Mercurial > hg > octave-lyh
comparison scripts/linear-algebra/null.m @ 557:e6ae50d8d4eb
[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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| 556:b805b12f3b66 | 557:e6ae50d8d4eb |
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| 1 function retval = null (A, tol) | |
| 2 | |
| 3 # usage: null (A, tol) | |
| 4 # null (A) | |
| 5 # | |
| 6 # Returns an orthonormal basis of the null space of A. | |
| 7 # | |
| 8 # The dimension of the null space is taken as the number of singular | |
| 9 # values of A not greater than tol; the default for tol is | |
| 10 # max (size (A)) * sigma_max (A) * eps, where sigma_max (A) is the | |
| 11 # maximal singular value of A. | |
| 12 | |
| 13 # written by KH (Kurt.Hornik@neuro.tuwien.ac.at) on Dec 24, 1993 | |
| 14 # copyright Dept of Probability Theory and Statistics TU Wien | |
| 15 | |
| 16 [U, S, V] = svd (A); | |
| 17 | |
| 18 [rows, cols] = size (A); | |
| 19 | |
| 20 s = diag (S); | |
| 21 | |
| 22 if (nargin == 1) | |
| 23 tol = max (size (A)) * s (1) * eps; | |
| 24 else (nargin != 2) | |
| 25 error("usage: null(A [, tol])"); | |
| 26 endif | |
| 27 | |
| 28 rank = sum (s > tol); | |
| 29 | |
| 30 if (rank < cols) | |
| 31 retval = V (:, rank+1:cols); | |
| 32 else | |
| 33 retval = zeros (cols, 0); | |
| 34 endif | |
| 35 | |
| 36 endfunction |