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annotate scripts/linear-algebra/orth.m @ 557:e6ae50d8d4eb

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[project @ 1994-07-25 20:23:22 by jwe] Initial revision
author jwe
date Mon, 25 Jul 1994 20:23:22 +0000
parents
children 4fcd2e68dd3b
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e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
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1 function retval = orth (A, tol)
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2
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3 # usage: orth (A, tol)
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4 # orth (A)
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5 #
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6 # Returns an orthonormal basis of the range of A.
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7 #
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8 # The dimension of the range space is taken as the number of singular
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9 # values of A greater than tol; the default for tol is
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10 # max (size (A)) * sigma_max (A) * eps, where sigma_max (A) is the
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11 # maximal singular value of A.
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12
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13 # written by KH (Kurt.Hornik@neuro.tuwien.ac.at) on Dec 24, 1993
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14 # copyright Dept of Probability Theory and Statistics TU Wien
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15
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16 [U, S, V] = svd (A);
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17
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18 [rows, cols] = size (A);
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19
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20 s = diag (S);
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21
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22 if (nargin == 1)
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23 tol = max (size (A)) * s (1) * eps;
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24 else if (nargin != 2)
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25 error ("usage: orth (A [, tol])");
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26 endif
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27
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28 rank = sum (s > tol);
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29
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30 if (rank > 0)
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31 retval = -U (:, 1:rank);
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32 else
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33 retval = zeros (rows, 0);
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34 endif
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35
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36 endfunction