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Create local repository for matrix toolboxes. Step #0 done.
author Antonio Pino Robles <data.script93@gmail.com>
date Wed, 06 May 2015 14:56:53 +0200
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8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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1 function [L, D] = ldlt_sytr(A)
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2 %LDLT_SYTR Block LDL^T factorization for a symmetric tridiagonal matrix.
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3 % [L, D] = LDLT_SYTR(A) factorizes A = L*D*L', where A is
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4 % Hermitian tridiagonal, L is unit lower triangular, and D is
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5 % block diagonal with 1x1 and 2x2 diagonal blocks. It uses
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6 % Bunch's strategy for choosing the pivots.
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7
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8 % References:
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9 % J. R. Bunch, Partial pivoting strategies for symmetric
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10 % matrices. SIAM J. Numer. Anal., 11(3):521-528, 1974.
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11 % N. J. Higham, Accuracy and Stability of Numerical Algorithms,
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12 % Second edition, Society for Industrial and Applied Mathematics,
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13 % Philadelphia, PA, 2002; sec. 11.1.4.
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14
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15 n = length(A);
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16 if norm( tril(A,-2), 1) | norm( triu(A,2), 1) | ~isequal(A,A')
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17 error('Matrix must be Hermitian tridiagonal.')
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18 end
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19
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20 s = norm(A(:), inf);
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21 a = (sqrt(5)-1)/2;
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22 L = eye(n);
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23 D = zeros(n);
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24 k = 1;
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25
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26 while k < n
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28 if s*abs(A(k,k)) >= a*abs(A(k+1,k))^2
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30 % 1-by-1 pivot.
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31 D(k,k) = A(k,k);
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32 L(k+1,k) = A(k+1,k)/A(k,k);
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33 A(k+1,k+1) = A(k+1,k+1) - abs(A(k+1,k))^2/A(k,k);
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34 k = k+1;
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35
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36 else
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37
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38 % 2-by-2 pivot.
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39 E = A(k:k+1,k:k+1);
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40 D(k:k+1,k:k+1) = E;
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41 if k+2 <= n
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42 L(k+2:n,k:k+1) = A(k+2:n,k:k+1)/E;
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43 A(k+2,k+2) = A(k+2,k+2) - abs(A(k+2,k+1))^2*A(k,k)/det(E);
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44 end
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45 k = k+2;
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47 end
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49 end
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50 if k == n
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51 D(k,k) = A(k,k);
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52 end