95 lines
3.9 KiB
Mathematica
95 lines
3.9 KiB
Mathematica
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function varargout = nnz(varargin)
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%NNZ (overloaded)
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%
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% n = nnz(X)
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%
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% NNZ applied to a constraint counts the number of satisfied constraints.
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%
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% The NNZ operator is implemented using the concept of nonlinear operators
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% in YALMIP. NNZ(X) creates a new so called derived variable that can be
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% treated as any other variable in YALMIP. When SOLVESDP is issued,
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% logic constraints are added to the problem to model the NNZ operator.
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switch class(varargin{1})
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case 'constraint'
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varargout{1} = yalmip('define','nnz',varargin{1});
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case 'char'
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t = varargin{2};
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x = varargin{3};
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switch varargin{1}
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case 'graph'
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x = lmi(x);
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if is(x,'elementwise')
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x = sdpvar(x);
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x = x(:);
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[M,m] = derivebounds(x);
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delta = binvar(length(x),1);
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F = (x >= m.*(1-delta)) + (sum(delta) == t);
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elseif is(x,'equality')
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x = sdpvar(x);
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x = x(:);
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[M,m,infbound] = derivebounds(x);
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if infbound
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warning('You have unbounded variables in IMPLIES leading to a lousy big-M relaxation.');
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end
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delta = binvar(length(x),1);
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F = (M.*(1-delta) >= x >= m.*(1-delta)) + (sum(delta) == t);
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else
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error('Constraint type not supported in cardinality. Make a feature request');
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end
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varargout{1} = F;
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varargout{2} = struct('convexity','concave','monotonicity','none','definiteness','none');
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varargout{3} = x;
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otherwise
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x = lmi(x);
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if is(x,'elementwise')
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x = sdpvar(x);
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x = x(:);
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[M,m,infbound] = derivebounds(x);
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if infbound
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warning('You have unbounded variables in NNZ leading to a lousy big-M relaxation.');
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end
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n = length(x);
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deltaD = binvar(n,1);
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deltaU = binvar(n,1);
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if all(ismember(getvariables(x),[yalmip('intvariables') yalmip('binvariables')]))
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% If an integer constraint not holds, it has to be
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% epsilon violated
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F = ((M+1e-4).*(1-deltaU)-1e-4 >= x >= m.*(1-deltaD));
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else
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% User has to think harder him self
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F = ((M).*(1-deltaU) >= x >= m.*(1-deltaD));
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end
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F = F + (sum(deltaD) == t);
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F = F + (deltaU + deltaD == 1);
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F = F + (0 <= t <= n);
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elseif is(x,'equality')
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x = sdpvar(x);
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x = x(:);
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n = length(x);
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[M,m] = derivebounds(x);
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deltaZ = binvar(n,1);
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deltaNZU = binvar(n,1);
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deltaNZD = binvar(n,1);
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eps = 1e-4;
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% deltaZ forces x to be zero
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% deltaZU 1 is x > eps
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% deltaZU 1 is x < -eps
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F = (M.*(1-deltaZ) >= x >= m.*(1-deltaZ));
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F = ((M+eps).*deltaNZU-eps>= x >= eps + (m-eps).*deltaNZD);
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F = F + (sum(deltaZ) == t);
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F = F + (deltaZ + deltaNZU + deltaNZD == 1);
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F = F + (0 <= t <= n);
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else
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error('Constraint type not supported in cardinality. Make a feature request');
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end
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varargout{1} = F;
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varargout{2} = struct('convexity','milp','monotonicity','milp','definiteness','milp');
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varargout{3} = x;
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end
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otherwise
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end
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