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########################################################################
##
## Copyright (C) 1996-2024 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{q} =} polyint (@var{p})
## @deftypefnx {} {@var{q} =} polyint (@var{p}, @var{k})
## Return the coefficients of the integral of the polynomial whose
## coefficients are represented by the vector @var{p}.
##
## The variable @var{k} is the constant of integration, which by default is
## set to zero.
## @seealso{polyder, polyval}
## @end deftypefn
function q = polyint (p, k)
if (nargin < 1)
print_usage ();
endif
if (nargin == 1)
k = 0;
elseif (! isscalar (k))
error ("polyint: the constant of integration must be a scalar");
endif
if (! (isvector (p) || isempty (p)))
error ("polyint: argument must be a vector");
endif
lp = length (p);
if (lp == 0)
q = [];
return;
endif
if (rows (p) > 1)
## Convert to column vector
p = p.';
endif
q = [(p ./ [lp:-1:1]), k];
endfunction
%!test
%! A = [3, 2, 1];
%! assert (polyint (A), polyint (A,0));
%! assert (polyint (A), polyint (A'));
%! assert (polyint (A), [1, 1, 1, 0]);
%! assert (polyint (A,1), ones (1,4));
%!test
%! A = ones (1,8);
%! B = [length(A):-1:1];
%! assert (polyint (A), [1./B, 0]);
%!error <Invalid call> polyint ()
%!error polyint (ones (2,2))
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