update packages

[CreaPhase.git] / octave_packages / m / polynomial / ppjumps.m

diff --git a/octave_packages/m/polynomial/ppjumps.m b/octave_packages/m/polynomial/ppjumps.m
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+## Copyright (C) 2008-2012 VZLU Prague, a.s., Czech Republic
+##
+## 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.
+##
+## This program 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 this software; see the file COPYING.  If not, see
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@var{jumps} =} ppjumps (@var{pp})
+## Evaluate the boundary jumps of a piecewise polynomial.
+## If there are @math{n} intervals, and the dimensionality of @var{pp} is
+## @math{d}, the resulting array has dimensions @code{[d, n-1]}.
+## @seealso{mkpp}
+## @end deftypefn
+
+function jumps = ppjumps (pp)
+  if (nargin != 1)
+    print_usage ();
+  endif
+
+  if (! (isstruct (pp) && strcmp (pp.form, "pp")))
+    error ("ppjumps: PP must be a structure");
+  endif
+
+  ## Extract info.
+  [x, P, n, k, d] = unmkpp(pp);
+  nd = length (d) + 1;
+
+  ## Offsets.
+  dx = diff(x(1:n));
+  dx = repmat (dx, [prod(d), 1]);
+  dx = reshape (dx, [d, n-1]);
+  dx = shiftdim (dx, nd - 1);
+
+  ## Use Horner scheme.
+  if (k>1)
+    llim = shiftdim (reshape (P(1:(n-1) * prod(d), 1), [d, n-1]), nd - 1);
+  endif
+
+  for i = 2 : k;
+    llim .*= dx;
+    llim += shiftdim (reshape (P(1:(n-1) * prod (d), i), [d, n-1]), nd - 1);
+  endfor
+
+  rlim = shiftdim (ppval (pp, x(2:end-1)), nd - 1);
+  jumps = shiftdim (rlim - llim, 1);
+endfunction
+
+
+%!test
+%! p = [1 6 11 6];
+%! x = linspace (5, 6, 4);
+%! y = polyval (p, x);
+%! pp = spline (x, y);
+%! jj = ppjumps (pp);
+%! assert (jj, [0 0], eps)
+
+%!test
+%!
+%! breaks = [0 1 2];
+%! pp1 = poly (-[1 2 3]);
+%! pp2 = poly (-([1 2 3]+1));
+%! pp = mkpp (breaks, [pp1;pp2]);
+%! assert (ppjumps (pp), 0, eps)
+
+%!test
+%!
+%! breaks = [0 1 2];
+%! pp1 = poly (-[1 2 3]);
+%! pp2 = poly (([1 2 3]+1));
+%! pp = mkpp (breaks, [pp1;pp2]);
+%! j  = - 2 * polyval (pp1, 1);
+%! assert (ppjumps (pp), j, eps)