90 lines
2.8 KiB
Mathematica
90 lines
2.8 KiB
Mathematica
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function varargout = cpower(varargin)
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%CPOWER Power of SDPVAR variable with convexity knowledge
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%
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% CPOWER is recommended if your goal is to obtain
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% a convex model, since the function CPOWER is implemented
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% as a so called nonlinear operator. (For p/q ==2 you can
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% however just as well use the overloaded power)
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%
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% t = cpower(x,p/q)
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%
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% For negative p/q, the operator is convex.
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% For positive p/q with p>q, the operator is convex.
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% For positive p/q with p<q, the operator is concave.
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%
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% A domain constraint x>0 is automatically added if
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% p/q not is an even integer.
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%
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% Note, the complexity of generating the conic representation
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% of these variables are O(2^L) where L typically is the
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% smallest integer such that 2^L >= min(p,q)
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switch class(varargin{1})
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case 'double'
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varargout{1} = power(varargin{1},varargin{2});
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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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if isreal(X)
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dim = size(X);
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X = reshape(X,prod(dim),1);
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y = [];
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for i = 1:prod(dim)
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y = [y;yalmip('define',mfilename,extsubsref(X,i),varargin{2})];
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end
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y = reshape(y,dim);
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varargout{1} = y;
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else
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error('CPOWER can only be applied to real vectors.');
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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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p = varargin{4};
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if p>0
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[p,q] = rat(abs(p));
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F = pospower(X,t,p,q);
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if p>q
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convexity = 'convex';
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monotonicity = 'increasing';
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else
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convexity = 'concave';
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monotonicity = 'decreasing';
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end
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else
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[p,q] = rat(abs(p));
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F = negpower(X,t,p,q);
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convexity = 'convex';
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monotonicity = 'decreasing';
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end
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varargout{1} = F;
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varargout{2} = struct('convexity',convexity,'monotonicity',monotonicity,'definiteness','positive','model','graph');
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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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function F = pospower(x,t,p,q)
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if p>q
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l = ceil(log2(abs(p)));
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r = 2^l-p;
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y = [ones(r,1)*x;ones(q,1)*t;ones(2^l-r-q,1)];
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F = detset(x,y);
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else
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l = ceil(log2(abs(q)));
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y = [ones(p,1)*x;ones(2^l-q,1)*t;ones(q-p,1)];
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F = detset(t,y);
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end
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function F = negpower(x,t,p,q)
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l = ceil(log2(abs(p+q)));
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p = abs(p);
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q = abs(q);
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y = [ones(2^l-p-q,1);ones(p,1)*x;ones(q,1)*t];
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F = detset(1,y);
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