|
5824
|
1 ## Copyright (C) 2000 Paul Kienzle |
|
|
2 ## |
|
|
3 ## This file is part of Octave. |
|
|
4 ## |
|
|
5 ## Octave is free software; you can redistribute it and/or modify it |
|
|
6 ## under the terms of the GNU General Public License as published by |
|
|
7 ## the Free Software Foundation; either version 2, or (at your option) |
|
|
8 ## any later version. |
|
|
9 ## |
|
|
10 ## Octave is distributed in the hope that it will be useful, but |
|
|
11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
|
|
12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
|
|
13 ## General Public License for more details. |
|
|
14 ## |
|
|
15 ## You should have received a copy of the GNU General Public License |
|
|
16 ## along with Octave; see the file COPYING. If not, write to the Free |
|
|
17 ## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
|
|
18 ## 02110-1301, USA. |
|
|
19 |
|
|
20 ## -*- texinfo -*- |
|
|
21 ## @deftypefn {Function File} {@var{pp} = } mkpp (@var{x}, @var{p}) |
|
|
22 ## @deftypefnx {Function File} {@var{pp} = } mkpp (@var{x}, @var{p}, @var{d}) |
|
|
23 ## |
|
|
24 ## Construct a piece-wise polynomial structure from sample points |
|
|
25 ## @var{x} and coefficients @var{p}. The ith row of @var{p}, |
|
|
26 ## @code{@var{p} (@var{i},:)}, contains the coefficients for the polynomial |
|
|
27 ## over the @var{i}-th interval, ordered from highest to |
|
|
28 ## lowest. There must be one row for each interval in @var{x}, so |
|
|
29 ## @code{rows (@var{p}) == length (@var{x}) - 1}. |
|
|
30 ## |
|
|
31 ## You can concatenate multiple polynomials of the same order over the |
|
|
32 ## same set of intervals using @code{@var{p} = [ @var{p1}; @var{p2}; |
|
|
33 ## @dots{}; @var{pd} ]}. In this case, @code{rows (@var{p}) == @var{d} |
|
|
34 ## * (length (@var{x}) - 1)}. |
|
|
35 ## |
|
|
36 ## @var{d} specifies the shape of the matrix @var{p} for all except the |
|
|
37 ## last dimension. If @var{d} is not specified it will be computed as |
|
|
38 ## @code{round (rows (@var{p}) / (length (@var{x}) - 1)) instead. |
|
|
39 ## |
|
|
40 ## @seealso{unmkpp, ppval, spline} |
|
|
41 ## @end deftypefn |
|
|
42 |
|
|
43 function pp = mkpp (x, P, d) |
|
|
44 if (nargin < 2 || nargin > 3) |
|
|
45 usage ("pp = mkpp(x,P,d)"); |
|
|
46 endif |
|
|
47 pp.x = x(:); |
|
|
48 pp.P = P; |
|
|
49 pp.n = length (x) - 1; |
|
|
50 pp.k = columns (P); |
|
|
51 if (nargin < 3) |
|
|
52 d = round (rows (P) / pp.n); |
|
|
53 endif |
|
|
54 pp.d = d; |
|
|
55 if (pp.n*d != rows (P)) |
|
|
56 error ("mkpp: num intervals in x doesn't match num polynomials in P"); |
|
|
57 endif |
|
|
58 endfunction |
|
|
59 |
|
|
60 %!demo # linear interpolation |
|
|
61 %! x=linspace(0,pi,5)'; |
|
|
62 %! t=[sin(x),cos(x)]; |
|
|
63 %! m=diff(t)./(x(2)-x(1)); |
|
|
64 %! b=t(1:4,:); |
|
|
65 %! pp = mkpp(x, [m(:),b(:)]); |
|
|
66 %! xi=linspace(0,pi,50); |
|
|
67 %! plot(x,t,"x;control;",xi,ppval(pp,xi),";interp;"); |
