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1 ## Copyright (C) 2000, 2006, 2007 Paul Kienzle |
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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 it |
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6 ## 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 (at |
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8 ## 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, but |
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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13 ## 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{pp} = } mkpp (@var{x}, @var{p}) |
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21 ## @deftypefnx {Function File} {@var{pp} = } mkpp (@var{x}, @var{p}, @var{d}) |
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22 ## |
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23 ## Construct a piece-wise polynomial structure from sample points |
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24 ## @var{x} and coefficients @var{p}. The ith row of @var{p}, |
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25 ## @code{@var{p} (@var{i},:)}, contains the coefficients for the polynomial |
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26 ## over the @var{i}-th interval, ordered from highest to |
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27 ## lowest. There must be one row for each interval in @var{x}, so |
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28 ## @code{rows (@var{p}) == length (@var{x}) - 1}. |
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29 ## |
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30 ## You can concatenate multiple polynomials of the same order over the |
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31 ## same set of intervals using @code{@var{p} = [ @var{p1}; @var{p2}; |
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32 ## @dots{}; @var{pd} ]}. In this case, @code{rows (@var{p}) == @var{d} |
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33 ## * (length (@var{x}) - 1)}. |
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34 ## |
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35 ## @var{d} specifies the shape of the matrix @var{p} for all except the |
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36 ## last dimension. If @var{d} is not specified it will be computed as |
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37 ## @code{round (rows (@var{p}) / (length (@var{x}) - 1))} instead. |
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38 ## |
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39 ## @seealso{unmkpp, ppval, spline} |
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40 ## @end deftypefn |
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41 |
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42 function pp = mkpp (x, P, d) |
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43 if (nargin < 2 || nargin > 3) |
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44 print_usage (); |
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45 endif |
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46 pp.x = x(:); |
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47 pp.P = P; |
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48 pp.n = length (x) - 1; |
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49 pp.k = columns (P); |
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50 if (nargin < 3) |
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51 d = round (rows (P) / pp.n); |
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52 endif |
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53 pp.d = d; |
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54 if (pp.n * prod (d) != rows (P)) |
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55 error ("mkpp: num intervals in x doesn't match num polynomials in P"); |
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56 endif |
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57 endfunction |
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58 |
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59 %!demo # linear interpolation |
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60 %! x=linspace(0,pi,5)'; |
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61 %! t=[sin(x),cos(x)]; |
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62 %! m=diff(t)./(x(2)-x(1)); |
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63 %! b=t(1:4,:); |
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64 %! pp = mkpp(x, [m(:),b(:)]); |
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65 %! xi=linspace(0,pi,50); |
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66 %! plot(x,t,"x",xi,ppval(pp,xi)); |
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67 %! legend("control","interp"); |
