if ismembc(getvariables(xmodel.arg{1}),allextvars)
x1 = expandand(xmodel.arg{1},allextvars);
end
if ismembc(getvariables(xmodel.arg{2}),allextvars)
x2 = expandand(xmodel.arg{2},allextvars);
end
x = [x1 x2];
end
function varargout = and(varargin)
%ANd (overloaded)
%
% z = and(x,y)
% z = x & y
%
% The AND operator is implemented using the concept of nonlinear operators
% in YALMIP. X|Y defines a new so called derived variable that can be
% treated as any other variable in YALMIP. When SOLVESDP is issued,
% constraints are added to the problem to model the AND operator. The new
% constraints add constraints to ensure that z, x and y satisfy the
% truth-table for AND.
%
% The model for ARE is set(z %
% It is assumed that x and y are binary variables (either explicitely
% declared using BINVAR, or constrained using BINARY.)
%
% See also SDPVAR/AND, BINVAR, BINARY
% Author Johan L鰂berg
% $Id: and.m,v 1.12 2006/04/28 14:47:32 joloef Exp $
switch class(varargin{1})
case 'char'
z = varargin{2};
x = varargin{3};
y = varargin{4};
% *******************************************************
% For *some* efficiency,we merge expressions like A&B&C&D
xvars = getvariables(x);
yvars = getvariables(y);
allextvars = yalmip('extvariables');
if (length(xvars)==1) & ismembc(xvars,allextvars)
x = expandand(x,allextvars);
end
if (length(yvars)==1) & ismembc(yvars,allextvars)
y = expandand(y,allextvars);
end
% *******************************************************
varargout{1} = set(x >= z) + set(y >= z) + set(length(x)+length(y)-1+z >= sum(x)+sum(y)) + set(binary(z));
varargout{2} = struct('convexity','milp','monotoncity','milp','definiteness','milp');
varargout{3} = [];
case 'sdpvar'
x = varargin{1};
y = varargin{2};
varargout{1} = yalmip('addextendedvariable','and',varargin{:});
otherwise
end
function x = expandand(x,allextvars)
xmodel = yalmip('extstruct',getvariables(x));
if isequal(xmodel.fcn,'and')
x1 = xmodel.arg{1};
x2 = xmodel.arg{2};
if ismembc(getvariables(xmodel.arg{1}),allextvars)
x1 = expandand(xmodel.arg{1},allextvars);
end
if ismembc(getvariables(xmodel.arg{2}),allextvars)
x2 = expandand(xmodel.arg{2},allextvars);
end
x = [x1 x2];
end