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function [fval, fjac] = brown(x)
% Copyright © 2021 Dynare Team
%
% This file is part of Dynare.
%
% Dynare is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% Dynare is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with Dynare. If not, see <https://www.gnu.org/licenses/>.
n = length(x);
if isnumeric(x) && isvector(x) && all(~isnan(x))
fval = zeros(n, 1);
sum = -(n+1);
prod = 1;
for j=1:n
sum = sum+x(j);
prod = prod*x(j);
end
for k=1:n-1
fval(k) = x(k)+sum;
end
fval(n) = prod-1;
if nargout>1
fjac = zeros(n);
prod = 1;
for j=1:n
prod = prod*x(j);
for k=1:n
fjac(k,j) = 1;
end
fjac(j,j) = 2;
end
for j=1:n
tmp = x(j);
if abs(tmp)<eps()
tmp = 1;
prod = 1;
for k=1:n
if k~=j
prod = prod*x(k);
end
end
end
fjac(n,j) = prod/tmp;
end
end
elseif isnumeric(x) && isvector(x) && all(isnan(x))
if nargout==1
fval = 0.5*ones(length(x), 1);
else
error('One output is required for initialization mode.')
end
else
error('Wrong input argument.')
end
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