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annotate scripts/polynomial/ppjumps.m @ 20654:b65888ec820e draft default tip gccjit

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dmalcom gcc jit import
author Stefan Mahr <dac922@gmx.de>
date Fri, 27 Feb 2015 16:59:36 +0100
parents f1d0f506ee78
children
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1 ## Copyright (C) 2008-2015 VZLU Prague, a.s., Czech Republic
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify
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6 ## it under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or
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8 ## (at your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful,
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11 ## but WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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13 ## GNU General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {@var{jumps} =} ppjumps (@var{pp})
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21 ## Evaluate the boundary jumps of a piecewise polynomial.
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22 ##
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23 ## If there are @math{n} intervals, and the dimensionality of @var{pp} is
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24 ## @math{d}, the resulting array has dimensions @code{[d, n-1]}.
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25 ## @seealso{mkpp}
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26 ## @end deftypefn
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27
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28 function jumps = ppjumps (pp)
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29 if (nargin != 1)
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30 print_usage ();
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31 endif
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32
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33 if (! (isstruct (pp) && strcmp (pp.form, "pp")))
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34 error ("ppjumps: PP must be a structure");
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35 endif
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36
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37 ## Extract info.
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38 [x, P, n, k, d] = unmkpp (pp);
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39 nd = length (d) + 1;
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40
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41 ## Offsets.
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42 dx = diff (x(1:n));
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43 dx = repmat (dx, [prod(d), 1]);
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44 dx = reshape (dx, [d, n-1]);
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45 dx = shiftdim (dx, nd - 1);
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46
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47 ## Use Horner scheme.
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48 if (k>1)
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49 llim = shiftdim (reshape (P(1:(n-1) * prod (d), 1), [d, n-1]), nd - 1);
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50 endif
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51
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52 for i = 2 : k;
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53 llim .*= dx;
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54 llim += shiftdim (reshape (P(1:(n-1) * prod (d), i), [d, n-1]), nd - 1);
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55 endfor
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56
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57 rlim = shiftdim (ppval (pp, x(2:end-1)), nd - 1);
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58 jumps = shiftdim (rlim - llim, 1);
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59 endfunction
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60
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61
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62 %!test
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63 %! p = [1 6 11 6];
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64 %! x = linspace (5, 6, 4);
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65 %! y = polyval (p, x);
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66 %! pp = spline (x, y);
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67 %! jj = ppjumps (pp);
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68 %! assert (jj, [0 0], eps);
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69
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70 %!test
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71 %! breaks = [0 1 2];
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72 %! pp1 = poly (-[1 2 3]);
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73 %! pp2 = poly (-([1 2 3]+1));
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74 %! pp = mkpp (breaks, [pp1;pp2]);
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75 %! assert (ppjumps (pp), 0, eps);
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76
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77 %!test
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78 %! breaks = [0 1 2];
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79 %! pp1 = poly (-[1 2 3]);
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80 %! pp2 = poly (([1 2 3]+1));
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81 %! pp = mkpp (breaks, [pp1;pp2]);
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82 %! j = - 2 * polyval (pp1, 1);
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83 %! assert (ppjumps (pp), j, eps);
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84