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########################################################################
##
## Copyright (C) 2000-2024 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{yi} =} ppval (@var{pp}, @var{xi})
## Evaluate the piecewise polynomial structure @var{pp} at the points @var{xi}.
##
## If @var{pp} describes a scalar polynomial function, the result is an array
## of the same shape as @var{xi}. Otherwise, the size of the result is
## @code{[pp.dim, length(@var{xi})]} if @var{xi} is a vector, or
## @code{[pp.dim, size(@var{xi})]} if it is a multi-dimensional array.
## @seealso{mkpp, unmkpp, spline, pchip}
## @end deftypefn
function yi = ppval (pp, xi)
if (nargin != 2)
print_usage ();
endif
if (! (isstruct (pp) && isfield (pp, "form") && strcmp (pp.form, "pp")))
error ("ppval: first argument must be a pp-form structure");
endif
## Extract info.
[x, P, n, k, d] = unmkpp (pp);
## dimension checks
sxi = size (xi);
if (isvector (xi))
xi = xi(:).';
endif
nd = length (d);
## Determine intervals.
xn = numel (xi);
idx = lookup (x, xi, "lr");
P = reshape (P, [d, n * k]);
P = shiftdim (P, nd);
P = reshape (P, [n, k, d]);
Pidx = P(idx(:), :); # 2-D matrix size: x = coefs*prod (d), y = prod (sxi)
if (isvector (xi))
Pidx = reshape (Pidx, [xn, k, d]);
Pidx = shiftdim (Pidx, 1);
dimvec = [d, xn];
else
Pidx = reshape (Pidx, [sxi, k, d]);
Pidx = shiftdim (Pidx, length (sxi));
dimvec = [d, sxi];
endif
ndv = length (dimvec);
## Offsets.
dx = (xi - x(idx))(:)';
dx = repmat (dx, [prod(d), 1]);
dx = reshape (dx, dimvec);
dx = shiftdim (dx, ndv - 1);
## Use Horner scheme.
if (k > 1)
yi = shiftdim (reshape (Pidx(1,:), dimvec), ndv - 1);
else
yi = shiftdim (reshape (Pidx, dimvec), ndv - 1);
endif
for i = 2 : k
yi .*= dx;
yi += shiftdim (reshape (Pidx(i,:), dimvec), ndv - 1);
endfor
## Adjust shape.
if ((numel (xi) > 1) || (length (d) == 1))
yi = reshape (shiftdim (yi, 1), dimvec);
endif
if (isvector (xi) && (d == 1))
yi = reshape (yi, sxi);
elseif (isfield (pp, "orient") && strcmp (pp.orient, "first"))
yi = shiftdim (yi, nd);
endif
if (d == 1)
yi = reshape (yi, sxi);
endif
endfunction
%!shared b, c, pp, pp2, xi, abserr
%! b = 1:3;
%! c = ones (2);
%! pp = mkpp (b, c);
%! abserr = 1e-14;
%! pp2 = mkpp (b, [c;c], 2);
%! xi = [1.1 1.3 1.9 2.1];
%!
%!assert (ppval (pp, 1.1), 1.1, abserr)
%!assert (ppval (pp, 2.1), 1.1, abserr)
%!assert (ppval (pp, xi), [1.1 1.3 1.9 1.1], abserr)
%!assert (ppval (pp, xi.'), [1.1 1.3 1.9 1.1].', abserr)
%!assert (ppval (pp2, 1.1), [1.1;1.1], abserr)
%!assert (ppval (pp2, 2.1), [1.1;1.1], abserr)
%!assert (ppval (pp2, xi), [1.1 1.3 1.9 1.1;1.1 1.3 1.9 1.1], abserr)
%!assert (ppval (pp2, xi'), [1.1 1.3 1.9 1.1;1.1 1.3 1.9 1.1], abserr)
%!assert (size (ppval (pp2, [xi;xi])), [2 2 4])
%!assert (ppval (mkpp([0 1],1), magic (3)), ones(3,3))
%!
%!test
%! breaks = [0, 1, 2, 3];
%! coefs = rand (6, 4);
%! pp = mkpp (breaks, coefs, 2);
%! ret = zeros (2, 4, 2);
%! ret(:,:,1) = ppval (pp, breaks');
%! ret(:,:,2) = ppval (pp, breaks');
%! assert (ppval (pp, [breaks',breaks']), ret);
## Test input validation
%!error <Invalid call> ppval ()
%!error <Invalid call> ppval (1)
%!error <argument must be a pp-form structure> ppval (1,2)
%!error <argument must be a pp-form structure> ppval (struct ("a", 1), 2)
%!error <argument must be a pp-form structure> ppval (struct ("form", "ab"), 2)
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