Mercurial > hg > octave-nkf

annotate scripts/linear-algebra/null.m @ 772:05cd8c8b13b3

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
[project @ 1994-10-05 22:10:27 by jwe]
author jwe
date Wed, 05 Oct 1994 22:12:21 +0000
parents e6ae50d8d4eb
children 4fcd2e68dd3b
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
557
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
1 function retval = null (A, tol)
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
2
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
3 # usage: null (A, tol)
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
4 # null (A)
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
5 #
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
6 # Returns an orthonormal basis of the null space of A.
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
7 #
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
8 # The dimension of the null space is taken as the number of singular
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
9 # values of A not greater than tol; the default for tol is
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
10 # max (size (A)) * sigma_max (A) * eps, where sigma_max (A) is the
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
11 # maximal singular value of A.
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
12
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
13 # written by KH (Kurt.Hornik@neuro.tuwien.ac.at) on Dec 24, 1993
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
14 # copyright Dept of Probability Theory and Statistics TU Wien
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
15
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
16 [U, S, V] = svd (A);
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
17
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
18 [rows, cols] = size (A);
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
19
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
20 s = diag (S);
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
21
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
22 if (nargin == 1)
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
23 tol = max (size (A)) * s (1) * eps;
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
24 else (nargin != 2)
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
25 error("usage: null(A [, tol])");
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
26 endif
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
27
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
28 rank = sum (s > tol);
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
29
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
30 if (rank < cols)
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
31 retval = V (:, rank+1:cols);
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
32 else
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
33 retval = zeros (cols, 0);
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
34 endif
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
35
e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
jwe
parents:
diff changeset
36 endfunction