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########################################################################
##
## Copyright (C) 1993-2024 The Octave Project Developers
##
## See the file COPYRIGHT.md in the top-level directory of this
## distribution or <https://octave.org/copyright/>.
##
## 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
## <https://www.gnu.org/licenses/>.
##
########################################################################
## -*- texinfo -*-
## @deftypefn {} {@var{V} =} vander (@var{c})
## @deftypefnx {} {@var{V} =} vander (@var{c}, @var{n})
## Return the @nospell{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 @nospell{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
function V = vander (c, n)
if (nargin < 1)
print_usage ();
endif
if (! isvector (c))
error ("vander: polynomial C must be a vector");
endif
if (nargin == 1)
n = length (c);
elseif (! isscalar (n))
error ("vander: N must be a positive scalar integer");
endif
## avoiding many ^s appears to be faster for n >= 100.
V = zeros (numel (c), n, class (c));
c = c(:);
d = 1;
for i = n:-1:1
V(:,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])
## Test input validation
%!error <Invalid call> vander ()
%!error <polynomial C must be a vector> vander ([1, 2; 3, 4])
%!error <N must be a positive scalar integer> vander (1, [1, 2])
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