[37] | 1 | function varargout = implies_internal(varargin) |
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| 2 | |
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| 3 | % Call recursicely on X -> (A,B,...) |
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| 4 | if isa(varargin{1},'sdpvar') & isa(varargin{2},'lmi') |
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| 5 | if length(varargin{1})==1 & length(varargin{2}) >1 |
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| 6 | F = set([]); |
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| 7 | for i = 1:length(varargin{2}) |
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| 8 | F = F + implies_internal(varargin{1},varargin{2}(i)); |
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| 9 | end |
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| 10 | varargout{1} = F; |
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| 11 | return |
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| 12 | end |
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| 13 | end |
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| 14 | |
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| 15 | X = varargin{1}; |
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| 16 | Y = varargin{2}; |
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| 17 | |
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| 18 | switch class(X) |
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| 19 | |
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| 20 | case 'sdpvar' |
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| 21 | |
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| 22 | switch class(Y) |
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| 23 | |
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| 24 | case 'sdpvar' % X --> Y |
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| 25 | varargout{1} = set(Y >= X); |
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| 26 | |
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| 27 | case {'lmi','constraint'} |
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| 28 | if isa(Y,'constraint') |
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| 29 | Y = set(Y,[],[],1); |
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| 30 | end |
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| 31 | switch settype(Y) |
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| 32 | |
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| 33 | case 'elementwise' % X --> (Y(:)>=0) |
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| 34 | Y = sdpvar(Y); |
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| 35 | [M,m,infbound]=derivebounds(Y); |
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| 36 | if infbound |
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| 37 | warning('You have unbounded variables in IMPLIES leading to a lousy big-M relaxation.'); |
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| 38 | end |
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| 39 | %varargout{1} = set(Y >= (1-X).*m); |
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| 40 | varargout{1} = set(Y - (1-X).*m); |
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| 41 | |
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| 42 | case 'equality' % X --> (Y(:)==0) |
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| 43 | Y = sdpvar(Y); |
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| 44 | [M,m,infbound]=derivebounds(Y); |
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| 45 | if infbound |
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| 46 | warning('You have unbounded variables in IMPLIES leading to a lousy big-M relaxation.'); |
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| 47 | end |
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| 48 | % varargout{1} = set((1-X).*M >= Y) + set(Y >= (1-X).*m); |
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| 49 | % Better display and somewhat faster |
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| 50 | temp = 1-X; |
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| 51 | varargout{1} = set([temp.*M - Y;Y - temp.*m]); |
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| 52 | |
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| 53 | case 'sdp' % X --> (Y>=0) |
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| 54 | if length(X)>1 |
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| 55 | error('IMPLIES not implemented for this case.'); |
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| 56 | end |
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| 57 | Y = sdpvar(Y); |
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| 58 | % Elements in matrix |
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| 59 | y = Y(find(triu(ones(length(Y))))); |
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| 60 | % Derive bounds on all elements |
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| 61 | [M,m,infbound]=derivebounds(y); |
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| 62 | if infbound |
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| 63 | warning('You have unbounded variables in IMPLIES leading to a lousy big-M relaxation.'); |
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| 64 | end |
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| 65 | % Crude lower bound eig(Y) > -max(abs(Y(:))*n*I |
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| 66 | m=-max(abs([M;m]))*length(Y); |
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| 67 | % Big-M relaxation... |
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| 68 | varargout{1} = set(Y >= (1-X)*m*eye(length(Y))); |
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| 69 | |
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| 70 | otherwise |
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| 71 | error('IMPLIES not implemented for this case'); |
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| 72 | end |
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| 73 | otherwise |
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| 74 | error('IMPLIES not implemented for this case'); |
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| 75 | end |
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| 76 | |
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| 77 | case {'lmi','constraint'} |
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| 78 | if isa(X,'constraint') |
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| 79 | X = set(X,[],[],1); |
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| 80 | end |
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| 81 | if isa(Y,'constraint') |
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| 82 | Y = set(Y,[],[],1); |
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| 83 | end |
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| 84 | if length(Y) == 1 |
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| 85 | if isa(Y,'sdpvar') | isequal(settype(Y),'elementwise') |
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| 86 | Y = sdpvar(Y); |
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| 87 | switch settype(X) |
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| 88 | case 'elementwise' |
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| 89 | X = sdpvar(X);X=X(:); |
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| 90 | [Mx,mx,infbound]=derivebounds(X); |
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| 91 | if infbound |
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| 92 | warning('You have unbounded variables in IMPLIES leading to a lousy big-M relaxation.'); |
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| 93 | end |
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| 94 | di = binvar(length(X),1); |
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| 95 | if is(Y,'binary') |
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| 96 | varargout{1} = set(X <= tol + Mx.*di) + set(Y>=0.5*(sum(di)-length(di)+1)); |
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| 97 | else |
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| 98 | [My,my]=derivebounds(Y); |
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| 99 | varargout{1} = set(X <= tol + Mx.*di) + set(Y>=my*(1-(sum(di)-length(di)+1))); |
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| 100 | end |
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| 101 | |
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| 102 | otherwise |
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| 103 | error('IMPLIES not implemented for this case'); |
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| 104 | end |
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| 105 | |
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| 106 | else |
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| 107 | error('IMPLIES not implemented for this case'); |
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| 108 | end |
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| 109 | end |
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| 110 | otherwise |
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| 111 | error('IMPLIES not implemented for this case'); |
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| 112 | end |
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| 113 | |
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