76 lines
2.2 KiB
Matlab
76 lines
2.2 KiB
Matlab
function d=hess_element(func,element1,element2,args)
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% function d=hess_element(func,element1,element2,args)
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% returns an entry of the finite differences approximation to the hessian of func
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%
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% INPUTS
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% func [function name] string with name of the function
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% element1 [int] the indices showing the element within the hessian that should be returned
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% element2 [int]
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% args [cell array] arguments provided to func
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%
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% OUTPUTS
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% d [double] the (element1,element2) entry of the hessian
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%
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% SPECIAL REQUIREMENTS
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% none
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% Copyright © 2010-2020 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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assert(element1 <= length(args) && element2 <= length(args));
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func = str2func(func);
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h=1e-6;
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p10 = args;
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p01 = args;
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m10 = args;
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m01 = args;
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p11 = args;
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m11 = args;
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p10{element1} = p10{element1} + h;
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m10{element1} = m10{element1} - h;
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p11{element1} = p11{element1} + h;
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m11{element1} = m11{element1} - h;
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p01{element2} = p01{element2} + h;
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m01{element2} = m01{element2} - h;
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p11{element2} = p11{element2} + h;
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m11{element2} = m11{element2} - h;
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% From Abramowitz and Stegun. Handbook of Mathematical Functions (1965)
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% formulas 25.3.24 and 25.3.27 p. 884
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if element1==element2
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d = (16*func(p10{:})...
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+16*func(m10{:})...
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-30*func(args{:})...
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-func(p11{:})...
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-func(m11{:}))/(12*h^2);
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else
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d = (func(p10{:})...
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+func(m10{:})...
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+func(p01{:})...
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+func(m01{:})...
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-2*func(args{:})...
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-func(p11{:})...
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-func(m11{:}))/(-2*h^2);
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end
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end
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