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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.
Antonio Pino Robles <data.script93@gmail.com>
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1 function [U, Q, L, S] = gqr(A, B, partial)
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2 %GQR Generalized QR factorization.
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3 % [U, Q, L, S] = GQR(A, B, partial) factorizes
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4 % the m-by-n A and p-by-n B, where m >= n >= p, as
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5 % A = U*L*Q^T, B = S*Q^T, with U and Q orthogonal
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6 % and L = [0; L1], S = [S1 0], with L1 and S1 lower triangular.
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7 % If a nonzero third argument is present then only a partial reduction
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8 % of A is performed: the first p columns of A are not reduced to
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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9 % triangular form (which is sufficient for solving the LSE problem).
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10
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11 % Reference:
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12 % N. J. Higham, Accuracy and Stability of Numerical Algorithms,
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13 % Second edition, Society for Industrial and Applied Mathematics,
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14 % Philadelphia, PA, 2002; sec. 20.9.
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15
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16 [m n] = size(A);
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17 [p n1] = size(B);
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18 if nargin < 3, partial = 0; end
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19
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20 if n ~= n1, error('A and B must have same number of columns!'), end
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21
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22 if partial
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23 limit = p+1;
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24 else
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25 limit = 1;
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26 end
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27
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28 [Q, S] = qr(B');
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29 S = S';
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30
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31 U = eye(m);
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32 A = A*Q;
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33
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34 % QL factorization of AQ.
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35
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36 for i = n:-1:limit
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37
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38 % Vector-reversal so that Householder eliminates leading
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39 % rather than trailing elements.
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40 temp = A(1:m-n+i,i); temp = temp(end:-1:1);
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41 [v, beta] = gallery('house',temp);
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42 v = v(end:-1:1);
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43
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44 temp = A(1:m-n+i,1:i);
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45 A(1:m-n+i,1:i) = temp - beta*v*(v'*temp);
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46
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47 % Put zeros where they're supposed to be!
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48 A(1:m-n+i-1,i) = zeros(m-n+i-1,1);
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49
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50 temp = U(:,1:m-n+i);
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51 U(:,1:m-n+i) = temp - beta*temp*v*v';
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52
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53 end
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55 L = A;