97 lines
2.6 KiB
Matlab
97 lines
2.6 KiB
Matlab
function T = reduced_rank_cholesky(X)
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% Computes the cholesky decomposition of a symetric semidefinite matrix or of a definite positive matrix.
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%@info:
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%! @deftypefn {Function File} { @var{T} =} reduced_rank_cholesky (@var{X})
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%! @anchor{reduced_rank_cholesky}
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%! @sp 1
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%! Computes the cholesky decomposition of a symetric semidefinite matrix or of a definite positive matrix.
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%! @sp 2
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%! @strong{Inputs}
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%! @sp 1
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%! @table @ @var
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%! @item X
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%! n*n matrix of doubles to be factorized (X is supposed to be semidefinite positive).
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%! @end table
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%! @sp 2
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%! @strong{Outputs}
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%! @sp 1
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%! @table @ @var
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%! @item T
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%! q*n matrix of doubles such that T'*T = X, where q is the number of positive eigenvalues in X.
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%! @end table
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%! @sp 2
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%! @strong{Remarks}
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%! @sp 1
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%! [1] If X is not positive definite, then X has to be a symetric semidefinite matrix.
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%! @sp 1
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%! [2] The matrix T is upper triangular iff X is positive definite.
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%! @sp 2
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%! @strong{This function is called by:}
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%! @sp 1
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%! @ref{particle/sequential_importance_particle_filter}
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%! @sp 2
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%! @strong{This function calls:}
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%! @sp 2
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%! @end deftypefn
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%@eod:
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% Copyright © 2009-2017 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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[T,X_is_not_positive_definite] = chol(X);
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if X_is_not_positive_definite
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n = length(X);
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[U,D] = eig(X);
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[tmp,max_elements_indices] = max(abs(U),[],1);
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negloc = (U(max_elements_indices+(0:n:(n-1)*n))<0);
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U(:,negloc) = -U(:,negloc);
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D = diag(D);
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tol = sqrt(eps(max(D))*length(D)*10);
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t = (abs(D) > tol);
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D = D(t);
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if ~(sum(D<0))
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T = diag(sqrt(D))*U(:,t)';
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else
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disp('reduced_rank_cholesky:: Input matrix is not semidefinite positive!')
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T = NaN;
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end
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end
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%@test:1
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%$ n = 10;
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%$ m = 100;
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%$
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%$ X = randn(n,m);
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%$ X = X*X';
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%$
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%$ t = ones(2,1);
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%$
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%$ try
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%$ T = reduced_rank_cholesky(X);
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%$ catch
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%$ t(1) = 0;
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%$ T = all(t);
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%$ return
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%$ end
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%$
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%$
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%$ % Check the results.
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%$ t(2) = dassert(T,chol(X),1e-16);
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%$ T = all(t);
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%@eof:1 |