1######################################################################## 2## 3## Copyright (C) 2009-2021 The Octave Project Developers 4## 5## See the file COPYRIGHT.md in the top-level directory of this 6## distribution or <https://octave.org/copyright/>. 7## 8## This file is part of Octave. 9## 10## Octave is free software: you can redistribute it and/or modify it 11## under the terms of the GNU General Public License as published by 12## the Free Software Foundation, either version 3 of the License, or 13## (at your option) any later version. 14## 15## Octave is distributed in the hope that it will be useful, but 16## WITHOUT ANY WARRANTY; without even the implied warranty of 17## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 18## GNU General Public License for more details. 19## 20## You should have received a copy of the GNU General Public License 21## along with Octave; see the file COPYING. If not, see 22## <https://www.gnu.org/licenses/>. 23## 24######################################################################## 25 26## -*- texinfo -*- 27## @deftypefn {} {} polyaffine (@var{f}, @var{mu}) 28## Return the coefficients of the polynomial vector @var{f} after an affine 29## transformation. 30## 31## If @var{f} is the vector representing the polynomial f(x), then 32## @code{@var{g} = polyaffine (@var{f}, @var{mu})} is the vector representing: 33## 34## @example 35## g(x) = f( (x - @var{mu}(1)) / @var{mu}(2) ) 36## @end example 37## 38## @seealso{polyval, polyfit} 39## @end deftypefn 40 41function g = polyaffine (f, mu) 42 43 if (nargin != 2) 44 print_usage (); 45 endif 46 47 if (! isvector (f)) 48 error ("polyaffine: F must be a vector"); 49 endif 50 51 if (! isvector (mu) || length (mu) != 2) 52 error ("polyaffine: MU must be a two-element vector"); 53 endif 54 55 lf = length (f); 56 57 ## Ensure that f is a row vector 58 if (rows (f) > 1) 59 f = f.'; 60 endif 61 62 g = f; 63 64 ## Scale. 65 if (mu(2) != 1) 66 g ./= mu(2) .^ (lf-1:-1:0); 67 endif 68 69 ## Translate. 70 if (mu(1) != 0) 71 w = (-mu(1)) .^ (0:lf-1); 72 ii = lf:-1:1; 73 g = g(ii) * (toeplitz (w) .* pascal (lf, -1)); 74 g = g(ii); 75 endif 76 77endfunction 78 79 80%!demo 81%! f = [1/5 4/5 -7/5 -2]; 82%! g = polyaffine (f, [1, 1.2]); 83%! x = linspace (-4,4,100); 84%! plot (x,polyval (f, x), x,polyval (g, x)); 85%! legend ("original", "affine"); 86%! axis ([-4 4 -3 5]); 87%! grid on; 88 89%!test 90%! f = [1/5 4/5 -7/5 -2]; 91%! mu = [1, 1.2]; 92%! g = polyaffine (f, mu); 93%! x = linspace (-4,4,100); 94%! assert (polyval (f, x, [], mu), polyval (g, x), 1e-10); 95