47 lines
1.4 KiB
Matlab
47 lines
1.4 KiB
Matlab
function g = knuth(a, b)
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% Returns gamma variates, see Knuth (1981) page 129.
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%
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% INPUTS
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% - a [double] n*1 vector, first hyperparameter.
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% - b [double] n*1 vector, second hyperparameter.
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%
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% OUTPUTS
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% - g [double] n*1 vector, gamma variates.
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% Copyright © 2006-2023 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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nn = length(a);
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mm = nn;
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bb = sqrt(2*a-1);
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Y = NaN(nn,1);
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X = NaN(nn,1);
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index = 1:mm;
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while mm
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Y(index) = tan(pi*rand(mm,1));
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X(index) = Y(index).*bb(index) + a(index) - 1;
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id1 = index(X(index)<=0); % Rejected draws.
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id2 = setdiff(index, id1);
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id3 = id2(rand(length(id2), 1)>(1+Y(id2).*Y(id2)).*exp((a(id2)-1).*(log(X(id2))-log(a(id2)-1))-bb(id2).*Y(id2))); % Rejected draws.
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index = [id1, id3];
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mm = length(index);
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end
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g = X.*b;
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