jens
7b34529b24
git-svn-id: http://moon:8086/svn/matlab/trunk@91 801c6759-fa7c-4059-a304-17956f83a07c
1 line
1.3 KiB
Matlab
1 line
1.3 KiB
Matlab
function [f,g,H,T] = autoTensor(x,type,funObj,varargin)
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% [f,g,H,T] = autoTensor(x,useComplex,funObj,varargin)
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% Numerically compute Tensor of 3rd-derivatives of objective function from Hessian values
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p = length(x);
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if type == 2
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mu = 2*sqrt(1e-12)*(1+norm(x));
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f1 = zeros(p,1);
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f2 = zeros(p,2);
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g1 = zeros(p);
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g2 = zeros(p);
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diff = zeros(p,p,p);
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for j = 1:p
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e_j = zeros(p,1);
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e_j(j) = 1;
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[f1(j) g1(:,j) diff1(:,:,j)] = funObj(x + mu*e_j,varargin{:});
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[f2(j) g2(:,j) diff2(:,:,j)] = funObj(x + mu*e_j,varargin{:});
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end
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f = mean([f1;f2]);
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g = mean([g1 g2],2);
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H = mean(cat(3,diff1,diff2),3);
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T = (diff1-diff2)/(2*mu);
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elseif type == 3 % Use Complex Differentials
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mu = 1e-150;
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f = zeros(p,1);
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g = zeros(p);
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diff = zeros(p,p,p);
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for j = 1:p
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e_j = zeros(p,1);
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e_j(j) = 1;
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[f(j) g(:,j) diff(:,:,j)] = funObj(x + mu*i*e_j,varargin{:});
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end
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f = mean(real(f));
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g = mean(real(g),2);
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H = mean(real(diff),3);
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T = imag(diff)/mu;
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else % Use finite differencing
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mu = 2*sqrt(1e-12)*(1+norm(x));
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[f,g,H] = funObj(x,varargin{:});
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diff = zeros(p,p,p);
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for j = 1:p
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e_j = zeros(p,1);
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e_j(j) = 1;
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[~ ~ diff(:,:,j)] = funObj(x + mu*e_j,varargin{:});
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end
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T = (diff-repmat(H,[1 1 p]))/mu;
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end
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