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function d = check(f, X, e, P1, P2, P3, P4, P5);
% checkgrad checks the derivatives in a function, by comparing them to finite
% differences approximations. The partial derivatives and the approximation
% are printed and the norm of the diffrence divided by the norm of the sum is
% returned as an indication of accuracy.
% usage: checkgrad('f', X, e, P1, P2, ...)
% where X is the argument and e is the small perturbation used for the finite
% differences. and the P1, P2, ... are optional additional parameters which
% get passed to f. The function f should be of the type
% [fX, dfX] = f(X, P1, P2, ...)
% where fX is the function value and dfX is a vector of partial derivatives.
% Carl Edward Rasmussen, 2001-08-01.
argstr = [f, '(X']; % assemble function call strings
argstrd = [f, '(X+dx'];
for i = 1:(nargin - 3)
argstr = [argstr, ',P', int2str(i)];
argstrd = [argstrd, ',P', int2str(i)];
argstr = [argstr, ')'];
argstrd = [argstrd, ')'];
[y dy] = eval(argstr); % get the partial derivatives dy
dh = zeros(length(X),1) ;
for j = 1:length(X)
dx = zeros(length(X),1);
dx(j) = dx(j) + e; % perturb a single dimension
y2 = eval(argstrd);
dx = -dx ;
y1 = eval(argstrd);
dh(j) = (y2 - y1)/(2*e);
disp([dy dh]) % print the two vectors
d = norm(dh-dy)/norm(dh+dy); % return norm of diff divided by norm of sum
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