rank.m

JAVA 数学程序库 提供常规的数值计算程序包

## Copyright (C) 1996, 1997 John W. Eaton
##
## This file is part of Octave.
##
## Octave is free software; you can redistribute it and/or modify it
## under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2, or (at your option)
## any later version.
##
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## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
## General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with Octave; see the file COPYING.  If not, write to the Free
## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
## 02110-1301, USA.

## -*- texinfo -*-
## @deftypefn {Function File} {} rank (@var{a}, @var{tol})
## Compute the rank of @var{a}, using the singular value decomposition.
## The rank is taken to be the number  of singular values of @var{a} that
## are greater than the specified tolerance @var{tol}.  If the second
## argument is omitted, it is taken to be
##
## @example
## tol = max (size (@var{a})) * sigma(1) * eps;
## @end example
##
## @noindent
## where @code{eps} is machine precision and @code{sigma(1)} is the largest
## singular value of @var{a}.
## @end deftypefn

## Author: jwe

function retval = rank (A, tol)

  if (nargin == 1)
    sigma = svd (A);
    if (isempty (sigma))
      tolerance = 0;
    else
      tolerance = max (size (A)) * sigma (1) * eps;
    endif
  elseif (nargin == 2)
    sigma = svd (A);
    tolerance = tol;
  else
    print_usage ();
  endif

  retval = sum (sigma > tolerance);

endfunction

/*
@GROUP
LinearAlgebra
@SYNTAX
rank()
@DOC
.
@EXAMPLES
<programlisting>
</programlisting>
@NOTES
@SEE
*/