length(X)==1
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if X
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varargout{1} = Y;
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else
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varargout{1} = [];
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end
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else
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if length(X) == length(Y)
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i = find(X);
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if isempty(i)
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varargout{1} = [];
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else
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varargout{1} = Y(i);
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end
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else
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error('Size mismatch in input arguments');
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end
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end
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end
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