update packages

[CreaPhase.git] / octave_packages / m / linear-algebra / rank.m

diff --git a/octave_packages/m/linear-algebra/rank.m b/octave_packages/m/linear-algebra/rank.m
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+## Copyright (C) 1993-2012 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 3 of the License, or (at
+## your option) any later version.
+##
+## Octave is distributed in the hope that it will be useful, but
+## WITHOUT ANY WARRANTY; without even the implied warranty of
+## 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, see
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn  {Function File} {} rank (@var{A})
+## @deftypefnx {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
+      if (isa (A, "single"))
+        tolerance = max (size (A)) * sigma (1) * eps ("single");
+      else
+        tolerance = max (size (A)) * sigma (1) * eps;
+      endif
+    endif
+  elseif (nargin == 2)
+    sigma = svd (A);
+    tolerance = tol;
+  else
+    print_usage ();
+  endif
+
+  retval = sum (sigma > tolerance);
+
+endfunction
+
+%!test
+%! A = [1 2 3 4 5 6 7;
+%!      4 5 6 7 8 9 12;
+%!      1 2 3.1 4 5 6 7;
+%!      2 3 4 5 6 7 8;
+%!      3 4 5 6 7 8 9;
+%!      4 5 6 7 8 9 10;
+%!      5 6 7 8 9 10 11];
+%! assert(rank(A),4);
+
+%!test
+%! A = [1 2 3 4 5 6 7;
+%!      4 5 6 7 8 9 12;
+%!      1 2 3.0000001 4 5 6 7;
+%!      4 5 6 7 8 9 12.00001;
+%!      3 4 5 6 7 8 9;
+%!      4 5 6 7 8 9 10;
+%!      5 6 7 8 9 10 11];
+%! assert(rank(A),4);
+
+%!test
+%! A = [1 2 3 4 5 6 7;
+%!      4 5 6 7 8 9 12;
+%!      1 2 3 4 5 6 7;
+%!      4 5 6 7 8 9 12.00001;
+%!      3 4 5 6 7 8 9;
+%!      4 5 6 7 8 9 10;
+%!      5 6 7 8 9 10 11];
+%! assert(rank(A),3);
+
+%!test
+%! A = [1 2 3 4 5 6 7;
+%!      4 5 6 7 8 9 12;
+%!      1 2 3 4 5 6 7;
+%!      4 5 6 7 8 9 12;
+%!      3 4 5 6 7 8 9;
+%!      4 5 6 7 8 9 10;
+%!      5 6 7 8 9 10 11];
+%! assert(rank(A),3);
+
+%!test
+%! A = eye(100);
+%! assert(rank(A),100);
+
+%!test
+%! A = [1, 2, 3; 1, 2.001, 3; 1, 2, 3.0000001];
+%! assert(rank(A),3)
+%! assert(rank(A,0.0009),1)
+%! assert(rank(A,0.0006),2)
+%! assert(rank(A,0.00000002),3)
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