| | DEFUN_DLD (svd, args, nargout,"-*- texinfo -*-\n\
@deftypefn {Loadable Function} {@var{s} =} svd (@var{A})\n\
@deftypefnx {Loadable Function} {[@var{U}, @var{S}, @var{V}] =} svd (@var{A})\n\
@deftypefnx {Loadable Function} {[@var{U}, @var{S}, @var{V}] =} svd (@var{A}, @var{econ})\n\
@cindex singular value decomposition\n\
Compute the singular value decomposition of @var{A}\n\
@tex\n\
$$\n\
A = U S V^H\n\
$$\n\
@end tex\n\
@ifnottex\n\
\n\
@example\n\
A = U*S*V'\n\
@end example\n\
\n\
@end ifnottex\n\
\n\
The function @code{svd} normally returns only the vector of singular values.\n\
When called with three return values, it computes\n\
@tex\n\
$U$, $S$, and $V$.\n\
@end tex\n\
@ifnottex\n\
@var{U}, @var{S}, and @var{V}.\n\
@end ifnottex\n\
For example,\n\
\n\
@example\n\
svd (hilb (3))\n\
@end example\n\
\n\
@noindent\n\
returns\n\
\n\
@example\n\
@group\n\
ans =\n\
\n\
1.4083189\n\
0.1223271\n\
0.0026873\n\
@end group\n\
@end example\n\
\n\
@noindent\n\
and\n\
\n\
@example\n\
[u, s, v] = svd (hilb (3))\n\
@end example\n\
\n\
@noindent\n\
returns\n\
\n\
@example\n\
@group\n\
u =\n\
\n\
-0.82704 0.54745 0.12766\n\
-0.45986 -0.52829 -0.71375\n\
-0.32330 -0.64901 0.68867\n\
\n\
s =\n\
\n\
1.40832 0.00000 0.00000\n\
0.00000 0.12233 0.00000\n\
0.00000 0.00000 0.00269\n\
\n\
v =\n\
\n\
-0.82704 0.54745 0.12766\n\
-0.45986 -0.52829 -0.71375\n\
-0.32330 -0.64901 0.68867\n\
@end group\n\
@end example\n\
\n\
If given a second argument, @code{svd} returns an economy-sized\n\
decomposition, eliminating the unnecessary rows or columns of @var{U} or\n\
@var{V}.\n\
@seealso{svd_driver, svds, eig}\n\
@end deftypefn") |
