update packages

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

diff --git a/octave_packages/m/linear-algebra/orth.m b/octave_packages/m/linear-algebra/orth.m
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+## Copyright (C) 1994-2012 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} {} orth (@var{A})
+## @deftypefnx {Function File} {} orth (@var{A}, @var{tol})
+## Return an orthonormal basis of the range space of @var{A}.
+##
+## The dimension of the range space is taken as the number of singular
+## values of @var{A} greater than @var{tol}.  If the argument @var{tol} is
+## missing, it is computed as
+##
+## @example
+## max (size (@var{A})) * max (svd (@var{A})) * eps
+## @end example
+## @seealso{null}
+## @end deftypefn
+
+## Author: KH <Kurt.Hornik@wu-wien.ac.at>
+## Created: 24 December 1993.
+## Adapted-By: jwe
+
+function retval = orth (A, tol)
+
+  if (nargin == 1 || nargin == 2)
+
+    if (isempty (A))
+      retval = [];
+      return;
+    endif
+
+    [U, S, V] = svd (A);
+
+    [rows, cols] = size (A);
+
+    [S_nr, S_nc] = size (S);
+
+    if (S_nr == 1 || S_nc == 1)
+      s = S(1);
+    else
+      s = diag (S);
+    endif
+
+    if (nargin == 1)
+      if (isa (A, "single"))
+        tol = max (size (A)) * s (1) * eps ("single");
+      else
+        tol = max (size (A)) * s (1) * eps;
+      endif
+    endif
+
+    rank = sum (s > tol);
+
+    if (rank > 0)
+      retval = -U (:, 1:rank);
+    else
+      retval = zeros (rows, 0);
+    endif
+
+  else
+
+    print_usage ();
+
+  endif
+
+endfunction
+
+%!test
+%! for ii=1:20
+%!   A = rand (10, 10);
+%!   V = orth (A);
+%!   if (det (A) != 0)
+%!     assert (V'*V, eye (10), 100*eps)
+%!   endif
+%! endfor