85 lines
2.2 KiB
Mathematica
85 lines
2.2 KiB
Mathematica
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function varargout = erf(varargin)
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%ERF (overloaded)
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switch class(varargin{1})
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case 'double'
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error('Overloaded SDPVAR/ERF CALLED WITH DOUBLE. Report error')
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case 'sdpvar'
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varargout{1} = InstantiateElementWise(mfilename,varargin{:});
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case 'char'
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operator = struct('convexity','none','monotonicity','increasing','definiteness','none','model','callback');
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operator.bounds = @bounds;
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operator.range = [-1 1];
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operator.derivative =@(x)exp(-x.^2)*2/sqrt(pi);
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operator.inverse = @(x)(erfinv(x));
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operator.convexhull = @convexhull;
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varargout{1} = [];
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varargout{2} = operator;
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varargout{3} = varargin{3};
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otherwise
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error('SDPVAR/ERF called with CHAR argument?');
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end
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function [L,U] = bounds(xL,xU)
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L = erf(xL);
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U = erf(xU);
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function [Ax, Ay, b, K] = convexhull(xL,xU)
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K = [];
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if xU <= 0
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xM = (xL+xU)/2;
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fL = erf(xL);
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fM = erf(xM);
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fU = erf(xU);
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dfL = exp(-xL.^2)*2/sqrt(pi);
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dfM = exp(-xM.^2)*2/sqrt(pi);
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dfU = exp(-xU.^2)*2/sqrt(pi);
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[Ax,Ay,b] = convexhullConvex(xL,xM,xU,fL,fM,fU,dfL,dfM,dfU);
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elseif xL >= 0
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xM = (xL+xU)/2;
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fL = erf(xL);
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fM = erf(xM);
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fU = erf(xU);
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dfL = exp(-xL.^2)*2/sqrt(pi);
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dfM = exp(-xM.^2)*2/sqrt(pi);
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dfU = exp(-xU.^2)*2/sqrt(pi);
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[Ax,Ay,b] = convexhullConcave(xL,xM,xU,fL,fM,fU,dfL,dfM,dfU);
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else
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z = linspace(xL,xU,1000);
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fz = erf(z);
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[minval,minpos] = min(fz);
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[maxval,maxpos] = max(fz);
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xtestmin = linspace(z(max([1 minpos-5])),z(min([100 minpos+5])),100);
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xtestmax = linspace(z(max([1 maxpos-5])),z(min([100 maxpos+5])),100);
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fz1 = erf(xtestmin);
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fz2 = erf(xtestmax);
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z = [z(:);xtestmin(:);xtestmax(:)];
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fz = [fz(:);fz1(:);fz2(:)];
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[z,sorter] = sort(z);
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fz = fz(sorter);
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[z,ii,jj]=unique(z);
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fz = fz(ii);
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k1 = max((fz(2:end)-fz(1))./(z(2:end)-xL))+1e-12;
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k2 = min((fz(2:end)-fz(1))./(z(2:end)-xL))-1e-12;
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k3 = min((fz(1:end-1)-fz(end))./(z(1:end-1)-xU))+1e-12;
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k4 = max((fz(1:end-1)-fz(end))./(z(1:end-1)-xU))-1e-12;
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Ax = [-k1;k2;-k3;k4];
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Ay = [1;-1;1;-1];
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b = [k1*(-z(1)) + fz(1);-(k2*(-z(1)) + fz(1));k3*(-z(end)) + fz(end);-(k4*(-z(end)) + fz(end))];
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end
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