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function [fval, fjac] = watson(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);
C9 = 29.0;
if isnumeric(x) && isvector(x) && all(~isnan(x))
fval = zeros(n, 1);
for i=1:29
ti = i/C9;
sum1 = 0;
tmp = 1;
for j=2:n
sum1 = sum1+(j-1)*tmp*x(j);
tmp = tmp*ti;
end
sum2 = 0;
tmp = 1;
for j=1:n
sum2 = sum2+tmp*x(j);
tmp = tmp*ti;
end
tmp1 = sum1-sum2*sum2-1;
tmp2 = 2*ti*sum2;
tmp = 1/ti;
for k=1:n
fval(k) = fval(k) + tmp*((k-1)-tmp2)*tmp1;
tmp = tmp*ti;
end
end
tmp = x(2)-x(1)*x(1)-1;
fval(1) = fval(1)+ x(1)*(1-2*tmp);
fval(2) = fval(2)+tmp;
if nargout>1
fjac = zeros(n);
for i=1:29
ti = i/C9;
sum1 = 0;
tmp = 1;
for j=2:n
sum1 = sum1 + (j-1)*tmp*x(j);
tmp = tmp*ti;
end
sum2 = 0;
tmp = 1;
for j=1:n
sum2 = sum2+tmp*x(j);
tmp = tmp*ti;
end
tmp1 = 2*(sum1-sum2*sum2-1);
tmp2 = 2*sum2;
tmp = ti*ti;
tk = 1;
for k=1:n
tj = tk;
for j=k:n
fjac(k,j) = fjac(k,j)+tj*(((k-1)/ti-tmp2)*((j-1)/ti-tmp2)-tmp1);
tj = tj*ti;
end
tk = tk*tmp;
end
end
fjac(1,1) = fjac(1,1)+6*x(1)*x(1)-2*x(2)+3;
fjac(1,2) = fjac(1,2)-2*x(1);
fjac(2,2) = fjac(2,2)+1;
for k=1:n
for j=k:n
fjac(j,k) = fjac(k,j);
end
end
end
elseif isnumeric(x) && isvector(x) && all(isnan(x))
if nargout==1
fval = zeros(length(x), 1);
else
error('One output is required for initialization mode.')
end
else
error('Wrong input argument.')
end
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