Mercurial > forge
changeset 11838:b9f4ede9342a octave-forge
data-smoothing: moved to a separate mercurial repo
| author | carandraug |
|---|---|
| date | Wed, 19 Jun 2013 02:15:35 +0000 |
| parents | 594aa2d7e0a5 |
| children | 569279ce3f71 |
| files | main/data-smoothing/COPYING main/data-smoothing/DESCRIPTION main/data-smoothing/NEWS main/data-smoothing/inst/ddmat.m main/data-smoothing/inst/regdatasmooth.m main/data-smoothing/inst/rgdtsmcore.m main/data-smoothing/inst/rgdtsmcorewrap.m main/data-smoothing/inst/smooth.m |
| diffstat | 8 files changed, 0 insertions(+), 1545 deletions(-) [+] |
line wrap: on
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--- a/main/data-smoothing/COPYING Wed Jun 19 01:54:25 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,674 +0,0 @@ - GNU GENERAL PUBLIC LICENSE - Version 3, 29 June 2007 - - Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/> - Everyone is permitted to copy and distribute verbatim copies - of this license document, but changing it is not allowed. - - Preamble - - The GNU General Public License is a free, copyleft license for -software and other kinds of works. - - The licenses for most software and other practical works are designed -to take away your freedom to share and change the works. By contrast, -the GNU General Public License is intended to guarantee your freedom to -share and change all versions of a program--to make sure it remains free -software for all its users. We, the Free Software Foundation, use the -GNU General Public License for most of our software; it applies also to -any other work released this way by its authors. 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Of course, your program's commands -might be different; for a GUI interface, you would use an "about box". - - You should also get your employer (if you work as a programmer) or school, -if any, to sign a "copyright disclaimer" for the program, if necessary. -For more information on this, and how to apply and follow the GNU GPL, see -<http://www.gnu.org/licenses/>. - - The GNU General Public License does not permit incorporating your program -into proprietary programs. If your program is a subroutine library, you -may consider it more useful to permit linking proprietary applications with -the library. If this is what you want to do, use the GNU Lesser General -Public License instead of this License. But first, please read -<http://www.gnu.org/philosophy/why-not-lgpl.html>.
--- a/main/data-smoothing/DESCRIPTION Wed Jun 19 01:54:25 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,12 +0,0 @@ -Name: data-smoothing -Version: 1.3.0 -Date: 2012-03-01 -Author: Jonathan Stickel <jonathan.stickel@nrel.gov> -Maintainer: Jonathan Stickel <jonathan.stickel@nrel.gov> -Title: Data smoothing -Description: Algorithms for smoothing noisy data -Categories: Data-smoothing -Depends: octave (>= 3.6.0), optim (>= 1.0.3) -Autoload: no -License: GPLv3+ -Url: http://octave.sf.net
--- a/main/data-smoothing/NEWS Wed Jun 19 01:54:25 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,9 +0,0 @@ -Summary of important user-visible changes for data-smoothing 1.3.0: -------------------------------------------------------------------- - - ** Package is no longer automatically loaded - - ** Code has been cleaned to remove warnings about `possible Matlab-style - short-circuit operator' - - ** Minimal input check for all functions has been implemented
--- a/main/data-smoothing/inst/ddmat.m Wed Jun 19 01:54:25 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,53 +0,0 @@ -## Copyright (C) 2003 Paul H. C. Eilers <p.eilers@erasmusmc.nl> -## -## This program is free software; you can redistribute it and/or modify it under -## the terms of the GNU General Public License as published by the Free Software -## Foundation; either version 3 of the License, or (at your option) any later -## version. -## -## This program 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 General Public License for more -## details. -## -## You should have received a copy of the GNU General Public License along with -## this program; if not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {@var{D} =} ddmat (@var{x}, @var{o}) -## Compute divided differencing matrix of order @var{o} -## -## @itemize @w -## @item Input -## @itemize @w -## @item @var{x}: vector of sampling positions -## @item @var{o}: order of diffferences -## @end itemize -## @item Output -## @itemize @w -## @item @var{D}: the matrix; @var{D} * Y gives divided differences of order @var{o} -## @end itemize -## @end itemize -## -## References: Anal. Chem. (2003) 75, 3631. -## -## @end deftypefn - -## corrected the recursion multiplier; JJS 2/25/08 -## added error check that x is a column vector; JJS 4/13/09 - -function D = ddmat(x, d) - if (nargin != 2) - print_usage; - elseif ( !iscolumn (x) ) - error("x should be a column vector") - endif - m = length(x); - if d == 0 - D = speye(m); - else - dx = x((d + 1):m) - x(1:(m - d)); - V = sparse(diag(1 ./ dx)); - D = d * V * diff(ddmat(x, d - 1)); - endif -endfunction
--- a/main/data-smoothing/inst/regdatasmooth.m Wed Jun 19 01:54:25 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,189 +0,0 @@ -## Copyright (C) 2008 Jonathan Stickel <jonathan.stickel@nrel.gov> -## -## This program is free software; you can redistribute it and/or modify it under -## the terms of the GNU General Public License as published by the Free Software -## Foundation; either version 3 of the License, or (at your option) any later -## version. -## -## This program 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 General Public License for more -## details. -## -## You should have received a copy of the GNU General Public License along with -## this program; if not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -##@deftypefn {Function File} {[@var{yhat}, @var{lambda}] =} regdatasmooth (@var{x}, @var{y}, [@var{options}]) -## -## Smooths the @var{y} vs. @var{x} values of 1D data by Tikhonov -## regularization. The smooth y-values are returned as @var{yhat}. The -## regularization parameter @var{lambda} that was used for the smoothing -## may also be returned. -## -## Note: the options have changed! -## Currently supported input options are (multiple options are allowed): -## -##@table @code -##@item "d", @var{value} -## the smoothing derivative to use (default = 2) -##@item "lambda", @var{value} -## the regularization paramater to use -##@item "stdev", @var{value} -## the standard deviation of the measurement of @var{y}; an optimal -## value for lambda will be determined by matching the provided -## @var{value} with the standard devation of @var{yhat}-@var{y}; -## if the option "relative" is also used, then a relative standard -## deviation is inferred -##@item "gcv" -## use generalized cross-validation to determine the optimal value for -## lambda; if neither "lambda" nor "stdev" options are given, this -## option is implied -##@item "lguess", @var{value} -## the initial value for lambda to use in the iterative minimization -## algorithm to find the optimal value (default = 1) -## @item "xhat", @var{vector} -## A vector of x-values to use for the smooth curve; must be -## monotonically increasing and must at least span the data -## @item "weights", @var{vector} -## A vector of weighting values for fitting each point in the data. -## @item "relative" -## use relative differences for the goodnes of fit term. Conflicts -## with the "weights" option. -##@item "midpointrule" -## use the midpoint rule for the integration terms rather than a direct -## sum; this option conflicts with the option "xhat" -##@end table -## -## Please run the demos for example usage. -## -## References: Anal. Chem. (2003) 75, 3631; AIChE J. (2006) 52, 325 -## @seealso{rgdtsmcorewrap, rgdtsmcore} -## @end deftypefn - -function [yhat, lambda] = regdatasmooth (x, y, varargin) - - if (nargin < 2) - print_usage; - elseif ( length(x) != length(y) ) - error("x and y must be equal length vectors") - endif - if ( isrow(x) ) x = x'; endif - if ( isrow(y) ) y = y'; endif - - ## defaults - d = 2; - lambda = 0; - stdev = 0; - guess = 0; - - ## parse options for d, lambda, stdev, gcv, lguess; - ## remaining options (gridx, Nhat, range, relative, midpointrule) - ## will be sent directly to the core function - idx = []; - if ( nargin > 2) - for i = 1:nargin-2 - arg = varargin{i}; - if ischar(arg) - switch arg - case "d" - d = varargin{i+1}; - idx = [idx,i,i+1]; - case "lambda" - lambda = varargin{i+1}; - idx = [idx,i,i+1]; - case "stdev" - stdev = varargin{i+1}; - idx = [idx,i,i+1]; - case "gcv" - idx = [idx,i]; - case "lguess" - guess = log10(varargin{i+1}); - idx = [idx,i,i+1]; - endswitch - endif - endfor - endif - varargin(idx) = []; - options = varargin; - ## add warning if more than one gcv, lambda, or stdev options provided? - - maxiter = 50; - if (lambda) - ## do nothing and use the provided lambda - else - ## find the "optimal" lambda - if ( stdev ) - ## match standard deviation - fhandle = @(log10lambda) rgdtsmcorewrap (log10lambda, x, y, d, {"stdev", stdev}, options{:}); - else - ## perform cross-validation - fhandle = @(log10lambda) rgdtsmcorewrap (log10lambda, x, y, d, {"cve"}, options{:}); - endif - ## "fminunc" works OK, but a derivative-free method (below) is better for this problem - ##opt = optimset("TolFun",1e-6,"MaxFunEvals",maxiter); - ##[log10lambda,fout,exitflag] = fminunc (fhandle, guess, opt); - ##[log10lambda,fout,exitflag] = fminunc_compat (fhandle, guess, opt); - ## derivative-free optimization; should use "fminsearch" for Matlab - ## compatibility, but fminsearch needs updates to be more compatible itself - [log10lambda, fout, niter] = nelder_mead_min (fhandle, guess, "ftol", 1e-6, "maxev", maxiter); - if (niter > maxiter) - exitflag = 0; - else - exitflag = 1; - endif - if (!exitflag) - warning("Iteration limit of %i exceeded\n",maxiter) - endif - lambda = 10^log10lambda; - endif - - yhat = rgdtsmcore (x, y, d, lambda, options{:}); - -endfunction - -%!demo -%! npts = 100; -%! x = linspace(0,2*pi,npts)'; -%! x = x + 2*pi/npts*(rand(npts,1)-0.5); -%! y = sin(x); -%! y = y + 1e-1*randn(npts,1); -%! yp = ddmat(x,1)*y; -%! y2p = ddmat(x,2)*y; -%! [yh, lambda] = regdatasmooth (x, y, "d",4,"stdev",1e-1,"midpointrule"); -%! lambda -%! yhp = ddmat(x,1)*yh; -%! yh2p = ddmat(x,2)*yh; -%! clf -%! subplot(221) -%! plot(x,y,'o','markersize',5,x,yh,x,sin(x)) -%! title("y(x)") -%! legend("noisy","smoothed","sin(x)","location","northeast"); -%! subplot(222) -%! plot(x(1:end-1),[yp,yhp,cos(x(1:end-1))]) -%! axis([min(x),max(x),min(yhp)-abs(min(yhp)),max(yhp)*2]) -%! title("y'(x)") -%! legend("noisy","smoothed","cos(x)","location","southeast"); -%! subplot(223) -%! plot(x(2:end-1),[y2p,yh2p,-sin(x(2:end-1))]) -%! axis([min(x),max(x),min(yh2p)-abs(min(yh2p)),max(yh2p)*2]) -%! title("y''(x)") -%! legend("noisy","smoothed","-sin(x)","location","southeast"); -%! %-------------------------------------------------------- -%! % smoothing of monotonic data, using "stdev" to determine the optimal lambda - -%!demo -%! npts = 20; -%! x = rand(npts,1)*2*pi; -%! y = sin(x); -%! y = y + 1e-1*randn(npts,1); -%! xh = linspace(0,2*pi,200)'; -%! [yh, lambda] = regdatasmooth (x, y, "d", 3, "xhat", xh); -%! lambda -%! clf -%! figure(1); -%! plot(x,y,'o','markersize',10,xh,yh,xh,sin(xh)) -%! title("y(x)") -%! legend("noisy","smoothed","sin(x)","location","northeast"); -%! %-------------------------------------------------------- -%! % smoothing of scattered data, using "gcv" to determine the optimal lambda
--- a/main/data-smoothing/inst/rgdtsmcore.m Wed Jun 19 01:54:25 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,166 +0,0 @@ -## Copyright (C) 2008 Jonathan Stickel <jonathan.stickel@nrel.gov> -## -## This program is free software; you can redistribute it and/or modify it under -## the terms of the GNU General Public License as published by the Free Software -## Foundation; either version 3 of the License, or (at your option) any later -## version. -## -## This program 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 General Public License for more -## details. -## -## You should have received a copy of the GNU General Public License along with -## this program; if not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -##@deftypefn {Function File} {[@var{yhat}, @var{v}] =} rgdtsmcore (@var{x}, @var{y}, @var{d}, @var{lambda}, [@var{options}]) -## -## Smooths @var{y} vs. @var{x} values by Tikhonov regularization. -## Although this function can be used directly, the more feature rich -## function "regdatasmooth" should be used instead. In addition to -## @var{x} and @var{y}, required input includes the smoothing derivative -## @var{d} and the regularization parameter @var{lambda}. The smooth -## y-values are returned as @var{yhat}. The generalized cross -## validation variance @var{v} may also be returned. -## -## Note: the options have changed! -## Currently supported input options are (multiple options are allowed): -## -## @table @code -## @item "xhat", @var{vector} -## A vector of x-values to use for the smooth curve; must be -## monotonically increasing and must at least span the data -## @item "weights", @var{vector} -## A vector of weighting values for fitting each point in the data. -## @item "relative" -## use relative differences for the goodnes of fit term. Conflicts -## with the "weights" option. -## @item "midpointrule" -## use the midpoint rule for the integration terms rather than a direct -## sum; this option conflicts with the option "xhat" -## @end table -## -## References: Anal. Chem. (2003) 75, 3631; AIChE J. (2006) 52, 325 -## @seealso{regdatasmooth} -## @end deftypefn - - -function [yhat, v] = rgdtsmcore (x, y, d, lambda, varargin) - - if (nargin < 4) - print_usage; - endif - - ## Defaults if not provided - xhatprov = 0; - xhat = x; - weights = 0; - relative = 0; - midpr = 0; - - ## parse the provided options - if ( length(varargin) ) - for i = 1:length(varargin) - arg = varargin{i}; - if ischar(arg) - switch arg - case "xhat" - xhatprov = 1; - xhat = varargin{i+1}; - case "weights" - weights = 1; - weightv = varargin{i+1}; - case "relative" - relative = 1; - case "midpointrule" - midpr = 1; - otherwise - printf("Option '%s' is not implemented;\n", arg) - endswitch - endif - endfor - endif - if (xhatprov && midpr) - warning("midpointrule is currently not used if xhat is provided (since x,y may be scattered)") - midpr = 0; - endif - if (weights && relative) - warning("relative differences is not used if a weighting vector is provided") - endif - - N = length(x); - Nhat = length(xhat); - - ## test that xhat is increasing - if !all(diff(xhat)>0) - if xhatprov - error("xhat must be monotonically increasing") - else - error("x must be monotonically increasing if xhat is not provided") - endif - endif - ## test that xhat spans x - if ( min(x) < min(xhat) || max(xhat) < max(x) ) - error("xhat must at least span the data") - endif - - ## construct M, D - M = speye(Nhat); - idx = interp1(xhat,1:Nhat,x,"nearest"); # works for unequally spaced xhat - M = M(idx,:); - D = ddmat(xhat,d); - - ## construct "weighting" matrices W and U - if (weights) - ## use arbitrary weighting as provided - W = diag(weightv); - elseif (relative) - ## use relative differences - Yinv = sparse(diag(1./y)); - W = Yinv^2; - else - W = speye(N); - endif - ## use midpoint rule integration (rather than simple sums) - if (midpr) - Bhat = sparse(diag(-ones(N-1,1),-1)) + sparse(diag(ones(N-1,1),1)); - Bhat(1,1) = -1; - Bhat(N,N) = 1; - B = 1/2*sparse(diag(Bhat*x)); - if ( floor(d/2) == d/2 ) # test if d is even - dh = d/2; - Btilda = B(dh+1:N-dh,dh+1:N-dh); - else # d is odd - dh = ceil(d/2); - Btilda = B(dh:N-dh,dh:N-dh); - endif - W = W*B; - U = Btilda; - else - ## W = W*speye(Nhat); - U = speye(Nhat-d); - endif - - ## Smoothing - delta = trace(D'*D)/Nhat^(2+d); # using "relative" or other weighting affects this! - yhat = (M'*W*M + lambda*delta^(-1)*D'*U*D) \ M'*W*y; - #[R,P,S] = splchol(M'*W*M + lambda*delta^(-1)*D'*U*D); - #yhat = S*(R'\(R\(S'*M'*W*y))); - - ## Computation of hat diagonal and cross-validation - if (nargout > 1) - ## from AIChE J. (2006) 52, 325 - ## note: chol factorization does not help speed up the computation of H; - ## should implement Eiler's partial H computation if many point smoothing by GCV is needed - ##H = M*(S*(R'\(R\(S'*M'*W)))); - H = M*((M'*W*M + lambda*delta^(-1)*D'*U*D)\M'*W); - ## note: this is variance, squared of the standard error that Eilers uses - v = (M*yhat - y)'*(M*yhat - y)/N / (1 - trace(H)/N)^2; - endif - - ## test mapping - ##figure(5) - ##plot(x,y,'o',x,M*yhat,'x') - -endfunction
--- a/main/data-smoothing/inst/rgdtsmcorewrap.m Wed Jun 19 01:54:25 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,71 +0,0 @@ -## Copyright (C) 2008 Jonathan Stickel <jonathan.stickel@nrel.gov> -## -## This program is free software; you can redistribute it and/or modify it under -## the terms of the GNU General Public License as published by the Free Software -## Foundation; either version 3 of the License, or (at your option) any later -## version. -## -## This program 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 General Public License for more -## details. -## -## You should have received a copy of the GNU General Public License along with -## this program; if not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {@var{cve} =} rgdtsmcorewrap (@var{log10lambda}, @var{x}, @var{y}, @var{d}, @var{mincell}, @var{options}) -## @deftypefnx {Function File} {@var{stdevdif} =} rgdtsmcorewrap (@var{log10lambda}, @var{x}, @var{y}, @var{d}, @var{mincell}, @var{options}) -## -## Wrapper function for rgdtsmcore in order to minimize over -## @var{lambda} w.r.t. cross-validation error OR the squared difference -## between the standard deviation of (@var{y}-@var{yhat}) and the given -## standard deviation. This function is called from regdatasmooth. -## @seealso{regdatasmooth} -## @end deftypefn - -function out = rgdtsmcorewrap (log10lambda, x, y, d, mincell, varargin) - - if (nargin < 5) - print_usage; - endif - - lambda = 10^(log10lambda); - - if ( length(mincell) == 2 ) # using stdev to find optimal lambda - stdev = mincell{2}; - yhat = rgdtsmcore (x, y, d, lambda, varargin{:}); - - xhatprov = 0; - relative = 0; - for i = 1:length(varargin) - if strcmp(varargin{i},"relative") - relative = 1; - elseif strcmp(varargin{i},"xhat") - xhatprov = 1; - xhat = varargin{i+1}; - endif - endfor - - if (xhatprov) - idx = interp1(xhat,1:length(xhat),x,"nearest"); - if relative - stdevd = std((y-yhat(idx))./y); - else - stdevd = std(y-yhat(idx)); - endif - else - if (relative) - stdevd = std((y-yhat)./y); - else - stdevd = std(y-yhat); - endif - endif - - out = (stdevd - stdev)^2; - - else # use gcv to find optimal lambda - [yhat, out] = rgdtsmcore (x, y, d, lambda, varargin{:}); - endif - -endfunction
--- a/main/data-smoothing/inst/smooth.m Wed Jun 19 01:54:25 2013 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,371 +0,0 @@ -## Copyright (C) 2013 Erik Kjellson <erikiiofph7@users.sourceforge.net> -## -## This program is free software; you can redistribute it and/or modify it under -## the terms of the GNU General Public License as published by the Free Software -## Foundation; either version 3 of the License, or (at your option) any later -## version. -## -## This program 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 General Public License for more -## details. -## -## You should have received a copy of the GNU General Public License along with -## this program; if not, see <http://www.gnu.org/licenses/>. - -## -*- texinfo -*- -## @deftypefn {Function File} {@var{yy} =} smooth (@var{y}) -## @deftypefnx {Function File} {@var{yy} =} smooth (@var{y}, @var{span}) -## @deftypefnx {Function File} {@var{yy} =} smooth (@var{y}, @var{method}) -## @deftypefnx {Function File} {@var{yy} =} smooth (@var{y}, @var{span}, @var{method}) -## @deftypefnx {Function File} {@var{yy} =} smooth (@var{y}, "sgolay", @var{degree}) -## @deftypefnx {Function File} {@var{yy} =} smooth (@var{y}, @var{span}, 'sgolay', @var{degree}) -## @deftypefnx {Function File} {@var{yy} =} smooth (@var{x}, @var{y}, ...) -## -## This is an implementation of the functionality of the @code{smooth} function in -## Matlab's Curve Fitting Toolbox. -## -## Smooths the @var{y} data with the chosen method, see the table below for available -## methods. -## -## The @var{x} data does not need to have uniform spacing. -## -## For the methods "moving" and "sgolay" the @var{span} parameter defines how many data -## points to use for the smoothing of each data point. Default is 5, i.e. the -## center point and two neighbours on each side. -## -## Smoothing methods specified by @var{method}: -## -## @table @asis -## @item "moving" -## Moving average (default). For each data point, the average value of the span -## is used. Corresponds to lowpass filtering. -## -## @item "sgolay" -## Savitzky-Golay filter. For each data point a polynomial of degree @var{degree} -## is fitted (using a least-square regression) to the span and evaluated for the -## current @var{x} value. Also known as digital smoothing polynomial filter or -## least-squares smoothing filter. Default value of @var{degree} is 2. -## -## @item "lowess" -## -## @item "loess" -## -## @item "rlowess" -## -## @item "rloess" -## -## @end table -## -## Documentation of the Matlab smooth function: -## @url{http://www.mathworks.se/help/curvefit/smooth.html} -## @url{http://www.mathworks.se/help/curvefit/smoothing-data.html} -## -## @end deftypefn - -function yy = smooth (varargin) - - ## Default values - - span = 5; - method = 'moving'; - degree = 2; ## for sgolay method - - ## Keep track of the order of the arguments - argidx_x = -1; - argidx_y = -1; - argidx_span = -1; - argidx_method = -1; - argidx_degree = -1; - - ## Check input arguments - - if (nargin < 1) - print_usage (); - else - ## 1 or more arguments - if (!isnumeric (varargin{1})) - error ('smooth: first argument must be a vector') - endif - if (nargin < 2) - ## first argument is y - argidx_y = 1; - y = varargin{1}; - else - ## 2 or more arguments - if ((isnumeric (varargin{2})) && (length (varargin{2}) > 1)) - ## both x and y are provided - argidx_x = 1; - argidx_y = 2; - x = varargin{1}; - y = varargin{2}; - if (length (x) != length (y)) - error ('smooth: x and y vectors must have the same length') - endif - else - ## Only y provided, create an evenly spaced x vector - argidx_y = 1; - y = varargin{1}; - x = 1:length (y); - if ((isnumeric (varargin{2})) && (length (varargin{2}) == 1)) - ## 2nd argument is span - argidx_span = 2; - span = varargin{2}; - elseif (ischar (varargin{2})) - ## 2nd argument is method - argidx_method = 2; - method = varargin{2}; - else - error ('smooth: 2nd argument is of unexpected type') - endif - endif - if (nargin > 2) - if ((argidx_y == 2) && (isnumeric (varargin{3}))) - ## 3rd argument is span - argidx_span = 3; - span = varargin{3}; - if (length (span) > 1) - error ('smooth: 3rd argument can''t be a vector') - endif - elseif (ischar (varargin{3})) - ## 3rd argument is method - argidx_method = 3; - method = varargin{3}; - elseif (strcmp (varargin{2}, 'sgolay') && (isnumeric (varargin{3}))) - ## 3rd argument is degree - argidx_degree = 3; - degree = varargin{3}; - if (length (degree) > 1) - error ('smooth: 3rd argument is of unexpected type') - endif - else - error ('smooth: 3rd argument is of unexpected type') - endif - if (nargin > 3) - if (argidx_span == 3) - ## 4th argument is method - argidx_mehod = 4; - method = varargin{4}; - if (!ischar (method)) - error ('smooth: 4th argument is of unexpected type') - endif - elseif (strcmp (varargin{3}, 'sgolay')) - ## 4th argument is degree - argidx_degree = 4; - degree = varargin{4}; - if ((!isnumeric (degree)) || (length (degree) > 1)) - error ('smooth: 4th argument is of unexpected type') - endif - else - error ('smooth: based on the first 3 arguments, a 4th wasn''t expected') - endif - if (nargin > 4) - if (strcmp (varargin{4}, 'sgolay')) - ## 5th argument is degree - argidx_degree = 5; - degree = varargin{5}; - if ((!isnumeric (degree)) || (length (degree) > 1)) - error ('smooth: 5th argument is of unexpected type') - endif - else - error ('smooth: based on the first 4 arguments, a 5th wasn''t expected') - endif - if (nargin > 5) - error ('smooth: too many input arguments') - endif - endif - endif - endif - endif - endif - - - ## Perform smoothing - - if (span > length (y)) - error ('smooth: span cannot be greater than ''length (y)''.') - endif - yy = []; - switch method - ## --- Moving average - case 'moving' - for i=1:length (y) - if (mod (span,2) == 0) - error ('smooth: span must be odd.') - endif - if (i <= (span-1)/2) - ## We're in the beginning of the vector, use as many y values as - ## possible and still having the index i in the center. - ## Use 2*i-1 as the span. - idx1 = 1; - idx2 = 2*i-1; - elseif (i <= length (y) - (span-1)/2) - ## We're somewhere in the middle of the vector. - ## Use full span. - idx1 = i-(span-1)/2; - idx2 = i+(span-1)/2; - else - ## We're near the end of the vector, reduce span. - ## Use 2*(length (y) - i) + 1 as span - idx1 = i - (length (y) - i); - idx2 = i + (length (y) - i); - endif - yy(i) = mean (y(idx1:idx2)); - endfor - - ## --- Savitzky-Golay filtering - case 'sgolay' - ## FIXME: Check how Matlab takes care of the beginning and the end. Reduce polynomial degree? - for i=1:length (y) - if (mod (span,2) == 0) - error ('smooth: span must be odd.') - endif - if (i <= (span-1)/2) - ## We're in the beginning of the vector, use as many y values as - ## possible and still having the index i in the center. - ## Use 2*i-1 as the span. - idx1 = 1; - idx2 = 2*i-1; - elseif (i <= length (y) - (span-1)/2) - ## We're somewhere in the middle of the vector. - ## Use full span. - idx1 = i-(span-1)/2; - idx2 = i+(span-1)/2; - else - ## We're near the end of the vector, reduce span. - ## Use 2*(length (y) - i) + 1 as span - idx1 = i - (length (y) - i); - idx2 = i + (length (y) - i); - endif - ## Fit a polynomial to the span using least-square method. - p = polyfit(x(idx1:idx2), y(idx1:idx2), degree); - ## Evaluate the polynomial in the center of the span. - yy(i) = polyval(p,x(i)); - endfor - - ## --- - case 'lowess' - ## FIXME: implement smoothing method 'lowess' - error ('smooth: method ''lowess'' not implemented yet') - - ## --- - case 'loess' - ## FIXME: implement smoothing method 'loess' - error ('smooth: method ''loess'' not implemented yet') - - ## --- - case 'rlowess' - ## FIXME: implement smoothing method 'rlowess' - error ('smooth: method ''rlowess'' not implemented yet') - - ## --- - case 'rloess' - ## FIXME: implement smoothing method 'rloess' - error ('smooth: method ''rloess'' not implemented yet') - - ## --- - otherwise - error ('smooth: unknown method') - endswitch -endfunction - - -######################################## - -%!test -%! ## 5 y values (same as default span) -%! y = [42 7 34 5 9]; -%! yy2 = y; -%! yy2(2) = (y(1) + y(2) + y(3))/3; -%! yy2(3) = (y(1) + y(2) + y(3) + y(4) + y(5))/5; -%! yy2(4) = (y(3) + y(4) + y(5))/3; -%! yy = smooth (y); -%! assert (yy, yy2); - -%!test -%! ## x vector provided -%! x = 1:5; -%! y = [42 7 34 5 9]; -%! yy2 = y; -%! yy2(2) = (y(1) + y(2) + y(3))/3; -%! yy2(3) = (y(1) + y(2) + y(3) + y(4) + y(5))/5; -%! yy2(4) = (y(3) + y(4) + y(5))/3; -%! yy = smooth (x, y); -%! assert (yy, yy2); - -%!test -%! ## span provided -%! y = [42 7 34 5 9]; -%! yy2 = y; -%! yy2(2) = (y(1) + y(2) + y(3))/3; -%! yy2(3) = (y(2) + y(3) + y(4))/3; -%! yy2(4) = (y(3) + y(4) + y(5))/3; -%! yy = smooth (y, 3); -%! assert (yy, yy2); - -%!test -%! ## x vector & span provided -%! x = 1:5; -%! y = [42 7 34 5 9]; -%! yy2 = y; -%! yy2(2) = (y(1) + y(2) + y(3))/3; -%! yy2(3) = (y(2) + y(3) + y(4))/3; -%! yy2(4) = (y(3) + y(4) + y(5))/3; -%! yy = smooth (x, y, 3); -%! assert (yy, yy2); - -%!test -%! ## method 'moving' provided -%! y = [42 7 34 5 9]; -%! yy2 = y; -%! yy2(2) = (y(1) + y(2) + y(3))/3; -%! yy2(3) = (y(1) + y(2) + y(3) + y(4) + y(5))/5; -%! yy2(4) = (y(3) + y(4) + y(5))/3; -%! yy = smooth (y, 'moving'); -%! assert (yy, yy2); - -%!test -%! ## x vector & method 'moving' provided -%! x = 1:5; -%! y = [42 7 34 5 9]; -%! yy2 = y; -%! yy2(2) = (y(1) + y(2) + y(3))/3; -%! yy2(3) = (y(1) + y(2) + y(3) + y(4) + y(5))/5; -%! yy2(4) = (y(3) + y(4) + y(5))/3; -%! yy = smooth (x, y, 'moving'); -%! assert (yy, yy2); - -%!test -%! ## span & method 'moving' provided -%! y = [42 7 34 5 9]; -%! yy2 = y; -%! yy2(2) = (y(1) + y(2) + y(3))/3; -%! yy2(3) = (y(2) + y(3) + y(4))/3; -%! yy2(4) = (y(3) + y(4) + y(5))/3; -%! yy = smooth (y, 3, 'moving'); -%! assert (yy, yy2); - -%!test -%! ## x vector, span & method 'moving' provided -%! x = 1:5; -%! y = [42 7 34 5 9]; -%! yy2 = y; -%! yy2(2) = (y(1) + y(2) + y(3))/3; -%! yy2(3) = (y(2) + y(3) + y(4))/3; -%! yy2(4) = (y(3) + y(4) + y(5))/3; -%! yy = smooth (x, y, 3, 'moving'); -%! assert (yy, yy2); - -######################################## - -%!demo -%! ## Moving average & Savitzky-Golay -%! x = linspace (0, 4*pi, 150); -%! y = sin (x) + 1*(rand (1, length (x)) - 0.5); -%! y_ma = smooth (y, 21, 'moving'); -%! y_sg = smooth (y, 21, 'sgolay', 2); -%! y_sg2 = smooth (y, 51, 'sgolay', 2); -%! figure -%! plot (x,y, x,y_ma, x,y_sg, x,y_sg2) -%! legend('Original', 'Moving Average (span 21)', 'Savitzky-Golay (span 21, degree 2)', 'Savitzky-Golay (span 51, degree 2)') -