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peakfit.m
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peakfit.m
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function [FitResults,LowestError,baseline,BestStart,xi,yi,BootResults]=peakfit(signal,center,window,NumPeaks,peakshape,extra,NumTrials,start,autozero,fixedparameters,plots,bipolar,minwidth)
% A command-line peak fitting program for time-series signals, written as a
% self-contained Matlab function in a single m-file. Uses a non-linear
% optimization algorithm to decompose a complex, overlapping-peak signal
% into its component parts. The objective is to determine whether your
% signal can be represented as the sum of fundamental underlying peaks
% shapes. Accepts signals of any length, including those with non-integer
% and non-uniform x-values. Fits any number of peaks of Gaussian,
% Lorentzian, equal-width Gaussian and Lorentzian, fixed-width Gaussian and
% Lorentzian, biburfated Gaussian, exponentially-broadened Gaussian,
% Pearson, Logistic, lognormal, exponential pulse, up and down sigmoids,
% Gaussian/ Lorentzian blend, Voigt, triangular, Breit-Wigner-Fano,
% triangular, or multiple combinations of those shapes (designated by using
% a vector as the 5th input argument; see examples 17 and 18). This is a
% command line version, usable from a remote terminal. It is capable of
% making multiple trial fits with sightly different starting values and
% taking the one with the lowest mean fit error (example 6), and it can
% estimate the standard deviation of peak parameters from a single signal
% using the bootstrap method (example 10).
%
% Version 5.7: August, 2014. Adds minimum width constraint as 13th input
% argument (See example 19); Can be a vector for multiple peak shapes. The
% default if not specified is the independent variable (x) interval.
%
% For more details, see
% http://terpconnect.umd.edu/~toh/spectrum/CurveFittingC.html and
% http://terpconnect.umd.edu/~toh/spectrum/InteractivePeakFitter.htm
%
% peakfit(signal);
% Performs an iterative least-squares fit of a single Gaussian
% peak to the data matrix "signal", which has x values
% in column 1 and Y values in column 2 (e.g. [x y])
%
% peakfit(signal,center,window);
% Fits a single Gaussian peak to a portion of the
% matrix "signal". The portion is centered on the
% x-value "center" and has width "window" (in x units).
%
% peakfit(signal,center,window,NumPeaks);
% "NumPeaks" = number of peaks in the model (default is 1 if not
% specified). No limit to maximum number of peaks in version 3.1
%
% peakfit(signal,center,window,NumPeaks,peakshape);
% "peakshape" specifies the peak shape of the model: (1=Gaussian
% (default), 2=Lorentzian, 3=logistic distribution, 4=Pearson,
% 5=exponentionally broadened Gaussian; 6=equal-width Gaussians;
% 7=Equal-width Lorentzians; 8=exponentionally broadened equal-width
% Gaussian, 9=exponential pulse, 10=up-sigmoid (logistic function),
% 11=Fixed-width Gaussian, 12=Fixed-width Lorentzian; 13=Gaussian/
% Lorentzian blend; 14=Bifurcated Gaussian, 15=Breit-Wigner-Fano,
% 16=Fixed-position Gaussians; 17=Fixed-position Lorentzians;
% 18=exponentionally broadened Lorentzian; 19=alpha function; 20=Voigt
% profile; 21=triangular; 22=multiple shapes; 23=down-sigmoid;
% 25=lognormal; 26=sine wave; 27=Gaussian first derivative.
%
% peakfit(signal,center,window,NumPeaks,peakshape,extra)
% 'extra' specifies the value of 'extra', used only in the Voigt, Pearson,
% exponentionally broadened Gaussian, Gaussian/Lorentzian blend, and
% bifurcated Gaussian and Lorentzian shapes to fine-tune the peak shape.
%
% peakfit(signal,center,window,NumPeaks,peakshape,extra,NumTrials);
% Performs "NumTrials" trial fits and selects the best one (with lowest
% fitting error). NumTrials can be any positive integer (default is 1).
%
% peakfit(signal,center,window,NumPeaks,peakshape,extra,NumTrials,start)
% Specifies the first guesses vector "firstguess" for the peak positions
% and widths. Must be expressed as a vector , in square brackets, e.g.
% start=[position1 width1 position2 width2 ...]
%
% peakfit(signal,center,window,NumPeaks,peakshape,extra,NumTrials,start,autozero)
% 'autozero' sets the baseline correction mode:
% autozero=0 (default) does not subtract baseline from data segment;
% autozero=1 interpolates a linear baseline from the edges of the data
% segment and subtracts it from the signal (assumes that the
% peak returns to the baseline at the edges of the signal);
% autozero=2 is like mode 1 except that it computes a quadratic curved baseline;
% autozero=3 compensates for a flat baseline without reference to the
% signal itself (best if the peak does not return to the
% baseline at the edges of the signal).
%
% peakfit(signal,center,window,NumPeaks,peakshape,extra,NumTrials,start,autozero,fixedparameters)
% 'fixedparameters' specifies fixed values for widths (shapes 10, 11) or
% positions (shapes 16, 17)
%
% peakfit(signal,center,window,NumPeaks,peakshape,extra,NumTrials,start,autozero,fixedparameters,plots)
% 'plots' controls graphic plotting: 0=no plot; 1=plots draw as usual (default)
%
% peakfit(signal,center,window,NumPeaks,peakshape,extra,NumTrials,start,autozero,fixedparameters,plots,bipolar)
% 'bipolar' = 0 constrain peaks heights to be positions; 'bipolar' = 1
% allows positive ands negative peak heights.
%
% peakfit(signal,center,window,NumPeaks,peakshape,extra,NumTrials,start,autozero,fixedparameters,plots,bipolar,minwidth)
% 'minwidth' sets the minmimum allowed peak width. The default if not
% specified is equal to the x-axis interval. Must be a vector of minimum
% widths, one value for each peak, if the multiple peak shape is chosen, as in
% example 17 and 18.
%
% [FitResults,FitError]=peakfit(signal,center,window...) Returns the
% FitResults vector in the order peak number, peak position, peak height,
% peak width, and peak area), and the FitError (the percent RMS
% difference between the data and the model in the selected segment of that
% data) of the best fit.
%
% [FitResults,LowestError,BestStart,xi,yi,BootResults]=peakfit(signal,...)
% Prints out parameter error estimates for each peak (bootstrap method).
%
% Optional output parameters
% 1. FitResults: a table of model peak parameters, one row for each peak,
% listing Peak number, Peak position, Height, Width, and Peak area.
% 2. LowestError: The rms fitting error of the best trial fit.
% 3. Baseline, used in the flat basline correction mode (autozero=3).
% 4. BestStart: the starting guesses that gave the best fit.
% 5. xi: vector containing 600 interploated x-values for the model peaks.
% 6. yi: matrix containing the y values of each model peak at each xi.
% Type plot(xi,yi(1,:)) to plot peak 1 or plot(xi,yi) to plot all peaks
% 7. BootResults: a table of bootstrap precision results for a each peak
% and peak parameter.
%
% Example 1:
% >> x=[0:.1:10]';y=exp(-(x-5).^2);peakfit([x y])
% Fits exp(-x)^2 with a single Gaussian peak model.
%
% Peak number Peak position Height Width Peak area
% 1 5 1 1.665 1.7725
%
% >> y=[0 1 2 4 6 7 6 4 2 1 0 ];x=1:length(y);
% >> peakfit([x;y],length(y)/2,length(y),0,0,0,0,0,0)
% Fits small set of manually entered y data to a single Gaussian peak model.
%
% Example 2:
% x=[0:.01:10];y=exp(-(x-5).^2)+randn(size(x));peakfit([x;y])
% Measurement of very noisy peak with signal-to-noise ratio = 1.
% ans =
% 1 5.0279 0.9272 1.7948 1.7716
%
% Example 3:
% x=[0:.1:10];y=exp(-(x-5).^2)+.5*exp(-(x-3).^2)+.1*randn(size(x));
% peakfit([x' y'],0,0,2)
% Fits a noisy two-peak signal with a double Gaussian model (NumPeaks=2).
% ans =
% 1 3.0001 0.49489 1.642 0.86504
% 2 4.9927 1.0016 1.6597 1.7696
%
% Example 4:
% >> x=1:100;y=ones(size(x))./(1+(x-50).^2);peakfit(y,0,0,1,2)
% Fit Lorentzian (peakshape=2) located at x=50, height=1, width=2.
% ans =
% 1 50 0.99974 1.9971 3.1079
%
% Example 5:
% >> x=[0:.005:1];y=humps(x);peakfit([x' y'],.3,.7,1,4,3);
% Fits a portion of the humps function, 0.7 units wide and centered on
% x=0.3, with a single (NumPeaks=1) Pearson function (peakshape=4) with
% extra=3 (controls shape of Pearson function).
%
% Example 6:
% >> x=[0:.005:1];y=(humps(x)+humps(x-.13)).^3;smatrix=[x' y'];
% >> [FitResults,FitError]=peakfit(smatrix,.4,.7,2,1,0,10)
% Creates a data matrix 'smatrix', fits a portion to a two-peak Gaussian
% model, takes the best of 10 trials. Returns FitResults and FitError.
% FitResults =
% 1 0.31056 2.0125e+006 0.11057 2.3689e+005
% 2 0.41529 2.2403e+006 0.12033 2.8696e+005
% FitError =
% 1.1899
%
% Example 7:
% >> peakfit([x' y'],.4,.7,2,1,0,10,[.3 .1 .5 .1]);
% As above, but specifies the first-guess position and width of the two
% peaks, in the order [position1 width1 position2 width2]
%
% Example 8: (Version 4 only)
% Demonstration of the four autozero modes, for a single Gaussian on flat
% baseline, with position=10, height=1, and width=1.66. Autozero mode
% is specified by the 9th input argument (0,1,2, or 3).
% >> x=8:.05:12;y=1+exp(-(x-10).^2);
% >> [FitResults,FitError]=peakfit([x;y],0,0,1,1,0,1,0,0)
% Autozero=0 means to ignore the baseline (default mode if not specified)
% FitResults =
% 1 10 1.8561 3.612 5.7641
% FitError =
% 5.387
% >> [FitResults,FitError]=peakfit([x;y],0,0,1,1,0,1,0,1)
% Autozero=1 subtracts linear baseline from edge to edge.
% Does not work well because signal does not return to baseline at edges.
% FitResults =
% 1 9.9984 0.96153 1.559 1.5916
% FitError =
% 1.9801
% >> [FitResults,FitError]=peakfit([x;y],0,0,1,1,0,1,0,2)
% Autozero=1 subtracts quadratic baseline from edge to edge.
% Does not work well because signal does not return to baseline at edges.
% FitResults =
% 1 9.9996 0.81749 1.4384 1.2503
% FitError =
% 1.8204
% Autozero=3: Flat baseline mode, measures baseline by regression
% >> [FitResults,Baseline,FitError]=peakfit([x;y],0,0,1,1,0,1,0,3)
% FitResults =
% 1 10 1.0001 1.6653 1.7645
% Baseline =
% 0.0037056
% FitError =
% 0.99985
%
% Example 9:
% x=[0:.1:10];y=exp(-(x-5).^2)+.5*exp(-(x-3).^2)+.1*randn(size(x));
% [FitResults,FitError]=peakfit([x' y'],0,0,2,11,0,0,0,0,1.666)
% Same as example 3, fit with fixed-width Gaussian (shape 11), width=1.666
%
% Example 10: (Version 3 or later; Prints out parameter error estimates)
% x=0:.05:9;y=exp(-(x-5).^2)+.5*exp(-(x-3).^2)+.01*randn(1,length(x));
% [FitResults,LowestError,BestStart,xi,yi,BootstrapErrors]=peakfit([x;y],0,0,2,6,0,1,0,0,0);
%
% Example 11: (Version 3.2 or later)
% x=[0:.005:1];y=humps(x);[FitResults,FitError]=peakfit([x' y'],0.54,0.93,2,13,15,10,0,0,0)
%
% FitResults =
% 1 0.30078 190.41 0.19131 23.064
% 2 0.89788 39.552 0.33448 6.1999
% FitError =
% 0.34502
% Fits both peaks of the Humps function with a Gaussian/Lorentzian blend
% (shape 13) that is 15% Gaussian (Extra=15).
%
% Example 12: (Version 3.2 or later)
% >> x=[0:.1:10];y=exp(-(x-4).^2)+.5*exp(-(x-5).^2)+.01*randn(size(x));
% >> [FitResults,FitError]=peakfit([x' y'],0,0,1,14,45,10,0,0,0)
% FitResults =
% 1 4.2028 1.2315 4.077 2.6723
% FitError =
% 0.84461
% Fit a slightly asymmetrical peak with a bifurcated Gaussian (shape 14)
%
% Example 13: (Version 3.3 or later)
% >> x=[0:.1:10]';y=exp(-(x-5).^2);peakfit([x y],0,0,1,1,0,0,0,0,0,0)
% Example 1 without plotting (11th input argument = 0, default is 1)
%
% Example 14: (Version 3.9 or later)
% Exponentially broadened Lorentzian with position=9, height=1.
% x=[0:.1:20];
% L=lorentzian(x,9,1);
% L1=ExpBroaden(L',-10)+0.02.*randn(size(x))';
% [FitResults,FitError]=peakfit([x;L1'],0,0,1,18,10)
%
% Example 15: Fitting the humps function with two Voigt profiles, flat
% baselinie mode
% [FitResults,FitError]=peakfit(humps(0:.01:2),71,140,2,20,1.7,1,[31 4.7 90 8.8],3)
%FitResults =
% 1 31.047 96.762 4.6785 2550.1
% 2 90.09 22.935 8.8253 1089.5
% FitError =
% 0.80501
%
% Example 16: (Version 4.3 or later) Set +/- mode to 1 (bipolar)
% >> x=[0:.1:10];y=exp(-(x-5).^2)-.5*exp(-(x-3).^2)+.1*randn(size(x));
% >> peakfit([x' y'],0,0,2,1,0,1,0,0,0,1,1)
% FitResults =
% 1 3.1636 -0.5433 1.62 -0.9369
% 2 4.9487 0.96859 1.8456 1.9029
% FitError =
% 8.2757
%
% Example 17: Version 5 or later. Fits humps function to a model consisting
% of one Pearson (shape=4, extra=3) and one Gaussian (shape=1), flat
% baseline mode=3, NumTrials=10.
% x=[0:.005:1.2];y=humps(x);[FitResults,FitError]=peakfit([x' y'],0,0,2,[2 1],[0 0])
% FitResults =
% 1 0.30154 84.671 0.27892 17.085
% 2 0.88522 11.545 0.20825 2.5399
% Baseline =
% 0.901
% FitError =
% 10.457
%
% Example 18: 5 peaks, 5 different shapes, all heights = 1, widths = 3.
% x=0:.1:60;
% y=modelpeaks2(x,[1 2 3 4 5],[1 1 1 1 1],[10 20 30 40 50],...
% [3 3 3 3 3],[0 0 0 2 -20])+.01*randn(size(x));
% peakfit([x' y'],0,0,5,[1 2 3 4 5],[0 0 0 2 -20])
%
% Example 19: Minimum width constraint (13th input argument)
% x=1:30;y=gaussian(x,15,8)+.05*randn(size(x));
% No constraint:
% peakfit([x;y],0,0,5,1,0,10,0,0,0,1,0,0);
% Widths constrained to values above 7:
% peakfit([x;y],0,0,5,1,0,10,0,0,0,1,0,7);
% Copyright (c) 2013, Thomas C. O'Haver
%
% Permission is hereby granted, free of charge, to any person obtaining a copy
% of this software and associated documentation files (the "Software"), to deal
% in the Software without restriction, including without limitation the rights
% to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
% copies of the Software, and to permit persons to whom the Software is
% furnished to do so, subject to the following conditions:
%
% The above copyright notice and this permission notice shall be included in
% all copies or substantial portions of the Software.
%
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% IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
% FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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%
global AA xxx PEAKHEIGHTS FIXEDPARAMETERS AUTOZERO delta BIPOLAR MINWIDTH
% peakfit.m version 5, February 2014
format short g
format compact
warning off all
NumArgOut=nargout;
datasize=size(signal);
if datasize(1)<datasize(2),signal=signal';end
datasize=size(signal);
if datasize(2)==1, % Must be isignal(Y-vector)
X=1:length(signal); % Create an independent variable vector
Y=signal;
else
% Must be isignal(DataMatrix)
X=signal(:,1); % Split matrix argument
Y=signal(:,2);
end
X=reshape(X,1,length(X)); % Adjust X and Y vector shape to 1 x n (rather than n x 1)
Y=reshape(Y,1,length(Y));
% If necessary, flip the data vectors so that X increases
if X(1)>X(length(X)),
disp('X-axis flipped.')
X=fliplr(X);
Y=fliplr(Y);
end
% Isolate desired segment from data set for curve fitting
if nargin==1 || nargin==2,center=(max(X)-min(X))/2;window=max(X)-min(X);end
% Y=Y-min(Y);
xoffset=0;
n1=val2ind(X,center-window/2);
n2=val2ind(X,center+window/2);
if window==0,n1=1;n2=length(X);end
xx=X(n1:n2)-xoffset;
yy=Y(n1:n2);
ShapeString='Gaussian';
% Define values of any missing arguments
switch nargin
case 1
NumPeaks=1;
peakshape=1;
extra=0;
NumTrials=1;
xx=X;yy=Y;
start=calcstart(xx,NumPeaks,xoffset);
AUTOZERO=0;
plots=1;
BIPOLAR=0;
MINWIDTH=xx(2)-xx(1);
case 2
NumPeaks=1;
peakshape=1;
extra=0;
NumTrials=1;
xx=signal;yy=center;
start=calcstart(xx,NumPeaks,xoffset);
AUTOZERO=0;
plots=1;
BIPOLAR=0;
MINWIDTH=xx(2)-xx(1);
case 3
NumPeaks=1;
peakshape=1;
extra=0;
NumTrials=1;
start=calcstart(xx,NumPeaks,xoffset);
AUTOZERO=0;
FIXEDPARAMETERS=0;
plots=1;
BIPOLAR=0;
MINWIDTH=xx(2)-xx(1);
case 4
peakshape=1;
extra=0;
NumTrials=1;
start=calcstart(xx,NumPeaks,xoffset);
AUTOZERO=0;
FIXEDPARAMETERS=0;
plots=1;
BIPOLAR=0;
MINWIDTH=xx(2)-xx(1);
case 5
extra=zeros(1,NumPeaks);
NumTrials=1;
start=calcstart(xx,NumPeaks,xoffset);
AUTOZERO=0;
FIXEDPARAMETERS=0;
plots=1;
BIPOLAR=0;
MINWIDTH=zeros(size(peakshape))+(xx(2)-xx(1));
case 6
NumTrials=1;
start=calcstart(xx,NumPeaks,xoffset);
AUTOZERO=0;
FIXEDPARAMETERS=0;
plots=1;
BIPOLAR=0;
MINWIDTH=zeros(size(peakshape))+(xx(2)-xx(1));
case 7
start=calcstart(xx,NumPeaks,xoffset);
AUTOZERO=0;
FIXEDPARAMETERS=0;
plots=1;
BIPOLAR=0;
MINWIDTH=zeros(size(peakshape))+(xx(2)-xx(1));
case 8
AUTOZERO=0;
FIXEDPARAMETERS=0;
plots=1;
BIPOLAR=0;
MINWIDTH=zeros(size(peakshape))+(xx(2)-xx(1));
case 9
AUTOZERO=autozero;
FIXEDPARAMETERS=0;
plots=1;
BIPOLAR=0;
MINWIDTH=zeros(size(peakshape))+(xx(2)-xx(1));
case 10
AUTOZERO=autozero;
FIXEDPARAMETERS=fixedparameters;
plots=1;
BIPOLAR=0;
MINWIDTH=zeros(size(peakshape))+(xx(2)-xx(1));
case 11
AUTOZERO=autozero;
FIXEDPARAMETERS=fixedparameters;
BIPOLAR=0;
case 12
AUTOZERO=autozero;
FIXEDPARAMETERS=fixedparameters;
BIPOLAR=bipolar;
MINWIDTH=zeros(size(peakshape))+(xx(2)-xx(1));
case 13
AUTOZERO=autozero;
FIXEDPARAMETERS=fixedparameters;
BIPOLAR=bipolar;
MINWIDTH=minwidth;
otherwise
end % switch nargin
% Default values for placeholder zeros1
if NumTrials==0;NumTrials=1;end
if isscalar(peakshape),
else
% disp('peakshape is vector');
shapesvector=peakshape;
NumPeaks=length(peakshape);
peakshape=22;
end
if peakshape==0;peakshape=1;end
if NumPeaks==0;NumPeaks=1;end
if start==0;start=calcstart(xx,NumPeaks,xoffset);end
if FIXEDPARAMETERS==0, FIXEDPARAMETERS=length(xx)/10;end
if peakshape==16;FIXEDPOSITIONS=fixedparameters;end
if peakshape==17;FIXEDPOSITIONS=fixedparameters;end
if AUTOZERO>3,AUTOZERO=3,end
if AUTOZERO<0,AUTOZERO=0,end
delta=1;
% % Remove linear baseline from data segment if AUTOZERO==1
bkgsize=round(length(xx)/10);
if bkgsize<2,bkgsize=2;end
lxx=length(xx);
if AUTOZERO==1, % linear autozero operation
XX1=xx(1:round(lxx/bkgsize));
XX2=xx((lxx-round(lxx/bkgsize)):lxx);
Y1=yy(1:(round(length(xx)/bkgsize)));
Y2=yy((lxx-round(lxx/bkgsize)):lxx);
bkgcoef=polyfit([XX1,XX2],[Y1,Y2],1); % Fit straight line to sub-group of points
bkg=polyval(bkgcoef,xx);
yy=yy-bkg;
end % if
if AUTOZERO==2, % Quadratic autozero operation
XX1=xx(1:round(lxx/bkgsize));
XX2=xx((lxx-round(lxx/bkgsize)):lxx);
Y1=yy(1:round(length(xx)/bkgsize));
Y2=yy((lxx-round(lxx/bkgsize)):lxx);
bkgcoef=polyfit([XX1,XX2],[Y1,Y2],2); % Fit parabola to sub-group of points
bkg=polyval(bkgcoef,xx);
yy=yy-bkg;
end % if autozero
PEAKHEIGHTS=zeros(1,NumPeaks);
n=length(xx);
newstart=start;
% Assign ShapStrings
switch peakshape(1)
case 1
ShapeString='Gaussian';
case 2
ShapeString='Lorentzian';
case 3
ShapeString='Logistic';
case 4
ShapeString='Pearson';
case 5
ShapeString='ExpGaussian';
case 6
ShapeString='Equal width Gaussians';
case 7
ShapeString='Equal width Lorentzians';
case 8
ShapeString='Exp. equal width Gaussians';
case 9
ShapeString='Exponential Pulse';
case 10
ShapeString='Up Sigmoid (logistic function)';
case 23
ShapeString='Down Sigmoid (logistic function)';
case 11
ShapeString='Fixed-width Gaussian';
case 12
ShapeString='Fixed-width Lorentzian';
case 13
ShapeString='Gaussian/Lorentzian blend';
case 14
ShapeString='BiGaussian';
case 15
ShapeString='Breit-Wigner-Fano';
case 16
ShapeString='Fixed-position Gaussians';
case 17
ShapeString='Fixed-position Lorentzians';
case 18
ShapeString='Exp. Lorentzian';
case 19
ShapeString='Alpha function';
case 20
ShapeString='Voigt profile';
case 21
ShapeString='triangular';
case 22
ShapeString=num2str(shapesvector);
case 24
ShapeString='Negative Binomial Distribution';
case 25
ShapeString='Lognormal Distribution';
case 26
ShapeString='Sine wave';
case 27
ShapeString='First derivative';
otherwise
end % switch peakshape
% Perform peak fitting for selected peak shape using fminsearch function
options = optimset('TolX',.001,'Display','off','MaxFunEvals',1000 );
LowestError=1000; % or any big number greater than largest error expected
FitParameters=zeros(1,NumPeaks.*2);
BestStart=zeros(1,NumPeaks.*2);
height=zeros(1,NumPeaks);
bestmodel=zeros(size(yy));
for k=1:NumTrials,
StartMatrix(k,:)=newstart;
% disp(['Trial number ' num2str(k) ] ) % optionally prints the current trial number as progress indicator
switch peakshape(1)
case 1
TrialParameters=fminsearch(@(lambda)(fitgaussian(lambda,xx,yy)),newstart,options);
for Peak=1:NumPeaks;
if TrialParameters(2*Peak)<MINWIDTH,
TrialParameters(2*Peak)=MINWIDTH;
end
end
case 2
TrialParameters=fminsearch(@(lambda)(fitlorentzian(lambda,xx,yy)),newstart,options);
for Peak=1:NumPeaks;
if TrialParameters(2*Peak)<MINWIDTH,
TrialParameters(2*Peak)=MINWIDTH;
end
end
case 3
TrialParameters=fminsearch(@(lambda)(fitlogistic(lambda,xx,yy)),newstart,options);
for Peak=1:NumPeaks;
if TrialParameters(2*Peak)<MINWIDTH,
TrialParameters(2*Peak)=MINWIDTH;
end
end
case 4
TrialParameters=fminsearch(@(lambda)(fitpearson(lambda,xx,yy,extra)),newstart,options);
for Peak=1:NumPeaks;
if TrialParameters(2*Peak)<MINWIDTH,
TrialParameters(2*Peak)=MINWIDTH;
end
end
case 5
zxx=[zeros(size(xx)) xx zeros(size(xx)) ];
zyy=[zeros(size(yy)) yy zeros(size(yy)) ];
TrialParameters=fminsearch(@(lambda)(fitexpgaussian(lambda,zxx,zyy,-extra)),newstart,options);
for Peak=1:NumPeaks;
if TrialParameters(2*Peak)<MINWIDTH,
TrialParameters(2*Peak)=MINWIDTH;
end
end
case 6
cwnewstart(1)=newstart(1);
for pc=2:NumPeaks,
cwnewstart(pc)=newstart(2.*pc-1);
end
cwnewstart(NumPeaks+1)=(max(xx)-min(xx))/5;
TrialParameters=fminsearch(@(lambda)(fitewgaussian(lambda,xx,yy)),cwnewstart,options);
for Peak=1:NumPeaks;
if TrialParameters(NumPeaks+1)<MINWIDTH,
TrialParameters(NumPeaks+1)=MINWIDTH;
end
end
case 7
cwnewstart(1)=newstart(1);
for pc=2:NumPeaks,
cwnewstart(pc)=newstart(2.*pc-1);
end
cwnewstart(NumPeaks+1)=(max(xx)-min(xx))/5;
TrialParameters=fminsearch(@(lambda)(fitewlorentzian(lambda,xx,yy)),cwnewstart,options);
for Peak=1:NumPeaks;
if TrialParameters(NumPeaks+1)<MINWIDTH,
TrialParameters(NumPeaks+1)=MINWIDTH;
end
end
case 8
cwnewstart(1)=newstart(1);
for pc=2:NumPeaks,
cwnewstart(pc)=newstart(2.*pc-1);
end
cwnewstart(NumPeaks+1)=(max(xx)-min(xx))/5;
TrialParameters=fminsearch(@(lambda)(fitexpewgaussian(lambda,xx,yy,-extra)),cwnewstart,options);
for Peak=1:NumPeaks;
if TrialParameters(NumPeaks+1)<MINWIDTH,
TrialParameters(NumPeaks+1)=MINWIDTH;
end
end
case 9
TrialParameters=fminsearch(@(lambda)(fitexppulse(lambda,xx,yy)),newstart,options);
for Peak=1:NumPeaks;
if TrialParameters(2*Peak)<MINWIDTH,
TrialParameters(2*Peak)=MINWIDTH;
end
end
case 10
TrialParameters=fminsearch(@(lambda)(fitupsigmoid(lambda,xx,yy)),newstart,options);
for Peak=1:NumPeaks;
if TrialParameters(2*Peak)<MINWIDTH,
TrialParameters(2*Peak)=MINWIDTH;
end
end
case 23
TrialParameters=fminsearch(@(lambda)(fitdownsigmoid(lambda,xx,yy)),newstart,options);
for Peak=1:NumPeaks;
if TrialParameters(2*Peak)<MINWIDTH,
TrialParameters(2*Peak)=MINWIDTH;
end
end
case 11
fixedstart=[];
for pc=1:NumPeaks,
fixedstart(pc)=min(xx)+pc.*(max(xx)-min(xx))./(NumPeaks+1);
end
TrialParameters=fminsearch(@(lambda)(FitFWGaussian(lambda,xx,yy)),fixedstart,options);
case 12
fixedstart=[];
for pc=1:NumPeaks,
fixedstart(pc)=min(xx)+pc.*(max(xx)-min(xx))./(NumPeaks+1);
end
TrialParameters=fminsearch(@(lambda)(FitFWLorentzian(lambda,xx,yy)),fixedstart,options);
case 13
TrialParameters=fminsearch(@(lambda)(fitGL(lambda,xx,yy,extra)),newstart,options);
for Peak=1:NumPeaks;
if TrialParameters(2*Peak)<MINWIDTH,
TrialParameters(2*Peak)=MINWIDTH;
end
end
case 14
TrialParameters=fminsearch(@(lambda)(fitBiGaussian(lambda,xx,yy,extra)),newstart,options);
for Peak=1:NumPeaks;
if TrialParameters(2*Peak)<MINWIDTH,
TrialParameters(2*Peak)=MINWIDTH;
end
end
case 15
TrialParameters=fminsearch(@(lambda)(fitBWF(lambda,xx,yy,extra)),newstart,options);
for Peak=1:NumPeaks;
if TrialParameters(2*Peak)<MINWIDTH,
TrialParameters(2*Peak)=MINWIDTH;
end
end
case 16
fixedstart=[];
for pc=1:NumPeaks,
fixedstart(pc)=(max(xx)-min(xx))./(NumPeaks+1);
fixedstart(pc)=fixedstart(pc)+.1*(rand-.5).*fixedstart(pc);
end
TrialParameters=fminsearch(@(lambda)(FitFPGaussian(lambda,xx,yy)),fixedstart,options);
for Peak=1:NumPeaks;
if TrialParameters(Peak)<MINWIDTH,
TrialParameters(Peak)=MINWIDTH;
end
end
case 17
fixedstart=[];
for pc=1:NumPeaks,
fixedstart(pc)=(max(xx)-min(xx))./(NumPeaks+1);
fixedstart(pc)=fixedstart(pc)+.1*(rand-.5).*fixedstart(pc);
end
TrialParameters=fminsearch(@(lambda)(FitFPLorentzian(lambda,xx,yy)),fixedstart,options);
for Peak=1:NumPeaks;
if TrialParameters(Peak)<MINWIDTH,
TrialParameters(Peak)=MINWIDTH;
end
end
case 18
zxx=[zeros(size(xx)) xx zeros(size(xx)) ];
zyy=[ones(size(yy)).*yy(1) yy zeros(size(yy)).*yy(length(yy)) ];
TrialParameters=fminsearch(@(lambda)(fitexplorentzian(lambda,zxx,zyy,-extra)),newstart,options);
for Peak=1:NumPeaks;
if TrialParameters(2*Peak)<MINWIDTH,
TrialParameters(2*Peak)=MINWIDTH;
end
end
case 19
TrialParameters=fminsearch(@(lambda)(fitalphafunction(lambda,xx,yy)),newstart,options);
for Peak=1:NumPeaks;
if TrialParameters(2*Peak)<MINWIDTH,
TrialParameters(2*Peak)=MINWIDTH;
end
end
case 20
TrialParameters=fminsearch(@(lambda)(fitvoigt(lambda,xx,yy,extra)),newstart,options);
for Peak=1:NumPeaks;
if TrialParameters(2*Peak)<MINWIDTH,
TrialParameters(2*Peak)=MINWIDTH;
end
end
case 21
TrialParameters=fminsearch(@(lambda)(fittriangular(lambda,xx,yy)),newstart,options);
for Peak=1:NumPeaks;
if TrialParameters(2*Peak)<MINWIDTH,
TrialParameters(2*Peak)=MINWIDTH;
end
end
case 22
TrialParameters=fminsearch(@(lambda)(fitmultiple(lambda,xx,yy,shapesvector,extra)),newstart,options);
for Peak=1:NumPeaks;
if TrialParameters(2*Peak)<MINWIDTH(Peak),
TrialParameters(2*Peak)=MINWIDTH(Peak);
end
end
case 24
TrialParameters=fminsearch(@(lambda)(fitnbinpdf(lambda,xx,yy)),newstart,options);
for Peak=1:NumPeaks;
if TrialParameters(2*Peak)<MINWIDTH,
TrialParameters(2*Peak)=MINWIDTH;
end
end
case 25
TrialParameters=fminsearch(@(lambda)(fitlognpdf(lambda,xx,yy)),newstart,options);
for Peak=1:NumPeaks;
if TrialParameters(2*Peak)<MINWIDTH,
TrialParameters(2*Peak)=MINWIDTH;
end
end
case 26
TrialParameters=fminsearch(@(lambda)(fitsine(lambda,xx,yy)),newstart,options);
case 27
TrialParameters=fminsearch(@(lambda)(fitd1gauss(lambda,xx,yy)),newstart,options);
otherwise
end % switch peakshape
% Construct model from Trial parameters
A=zeros(NumPeaks,n);
for m=1:NumPeaks,
switch peakshape(1)
case 1
A(m,:)=gaussian(xx,TrialParameters(2*m-1),TrialParameters(2*m));
case 2
A(m,:)=lorentzian(xx,TrialParameters(2*m-1),TrialParameters(2*m));
case 3
A(m,:)=logistic(xx,TrialParameters(2*m-1),TrialParameters(2*m));
case 4
A(m,:)=pearson(xx,TrialParameters(2*m-1),TrialParameters(2*m),extra);
case 5
A(m,:)=expgaussian(xx,TrialParameters(2*m-1),TrialParameters(2*m),-extra)';
case 6
A(m,:)=gaussian(xx,TrialParameters(m),TrialParameters(NumPeaks+1));
case 7
A(m,:)=lorentzian(xx,TrialParameters(m),TrialParameters(NumPeaks+1));
case 8
A(m,:)=expgaussian(xx,TrialParameters(m),TrialParameters(NumPeaks+1),-extra)';
case 9
A(m,:)=exppulse(xx,TrialParameters(2*m-1),TrialParameters(2*m));
case 10
A(m,:)=upsigmoid(xx,TrialParameters(2*m-1),TrialParameters(2*m));
case 11
A(m,:)=gaussian(xx,TrialParameters(m),FIXEDPARAMETERS);
case 12
A(m,:)=lorentzian(xx,TrialParameters(m),FIXEDPARAMETERS);
case 13
A(m,:)=GL(xx,TrialParameters(2*m-1),TrialParameters(2*m),extra);
case 14
A(m,:)=BiGaussian(xx,TrialParameters(2*m-1),TrialParameters(2*m),extra);
case 15
A(m,:)=BWF(xx,TrialParameters(2*m-1),TrialParameters(2*m),extra);
case 16
A(m,:)=gaussian(xx,FIXEDPOSITIONS(m),TrialParameters(m));
case 17
A(m,:)=lorentzian(xx,FIXEDPOSITIONS(m),TrialParameters(m));
case 18
A(m,:)=explorentzian(xx,TrialParameters(2*m-1),TrialParameters(2*m),-extra)';
case 19
A(m,:)=alphafunction(xx,TrialParameters(2*m-1),TrialParameters(2*m));
case 20
A(m,:)=voigt(xx,TrialParameters(2*m-1),TrialParameters(2*m),extra);
case 21
A(m,:)=triangular(xx,TrialParameters(2*m-1),TrialParameters(2*m));
case 22
A(m,:)=peakfunction(shapesvector(m),xx,TrialParameters(2*m-1),TrialParameters(2*m),extra(m));
case 23
A(m,:)=downsigmoid(xx,TrialParameters(2*m-1),TrialParameters(2*m));
case 24
A(m,:)=nbinpdf(xx,TrialParameters(2*m-1),TrialParameters(2*m));
case 25
A(m,:)=lognormal(xx,TrialParameters(2*m-1),TrialParameters(2*m));
case 26
A(m,:)=sine(xx,TrialParameters(2*m-1),TrialParameters(2*m));
case 27
A(m,:)=d1gauss(xx,TrialParameters(2*m-1),TrialParameters(2*m));
otherwise
end % switch
for parameter=1:2:2*NumPeaks,
newstart(parameter)=newstart(parameter)*(1+delta*(rand-.5)/500);
newstart(parameter+1)=newstart(parameter+1)*(1+delta*(rand-.5)/100);
end
end % for NumPeaks
% Multiplies each row by the corresponding amplitude and adds them up
if AUTOZERO==3,
baseline=PEAKHEIGHTS(1);
Heights=PEAKHEIGHTS(2:1+NumPeaks);
model=Heights'*A+baseline;
else
model=PEAKHEIGHTS'*A;
Heights=PEAKHEIGHTS;
baseline=0;
end
% Compare trial model to data segment and compute the fit error
MeanFitError=100*norm(yy-model)./(sqrt(n)*max(yy));
% Take only the single fit that has the lowest MeanFitError
if MeanFitError<LowestError,
if min(Heights)>=-BIPOLAR*10^100, % Consider only fits with positive peak heights
LowestError=MeanFitError; % Assign LowestError to the lowest MeanFitError
FitParameters=TrialParameters; % Assign FitParameters to the fit with the lowest MeanFitError
BestStart=newstart; % Assign BestStart to the start with the lowest MeanFitError
height=Heights; % Assign height to the PEAKHEIGHTS with the lowest MeanFitError
bestmodel=model; % Assign bestmodel to the model with the lowest MeanFitError
end % if min(PEAKHEIGHTS)>0
end % if MeanFitError<LowestError
% ErrorVector(k)=MeanFitError;
end % for k (NumTrials)
% Uncomment following 4 lines to monitor trail fit starts and errors.
% StartMatrix=StartMatrix;
% ErrorVector=ErrorVector;
% matrix=[StartMatrix ErrorVector']
% std(StartMatrix)
% Construct model from best-fit parameters
AA=zeros(NumPeaks,600);
xxx=linspace(min(xx),max(xx),600);
% xxx=linspace(min(xx)-length(xx),max(xx)+length(xx),200);
for m=1:NumPeaks,
switch peakshape(1)
case 1
AA(m,:)=gaussian(xxx,FitParameters(2*m-1),FitParameters(2*m));
case 2
AA(m,:)=lorentzian(xxx,FitParameters(2*m-1),FitParameters(2*m));
case 3
AA(m,:)=logistic(xxx,FitParameters(2*m-1),FitParameters(2*m));
case 4
AA(m,:)=pearson(xxx,FitParameters(2*m-1),FitParameters(2*m),extra);
case 5
AA(m,:)=expgaussian(xxx,FitParameters(2*m-1),FitParameters(2*m),-extra*length(xxx)./length(xx))';
case 6
AA(m,:)=gaussian(xxx,FitParameters(m),FitParameters(NumPeaks+1));
case 7
AA(m,:)=lorentzian(xxx,FitParameters(m),FitParameters(NumPeaks+1));
case 8
AA(m,:)=expgaussian(xxx,FitParameters(m),FitParameters(NumPeaks+1),-extra*length(xxx)./length(xx))';
case 9
AA(m,:)=exppulse(xxx,FitParameters(2*m-1),FitParameters(2*m));
case 10
AA(m,:)=upsigmoid(xxx,FitParameters(2*m-1),FitParameters(2*m));
case 11
AA(m,:)=gaussian(xxx,FitParameters(m),FIXEDPARAMETERS);
case 12
AA(m,:)=lorentzian(xxx,FitParameters(m),FIXEDPARAMETERS);
case 13
AA(m,:)=GL(xxx,FitParameters(2*m-1),FitParameters(2*m),extra);
case 14
AA(m,:)=BiGaussian(xxx,FitParameters(2*m-1),FitParameters(2*m),extra);
case 15
AA(m,:)=BWF(xxx,FitParameters(2*m-1),FitParameters(2*m),extra);
case 16
AA(m,:)=gaussian(xxx,FIXEDPOSITIONS(m),FitParameters(m));
case 17
AA(m,:)=lorentzian(xxx,FIXEDPOSITIONS(m),FitParameters(m));
case 18
AA(m,:)=explorentzian(xxx,FitParameters(2*m-1),FitParameters(2*m),-extra*length(xxx)./length(xx))';
case 19
AA(m,:)=alphafunction(xxx,FitParameters(2*m-1),FitParameters(2*m));
case 20
AA(m,:)=voigt(xxx,FitParameters(2*m-1),FitParameters(2*m),extra);
case 21
AA(m,:)=triangular(xxx,FitParameters(2*m-1),FitParameters(2*m));
case 22
AA(m,:)=peakfunction(shapesvector(m),xxx,FitParameters(2*m-1),FitParameters(2*m),extra(m));
case 23
AA(m,:)=downsigmoid(xxx,FitParameters(2*m-1),FitParameters(2*m));
case 24
AA(m,:)=nbinpdf(xxx,FitParameters(2*m-1),FitParameters(2*m));
case 25
AA(m,:)=lognormal(xxx,FitParameters(2*m-1),FitParameters(2*m));
case 26
AA(m,:)=sine(xxx,FitParameters(2*m-1),FitParameters(2*m));
case 27
AA(m,:)=d1gauss(xxx,FitParameters(2*m-1),FitParameters(2*m));
otherwise
end % switch
end % for NumPeaks
% Multiplies each row by the corresponding amplitude and adds them up
heightsize=size(height');
AAsize=size(AA);
if heightsize(2)==AAsize(1),
mmodel=height'*AA+baseline;
else
mmodel=height*AA+baseline;
end
% Top half of the figure shows original signal and the fitted model.
if plots,
subplot(2,1,1);plot(xx+xoffset,yy,'b.'); % Plot the original signal in blue dots
hold on
end
for m=1:NumPeaks,
if plots, plot(xxx+xoffset,height(m)*AA(m,:)+baseline,'g'),end % Plot the individual component peaks in green lines
area(m)=trapz(xxx+xoffset,height(m)*AA(m,:)); % Compute the area of each component peak using trapezoidal method
yi(m,:)=height(m)*AA(m,:); % (NEW) Place y values of individual model peaks into matrix yi
end
xi=xxx+xoffset; % (NEW) Place the x-values of the individual model peaks into xi
if plots,
% Mark starting peak positions with vertical dashed lines
if peakshape(1)==16||peakshape(1)==17
else
for marker=1:NumPeaks,
markx=BestStart((2*marker)-1);
subplot(2,1,1);plot([markx+xoffset markx+xoffset],[0 max(yy)],'m--')
end % for
end % if peakshape
plot(xxx+xoffset,mmodel,'r'); % Plot the total model (sum of component peaks) in red lines
hold off;
lyy=min(yy);
uyy=max(yy)+(max(yy)-min(yy))/10;
if BIPOLAR,
axis([min(xx) max(xx) lyy uyy]);
ylabel('+ - mode')
else
axis([min(xx) max(xx) 0 uyy]);
ylabel('+ mode')
end
switch AUTOZERO,
case 0
title(['peakfit 5.7 No baseline correction'])
case 1
title(['peakfit 5.7 Linear baseline subtraction'])
case 2
title(['peakfit 5.7 Quadratic subtraction baseline'])
case 3
title(['peakfit 5.7 Flat baseline correction'])
end
switch peakshape(1)
case {4,20}
xlabel(['Peaks = ' num2str(NumPeaks) ' Shape = ' ShapeString ' Min. Width = ' num2str(MINWIDTH) ' Shape Constant = ' num2str(extra) ' Error = ' num2str(round(1000*LowestError)/1000) '%' ] )
case {5,8,18}
xlabel(['Peaks = ' num2str(NumPeaks) ' Shape = ' ShapeString ' Min. Width = ' num2str(MINWIDTH) ' Time Constant = ' num2str(extra) ' Error = ' num2str(round(1000*LowestError)/1000) '%' ] )
case 13
xlabel(['Peaks = ' num2str(NumPeaks) ' Shape = ' ShapeString ' Min. Width = ' num2str(MINWIDTH) ' % Gaussian = ' num2str(extra) ' Error = ' num2str(round(1000*LowestError)/1000) '% ' ] )
case {14,15,22}
xlabel(['Peaks = ' num2str(NumPeaks) ' Shape = ' ShapeString ' Min. Width = ' num2str(MINWIDTH) ' extra = ' num2str(extra) ' Error = ' num2str(round(1000*LowestError)/1000) '% ' ] )
otherwise
xlabel(['Peaks = ' num2str(NumPeaks) ' Shape = ' ShapeString ' Min. Width = ' num2str(MINWIDTH) ' Error = ' num2str(round(1000*LowestError)/1000) '% ' ] )
end