testfunctiondD.m

% tf = testfunctiondD(x)
% Evaluates one of the testfunctions below at d-dimensional points

function testfunction = testfunctiondD(x)

[N,d] = size(x);

% Franke type function
%a1 = repmat([7 sqrt(10)],N,floor((d+1)/2));
%a2 = repmat([7 3],N,floor((d+1)/2));
%a3 = repmat([4 7],N,floor((d+1)/2));
%testfunction = 0.75*exp(-sum((9*x-2).^2,2)/4) + 0.75*exp(-sum(((9*x+1)./a1(:,1:d)).^2,2)) ...
%    + 0.5*exp(-sum((9*x-a2(:,1:d)).^2,2)/4) - 0.2*exp(-sum((9*x-a3(:,1:d)).^2,2));

% tensor-product multi-linear function 
testfunction = 4^d*prod(x.*(1-x),2);
    
% d-D sinc function
%testfunction = prod(sinc(x),2);

% tensor-product weighted
%alpha = .1;
%testfunction = prod(1-alpha*x.*(1-x),2);

% borehole function
%rw=0.05 + 0.1*x(:,1);
%if d<2; r=(50000+100)/2; else r=100 + (50000-100)*x(:,2); end
%if d<3; Tu=(115600-63070)/2; else Tu=63070 + (115600-63070)*x(:,3); end
%if d<4; Tl=(116+63.1)/2; else Tl=63.1 + (116-63.1)*x(:,4); end
%if d<5; Hu=(1110+990)/2; else Hu=990 + (1110-990)*x(:,5); end
%if d<6; Hl=(820+700)/2; else Hl=700 + (820-700)*x(:,6); end
%if d<7; L=(1680+1120)/2; else L=1120 + (1680-1120)*x(:,7); end
%if d<8; Kw=(12045+9855)/2; else Kw=9855 + (12045-9855)*x(:,8); end
%logrrw=log(r./rw);
%testfunction = 2*pi*Tu.*(Hu-Hl)./(logrrw.*(1+2*L.*Tu./(logrrw.*rw.*rw.*Kw) + Tu./Tl));

% robotic arm function
%z = floor(d/2);
%theta = (2*pi)*x(:,1:z);
%len = x(:,(z+1):(2*z));
%sumtheta = cumsum(theta,2);
%u = sum(len.*cos(sumtheta),2);
%v = sum(len.*sin(sumtheta),2);
%testfunction = sqrt(u.*u+v.*v);

% product function
%alpha = .1;
%testfunction = prod(1+alpha*x,2);

% only 2D
%testfunction = (tanh(9*(x(:,2)-x(:,1)))+1)/(tanh(9)+1);