126 lines
4.2 KiB
Mathematica
126 lines
4.2 KiB
Mathematica
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function varargout = geomean(varargin)
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%GEOMEAN (overloaded)
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%
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% t = GEOMEAN(X)
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%
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% For Hermitian matrix X, returns det(X)^(1/length(X))
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%
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% For real vector X, returns prod(X)^(1/length(X))
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%
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% This concave function is monotonically growing in det(P)
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% for P>0, so it can be used for maximizing det(P),
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% or to add lower bound constraints on the determinant.
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%
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% When GEOMEAN is used in a problem, the domain constraint
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% (X>=0) is automatically added to the problem.
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%
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% If you only use GEOMEAN as the objective function, you
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% may want to consider GEOMEAN2 which may results in a
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% slightly smaller SDP model.
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%
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% See also SDPVAR, GEOMEAN2, SUMK, SUMABSK
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switch class(varargin{1})
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case 'sdpvar' % Overloaded operator for SDPVAR objects. Pass on args and save them.
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X = varargin{1};
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[n,m] = size(X);
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if is(varargin{1},'hermitian') | min(n,m)==1
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varargout{1} = yalmip('addextendedvariable',mfilename,varargin{:});
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else
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% Create one variable for each column
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y = [];
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for i = 1:m
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index = (1+n*(i-1)):i*n;
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x = extsubsref(X,index);
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y = [y yalmip('addextendedvariable',mfilename,x)];
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end
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varargout{1} = y;
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end
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case 'char' % YALMIP send 'model' when it wants the epigraph or hypograph
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if isequal(varargin{1},'graph')
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t = varargin{2}; % Second arg is the extended operator variable
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X = varargin{3}; % Third arg and above are the args user used when defining t.
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% Extend if not power of 2
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n = length(X);
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m=2^ceil(log2(n));
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X0=X;
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F = ([]);
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if n ~= m
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d=m-n;
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if size(X,1)==size(X,2)
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% model determinant
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% Convert to a real problem
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if is(X,'complex')
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X = [real(X) imag(X);-imag(X) real(X)];
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n = length(X);
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% We will now get (detX)^2, so we need to pad
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% differently to get (detX)^(1/n)
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d=2*m-n;
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end
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D = tril(sdpvar(n,n));
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delta = diag(D);
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F = ([X D;D' diag(delta)] > 0);
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p = 2^ceil(log2(n));
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if 1
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x = [delta;ones(d,1)*t];
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else
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% More efficient in detset, but not tested
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% sufficiently yet
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x = delta;
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end
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elseif size(X,1)>size(X,2)
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x = [X;ones(d,1)*t];
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else
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x = [X ones(1,d)*t];
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end
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else
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if size(X,1)==size(X,2)
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% model determinant
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% Convert to a real problem
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if is(X,'complex')
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X = [real(X) imag(X);-imag(X) real(X)];
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n = length(X);
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% We will now get (detX)^2, so we need to pad
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% differently to get (detX)^(1/n)
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d=2*m-n;
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end
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D = tril(sdpvar(n,n));
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delta = diag(D);
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F = ([X D;D' diag(delta)] > 0);
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p = 2^ceil(log2(n));
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x = delta;
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elseif size(X,1)>size(X,2)
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x = X;
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elseif size(X,1)<size(X,2)
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x = X;
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end
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end
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varargout{1} = F + detset(t,x);
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if (min(size(X))>1) & ishermitian(X0)
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varargout{2} = struct('convexity','concave','monotonicity','none','definiteness','positive');
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else
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varargout{2} = struct('convexity','concave','monotonicity','increasing','definiteness','positive');
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end
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varargout{3} = X0; %We have altered the original input, lucky we saved it!
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elseif isequal(varargin{1},'milp')
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varargout{1} = [];
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varargout{2} = [];
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varargout{3} = [];
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else
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end
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otherwise
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end
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