89 lines
2.5 KiB
Mathematica
89 lines
2.5 KiB
Mathematica
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function varargout = power_internal1(varargin)
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%power_internal1
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% Used for cases such as 2^x, and is treated as evaluation-based operators
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switch class(varargin{1})
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case 'double'
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varargout{1} = varargin{2}.^varargin{1};
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case 'sdpvar'
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if isa(varargin{2},'sdpvar')
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x = varargin{2};
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y = varargin{1};
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varargout{1} = exp(y*log(x)); %x^y = exp(log(x^y))
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else
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if length(varargin{1}) > 1 || size(varargin{2},1) ~= size(varargin{2},2)
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error('Inputs must be a scalar and a square matrix. To compute elementwise POWER, use POWER (.^) instead.');
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end
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x = varargin{2};
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y = varargin{1};
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if isa(x,'double') && x==1 && length(y)==1
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varargout{1} = 1;
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else
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varargout{1} = InstantiateElementWise(mfilename,varargin{:});
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end
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end
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case 'char'
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X = varargin{3};
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Y = varargin{4};
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F=[];
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if Y>=1
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operator = struct('convexity','none','monotonicity','increasing','definiteness','positve','model','callback');
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elseif Y>=0
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operator = struct('convexity','none','monotonicity','decreasing','definiteness','positive','model','callback');
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else
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% Base is negative, so the power has to be an integer
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F = (integer(X));
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operator = struct('convexity','none','monotonicity','decreasing','definiteness','none','model','callback');
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end
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operator.bounds = @bounds_power;
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operator.convexhull = @convexhull_power;
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operator.derivative = @(x)derivative(x,Y);
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if Y >= 0
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operator.inverse = @(x,Y)inverse(x,Y);
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end
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varargout{1} = F;
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varargout{2} = operator;
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varargout{3} = [X(:);Y(:)];
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otherwise
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error('SDPVAR/power_internal1 called with CHAR argument?');
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end
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% This should not be hidden here....
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function [L,U] = bounds_power(xL,xU,base)
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if base >= 1
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L = base^xL;
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U = base^xU;
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elseif base>= 0
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L = base^xU;
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U = base^xL;
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else
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disp('Not implemented yet. Report bug if you need this')
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error
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end
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function x = inverse(y,base)
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if y <=0
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x = -inf;
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else
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x = log(y)/log(base);
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end
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function df = derivative(x,base)
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if length(base)~=length(x)
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base = base*ones(size(x));
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end
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f = base.^x;
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df = log(base)*f;
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function [Ax, Ay, b] = convexhull_power(xL,xU,base)
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fL = base^xL;
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fU = base^xU;
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dfL = log(base)*fL;
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dfU = log(base)*fU;
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[Ax,Ay,b] = convexhullConvex(xL,xU,fL,fU,dfL,dfU);
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