Documentation of detrend

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Function Synopsis

y = detrend(x,o,bp)

Help text

DETREND Remove a linear trend from a vector, usually for FFT processing.
   Y = DETREND(X) removes the best straight-line fit linear trend from 
   the data in vector X and returns it in vector Y.  If X is a matrix,
   DETREND removes the trend from each column of the matrix.

   Y = DETREND(X,'constant') removes just the mean value from the vector X,
   or the mean value from each column, if X is a matrix.

   Y = DETREND(X,'linear',BP) removes a continuous, piecewise linear trend.
   Breakpoint indices for the linear trend are contained in the vector BP.
   The default is no breakpoints, such that one single straight line is
   removed from each column of X.

   See also MEAN

Cross-Reference Information

This function calls	This function is called by
dc	reemerge1 heat_ceof heat_ceof eq_tend_terms2 lagged_correlation ml_coup_slp_eof get_hctend_terms hc_eof plot_lp_pac_regressions plot_regressions heat_ceof ceof_regress_on_all_2 compare_cts compare_cts3 regress_flux eq_tend_terms heat_ceof eq_tend_terms eq_tend_terms2 heat_ceof plot_30s30n_EOF_regressions eq_tend_terms pdo_statistics gu_philander ml_slp_pcs_ppcs_2 check_atl_trop_vwnd check_nh_sh_eq_corr check_old_new_stats check_pac_trop_vwnd comp_eof_sst_regress_on_all compare_cts compare_cts2 complex_eof_heat_content composite composite_1 corr_ct_mlcurl corr_indices cospectrum coup_run_stats ct_lagged_correlation ct_lpct_regs ct_seasonal ct_spectrum2 ct_statistics curlt_eof dtrend eof_20deg_isotherm eof_heat_content eof_height eof_slp eof_sst eq_ind_corr eq_tend_terms eq_tend_terms2 fig1 get_taux_std gu_philander gu_philander2 gu_philander3 gu_philander4 gu_philander5 gu_philander_HP gu_philander_thesis hc_eof hc_eofs hc_sst_lagged_regression heat_ceof hoffmoeller_corr_plot hoffmoeller_plot hofmoeller_depth_temp hofmoeller_depth_temp2 hofmoeller_depth_temp3 hofmoeller_depth_temp4 HP_HC_evolution_30s30n hp_lp_SST_hoffmoeller lag_regress_on_ct lagged_corr_slpx_ct lagged_correlation lagged_filt_ct_regressions look_3dceof_vort_div look_at_coup_run look_at_stoc_run look_hc_terms LP_HC_evolution_30s30n LPPC1_regression make_regressions MIX_regressions ml_coup_slp_eof ml_ppcs_thesis ML_projections ml_run_stats ml_run_stats2 ml_run_stats3 ml_run_stats4 ml_slp_pcs_ppcs ml_slp_pcs_ppcs_2 model_ekman_upwelling movie_hc_25yrlp npac_sst_eofs pac_atl_3dCEOF_look pc_spectrum pc_statistics pdo_calc pdo_statistics plot_lag_regress2 plot_lp_pac_regressions plot_pac_regressions plot_reg_HEAT_SFC plot_reg_TAUX_z250 plot_regressions plot_regressions_HP_LP plot_regressions_HP_LP_thesis plot_variance_explained pop_anal_tropics pop_anal_tropics2 pos_vs_neg_LPCT project_windstress reg_SST_onto_SLP_variosBPs reg_stuff_onto_BPppcs regress_flux regress_hp_lp_ct regress_taux_hanom regress_taux_hanom2 regress_velocity regress_vertical_temp regress_wbc save_20deg_ceof seasonal_spect sst_ceof sst_complex_eof sst_eof sst_eof2 sst_eof_heat_regress std_ct svd_slp_taux table_correlation temp_3d_eof test_AR2_spect thermocline_structure time_freq_anal vert_ubtp_uptb vert_vdtdy_wdtdz vert_vptb_wptb vertical_ocean_structure windstress_regcoef

This function calls

This function is called by

Listing of function detrend

function y = detrend(x,o,bp)

%   Author(s): J.N. Little, 6-08-86
%   	   J.N. Little, 2-29-88, revised
%   	   G. Wolodkin, 2-02-98, added piecewise linear fit of L. Ljung
%   Copyright (c) 1984-98 by The MathWorks, Inc.
%   $Revision: 1.4 $  $Date: 1998/06/08 21:34:05 $

if nargin < 2, o  = 1; end
if nargin < 3, bp = 0; end

%  Reshape x if necessary, assuming the dimension to be 
%  detrended is the first

szx = size(x); ndimx = length(szx);
if ndimx > 2;
  x = reshape(x, szx(1), prod(szx(2:ndimx)));
end
 
n = size(x,1);
if n == 1,
  x = x(:);			% If a row, turn into column vector
end
N = size(x,1);

switch o
case {0,'c','constant'}
  y = x - ones(N,1)*mean(x);	% Remove just mean from each column

case {1,'l','linear'}
  bp = unique([0;bp(:);N-1]);	% Include both endpoints
  lb = length(bp)-1;
  a  = [zeros(N,lb) ones(N,1)];	% Build regressor with linear pieces + DC
  for kb = 1:lb
    M = N - bp(kb);
    a([1:M]+bp(kb),kb) = [1:M]'/M;
  end
  y = x - a*(a\x);		% Remove best fit

otherwise
  % This should eventually become an error.
  warning(['Invalid trend type ''' num2str(o) '''.. assuming ''linear''.']);
  y = detrend(x,1,bp); 

end

if n == 1
  y = y.';
end

%  Reshape output so it is the same dimension as input

if ndimx > 2;
  y = reshape(y, szx);
end