Skip to content

Instantly share code, notes, and snippets.

@tonyfast

tonyfast/.description.markdown

Last active August 29, 2015 14:07
Show Gist options

  • Select an option

    Learn more about clone URLs
  • Save tonyfast/de3d7b841cea38dc40fa to your computer and use it in GitHub Desktop.

Select an option

Learn more about clone URLs
Save tonyfast/de3d7b841cea38dc40fa to your computer and use it in GitHub Desktop.
Download ZIP
A naive segmentation function for N-D datasets
Raw
.description.markdown

A non-thresholding method for image segment

This naive function:

  • Computes the PDF and CDF of a 2-D or 3-D images with nbins in the histogram.
  • Fit npeaks number of peaks to the PDF
  • Compute the probability of each voxel belonging to each phase.
  • Decide on the phase based on the greatest probability.

Usage

  1. Choose an image
  2. Toggle nbins and npeaks
  3. Check for the fit of the distribution
  4. Check for qualitative accuracy of the phases.

Example

The image below is a Atomic Force Microscopy Image of an Organic Field Effect Transistor.

Original

The pixels values suggest a phase of interest. segmentprob returns the following segmentation.

Segmented

Other Examples

Problems

  • The Gaussian is not computed right. It is missing the scaling factor.
  • I am unsure about how to interpret the standard deviation from the FWHM report by peakfind.m
Raw
driver.m
% Download and Image from the web and fit the phases
url = 'https://farm3.staticflickr.com/2949/15392865571_eaf436ba03_o.png';
out = segmentprob( mean(double( imread(url) ), 3), ... A 2-D (could be 3-D) image, average the RGB channels
51, ... Number of bins in the histogram
4 ... Number of peaks of phases to find
);
Raw
peakfit.m
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.
%
% 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 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
% 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,'r.')
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,
% Display Fit Results on lower graph
subplot(2,1,2);
startx=min(xx)+(max(xx)-min(xx))./20;
dxx=(max(xx)-min(xx))./10;
dyy=((max(residual)-min(residual))./10);
starty=max(residual)-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 MINWIDTH
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);
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)),newstar,optionst);
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);
for Peak=1:NumPeaks;
if TrialParameters(2*Peak)<MINWIDTH,
TrialParameters(2*Peak)=MINWIDTH;
end
end
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);
for Peak=1:NumPeaks;
if TrialParameters(2*Peak)<MINWIDTH,
TrialParameters(2*Peak)=MINWIDTH;
end
end
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);
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);
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=[zeros(size(yy)) yy zeros(size(yy)) ];
TrialParameters=fminsearch(@(lambda)(fitexplorentzian(lambda,zxx,zyy,-extra)),newstart,options);
case 19
TrialParameters=fminsearch(@(lambda)(alphafunction(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 23
TrialParameters=fminsearch(@(lambda)(fitdownsigmoid(lambda,xx,yy)),newstar,optionst);
for Peak=1:NumPeaks;
if TrialParameters(2*Peak)<MINWIDTH,
TrialParameters(2*Peak)=MINWIDTH;
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);
for Peak=1:NumPeaks;
if TrialParameters(2*Peak)<MINWIDTH,
TrialParameters(2*Peak)=MINWIDTH;
end
end
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));
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,:)=sin(xx,TrialParameters(2*m-1),TrialParameters(2*m));
case 27
A(m,:)=d1gauss(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,
% if lambda(2*j)<MINWIDTH,lambda(2*j)=MINWIDTH;end
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)
%trianglar(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,trianglar(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)
% down step sigmoid
g=.5-.5*erf(real((x-t1)/sqrt(2*t2)));
% ----------------------------------------------------------------------
function g=upsigmoid(x,t1,t2)
% up step sigmoid
g=1/2 + 1/2* erf(real((x-t1)/sqrt(2*t2)));
% ----------------------------------------------------------------------
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 err = fitnbinpdf(tau,x,y)
% Fitting function for iterative fit to the sum of
% Negative Binomial Distributions
% (http://www.mathworks.com/help/stats/negative-binomial-distribution.html)
global PEAKHEIGHTS AUTOZERO BIPOLAR LOGPLOT
A = zeros(length(x),round(length(tau)/2));
for j = 1:length(tau)/2,
A(:,j) = nbinpdf(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 = fitlognpdf(tau,x,y)
% Fitting function for iterative fit to the sum of
% Lognormal Distributions
% (http://www.mathworks.com/help/stats/lognormal-distribution.html)
global PEAKHEIGHTS AUTOZERO BIPOLAR LOGPLOT
A = zeros(length(x),round(length(tau)/2));
for j = 1:length(tau)/2,
A(:,j) = lognormal(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 = lognormal(x,pos,wid)
% lognormal function. pos=position; wid=half-width (both scalar)
% lognormal(x,pos,wid), where x may be scalar, vector, or matrix
% pos=position; wid=half-width (both scalar)
% T. C. O'Haver, 1991
g = exp(-(log(x/pos)/(0.01.*wid)) .^2);
% ----------------------------------------------------------------------
function err = fitsine(tau,x,y)
% Fitting function for iterative fit to the sum of
% sine waves (alpha test, NRFPT)
global PEAKHEIGHTS AUTOZERO BIPOLAR LOGPLOT
A = zeros(length(x),round(length(tau)/2));
for j = 1:length(tau)/2,
A(:,j) = sine(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 y=d1gauss(x,p,w)
% First derivative of Gaussian (alpha test)
y=-(5.54518.*(x-p).*exp(-(2.77259.*(p-x).^2)./w^2))./w.^2;
y=y./max(y);
% ----------------------------------------------------------------------
function g=sine(x,f,phase)
% Sine wave (alpha test)
g=sin(2*pi*f*(x+phase));
% ----------------------------------------------------------------------
function err = fitd1gauss(lambda,t,y)
% Fitting functions for the first derivative of a Gaussian
% T. C. O'Haver, 2014
global PEAKHEIGHTS AUTOZERO BIPOLAR
A = zeros(length(t),round(length(lambda)/2));
for j = 1:length(lambda)/2,
A(:,j) = d1gauss(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;
err = norm(z-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)
% function that generates any of 20 peak types specified by number. 'shape'
% specifies the shape type of each peak in the signal: "peakshape" = 1-20.
% 1=Gaussian 2=Lorentzian, 3=logistic, 4=Pearson, 5=exponentionally
% broadened Gaussian; 9=exponential pulse, 10=up sigmoid,
% 13=Gaussian/Lorentzian blend; 14=BiGaussian, 15=Breit-Wigner-Fano (BWF) ,
% 18=exponentionally broadened Lorentzian; 19=alpha function; 20=Voigt
% profile; 21=triangular; 23=down sigmoid; 25=lognormal. "m" is required
% for variable-shape peaks only.
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=downsigmoid(x,pos,wid);
case 25
p=lognormal(x,pos,wid);
case 26
p=sine(x,pos,wid);
case 27
p=d1gauss(x,pos,wid);
otherwise
end % switch
Raw
segmentprob.m
function param = segmentprob( I, nhist, npeak )
%%
% I is a signal or image with distinct phases.
% nhist - number of histogram bins
% npeak - number of peaks to find in the histogram
nd = ndims( I );
sz = size(I);
if ~exist( 'nhist','var') || numel(nhist) == 0
nhist = 101;
end
if ~exist( 'npeak','var') || numel(nhist) == 0
nhist = 3;
end
param = struct( 'hist', struct( 'n', nhist, ...
'pixel',[], ...
'cdf',[], ...
'intensity', [] ), ...
'peak', struct( 'n', npeak, ...
'info', [] ), ...
'out', struct( 'ci', zeros( sz ), ...
'phase', zeros( sz ) ) );
%%
normalize = @(A)( A-min(A(:)) ) ./ ( max(A(:)) - min(A(:)) );
adjust = @(A)reshape( ... back to original shape
imadjust( ... adjust image
reshape( ... flatten to 2-D image
normalize(A), ... normalize from zero to one
size(A,1), numel(A)./size(A,1))), ... Reshape to 2-D array
size(A) ... Reshape back to original size
);
%%
I(:) = normalize(I);
I(:) = adjust(I);
%% Histogram for Signal
[ param.hist.intensity, ...
param.hist.pixel ] = hist( I(:), param.hist.n );
param.hist.cdf = cumsum( param.hist.intensity )./sum( param.hist.intensity );
%% Fit peak
% Fit the peak with the default Gaussian fit.
% No initial Guesses
p = peakfit( param.hist.intensity(:)', 0, 0, param.peak.n );
% peak index - peak center - peak
param.peak.center = interp1( 1: param.hist.n, param.hist.pixel, p(:,2) );
[ param.peak.area, ...
param.peak.fwhm, ...
param.peak.intensity ] = deal( p(:,3), p(:,4), p(:,5 ) );
D = bsxfun( @minus, I, permute( param.peak.center , ...
circshift( 1 : ( nd+1), [1 -1]) ) ).^2;
D(:) = 2 .* bsxfun( @rdivide, D, permute( param.peak.center , ...
circshift( 1 : ( nd+1), [1 -1]) ) );
D(:) = exp(-1.*D.^2);
% How do I actualy compute the confidence index
[ param.out.ci, param.out.phase ] = max( D, [], nd + 1 );
%%
if all(size(I) > 1) & ndims( I ) == 2
figure;
sp = [ 3 1];
subplot(sp(1),sp(2),1)
pcolor( I ); ; title('Original')
subplot(sp(1),sp(2),2)
pcolor( param.out.phase ); title('Phase')
subplot(sp(1),sp(2),3)
pcolor( param.out.ci ); title('Relative Confidence')
for ii = 1 : 3
ax(ii) = subplot(sp(1),sp(2),ii);
axis equal; axis tight
shading flat;
colorbar
end
linkaxes( ax );
figure(gcf-1);
end
@tonyfast

tonyfast commented Oct 14, 2014

Copy link
Copy Markdown
Author

A Non-thresholding technique for image segmentation

peakfit.m is from Mathworks Central

Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment