1######################################################################## 2## 3## Copyright (C) 1995-2021 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 {} {} detrend (@var{x}, @var{p}) 28## If @var{x} is a vector, @code{detrend (@var{x}, @var{p})} removes the 29## best fit of a polynomial of order @var{p} from the data @var{x}. 30## 31## If @var{x} is a matrix, @code{detrend (@var{x}, @var{p})} does the same 32## for each column in @var{x}. 33## 34## The second argument @var{p} is optional. If it is not specified, a value of 35## 1 is assumed. This corresponds to removing a linear trend. 36## 37## The order of the polynomial can also be given as a string, in which case 38## @var{p} must be either @qcode{"constant"} (corresponds to @code{@var{p}=0}) 39## or @qcode{"linear"} (corresponds to @code{@var{p}=1}). 40## @seealso{polyfit} 41## @end deftypefn 42 43function y = detrend (x, p = 1) 44 45 if (nargin < 1 || nargin > 2) 46 print_usage (); 47 endif 48 49 if (! isnumeric (x) || ndims (x) > 2) 50 error ("detrend: X must be a numeric vector or matrix"); 51 endif 52 53 if (ischar (p) && strcmpi (p, "constant")) 54 p = 0; 55 elseif (ischar (p) && strcmpi (p, "linear")) 56 p = 1; 57 elseif (! isscalar (p) || p < 0 || p != fix (p)) 58 error ("detrend: P must be \"constant\", \"linear\", or a positive integer"); 59 endif 60 61 [m, n] = size (x); 62 if (m == 1) 63 x = x.'; 64 endif 65 66 r = rows (x); 67 b = ((1 : r).' * ones (1, p + 1)) .^ (ones (r, 1) * (0 : p)); 68 y = x - b * (b \ x); 69 70 if (m == 1) 71 y = y.'; 72 endif 73 74endfunction 75 76 77%!test 78%! N = 32; 79%! x = (0:1:N-1)/N + 2; 80%! y = detrend (x); 81%! assert (abs (y(:)) < 20*eps); 82 83%!test 84%! N = 32; 85%! t = (0:1:N-1)/N; 86%! x = t .* t + 2; 87%! y = detrend (x,2); 88%! assert (abs (y(:)) < 30*eps); 89 90%!test 91%! N = 32; 92%! t = (0:1:N-1)/N; 93%! x = [t;4*t-3].'; 94%! y = detrend (x); 95%! assert (abs (y(:)) < 20*eps); 96 97%!test 98%! N = 32; 99%! x = ((0:1:N-1)/N + 2) * 1i; 100%! y = detrend (x); 101%! assert (abs (y(:)) < 20*eps); 102 103## Test input validation 104%!error detrend () 105%!error detrend (1, 2, 3) 106%!error detrend ("a") 107%!error detrend (true) 108%!error detrend (1, "invalid") 109%!error detrend (1, -1) 110%!error detrend (1, 1.25) 111 112