www.gusucode.com > 时间序列分析工具箱 - tsa源码程序 > tsa/detrend.m
function [X,T]=detrend(t,X,p) % DETREND removes the trend from data, NaN's are considered as missing values % % DETREND is fully compatible to previous Matlab and Octave DETREND with the following features added: % - handles NaN's by assuming that these are missing values % - handles unequally spaced data % - second output parameter gives the trend of the data % - compatible to Matlab and Octave % % [...]=detrend([t,] X [,p]) % removes trend for unequally spaced data % t represents the time points % X(i) is the value at time t(i) % p must be a scalar % % [...]=detrend(X,0) % removes the mean % % [...]=detrend(X,p) % removes polynomial of order p (default p=1) % % [...]=detrend(X,1) - default % removes linear trend % % [X,T]=detrend(...) % % X is the detrended data % T is the removed trend % % see also: SUMSKIPNAN % This library is free software; you can redistribute it and/or % modify it under the terms of the GNU Library General Public % License as published by the Free Software Foundation; either % Version 2 of the License, or (at your option) any later version. % % This library is distributed in the hope that it will be useful, % but WITHOUT ANY WARRANTY; without even the implied warranty of % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU % Library General Public License for more details. % % You should have received a copy of the GNU Library General Public % License along with this library; if not, write to the % Free Software Foundation, Inc., 59 Temple Place - Suite 330, % Boston, MA 02111-1307, USA. % Copyright (C) 1995, 1996 Kurt Hornik <Kurt.Hornik@ci.tuwien.ac.at> % Copyright (C) 2001 by Alois Schloegl <a.schloegl@ieee.org> % last revision 13 Apr 2001, Ver 2.74 if (nargin == 1) p = 1; X = t; t = []; elseif (nargin == 2) if all(size(X)==1), p = X; X = t; t = []; else p = 1; end; elseif (nargin == 3) elseif (nargin > 3) fprintf (1,'usage: detrend (x [, p])\n'); end; % check data, must be in culomn order [m, n] = size (X); if (m == 1) X = X'; r=n; else r=m; end % check time scale if isempty(t), t = (1:r).'; % make time scale elseif ~all(size(t)==size(X)) t = t(:); end; % check dimension of t and X if ~all(size(X,1)==size(t,1)) fprintf (2,'detrend: size(t,1) must same as size(x,1) \n'); end; % check the order of the polynomial if (~(all(size(p)==1) & (p == round (p)) & (p >= 0))) fprintf (2,'detrend: p must be a nonnegative integer\n'); end if (nargout>1) , % needs more memory T = zeros(size(X))+nan; %T=repmat(nan,size(X)); % not supported by Octave 2.0.16 if (size(t,2)>1), % for multiple time scales for k=1:size(X,2), idx=find(~isnan(X(:,k))); b = (t(idx,k) * ones (1, p + 1)) .^ (ones (length(idx),1) * (0 : p)); T(idx,k) = b * (b \ X(idx,k)); end; else % if only one time scale is used b = (t * ones (1, p + 1)) .^ (ones (length(t),1) * (0 : p)); for k=1:size(X,2), idx=find(~isnan(X(:,k))); T(idx,k) = b(idx,:) * (b(idx,:) \ X(idx,k)); %X(idx,k) = X(idx,k) - T(idx,k); % 1st alternative implementation %X(:,k) = X(:,k) - T(:,k); % 2nd alternative end; end; X = X-T; % 3nd alternative if (m == 1) X = X'; T = T'; end else % needs less memory if (size(t,2)>1), % for multiple time scales for k = 1:size(X,2), idx = find(~isnan(X(:,k))); b = (t(idx,k) * ones (1, p + 1)) .^ (ones (length(idx),1) * (0 : p)); X(idx,k) = X(idx,k) - b * (b \ X(idx,k)); end; else % if only one time scale is used b = (t * ones (1, p + 1)) .^ (ones (length(t),1) * (0 : p)); for k = 1:size(X,2), idx = find(~isnan(X(:,k))); X(idx,k) = X(idx,k) - b(idx,:) * (b(idx,:) \ X(idx,k)); end; end; if (m == 1) X = X'; end end;