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Peak Fitter

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Peak Fitter

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09 Apr 2009 (Updated )

Command-line peak fitter for time-series signals. Version 5.4, June, 2014

[FitResults,LowestError,baseline,BestStart,xi,yi,BootResults]=peakfit(signal,center,window,NumPeaks,peakshape,extra,NumTrials,start,autozero,fixedparameters,plots,bipolar)
function [FitResults,LowestError,baseline,BestStart,xi,yi,BootResults]=peakfit(signal,center,window,NumPeaks,peakshape,extra,NumTrials,start,autozero,fixedparameters,plots,bipolar)
% 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, exponential pulse, up and down sigmoids, Gaussian/
% Lorentzian blend, Voigt, triangular, Breit-Wigner-Fano, 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 5.4: June, 2014. Replaces bifurcated Lorentzian with 
% Breit-Wigner-Fano resonance peak (Shape=15).
%
% 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); 
% Specifies the peak shape of the model: "peakshape" = 1-20. (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.
%
% peakfit(signal,center,window,NumPeaks,peakshape,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) 
% Sets autozero mode in the last argument: 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,  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).
%
% [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 fit.
%
% 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 funciton 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.
% [FitResults,Baseline,FitError]=peakfit([x;y],0.6,1,2,[4 1],[3 0],10,0,3)
% 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])
%

% 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.
% 
% THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
% IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
% FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
% AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
% LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
% OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
% THE SOFTWARE.
% 
global AA xxx PEAKHEIGHTS FIXEDPARAMETERS AUTOZERO delta BIPOLAR
% 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;
    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;
    case 3
        NumPeaks=1;
        peakshape=1;
        extra=0;
        NumTrials=1;
        start=calcstart(xx,NumPeaks,xoffset);
        AUTOZERO=0;
        FIXEDPARAMETERS=0;
        plots=1;
        BIPOLAR=0;
    case 4
        peakshape=1;
        extra=0;
        NumTrials=1;
        start=calcstart(xx,NumPeaks,xoffset);
        AUTOZERO=0;
        FIXEDPARAMETERS=0;
        plots=1;
        BIPOLAR=0;
    case 5
        extra=zeros(1,NumPeaks);
        NumTrials=1;
        start=calcstart(xx,NumPeaks,xoffset);
        AUTOZERO=0;
        FIXEDPARAMETERS=0;
        plots=1;
        BIPOLAR=0;
    case 6
        NumTrials=1;
        start=calcstart(xx,NumPeaks,xoffset);
        AUTOZERO=0;
        FIXEDPARAMETERS=0;
        plots=1;
        BIPOLAR=0;
    case 7
        start=calcstart(xx,NumPeaks,xoffset);
        AUTOZERO=0;
        FIXEDPARAMETERS=0;
        plots=1;
        BIPOLAR=0;
    case 8
        AUTOZERO=0;
        FIXEDPARAMETERS=0;
        plots=1;
        BIPOLAR=0;
    case 9
        AUTOZERO=autozero;
        FIXEDPARAMETERS=0;
        plots=1;
        BIPOLAR=0;
    case 10
        AUTOZERO=autozero;
        FIXEDPARAMETERS=fixedparameters;
        plots=1;
        BIPOLAR=0;
    case 11
        AUTOZERO=autozero;
        FIXEDPARAMETERS=fixedparameters;
        BIPOLAR=0;
    case 12
        AUTOZERO=autozero;
        FIXEDPARAMETERS=fixedparameters;
        BIPOLAR=bipolar;
    otherwise
end % switch nargin

% Default values for placeholder zeros
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);
    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, 
    % StartVector=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);
    case 2
        TrialParameters=fminsearch(@(lambda)(fitlorentzian(lambda,xx,yy)),newstart,options);
    case 3
        TrialParameters=fminsearch(@(lambda)(fitlogistic(lambda,xx,yy)),newstart,options);
    case 4
        TrialParameters=fminsearch(@(lambda)(fitpearson(lambda,xx,yy,extra)),newstart,options);
    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);
    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);
    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);
    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);
      case 9
          TrialParameters=fminsearch(@(lambda)(fitexppulse(lambda,xx,yy)),newstart,options);
      case 10
          TrialParameters=fminsearch(@(lambda)(fitupsigmoid(lambda,xx,yy)),newstart,options);
      case 23
          TrialParameters=fminsearch(@(lambda)(fitdownsigmoid(lambda,xx,yy)),newstart,options);
      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);
      case 14
          TrialParameters=fminsearch(@(lambda)(fitBiGaussian(lambda,xx,yy,extra)),newstart,options);
      case 15
          TrialParameters=fminsearch(@(lambda)(fitBWF(lambda,xx,yy,extra)),newstart,options);
      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);
      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);
      case 18
        zxx=[zeros(size(xx)) xx zeros(size(xx)) ];
        zyy=[ones(size(yy)).*yy(1) yy zeros(size(yy)).*yy(length(yy)) ];
%         plot(zxx,zyy);pause
        TrialParameters=fminsearch(@(lambda)(fitexplorentzian(lambda,zxx,zyy,-extra)),newstart,options);     
      case 19
          TrialParameters=fminsearch(@(lambda)(fitalphafunction(lambda,xx,yy)),newstart,options);
      case 20
          TrialParameters=fminsearch(@(lambda)(fitvoigt(lambda,xx,yy,extra)),newstart,options);
      case 21
          TrialParameters=fminsearch(@(lambda)(fittriangular(lambda,xx,yy)),newstart,options);
      case 22
          TrialParameters=fminsearch(@(lambda)(fitmultiple(lambda,xx,yy,shapesvector,extra)),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));        
        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
end % for k (NumTrials)
%
% 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));  
    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 5.3   No baseline correction'])
        case 1
            title(['peakfit 5.3   Linear baseline subtraction'])
        case 2
            title(['peakfit 5.3   Quadratic subtraction baseline'])
        case 3
            title(['peakfit 5.3   Flat baseline correction'])
    end
 
    switch peakshape(1)
    case {4,20}
        xlabel(['Peaks = ' num2str(NumPeaks) '     Shape = ' ShapeString '      Shape Constant = ' num2str(extra) '   Error = ' num2str(round(1000*LowestError)/1000) '%' ] )
    case {5,8,18}
        xlabel(['Peaks = ' num2str(NumPeaks) '     Shape = ' ShapeString '      Time Constant = ' num2str(extra) '   Error = ' num2str(round(1000*LowestError)/1000) '%' ] )
    case 13
        xlabel(['Peaks = ' num2str(NumPeaks) '     Shape = ' ShapeString '      % Gaussian = ' num2str(extra)  '     Error = ' num2str(round(1000*LowestError)/1000) '% ' ] )
    case {14,15,22}
        xlabel(['Peaks = ' num2str(NumPeaks) '     Shape = ' ShapeString '      extra = ' num2str(extra) '     Error = ' num2str(round(1000*LowestError)/1000)  '% ' ] )
    otherwise
        xlabel(['Peaks = ' num2str(NumPeaks) '     Shape = ' ShapeString '     Error = ' num2str(round(1000*LowestError)/1000) '% ' ] )
    end

    % Bottom half of the figure shows the residuals and displays RMS error
    % between original signal and model
    residual=yy-bestmodel;
    subplot(2,1,2);plot(xx+xoffset,residual,'b.')
    axis([min(xx)+xoffset max(xx)+xoffset min(residual) max(residual)]);
    xlabel('Residual Plot')
end % if plots

% Put results into a matrix, one row for each peak, showing peak index number,
% position, amplitude, and width.
for m=1:NumPeaks,
    if m==1,
        if peakshape(1)==6||peakshape(1)==7||peakshape(1)==8, % equal-width peak models only
            FitResults=[[round(m) FitParameters(m)+xoffset height(m) abs(FitParameters(NumPeaks+1)) area(m)]];
        else
            if peakshape(1)==11||peakshape(1)==12, % Fixed-width shapes only
                FitResults=[[round(m) FitParameters(m)+xoffset height(m) FIXEDPARAMETERS area(m)]];
            else
                if peakshape(1)==16||peakshape(1)==17, % Fixed-position shapes only
                    FitResults=[round(m) FIXEDPOSITIONS(m) height(m) FitParameters(m) area(m)];
                else
                    FitResults=[round(m) FitParameters(2*m-1)+xoffset height(m) abs(FitParameters(2*m)) area(m)];
                end
            end
        end % if peakshape
    else
        if peakshape(1)==6||peakshape(1)==7||peakshape(1)==8, % equal-width peak models only
            FitResults=[FitResults ; [round(m) FitParameters(m)+xoffset height(m) abs(FitParameters(NumPeaks+1)) area(m)]];
        else
            if peakshape(1)==11||peakshape(1)==12, % Fixed-width shapes only
                FitResults=[FitResults ; [round(m) FitParameters(m)+xoffset height(m) FIXEDPARAMETERS area(m)]];
            else
                if peakshape(1)==16||peakshape(1)==17, % Fixed-position shapes only
                    FitResults=[FitResults ; [round(m) FIXEDPOSITIONS(m) height(m) FitParameters(m) area(m)]];
                else
                    FitResults=[FitResults ; [round(m) FitParameters(2*m-1)+xoffset height(m) abs(FitParameters(2*m)) area(m)]];
                end
            end
        end % if peakshape
    end % m==1
end % for m=1:NumPeaks
% Display Fit Results on lower graph
if plots,
    subplot(2,1,2);
    startx=min(xx)+xoffset+(max(xx)-min(xx))./20;
    dxx=(max(xx)-min(xx))./10;
    dyy=(max(yy)-min(yy))./10;
    starty=max(yy)-dyy;
    FigureSize=get(gcf,'Position');
    if peakshape(1)==9||peakshape(1)==10||peakshape(1)==19,  % Pulse and sigmoid shapes only
        text(startx,starty+dyy/2,['Peak #          tau1           Height           tau2             Area'] );
    else
        text(startx,starty+dyy/2,['Peak #          Position        Height         Width             Area'] );
    end
    % Display FitResults using sprintf
    for peaknumber=1:NumPeaks,
        for column=1:5,
            itemstring=sprintf('%0.4g',FitResults(peaknumber,column));
            xposition=startx+(1.7.*dxx.*(column-1).*(600./FigureSize(3)));
            yposition=starty-peaknumber.*dyy.*(400./FigureSize(4));
            text(xposition,yposition,itemstring);
        end
    end
    xposition=startx;
    yposition=starty-(peaknumber+1).*dyy.*(400./FigureSize(4));
    if AUTOZERO==3,
       text(xposition,yposition,[ 'Baseline= ' num2str(baseline) ]);
    end
end % if plots

if NumArgOut==7,
    if plots,disp('Computing bootstrap sampling statistics.....'),end
    BootstrapResultsMatrix=zeros(5,100,NumPeaks);
    BootstrapErrorMatrix=zeros(1,100,NumPeaks);
    clear bx by
    tic;
    for trial=1:100,
        n=1;
        bx=xx;
        by=yy;
        while n<length(xx)-1,
            if rand>.5,
                bx(n)=xx(n+1);
                by(n)=yy(n+1);
            end
            n=n+1;
        end
        bx=bx+xoffset;
        [FitResults,BootFitError]=fitpeaks(bx,by,NumPeaks,peakshape,extra,NumTrials,start,AUTOZERO,FIXEDPARAMETERS);
        for peak=1:NumPeaks,
            BootstrapResultsMatrix(:,trial,peak)=FitResults(peak,:);
            BootstrapErrorMatrix(:,trial,peak)=BootFitError;
        end
    end
    if plots,toc;end
    for peak=1:NumPeaks,
        if plots,
            disp(' ')
            disp(['Peak #',num2str(peak) '         Position    Height       Width       Area']);
        end % if plots
        BootstrapMean=mean(real(BootstrapResultsMatrix(:,:,peak)'));
        BootstrapSTD=std(BootstrapResultsMatrix(:,:,peak)');
        BootstrapIQR=iqr(BootstrapResultsMatrix(:,:,peak)');
        PercentRSD=100.*BootstrapSTD./BootstrapMean;
        PercentIQR=100.*BootstrapIQR./BootstrapMean;
        BootstrapMean=BootstrapMean(2:5);
        BootstrapSTD=BootstrapSTD(2:5);
        BootstrapIQR=BootstrapIQR(2:5);
        PercentRSD=PercentRSD(2:5);
        PercentIQR=PercentIQR(2:5);
        if plots,
            disp(['Bootstrap Mean: ', num2str(BootstrapMean)])
            disp(['Bootstrap STD:  ', num2str(BootstrapSTD)])
            disp(['Bootstrap IQR:  ', num2str(BootstrapIQR)])
            disp(['Percent RSD:    ', num2str(PercentRSD)])
            disp(['Percent IQR:    ', num2str(PercentIQR)])
        end % if plots
        BootResults(peak,:)=[BootstrapMean BootstrapSTD PercentRSD BootstrapIQR PercentIQR];
    end % peak=1:NumPeaks,
end % if NumArgOut==6,
% ----------------------------------------------------------------------
function [FitResults,LowestError]=fitpeaks(xx,yy,NumPeaks,peakshape,extra,NumTrials,start,AUTOZERO,fixedparameters)
% Based on peakfit Version 3: June, 2012. 
global PEAKHEIGHTS FIXEDPARAMETERSS AUTOZERO BIPOLAR
format short g
format compact
warning off all
FIXEDPARAMETERS=fixedparameters;
xoffset=0;
if start==0;start=calcstart(xx,NumPeaks,xoffset);end
PEAKHEIGHTS=zeros(1,NumPeaks);
n=length(xx);
newstart=start;

% 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,
    % StartVector=newstart
    switch peakshape(1)
        case 1
            TrialParameters=fminsearch(@(lambda)(fitgaussian(lambda,xx,yy)),newstart,options);
        case 2
            TrialParameters=fminsearch(@(lambda)(fitlorentzian(lambda,xx,yy)),newstart,options);
        case 3
            TrialParameters=fminsearch(@(lambda)(fitlogistic(lambda,xx,yy)),newstart,options);
        case 4
            TrialParameters=fminsearch(@(lambda)(fitpearson(lambda,xx,yy,extra)),newstart,options);
        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);
        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);
        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);
        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);
        case 9
            TrialParameters=fminsearch(@(lambda)(fitexppulse(lambda,xx,yy)),newstart,options);
        case 10
            TrialParameters=fminsearch(@(lambda)(fitupsigmoid(lambda,xx,yy)),newstar,optionst);
        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);
        case 14
            TrialParameters=fminsearch(@(lambda)(fitBiGaussian(lambda,xx,yy,extra)),newstart,options);
        case 15
            TrialParameters=fminsearch(@(lambda)(fitBWF(lambda,xx,yy,extra)),newstart,options);
        case 16
            fixedstart=[];
            for pc=1:NumPeaks,
                fixedstart(pc)=(max(xx)-min(xx))./(NumPeaks+1);
            end
            TrialParameters=fminsearch(@(lambda)(FitFPGaussian(lambda,xx,yy)),fixedstart,options);
        case 17
            fixedstart=[];
            for pc=1:NumPeaks,
                fixedstart(pc)=(max(xx)-min(xx))./(NumPeaks+1);
            end
            TrialParameters=fminsearch(@(lambda)(FitFPLorentzian(lambda,xx,yy)),fixedstart,options);
        case 18
            zxx=[zeros(size(xx)) xx zeros(size(xx)) ];
            zyy=[zeros(size(yy)) yy zeros(size(yy)) ];
            TrialParameters=fminsearch(@(lambda)(fitlorentzian(lambda,zxx,zyy,-extra)),newstart,options);
        case 19
            TrialParameters=fminsearch(@(lambda)(alphafunction(lambda,xx,yy)),newstart,options);
        case 20
            TrialParameters=fminsearch(@(lambda)(fitvoigt(lambda,xx,yy,extra)),newstart,options);
        case 21
            TrialParameters=fminsearch(@(lambda)(fittriangular(lambda,xx,yy)),newstart,options);
        case 22
            TrialParameters=fminsearch(@(lambda)(fitmultiple(lambda,xx,yy,shapesvector,extra)),newstart,options);
        case 23
            TrialParameters=fminsearch(@(lambda)(fitdownsigmoid(lambda,xx,yy)),newstar,optionst);
        otherwise
    end % switch peakshape
    
    
for peaks=1:NumPeaks,
     peakindex=2*peaks-1;
     newstart(peakindex)=start(peakindex)-xoffset;
end

    % 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));      
        end % switch
        %     for parameter=1:2:2*NumPeaks,
        %         newstart(parameter)=newstart(parameter)*(1+(rand-.5)/50);
        %         newstart(parameter+1)=newstart(parameter+1)*(1+(rand-.5)/10);
        %     end
    end % for
    
    % 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
            height=Heights; % Assign height to the PEAKHEIGHTS with the lowest MeanFitError
        end % if min(PEAKHEIGHTS)>0
    end % if MeanFitError<LowestError
end % for k (NumTrials)

for m=1:NumPeaks,
    area(m)=trapz(xx+xoffset,height(m)*A(m,:)); % Compute the area of each component peak using trapezoidal method
end

for m=1:NumPeaks,
    if m==1,
        if peakshape(1)==6||peakshape(1)==7||peakshape(1)==8, % equal-width peak models
            FitResults=[[round(m) FitParameters(m)+xoffset height(m) abs(FitParameters(NumPeaks+1)) area(m)]];
        else
            if peakshape(1)==11||peakshape(1)==12,  % Fixed-width shapes only
                FitResults=[[round(m) FitParameters(m)+xoffset height(m) FIXEDPARAMETERS area(m)]];
            else
                FitResults=[[round(m) FitParameters(2*m-1)+xoffset height(m) abs(FitParameters(2*m)) area(m)]];
            end
        end % if peakshape
    else
        if peakshape(1)==6||peakshape(1)==7||peakshape(1)==8, % equal-width peak models
            FitResults=[FitResults ; [round(m) FitParameters(m)+xoffset height(m) abs(FitParameters(NumPeaks+1)) area(m)]];
        else
            if peakshape(1)==11||peakshape(1)==12, % Fixed-width shapes only
                FitResults=[FitResults ; [round(m) FitParameters(m)+xoffset height(m) FIXEDPARAMETERS area(m)]];
            else
                FitResults=[FitResults ; [round(m) FitParameters(2*m-1)+xoffset height(m) abs(FitParameters(2*m)) area(m)]];
            end
        end % if peakshape
    end % m==1
end % for m=1:NumPeaks
% ----------------------------------------------------------------------
function start=calcstart(xx,NumPeaks,xoffset)
  n=max(xx)-min(xx);
  start=[];
  startpos=[n/(NumPeaks+1):n/(NumPeaks+1):n-(n/(NumPeaks+1))]+min(xx);
  for marker=1:NumPeaks,
      markx=startpos(marker)+ xoffset;
      start=[start markx n/ (3.*NumPeaks)];
  end % for marker
% ----------------------------------------------------------------------
function [index,closestval]=val2ind(x,val)
% Returns the index and the value of the element of vector x that is closest to val
% If more than one element is equally close, returns vectors of indicies and values
% Tom O'Haver (toh@umd.edu) October 2006
% Examples: If x=[1 2 4 3 5 9 6 4 5 3 1], then val2ind(x,6)=7 and val2ind(x,5.1)=[5 9]
% [indices values]=val2ind(x,3.3) returns indices = [4 10] and values = [3 3]
dif=abs(x-val);
index=find((dif-min(dif))==0);
closestval=x(index);
% ----------------------------------------------------------------------
function err = fitgaussian(lambda,t,y)
% Fitting function for a Gaussian band signal.
global PEAKHEIGHTS AUTOZERO BIPOLAR logplot
numpeaks=round(length(lambda)/2);
A = zeros(length(t),numpeaks);
for j = 1:numpeaks,
    A(:,j) = gaussian(t,lambda(2*j-1),lambda(2*j))';
end 
if AUTOZERO==3,A=[ones(size(y))' A];end
if BIPOLAR,PEAKHEIGHTS=A\y';else PEAKHEIGHTS=abs(A\y');end
z = A*PEAKHEIGHTS;
if logplot,
    err = norm(log10(z)-log10(y)');
else
    err = norm(z-y');
end
% ----------------------------------------------------------------------
function err = fitewgaussian(lambda,t,y)
% Fitting function for a Gaussian band signal with equal peak widths.
global PEAKHEIGHTS AUTOZERO BIPOLAR logplot
numpeaks=round(length(lambda)-1);
A = zeros(length(t),numpeaks);
for j = 1:numpeaks,
    A(:,j) = gaussian(t,lambda(j),lambda(numpeaks+1))';
end
if AUTOZERO==3,A=[ones(size(y))' A];end
if BIPOLAR,PEAKHEIGHTS=A\y';else PEAKHEIGHTS=abs(A\y');end
z = A*PEAKHEIGHTS;
if logplot,
    err = norm(log10(z)-log10(y)');
else
    err = norm(z-y');
end
% ----------------------------------------------------------------------
function err = FitFWGaussian(lambda,t,y)
%	Fitting function for a fixed width Gaussian
global PEAKHEIGHTS AUTOZERO FIXEDPARAMETERS BIPOLAR logplot
numpeaks=round(length(lambda));
A = zeros(length(t),numpeaks);
for j = 1:numpeaks,
    A(:,j) = gaussian(t,lambda(j),FIXEDPARAMETERS)';
end
if AUTOZERO==3,A=[ones(size(y))' A];end
if BIPOLAR,PEAKHEIGHTS=A\y';else PEAKHEIGHTS=abs(A\y');end
z = A*PEAKHEIGHTS;
if logplot,
    err = norm(log10(z)-log10(y)');
else
    err = norm(z-y');
end
% ----------------------------------------------------------------------
function err = FitFPGaussian(lambda,t,y)
%	Fitting function for fixed-position Gaussians
global PEAKHEIGHTS AUTOZERO FIXEDPARAMETERS BIPOLAR logplot
numpeaks=round(length(lambda));
A = zeros(length(t),numpeaks);
for j = 1:numpeaks,
    A(:,j) = gaussian(t,FIXEDPARAMETERS(j), lambda(j))';
end
if AUTOZERO==3,A=[ones(size(y))' A];end
if BIPOLAR,PEAKHEIGHTS=A\y';else PEAKHEIGHTS=abs(A\y');end
z = A*PEAKHEIGHTS;
if logplot,
    err = norm(log10(z)-log10(y)');
else
    err = norm(z-y');
end
% ----------------------------------------------------------------------
function err = FitFPLorentzian(lambda,t,y)
%	Fitting function for fixed-position Lorentzians
global PEAKHEIGHTS AUTOZERO FIXEDPARAMETERS BIPOLAR
numpeaks=round(length(lambda));
A = zeros(length(t),numpeaks);
for j = 1:numpeaks,
    A(:,j) = lorentzian(t,FIXEDPARAMETERS(j), lambda(j))';
end
if AUTOZERO==3,A=[ones(size(y))' A];end
if BIPOLAR,PEAKHEIGHTS=A\y';else PEAKHEIGHTS=abs(A\y');end
z = A*PEAKHEIGHTS;
err = norm(z-y');
% ----------------------------------------------------------------------
function err = FitFWLorentzian(lambda,t,y)
%	Fitting function for fixed width Lorentzian
global PEAKHEIGHTS AUTOZERO FIXEDPARAMETERS BIPOLAR logplot
numpeaks=round(length(lambda));
A = zeros(length(t),numpeaks);
for j = 1:numpeaks,
    A(:,j) = lorentzian(t,lambda(j),FIXEDPARAMETERS)';
end
if AUTOZERO==3,A=[ones(size(y))' A];end
if BIPOLAR,PEAKHEIGHTS=A\y';else PEAKHEIGHTS=abs(A\y');end
z = A*PEAKHEIGHTS;
if logplot,
    err = norm(log10(z)-log10(y)');
else
    err = norm(z-y');
end
% ----------------------------------------------------------------------
function err = fitewlorentzian(lambda,t,y)
% Fitting function for a Lorentzian band signal with equal peak widths.
global PEAKHEIGHTS AUTOZERO BIPOLAR logplot
numpeaks=round(length(lambda)-1);
A = zeros(length(t),numpeaks);
for j = 1:numpeaks,
    A(:,j) = lorentzian(t,lambda(j),lambda(numpeaks+1))';
end
if AUTOZERO==3,A=[ones(size(y))' A];end
if BIPOLAR,PEAKHEIGHTS=A\y';else PEAKHEIGHTS=abs(A\y');end
z = A*PEAKHEIGHTS;
if logplot,
    err = norm(log10(z)-log10(y)');
else
    err = norm(z-y');
end
% ----------------------------------------------------------------------
function g = gaussian(x,pos,wid)
%  gaussian(X,pos,wid) = gaussian peak centered on pos, half-width=wid
%  X may be scalar, vector, or matrix, pos and wid both scalar
% Examples: gaussian([0 1 2],1,2) gives result [0.5000    1.0000    0.5000]
% plot(gaussian([1:100],50,20)) displays gaussian band centered at 50 with width 20.
g = exp(-((x-pos)./(0.6005615.*wid)).^2);
% ----------------------------------------------------------------------
function err = fitlorentzian(lambda,t,y)
%	Fitting function for single lorentzian, lambda(1)=position, lambda(2)=width
%	Fitgauss assumes a lorentzian function 
global PEAKHEIGHTS AUTOZERO BIPOLAR logplot
A = zeros(length(t),round(length(lambda)/2));
for j = 1:length(lambda)/2,
    A(:,j) = lorentzian(t,lambda(2*j-1),lambda(2*j))';
end
if AUTOZERO==3,A=[ones(size(y))' A];end
if BIPOLAR,PEAKHEIGHTS=A\y';else PEAKHEIGHTS=abs(A\y');end
z = A*PEAKHEIGHTS;
if logplot,
    err = norm(log10(z)-log10(y)');
else
    err = norm(z-y');
end
% ----------------------------------------------------------------------
function g = lorentzian(x,position,width)
% lorentzian(x,position,width) Lorentzian function.
% where x may be scalar, vector, or matrix
% position and width scalar
% T. C. O'Haver, 1988
% Example: lorentzian([1 2 3],2,2) gives result [0.5 1 0.5]
g=ones(size(x))./(1+((x-position)./(0.5.*width)).^2);
% ----------------------------------------------------------------------
function err = fitlogistic(lambda,t,y)
%	Fitting function for logistic, lambda(1)=position, lambda(2)=width
%	between the data and the values computed by the current
%	function of lambda.  Fitlogistic assumes a logistic function 
%  T. C. O'Haver, May 2006
global PEAKHEIGHTS AUTOZERO BIPOLAR logplot
A = zeros(length(t),round(length(lambda)/2));
for j = 1:length(lambda)/2,
    A(:,j) = logistic(t,lambda(2*j-1),lambda(2*j))';
end
if AUTOZERO==3,A=[ones(size(y))' A];end
if BIPOLAR,PEAKHEIGHTS=A\y';else PEAKHEIGHTS=abs(A\y');end
z = A*PEAKHEIGHTS;
if logplot,
    err = norm(log10(z)-log10(y)');
else
    err = norm(z-y');
end
% ----------------------------------------------------------------------
function g = logistic(x,pos,wid)
% logistic function.  pos=position; wid=half-width (both scalar)
% logistic(x,pos,wid), where x may be scalar, vector, or matrix
% pos=position; wid=half-width (both scalar)
% T. C. O'Haver, 1991 
n = exp(-((x-pos)/(.477.*wid)) .^2);
g = (2.*n)./(1+n);
% ----------------------------------------------------------------------
function err = fittriangular(lambda,t,y)
%	Fitting function for triangular, lambda(1)=position, lambda(2)=width
%	between the data and the values computed by the current
%	function of lambda.  Fittriangular assumes a triangular function 
%  T. C. O'Haver, May 2006
global PEAKHEIGHTS AUTOZERO BIPOLAR logplot
A = zeros(length(t),round(length(lambda)/2));
for j = 1:length(lambda)/2,
    A(:,j) = triangular(t,lambda(2*j-1),lambda(2*j))';
end
if AUTOZERO==3,A=[ones(size(y))' A];end
if BIPOLAR,PEAKHEIGHTS=A\y';else PEAKHEIGHTS=abs(A\y');end
z = A*PEAKHEIGHTS;
if logplot,
    err = norm(log10(z)-log10(y)');
else
    err = norm(z-y');
end
% ----------------------------------------------------------------------
function g = triangular(x,pos,wid)
%triangle function.  pos=position; wid=half-width (both scalar)
%triangle(x,pos,wid), where x may be scalar or vector,
%pos=position; wid=half-width (both scalar)
% T. C. O'Haver, 1991
% Example
% x=[0:.1:10];plot(x,triangle(x,5.5,2.3),'.')
g=1-(1./wid) .*abs(x-pos);
for i=1:length(x),  
if g(i)<0,g(i)=0;end
end
% ----------------------------------------------------------------------
function err = fitpearson(lambda,t,y,shapeconstant)
%   Fitting functions for a Pearson 7 band signal.
% T. C. O'Haver (toh@umd.edu),   Version 1.3, October 23, 2006.
global PEAKHEIGHTS AUTOZERO BIPOLAR logplot
A = zeros(length(t),round(length(lambda)/2));
for j = 1:length(lambda)/2,
    A(:,j) = pearson(t,lambda(2*j-1),lambda(2*j),shapeconstant)';
end
if AUTOZERO==3,A=[ones(size(y))' A];end
if BIPOLAR,PEAKHEIGHTS=A\y';else PEAKHEIGHTS=abs(A\y');end
z = A*PEAKHEIGHTS;
if logplot,
    err = norm(log10(z)-log10(y)');
else
    err = norm(z-y');
end
% ----------------------------------------------------------------------
function g = pearson(x,pos,wid,m)
% Pearson VII function. 
% g = pearson7(x,pos,wid,m) where x may be scalar, vector, or matrix
% pos=position; wid=half-width (both scalar)
% m=some number
%  T. C. O'Haver, 1990  
g=ones(size(x))./(1+((x-pos)./((0.5.^(2/m)).*wid)).^2).^m;
% ----------------------------------------------------------------------
function err = fitexpgaussian(lambda,t,y,timeconstant)
%   Fitting functions for a exponentially-broadened Gaussian band signal.
%  T. C. O'Haver, October 23, 2006.
global PEAKHEIGHTS AUTOZERO BIPOLAR logplot
A = zeros(length(t),round(length(lambda)/2));
for j = 1:length(lambda)/2,
    A(:,j) = expgaussian(t,lambda(2*j-1),lambda(2*j),timeconstant);
end
if AUTOZERO==3,A=[ones(size(y))' A];end
if BIPOLAR,PEAKHEIGHTS=A\y';else PEAKHEIGHTS=abs(A\y');end
z = A*PEAKHEIGHTS;
if logplot,
    err = norm(log10(z)-log10(y)');
else
    err = norm(z-y');
end
% ----------------------------------------------------------------------
function err = fitexplorentzian(lambda,t,y,timeconstant)
%   Fitting functions for a exponentially-broadened lorentzian band signal.
%  T. C. O'Haver, 2013.
global PEAKHEIGHTS AUTOZERO BIPOLAR logplot
A = zeros(length(t),round(length(lambda)/2));
for j = 1:length(lambda)/2,
    A(:,j) = explorentzian(t,lambda(2*j-1),lambda(2*j),timeconstant);
end
if AUTOZERO==3,A=[ones(size(y))' A];end
if BIPOLAR,PEAKHEIGHTS=A\y';else PEAKHEIGHTS=abs(A\y');end
z = A*PEAKHEIGHTS;
if logplot,
    err = norm(log10(z)-log10(y)');
else
    err = norm(z-y');
end
% ----------------------------------------------------------------------
function err = fitexpewgaussian(lambda,t,y,timeconstant)
% Fitting function for exponentially-broadened Gaussian bands with equal peak widths.
global PEAKHEIGHTS AUTOZERO BIPOLAR logplot
numpeaks=round(length(lambda)-1);
A = zeros(length(t),numpeaks);
for j = 1:numpeaks,
    A(:,j) = expgaussian(t,lambda(j),lambda(numpeaks+1),timeconstant);
end
if AUTOZERO==3,A=[ones(size(y))' A];end
if BIPOLAR,PEAKHEIGHTS=A\y';else PEAKHEIGHTS=abs(A\y');end
z = A*PEAKHEIGHTS;
if logplot,
    err = norm(log10(z)-log10(y)');
else
    err = norm(z-y');
end
% ----------------------------------------------------------------------
function g = expgaussian(x,pos,wid,timeconstant)
%  Exponentially-broadened gaussian(x,pos,wid) = gaussian peak centered on pos, half-width=wid
%  x may be scalar, vector, or matrix, pos and wid both scalar
%  T. C. O'Haver, 2006
g = exp(-((x-pos)./(0.6005615.*wid)) .^2);
g = ExpBroaden(g',timeconstant);
% ----------------------------------------------------------------------
function g = explorentzian(x,pos,wid,timeconstant)
%  Exponentially-broadened lorentzian(x,pos,wid) = lorentzian peak centered on pos, half-width=wid
%  x may be scalar, vector, or matrix, pos and wid both scalar
%  T. C. O'Haver, 2013
g = ones(size(x))./(1+((x-pos)./(0.5.*wid)).^2);
g = ExpBroaden(g',timeconstant);
% ----------------------------------------------------------------------
function yb = ExpBroaden(y,t)
% ExpBroaden(y,t) zero pads y and convolutes result by an exponential decay
% of time constant t by multiplying Fourier transforms and inverse
% transforming the result.
hly=round(length(y)./2);
ey=[y(1).*ones(1,hly)';y;y(length(y)).*ones(1,hly)'];
% figure(2);plot(ey);figure(1);
fy=fft(ey);
a=exp(-(1:length(fy))./t);
fa=fft(a);
fy1=fy.*fa';
ybz=real(ifft(fy1))./sum(a);
yb=ybz(hly+2:length(ybz)-hly+1);
% ----------------------------------------------------------------------
function err = fitexppulse(tau,x,y)
% Iterative fit of the sum of exponential pulses
% of the form Height.*exp(-tau1.*x).*(1-exp(-tau2.*x)))
global PEAKHEIGHTS AUTOZERO BIPOLAR logplot
A = zeros(length(x),round(length(tau)/2));
for j = 1:length(tau)/2,
    A(:,j) = exppulse(x,tau(2*j-1),tau(2*j));
end
if AUTOZERO==3,A=[ones(size(y))' A];end
if BIPOLAR,PEAKHEIGHTS=A\y';else PEAKHEIGHTS=abs(A\y');end
z = A*PEAKHEIGHTS;
if logplot,
    err = norm(log10(z)-log10(y)');
else
    err = norm(z-y');
end
% ----------------------------------------------------------------------
function g = exppulse(x,t1,t2)
% Exponential pulse of the form 
% g = (x-spoint)./pos.*exp(1-(x-spoint)./pos);
e=(x-t1)./t2;
p = 4*exp(-e).*(1-exp(-e));
p=p .* (p>0);
g = p';
% ----------------------------------------------------------------------
function err = fitalphafunction(tau,x,y)
% Iterative fit of the sum of alpha funciton
% of the form Height.*exp(-tau1.*x).*(1-exp(-tau2.*x)))
global PEAKHEIGHTS AUTOZERO BIPOLAR logplot
A = zeros(length(x),round(length(tau)/2));
for j = 1:length(tau)/2,
    A(:,j) = alphafunction(x,tau(2*j-1),tau(2*j));
end
if AUTOZERO==3,A=[ones(size(y))' A];end
if BIPOLAR,PEAKHEIGHTS=A\y';else PEAKHEIGHTS=abs(A\y');end
z = A*PEAKHEIGHTS;
if logplot,
    err = norm(log10(z)-log10(y)');
else
    err = norm(z-y');
end
% ----------------------------------------------------------------------
function g = alphafunction(x,pos,spoint)
% alpha function.  pos=position; wid=half-width (both scalar)
% alphafunction(x,pos,wid), where x may be scalar, vector, or matrix
% pos=position; wid=half-width (both scalar)
% Taekyung Kwon, July 2013  
g = (x-spoint)./pos.*exp(1-(x-spoint)./pos);
for m=1:length(x);if g(m)<0;g(m)=0;end;end
% ----------------------------------------------------------------------
function err = fitdownsigmoid(tau,x,y)
% Fitting function for iterative fit to the sum of
% downward moving sigmiods 
global PEAKHEIGHTS AUTOZERO BIPOLAR logplot
A = zeros(length(x),round(length(tau)/2));
for j = 1:length(tau)/2,
    A(:,j) = downsigmoid(x,tau(2*j-1),tau(2*j));
end
if AUTOZERO==3,A=[ones(size(y))' A];end
if BIPOLAR,PEAKHEIGHTS=A\y';else PEAKHEIGHTS=abs(A\y');end
z = A*PEAKHEIGHTS;
if logplot,
    err = norm(log10(z)-log10(y)');
else
    err = norm(z-y');
end
% ----------------------------------------------------------------------
function err = fitupsigmoid(tau,x,y)
% Fitting function for iterative fit to the sum of
% upwards moving sigmiods
global PEAKHEIGHTS AUTOZERO BIPOLAR logplot
A = zeros(length(x),round(length(tau)/2));
for j = 1:length(tau)/2,
    A(:,j) = upsigmoid(x,tau(2*j-1),tau(2*j));
end
if AUTOZERO==3,A=[ones(size(y))' A];end
if BIPOLAR,PEAKHEIGHTS=A\y';else PEAKHEIGHTS=abs(A\y');end
z = A*PEAKHEIGHTS;
if logplot,
    err = norm(log10(z)-log10(y)');
else
    err = norm(z-y');
end
% ----------------------------------------------------------------------
function g=downsigmoid(x,t1,t2)
% g=1./(1 + exp((t1 - x)./t2))'; % old version of sigmoid
g=.5-.5*erf(real((x-t1)/sqrt(2*t2))); % down step sigmoid
% ----------------------------------------------------------------------
function g=upsigmoid(x,t1,t2)
% g=1./(1 + exp((t1 - x)./t2))'; % old version of sigmoid
g=1/2 + 1/2* erf(real((x-t1)/sqrt(2*t2))); % up step sigmoid
% ----------------------------------------------------------------------
function err = fitGL(lambda,t,y,shapeconstant)
%   Fitting functions for Gaussian/Lorentzian blend.
% T. C. O'Haver (toh@umd.edu), 2012.
global PEAKHEIGHTS AUTOZERO BIPOLAR logplot
A = zeros(length(t),round(length(lambda)/2));
for j = 1:length(lambda)/2,
    A(:,j) = GL(t,lambda(2*j-1),lambda(2*j),shapeconstant)';
end
if AUTOZERO==3,A=[ones(size(y))' A];end
if BIPOLAR,PEAKHEIGHTS=A\y';else PEAKHEIGHTS=abs(A\y');end
z = A*PEAKHEIGHTS;
if logplot,
    err = norm(log10(z)-log10(y)');
else
    err = norm(z-y');
end
% ----------------------------------------------------------------------
function g = GL(x,pos,wid,m)
% Gaussian/Lorentzian blend. m = percent Gaussian character
% pos=position; wid=half-width
% m = percent Gaussian character.
%  T. C. O'Haver, 2012
% sizex=size(x)
% sizepos=size(pos)
% sizewid=size(wid)
% sizem=size(m)
g=2.*((m/100).*gaussian(x,pos,wid)+(1-(m(1)/100)).*lorentzian(x,pos,wid))/2;
% ----------------------------------------------------------------------
function err = fitvoigt(lambda,t,y,shapeconstant)
% Fitting functions for Voigt profile function
% T. C. O'Haver (toh@umd.edu), 2013.
global PEAKHEIGHTS AUTOZERO BIPOLAR logplot
A = zeros(length(t),round(length(lambda)/2));
for j = 1:length(lambda)/2,
    A(:,j) = voigt(t,lambda(2*j-1),lambda(2*j),shapeconstant)';
end
if AUTOZERO==3,A=[ones(size(y))' A];end
if BIPOLAR,PEAKHEIGHTS=A\y';else PEAKHEIGHTS=abs(A\y');end
z = A*PEAKHEIGHTS;
if logplot,
    err = norm(log10(z)-log10(y)');
else
    err = norm(z-y');
end
% ----------------------------------------------------------------------
function g=voigt(xx,pos,gD,alpha)
% Voigt profile function. xx is the independent variable (energy,
% wavelength, etc), gD is the Doppler (Gaussian) width, and alpha is the
% shape constant (ratio of the Lorentzian width gL to the Doppler width gD.
% Based on Chong Tao's "Voigt lineshape spectrum simulation", 
% File ID: #26707
% alpha=alpha
gL=alpha.*gD;
gV = 0.5346*gL + sqrt(0.2166*gL.^2 + gD.^2);
x = gL/gV;
y = abs(xx-pos)/gV;
g = 1/(2*gV*(1.065 + 0.447*x + 0.058*x^2))*((1-x)*exp(-0.693.*y.^2) + (x./(1+y.^2)) + 0.016*(1-x)*x*(exp(-0.0841.*y.^2.25)-1./(1 + 0.021.*y.^2.25)));
g=g./max(g);
% ----------------------------------------------------------------------
function err = fitBiGaussian(lambda,t,y,shapeconstant)
%   Fitting functions for BiGaussian.
% T. C. O'Haver (toh@umd.edu),  2012.
global PEAKHEIGHTS AUTOZERO BIPOLAR logplot
A = zeros(length(t),round(length(lambda)/2));
for j = 1:length(lambda)/2,
    A(:,j) = BiGaussian(t,lambda(2*j-1),lambda(2*j),shapeconstant)';
end
if AUTOZERO==3,A=[ones(size(y))' A];end
if BIPOLAR,PEAKHEIGHTS=A\y';else PEAKHEIGHTS=abs(A\y');end
z = A*PEAKHEIGHTS;
if logplot,
    err = norm(log10(z)-log10(y)');
else
    err = norm(z-y');
end
% ----------------------------------------------------------------------
function g = BiGaussian(x,pos,wid,m)
% BiGaussian (different widths on leading edge and trailing edge).
% pos=position; wid=width 
% m determines shape; symmetrical if m=50.
%  T. C. O'Haver, 2012
lx=length(x);
hx=val2ind(x,pos);
g(1:hx)=gaussian(x(1:hx),pos,wid*(m/100));
g(hx+1:lx)=gaussian(x(hx+1:lx),pos,wid*(1-m/100));
% ----------------------------------------------------------------------
function err = fitBWF(lambda,t,y,shapeconstant)
%   Fitting function for Breit-Wigner-Fano.
% T. C. O'Haver (toh@umd.edu),  2014.
global PEAKHEIGHTS AUTOZERO BIPOLAR logplot
A = zeros(length(t),round(length(lambda)/2));
for j = 1:length(lambda)/2,
    A(:,j) = BWF(t,lambda(2*j-1),lambda(2*j),shapeconstant)';
end
if AUTOZERO==3,A=[ones(size(y))' A];end
if BIPOLAR,PEAKHEIGHTS=A\y';else PEAKHEIGHTS=abs(A\y');end
z = A*PEAKHEIGHTS;
if logplot,
    err = norm(log10(z)-log10(y)');
else
    err = norm(z-y');
end
% ----------------------------------------------------------------------
function g = BWF(x,pos,wid,m)
% BWF (Breit-Wigner-Fano) http://en.wikipedia.org/wiki/Fano_resonance
% pos=position; wid=width; m=Fano factor
%  T. C. O'Haver, 2014
y=((m*wid/2+x-pos).^2)./(((wid/2).^2)+(x-pos).^2);
% y=((1+(x-pos./(m.*wid))).^2)./(1+((x-pos)./wid).^2);
g=y./max(y);
% ----------------------------------------------------------------------
function b=iqr(a)
% b = IQR(a)  returns the interquartile range of the values in a.  For
%  vector input, b is the difference between the 75th and 25th percentiles
%  of a.  For matrix input, b is a row vector containing the interquartile
%  range of each column of a.
%  T. C. O'Haver, 2012
mina=min(a);
sizea=size(a);
NumCols=sizea(2);
for n=1:NumCols,b(:,n)=a(:,n)-mina(n);end
Sorteda=sort(b);
lx=length(Sorteda);
SecondQuartile=round(lx/4);
FourthQuartile=3*round(lx/4);
b=abs(Sorteda(FourthQuartile,:)-Sorteda(SecondQuartile,:));
% ----------------------------------------------------------------------
function err = fitmultiple(lambda,t,y,shapesvector,m)
% Fitting function for a multiple-shape band signal.
% The sequence of peak shapes are defined by the vector "shape".
% The vector "m" determines the shape of variable-shape peaks.
global PEAKHEIGHTS AUTOZERO BIPOLAR logplot
numpeaks=round(length(lambda)/2);
A = zeros(length(t),numpeaks);
for j = 1:numpeaks,
    A(:,j) = peakfunction(shapesvector(j),t,lambda(2*j-1),lambda(2*j),m(j))';
end 
if AUTOZERO==3,A=[ones(size(y))' A];end
if BIPOLAR,PEAKHEIGHTS=A\y';else PEAKHEIGHTS=abs(A\y');end
z = A*PEAKHEIGHTS;
if logplot,
    err = norm(log10(z)-log10(y)');
else
    err = norm(z-y');
end
% ----------------------------------------------------------------------
function p=peakfunction(shape,x,pos,wid,m)
switch shape,
    case 1
        p=gaussian(x,pos,wid);
    case 2
        p=lorentzian(x,pos,wid);
    case 3
        p=logistic(x,pos,wid);
    case 4
        p=pearson(x,pos,wid,m);
    case 5
        p=expgaussian(x,pos,wid,m)';
    case 6
        p=gaussian(x,pos,wid);
    case 7
        p=lorentzian(x,pos,wid);
    case 8
        p=expgaussian(x,pos,wid,m)';
    case 9
        p=exppulse(x,pos,wid);
    case 10
        p=upsigmoid(x,pos,wid);
    case 11
        p=gaussian(x,pos,wid);
    case 12
        p=lorentzian(x,pos,wid);
    case 13
        p=GL(x,pos,wid,m);
    case 14
        p=BiGaussian(x,pos,wid,m);
    case 15
        p=BWF(x,pos,wid,m);
    case 16
        p=gaussian(x,pos,wid);
    case 17
        p=lorentzian(x,pos,wid);
    case 18
        p=explorentzian(x,pos,wid,m)';
    case 19
        p=alphafunction(x,pos,wid);
    case 20
        p=voigt(x,pos,wid,m);
    case 21
        p=triangular(x,pos,wid);
    case 23
        p=downpsigmoid(x,pos,wid);
    otherwise
end % switch

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