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view scripts/polynomial/ppval.m @ 17338:1c89599167a6
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author | Rik <rik@octave.org> |
---|---|
date | Wed, 28 Aug 2013 08:33:02 -0700 |
parents | b81b9d079515 |
children | 3f02bcf2bdcc |
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## Copyright (C) 2000-2012 Paul Kienzle ## ## 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{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) && 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(:), :);#2d 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. yi = Pidx; if (k > 1) yi = shiftdim (reshape (Pidx(1,:), 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 ## FIXME: Why is this commented out, rather than just removed? #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]) %!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)