update packages

[CreaPhase.git] / octave_packages / m / special-matrix / vander.m

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+## Copyright (C) 1993-2012 John W. Eaton
+## 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} {} vander (@var{c})
+## @deftypefnx {Function File} {} vander (@var{c}, @var{n})
+## Return the Vandermonde matrix whose next to last column is @var{c}.
+## If @var{n} is specified, it determines the number of columns;
+## otherwise, @var{n} is taken to be equal to the length of @var{c}.
+##
+## A Vandermonde matrix has the form:
+## @tex
+## $$
+## \left[\matrix{c_1^{n-1}  & \cdots & c_1^2  & c_1    & 1      \cr
+##               c_2^{n-1}  & \cdots & c_2^2  & c_2    & 1      \cr
+##               \vdots     & \ddots & \vdots & \vdots & \vdots \cr
+##               c_n^{n-1}  & \cdots & c_n^2  & c_n    & 1      }\right]
+## $$
+## @end tex
+## @ifnottex
+##
+## @example
+## @group
+## c(1)^(n-1) @dots{} c(1)^2  c(1)  1
+## c(2)^(n-1) @dots{} c(2)^2  c(2)  1
+##     .     .      .      .    .
+##     .       .    .      .    .
+##     .         .  .      .    .
+## c(n)^(n-1) @dots{} c(n)^2  c(n)  1
+## @end group
+## @end example
+##
+## @end ifnottex
+## @seealso{polyfit}
+## @end deftypefn
+
+## Author: jwe
+
+function retval = vander (c, n)
+
+  if (nargin == 1)
+    n = length (c);
+  elseif (nargin != 2)
+    print_usage ();
+  endif
+
+  if (! isvector (c))
+    error ("vander: polynomial C must be a vector");
+  endif
+
+  ## avoiding many ^s appears to be faster for n >= 100.
+  retval = zeros (length (c), n, class (c));
+  d = 1;
+  c = c(:);
+  for i = n:-1:1
+    retval(:,i) = d;
+    d .*= c;
+  endfor
+
+endfunction
+
+
+%!test
+%! c = [0,1,2,3];
+%! expect = [0,0,0,1; 1,1,1,1; 8,4,2,1; 27,9,3,1];
+%! assert(vander (c), expect);
+
+%!assert (vander (1), 1)
+%!assert (vander ([1, 2, 3]), vander ([1; 2; 3]))
+%!assert (vander ([1, 2, 3]), [1, 1, 1; 4, 2, 1; 9, 3, 1])
+%!assert (vander ([1, 2, 3]*i), [-1, i, 1; -4, 2i, 1; -9, 3i, 1])
+
+%!assert(vander (2, 3), [4, 2, 1])
+%!assert(vander ([2, 3], 3), [4, 2, 1; 9, 3, 1])
+
+%!error vander ();
+%!error vander (1, 2, 3);
+%!error <polynomial C must be a vector> vander ([1, 2; 3, 4]);
+