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annotate toolbox/poldec.m @ 2:c124219d7bfa draft

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Re-add the 1995 toolbox after noticing the statement in the ~higham/mctoolbox/ webpage.
author Antonio Pino Robles <data.script93@gmail.com>
date Thu, 07 May 2015 18:36:24 +0200
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1 function [U, H] = poldec(A)
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2 %POLDEC Polar decomposition.
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3 % [U, H] = POLDEC(A) computes a matrix U of the same dimension
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4 % (m-by-n) as A, and a Hermitian positive semi-definite matrix H,
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5 % such that A = U*H.
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6 % U has orthonormal columns if m >= n, and orthonormal rows if m <= n.
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7 % U and H are computed via an SVD of A.
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8 % U is a nearest unitary matrix to A in both the 2-norm and the
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9 % Frobenius norm.
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11 % Reference:
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12 % N.J. Higham, Computing the polar decomposition---with applications,
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13 % SIAM J. Sci. Stat. Comput., 7(4):1160--1174, 1986.
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14 %
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15 % (The name `polar' is reserved for a graphics routine.)
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16
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17 [m, n] = size(A);
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19 [P, S, Q] = svd(A, 0); % Economy size.
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20 if m < n % Ditto for the m<n case.
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21 S = S(:, 1:m);
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22 Q = Q(:, 1:m);
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23 end
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24 U = P*Q';
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25 if nargout == 2
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26 H = Q*S*Q';
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27 H = (H + H')/2; % Force Hermitian by taking nearest Hermitian matrix.
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28 end