97 lines
2.6 KiB
Matlab
97 lines
2.6 KiB
Matlab
function [fval, fjac] = watson(x)
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% Copyright © 2021 Dynare Team
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%
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% This file is part of Dynare.
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <https://www.gnu.org/licenses/>.
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n = length(x);
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C9 = 29.0;
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if isnumeric(x) && isvector(x) && all(~isnan(x))
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fval = zeros(n, 1);
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for i=1:29
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ti = i/C9;
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sum1 = 0;
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tmp = 1;
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for j=2:n
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sum1 = sum1+(j-1)*tmp*x(j);
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tmp = tmp*ti;
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end
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sum2 = 0;
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tmp = 1;
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for j=1:n
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sum2 = sum2+tmp*x(j);
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tmp = tmp*ti;
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end
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tmp1 = sum1-sum2*sum2-1;
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tmp2 = 2*ti*sum2;
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tmp = 1/ti;
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for k=1:n
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fval(k) = fval(k) + tmp*((k-1)-tmp2)*tmp1;
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tmp = tmp*ti;
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end
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end
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tmp = x(2)-x(1)*x(1)-1;
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fval(1) = fval(1)+ x(1)*(1-2*tmp);
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fval(2) = fval(2)+tmp;
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if nargout>1
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fjac = zeros(n);
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for i=1:29
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ti = i/C9;
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sum1 = 0;
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tmp = 1;
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for j=2:n
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sum1 = sum1 + (j-1)*tmp*x(j);
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tmp = tmp*ti;
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end
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sum2 = 0;
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tmp = 1;
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for j=1:n
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sum2 = sum2+tmp*x(j);
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tmp = tmp*ti;
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end
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tmp1 = 2*(sum1-sum2*sum2-1);
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tmp2 = 2*sum2;
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tmp = ti*ti;
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tk = 1;
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for k=1:n
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tj = tk;
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for j=k:n
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fjac(k,j) = fjac(k,j)+tj*(((k-1)/ti-tmp2)*((j-1)/ti-tmp2)-tmp1);
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tj = tj*ti;
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end
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tk = tk*tmp;
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end
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end
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fjac(1,1) = fjac(1,1)+6*x(1)*x(1)-2*x(2)+3;
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fjac(1,2) = fjac(1,2)-2*x(1);
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fjac(2,2) = fjac(2,2)+1;
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for k=1:n
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for j=k:n
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fjac(j,k) = fjac(k,j);
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end
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end
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end
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elseif isnumeric(x) && isvector(x) && all(isnan(x))
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if nargout==1
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fval = zeros(length(x), 1);
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else
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error('One output is required for initialization mode.')
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end
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else
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error('Wrong input argument.')
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end |