update packages

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

diff --git a/octave_packages/m/linear-algebra/normest.m b/octave_packages/m/linear-algebra/normest.m
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+## Copyright (C) 2006-2012 David Bateman and Marco Caliari
+## Copyright (C) 2009 VZLU Prague
+##
+## 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} {@var{n} =} normest (@var{A})
+## @deftypefnx {Function File} {@var{n} =} normest (@var{A}, @var{tol})
+## @deftypefnx {Function File} {[@var{n}, @var{c}] =} normest (@dots{})
+## Estimate the 2-norm of the matrix @var{A} using a power series
+## analysis.  This is typically used for large matrices, where the cost
+## of calculating @code{norm (@var{A})} is prohibitive and an approximation
+## to the 2-norm is acceptable.
+##
+## @var{tol} is the tolerance to which the 2-norm is calculated.  By default
+## @var{tol} is 1e-6.  @var{c} returns the number of iterations needed for
+## @code{normest} to converge.
+## @end deftypefn
+
+function [n, c] = normest (A, tol = 1e-6)
+
+  if (nargin != 1 && nargin != 2)
+    print_usage ();
+  endif
+
+  if (! (isnumeric (A) && ndims (A) == 2))
+    error ("normest: A must be a numeric 2-D matrix");
+  endif
+
+  if (! (isscalar (tol) && isreal (tol)))
+    error ("normest: TOL must be a real scalar");
+  endif
+
+  if (! isfloat (A))
+    A = double (A);
+  endif
+
+  tol = max (tol, eps (class (A)));
+  ## Set random number generator to depend on target matrix
+  v = rand ("state");
+  rand ("state", trace (A));
+  ncols = columns (A);
+  ## Randomize y to avoid bad guesses for important matrices.
+  y = rand (ncols, 1);
+  c = 0;
+  n = 0;
+  do
+    n0 = n;
+    x = A * y;
+    normx = norm (x);
+    if (normx == 0)
+      x = rand (ncols, 1);
+    else
+      x = x / normx;
+    endif
+    y = A' * x;
+    n = norm (y);
+    c += 1;
+  until (abs (n - n0) <= tol * n)
+
+  rand ("state", v);    # restore state of random number generator
+endfunction
+
+%!test
+%! A = toeplitz ([-2,1,0,0]);
+%! assert (normest(A), norm(A), 1e-6);
+
+%!test
+%! A = rand (10);
+%! assert (normest(A), norm(A), 1e-6);
+
+%% Test input validation
+%!error normest ()
+%!error normest (1, 2, 3)
+%!error normest ([true true])
+%!error normest (ones (3,3,3))
+%!error normest (1, [1, 2])
+%!error normest (1, 1+1i)
+