Code covered by the BSD License

# Peak finding and measurement

### Tom O'Haver (view profile)

20 Jul 2006 (Updated )

Function to locate and measure the positive peaks and valleys in noisy data sets.

idemo2
```function idemo2
% Self-contained demonstration function for comparing the iPeak and.
% Peakfit functions applied to a test signal consisting of 16 peaks
% with random peak heights and gradually increasing peak widths.
%   T. C. O'Haver, July 2012
increment=1;
x=1:increment:4000;

% For each simulated peak, compute the amplitude, position, and width
pos=[400 900 1000 1100 1500 1700 2200 2400 2500 2700 2800 3100 3200 3300 3400 3800];   % Positions of the peaks (Change if desired)
amp=round(1+5.*rand(1,length(pos)));  % Amplitudes of the peaks  (Change if desired)
wid=60+60.*pos./10000;   % Widths of the peaks (Change if desired)
Noise=0.05; % Amount of random noise added to the signal. (Change if desired)

% A = matrix containing one of the unit-amplidude peak in each of its rows
A = zeros(length(pos),length(x));
ActualPeaks=[0 0 0 0 0];
p=1;
for k=1:length(pos)
A(k,:)=exp(-((x-pos(k))./(0.6005612.*wid(k))).^2); % Gaussian peaks
% A(k,:)=ones(size(x))./(1+((x-pos(k))./(0.5.*wid(k))).^2);  % Lorentzian peaks
% Assembles actual parameters into ActualPeaks matrix: each row = 1
% peak; columns are Peak #, Position, Height, Width, Area
ActualPeaks(k,:) = [k pos(k) amp(k) wid(k) 1.0646.*amp(k).*wid(k)];
end
z=amp*A;  % Multiplies each row by the corresponding amplitude and adds them up
y=z+Noise.*randn(size(z));  % Optionally adds random noise
demodata=[x' y']; % Assembles x and y vectors into data matrix

% Initial values of variable peak detection parameters
WidthPoints=mean(wid)/increment; % Average number of points in half-width of peaks
SlopeThreshold=0.5*WidthPoints^-2; % Formula for estimating value of SlopeThreshold
AmpThreshold=0.05*max(y);
SmoothWidth=25;  % SmoothWidth should be roughly equal to 1/2 the peak width (in points)
FitWidth=round(WidthPoints/2); % FitWidth should be roughly equal to 1/2 the peak widths(in points)

% Now call iPeak, with specified values of AmpT, SlopeT, SmoothW, and FitW.
% (You can change theses values if desired).
tic;
iPeakResults=ipeak(demodata,0,AmpThreshold,SlopeThreshold,SmoothWidth,FitWidth,ActualPeaks(1,2),200,1);
TiPeak=toc;
disp('-----------------------------------------------------------------')
disp('Comparison of the iPeak and Peakfit functions for a test signal ')
disp('consisting of multiple peaks with random peak heights and gradually')
disp('increasing peak widths, superimposed on a curved sloping background. ')
disp(' ')
disp('         Peak #    Position      Height       Width        Area')
ActualPeaks
disp('  ')
fprintf(2,'Press any key to continue.....or press Ctrl-C to abort.\n')
pause

% Compare iPeakResults to ActualPeaks
disp('  ')
disp('Using iPeak:')
disp('>> iPeakResults=ipeak(demodata,0,AmpThreshold,SlopeThreshold,SmoothWidth,FitWidth,ActualPeaks(1,2),200,1);')
NumPeaks=max(iPeakResults(:,1));
disp(['Number of peaks detected = ' num2str(NumPeaks)])
iPeakResults

SizeResults=size(iPeakResults);
error=zeros(SizeResults(1),5);
for n=1:SizeResults(1),
indexn=val2ind(ActualPeaks(:,2),iPeakResults(n,2));
error(n,:)=100.*abs(ActualPeaks(indexn,:)-iPeakResults(n,:))./ActualPeaks(indexn,:);
error(n,1)=iPeakResults(n,1);
% MeasuredPeaks(n,1)=indexn;
end
AverageiPeakError=mean(error)
disp(['Elapsed time is ' num2str(TiPeak) ' seconds'])
disp(' ')
disp('Comparing ActualPeaks to iPeakResults, you can see that iPeak')
disp('works well for isolated peaks (like peak 1), but does not')
disp('accurately correct for the background when the peaks are close ')
disp('together, like peak 2.  Also it sometimes misses the small peaks.')
disp(' ')
fprintf(2,'Press any key to continue.....or press Ctrl-C to abort.\n')
pause
% -------------------------------------------------------------------
disp('  ')
disp('Using peakfit:')
disp('To use peakfit on a signal with lots of peaks, it is best to')
disp('fit each group of overlapping peaks separately. In this signal,')
disp('there are 8 groups ranging from 1 peak to 4 peaks per group.')
disp('  ')

% Group 1
disp('Group 1')
disp('>> FitResults=peakfit(demodata,400,265,1,1,0,10,0,1,0);')
disp('         Peak #    Position      Height       Width        Area')
figure(2)
PeakfitErrors=0;
tic;
FitResults=peakfit(demodata,400,265,1,1,0,10,0,1,0);
Tpeakfit1=toc;
SizeResults=size(FitResults);
error=zeros(SizeResults(1),5);
for n=1:SizeResults(1),
indexn=val2ind(ActualPeaks(:,2),FitResults(n,2));
error(n,:)=100.*abs(ActualPeaks(indexn,:)-FitResults(n,:))./ActualPeaks(indexn,:);
error(n,1)=indexn;
FitResults(n,1)=indexn;
end
ActualPeaksInThisGroup=ActualPeaks(FitResults(:,1),:)
FitResults
if SizeResults(1)==1,
AveragePercentErrors=error;
else
AveragePercentErrors=mean(error);
end
AveragePercentErrors(1)=0;
AveragePercentErrors
disp(['Elapsed time is ' num2str(Tpeakfit1) ' seconds'])
drawnow
PeakfitErrors=AveragePercentErrors;
disp(' ')
fprintf(2,'Press any key to continue.....or press Ctrl-C to abort.\n')
pause

% Group 2
disp('  ')
disp('Group 2  ')
disp('>> FitResults=peakfit(demodata,1000,3,1,0,10,0,1,0);')
disp('         Peak #    Position      Height       Width        Area')
tic
FitResults=peakfit(demodata,1000,438,3,1,0,10,0,1,0);
Tpeakfit2=toc;
SizeResults=size(FitResults);
error=zeros(SizeResults(1),5);
for n=1:SizeResults(1),
indexn=val2ind(ActualPeaks(:,2),FitResults(n,2));
error(n,:)=100.*abs(ActualPeaks(indexn,:)-FitResults(n,:))./ActualPeaks(indexn,:);
error(n,1)=indexn;
FitResults(n,1)=indexn;
end
ActualPeaksInThisGroup=ActualPeaks(FitResults(:,1),:)
FitResults
if SizeResults(1)==1,
AveragePercentErrors=error;
else
AveragePercentErrors=mean(error);
end
AveragePercentErrors(1)=0;
AveragePercentErrors
disp(['Elapsed time is ' num2str(Tpeakfit2) ' seconds'])
drawnow
PeakfitErrors=[PeakfitErrors;AveragePercentErrors];
disp(' ')
fprintf(2,'Press any key to continue.....or press Ctrl-C to abort.\n')
pause

% Group 3
disp('  ')
disp(' Group 3  ')
disp('>> FitResults=peakfit(demodata,1595,477,2,1,0,10,0,1,0);')
disp('         Peak #    Position      Height       Width        Area')
tic;
FitResults=peakfit(demodata,1595,477,2,1,0,10,0,1,0);
Tpeakfit3=toc;
SizeResults=size(FitResults);
error=zeros(SizeResults(1),5);
for n=1:SizeResults(1),
indexn=val2ind(ActualPeaks(:,2),FitResults(n,2));
error(n,:)=100.*abs(ActualPeaks(indexn,:)-FitResults(n,:))./ActualPeaks(indexn,:);
error(n,1)=indexn;
FitResults(n,1)=indexn;
end
ActualPeaksInThisGroup=ActualPeaks(FitResults(:,1),:)
FitResults
if SizeResults(1)==1,
AveragePercentErrors=error;
else
AveragePercentErrors=mean(error);
end
AveragePercentErrors(1)=0;
AveragePercentErrors
disp(['Elapsed time is ' num2str(Tpeakfit3) ' seconds'])
drawnow
PeakfitErrors=[PeakfitErrors;AveragePercentErrors];
disp(' ')
fprintf(2,'Press any key to continue.....or press Ctrl-C to abort.\n')
pause

% Group 4
disp('  ')
disp('Group 4  ')
disp('>> FitResults=peakfit(demodata,2187,246,1,1,0,10,0,1,0);')
disp('         Peak #    Position      Height       Width        Area')
tic;
FitResults=peakfit(demodata,2187,246,1,1,0,10,0,1,0);
Tpeakfit4=toc;
SizeResults=size(FitResults);
error=zeros(SizeResults(1),5);
for n=1:SizeResults(1),
indexn=val2ind(ActualPeaks(:,2),FitResults(n,2));
error(n,:)=100.*abs(ActualPeaks(indexn,:)-FitResults(n,:))./ActualPeaks(indexn,:);
error(n,1)=indexn;
FitResults(n,1)=indexn;
end
ActualPeaksInThisGroup=ActualPeaks(FitResults(:,1),:)
FitResults
if SizeResults(1)==1,
AveragePercentErrors=error;
else
AveragePercentErrors=mean(error);
end
AveragePercentErrors(1)=0;
AveragePercentErrors
disp(['Elapsed time is ' num2str(Tpeakfit4) ' seconds'])
drawnow
PeakfitErrors=[PeakfitErrors;AveragePercentErrors];

disp(' ')
fprintf(2,'Press any key to continue.....or press Ctrl-C to abort.\n')
pause

% Group 5
disp('  ')
disp('Group 5  ')
disp('>> FitResults=peakfit(demodata,2450,325,2,1,0,10,0,1,0);')
disp('         Peak #    Position      Height       Width        Area')
tic;
FitResults=peakfit(demodata,2450,325,2,1,0,10,0,1,0);
Tpeakfit5=toc;
SizeResults=size(FitResults);
error=zeros(SizeResults(1),5);
for n=1:SizeResults(1),
indexn=val2ind(ActualPeaks(:,2),FitResults(n,2));
error(n,:)=100.*abs(ActualPeaks(indexn,:)-FitResults(n,:))./ActualPeaks(indexn,:);
error(n,1)=indexn;
FitResults(n,1)=indexn;
end
ActualPeaksInThisGroup=ActualPeaks(FitResults(:,1),:)
FitResults
if SizeResults(1)==1,
AveragePercentErrors=error;
else
AveragePercentErrors=mean(error);
end
AveragePercentErrors(1)=0;
AveragePercentErrors
disp(['Elapsed time is ' num2str(Tpeakfit5) ' seconds'])
drawnow
PeakfitErrors=[PeakfitErrors;AveragePercentErrors];
disp(' ')
fprintf(2,'Press any key to continue.....or press Ctrl-C to abort.\n')
pause

% Group 6
disp('  ')
disp('Group 6  ')
disp('>> FitResults=peakfit(demodata,2742,325,2,1,0,10,0,1,0);')
disp('         Peak #    Position      Height       Width        Area')
tic;
FitResults=peakfit(demodata,2742,325,2,1,0,10,0,1,0);
Tpeakfit6=toc;
SizeResults=size(FitResults);
error=zeros(SizeResults(1),5);
for n=1:SizeResults(1),
indexn=val2ind(ActualPeaks(:,2),FitResults(n,2));
error(n,:)=100.*abs(ActualPeaks(indexn,:)-FitResults(n,:))./ActualPeaks(indexn,:);
error(n,1)=indexn;
FitResults(n,1)=indexn;
end
ActualPeaksInThisGroup=ActualPeaks(FitResults(:,1),:)
FitResults
if SizeResults(1)==1,
AveragePercentErrors=error;
else
AveragePercentErrors=mean(error);
end
AveragePercentErrors(1)=0;
AveragePercentErrors
disp(['Elapsed time is ' num2str(Tpeakfit6) ' seconds'])
drawnow
PeakfitErrors=[PeakfitErrors;AveragePercentErrors];
disp(' ')
fprintf(2,'Press any key to continue.....or press Ctrl-C to abort.\n')
pause

% Group 7
disp('  ')
disp('Group 7  ')
disp('>> FitResults=peakfit(demodata,3260,600,4,6,0,10,0,1,0);')
disp('         Peak #    Position      Height       Width        Area')
tic;
FitResults=peakfit(demodata,3260,600,4,6,0,10,0,1,0);
Tpeakfit7=toc;
SizeResults=size(FitResults);
error=zeros(SizeResults(1),5);
for n=1:SizeResults(1),
indexn=val2ind(ActualPeaks(:,2),FitResults(n,2));
error(n,:)=100.*abs(ActualPeaks(indexn,:)-FitResults(n,:))./ActualPeaks(indexn,:);
error(n,1)=indexn;
FitResults(n,1)=indexn;
end
ActualPeaksInThisGroup=ActualPeaks(FitResults(:,1),:)
FitResults
if SizeResults(1)==1,
AveragePercentErrors=error;
else
AveragePercentErrors=mean(error);
end
AveragePercentErrors(1)=0;
AveragePercentErrors
disp(['Elapsed time is ' num2str(Tpeakfit7) ' seconds'])
drawnow
PeakfitErrors=[PeakfitErrors;AveragePercentErrors];
disp(' ')
fprintf(2,'Press any key to continue.....or press Ctrl-C to abort.\n')
pause

% Group 8
disp('  ')
disp('Group 8  ')
disp('>> FitResults=peakfit(demodata,3795,410,1,1,0,10,0,1,0);')
disp('         Peak #    Position      Height       Width        Area')
tic;
FitResults=peakfit(demodata,3795,410,1,1,0,10,0,1,0);
Tpeakfit8=toc;
SizeResults=size(FitResults);
error=zeros(SizeResults(1),5);
for n=1:SizeResults(1),
indexn=val2ind(ActualPeaks(:,2),FitResults(n,2));
error(n,:)=100.*abs(ActualPeaks(indexn,:)-FitResults(n,:))./ActualPeaks(indexn,:);
error(n,1)=indexn;
FitResults(n,1)=indexn;
end
ActualPeaksInThisGroup=ActualPeaks(FitResults(:,1),:)
FitResults
if SizeResults(1)==1,
AveragePercentErrors=error;
else
AveragePercentErrors=mean(error);
end
AveragePercentErrors(1)=0;
AveragePercentErrors
disp(['Elapsed time is ' num2str(Tpeakfit8) ' seconds'])
PeakfitErrors=[PeakfitErrors;AveragePercentErrors];
TotalPeakfitComputationTime=Tpeakfit1+Tpeakfit2+Tpeakfit3+Tpeakfit4+Tpeakfit5+Tpeakfit6+Tpeakfit7+Tpeakfit8
disp('  ')
disp('In summary, we can compare the average percent errors and the')
disp('computation time of the iPeak and Peakfit methods:')
disp('  ')
AverageiPeakError=AverageiPeakError(2:5)
iPeakComputationTime=TiPeak
AveragePeakfitErrors=mean(PeakfitErrors);
AveragePeakfitErrors=AveragePeakfitErrors(2:5)
TotalPeakfitComputationTime
disp('  ')
disp('You can see that the errors of the peakfit method are quite a bit')
disp(['lower (by about a factor of ' num2str(round(mean(AverageiPeakError./AveragePeakfitErrors))) '), but that the execution time' ])
disp(['is longer (by about a factor of ' num2str(round(TotalPeakfitComputationTime/TiPeak)) ').' ])
disp('For both methods, the peak positions are measured most accurately and')
disp('the peak widths and areas least accurately.')
disp('  ')
disp('For a more challenging test, change line 13 to read Noise=.5 ')
disp('and re-run this script.')
fprintf(2,'End of demo\n')

function P=ipeak(DataMatrix,PeakD,AmpT,SlopeT,SmoothW,FitW,xcenter,xrange,MaxError,positions,names)
global X Y xo dx SlopeThreshold AmpThreshold SmoothWidth FitWidth AUTOZERO valleymode
global PeakLabels PeakID Names Positions maxerror logplot plotcolor showpeak

format short g
format compact
warning off all
switch nargin
% 'nargin' is the number of arguments
case 1  % One argument only
% Assumne that the argument must be a matrix of data.
% If DataMatrix is in the wrong transposition, fix it.
datasize=size(DataMatrix);
if datasize(1)<datasize(2),DataMatrix=DataMatrix';end
datasize=size(DataMatrix);
if datasize(2)==1, %  Must be ipeak(Y-vector)
X=[1:length(DataMatrix)]'; % Create an independent variable vector
Y=DataMatrix;
else
% Must be ipeak(DataMatrix)
X=DataMatrix(:,1); % Split matrix argument
Y=DataMatrix(:,2);
end
% Calculate default values of peak detection parameters
PeakDensity=20;
% Estimate approx number of points in a peak half-width
WidthPoints=length(Y)/PeakDensity;
SlopeThreshold=WidthPoints^-2;
AmpThreshold=abs(min(Y)+0.1*(max(Y)-min(Y)));
SmoothWidth=round(WidthPoints/3);
FitWidth=round(WidthPoints/3);
if FitWidth>100,FitWidth=100;end   % Keep FitWidth below 100
if SmoothWidth>100,SmoothWidth=100;end   % Keep SmoothWidth below 100
xo=length(Y)/2; % Initial Pan setting
dx=length(Y)/4; % Initial Zoom setting
AUTOZERO=0;
case 2
% Two arguments; might be separate x and y data vectors,
% data matrix + number, or y vector + number (peak density estimate)
if isscalar(PeakD)
% Must be one data matrix and a peak density estimate.
% If DataMatrix is in the wrong transposition, fix it.
datasize=size(DataMatrix);
if datasize(1)<datasize(2),DataMatrix=DataMatrix';end
datasize=size(DataMatrix);
if datasize(2)==1, %  Must be ipeak(Y-vector)
X=[1:length(DataMatrix)]'; % Create an independent variable vector
Y=DataMatrix;
else
% Must be ipeak(DataMatrix)
X=DataMatrix(:,1); % Split matrix argument
Y=DataMatrix(:,2);
end
% Calculate values of peak detection parameters
% arguments based on the peak density, PeakD
PeakDensity=PeakD;
% Estimate approx number of points in a peak half-width
WidthPoints=length(Y)/PeakDensity;
SlopeThreshold=WidthPoints^-2;
AmpThreshold=abs(min(Y)+0.1*(max(Y)-min(Y)));
SmoothWidth=round(WidthPoints/3);
FitWidth=round(WidthPoints/3);
if FitWidth>100,FitWidth=100;end   % Keep FitWidth below 100
if SmoothWidth>100,SmoothWidth=100;end   % Keep SmoothWidth below      xo=length(Y)/2; % Initial Pan setting
xo=length(Y)/2; % Initial Pan setting
dx=length(Y)/4; % Initial Zoom setting
AUTOZERO=0;
else % if not isscalar
% Must be separate x and y data vectors
X=DataMatrix;
Y=PeakD;
PeakDensity=20;
% Estimate approx number of points in a peak half-width
WidthPoints=length(Y)/PeakDensity;
SlopeThreshold=WidthPoints^-2;
AmpThreshold=abs(min(Y)+0.1*(max(Y)-min(Y)));
SmoothWidth=round(WidthPoints/3);
FitWidth=round(WidthPoints/3);
if FitWidth>100,FitWidth=100;end   % Keep FitWidth below 100
if SmoothWidth>100,SmoothWidth=100;end   % Keep SmoothWidth below 100
xo=length(Y)/2; % Initial Pan setting
dx=length(Y)/4; % Initial Zoom setting
end  % if isscalar
AUTOZERO=0;
case 3
% Must be separate x and y data vectors plus a peak density estimate.
X=DataMatrix;
Y=PeakD;
% Calculate values of peak detection parameters
% arguments based on the peak density, PeakD
PeakDensity=AmpT;
% Estimate approx number of points in a peak half-width
WidthPoints=length(Y)/PeakDensity;
SlopeThreshold=WidthPoints^-2;
AmpThreshold=abs(min(Y)+0.02*(max(Y)-min(Y)));
SmoothWidth=round(WidthPoints/3);
FitWidth=round(WidthPoints/3);
if FitWidth>100,FitWidth=100;end   % Keep FitWidth below 100
if SmoothWidth>100,SmoothWidth=100;end   % Keep SmoothWidth below 100
xo=length(Y)/2; % Initial Pan setting
dx=length(Y)/4; % Initial Zoom setting
AUTOZERO=0;
case 6
% Must be one data matrix and all peak detection parameters
% specified in arguments
% If DataMatrix is in the wrong transposition, fix it.
datasize=size(DataMatrix);
if datasize(1)<datasize(2),DataMatrix=DataMatrix';end
X=DataMatrix(:,1); % Split matrix argument
Y=DataMatrix(:,2);
SlopeThreshold=SlopeT;
AmpThreshold=AmpT;
SmoothWidth=SmoothW;
FitWidth=FitW;
xo=length(Y)/2; % Initial Pan setting
dx=length(Y)/4; % Initial Zoom setting
AUTOZERO=0;
case 8
% One data matrix, all peak detection parameters specified
% in arguments, initial values of xcenter and xrange specified.
% If DataMatrix is in the wrong transposition, fix it.
datasize=size(DataMatrix);
if datasize(1)<datasize(2),DataMatrix=DataMatrix';end
X=DataMatrix(:,1); % Split matrix argument
Y=DataMatrix(:,2);
SlopeThreshold=SlopeT;
AmpThreshold=AmpT;
SmoothWidth=SmoothW;
FitWidth=FitW;
if xcenter<min(X),
disp(['Lowest X value is ' num2str(min(X)) ]),
xcenter=min(X)+xrange;
end
if xcenter>max(X),
disp(['Highest X value is ' num2str(max(X)) ]),
xcenter=max(X)-xrange;
end
xo=val2ind(X,xcenter);
hirange=val2ind(X,xcenter+xrange./2);
lorange=val2ind(X,xcenter-xrange./2);
dx=(hirange-lorange);
AUTOZERO=0;
case 9
% Like case 9, except initial AUTOZERO mode is specified
% in arguments, initial values of xcenter and xrange specified.
% If DataMatrix is in the wrong transposition, fix it.
datasize=size(DataMatrix);
if datasize(1)<datasize(2),DataMatrix=DataMatrix';end
X=DataMatrix(:,1); % Split matrix argument
Y=DataMatrix(:,2);
SlopeThreshold=SlopeT;
AmpThreshold=AmpT;
SmoothWidth=SmoothW;
FitWidth=FitW;
xo=val2ind(X,xcenter);
hirange=val2ind(X,xcenter+xrange./2);
lorange=val2ind(X,xcenter-xrange./2);
dx=(hirange-lorange);
if xcenter<min(X),
disp(['Lowest X value is ' num2str(min(X)) ]),
xcenter=min(X)+xrange;
end
if xcenter>max(X),
disp(['Highest X value is ' num2str(max(X)) ]),
xcenter=max(X)-xrange;
end
AUTOZERO=MaxError;
case 11 % last 3 options arguments provided
datasize=size(DataMatrix);
if datasize(1)<datasize(2),DataMatrix=DataMatrix';end
X=DataMatrix(:,1); % Split matrix argument
Y=DataMatrix(:,2);
SlopeThreshold=SlopeT;
AmpThreshold=AmpT;
SmoothWidth=SmoothW;
FitWidth=FitW;
xo=val2ind(X,xcenter);
hirange=val2ind(X,xcenter+xrange./2);
lorange=val2ind(X,xcenter-xrange./2);
dx=(hirange-lorange);
if xcenter<min(X),
disp(['Lowest X value is ' num2str(min(X)) ]),
xcenter=min(X)+xrange;
end
if xcenter>max(X),
disp(['Highest X value is ' num2str(max(X)) ]),
xcenter=max(X)-xrange;
end
maxerror=MaxError;
Positions=positions;
Names=names;
AUTOZERO=0;
otherwise
disp('Invalid number of arguments')
disp('Expected forms are:')
disp('ipeak(y);  % Data in single y vector')
disp('ipeak(x,y);  % Data in separate x and y vectors')
disp('ipeak(DataMatrix); % Data in two columns of DataMatrix')
disp('ipeak(x,y,10), ipeak([x;y],10) or ipeak(y,10), specifying peak density')
disp('ipeak(DataMatrix,0,.5,.0001,33,33);  specifying peak density, AmpT, SlopeT, SmoothW, FitW')
disp('ipeak(DataMatrix,PeakD,AmpT,SlopeT,SmoothW,FitW,xcenter,xrange)')
disp('ipeak(DataMatrix,PeakD,AmpT,SlopeT,SmoothW,FitW,xcenter,xrange,MaxError,positions,names)')
beep
return
end % switch nargin
% 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
if FitWidth<3,FitWidth=3;end   % Keep FitWidth above 2
PeakLabels=0; % Peak numbers only, no parameter labels, in upper window
valleymode=0;
% Plot the signal
P=findpeaks(X,Y,SlopeThreshold,AmpThreshold,SmoothWidth,FitWidth,3);
[xx,yy]=RedrawSignal(X,Y,xo,dx);
sizeP=size(P);
NumPeaks=sizeP(1);
P=MeasurePeaks(NumPeaks,X,Y,P,dx,SmoothWidth,FitWidth,AUTOZERO,valleymode);
% Attaches KeyPress test function to the figure.
uicontrol('Style','text')
% end of outer function
% ----------------------------SUBFUNCTIONS--------------------------------
% Interprets key presses from the Figure window. When a key is pressed,
% executes the code in the corresponding section in the SWITCH statement.
% Note: If you don't like my key assignments, you can change the numbers
% in the case statements here to re-assign that function to any other key.
% If you press a key that has not yet been assigned to a function, it
% displays the key code number in the command window so you can easily
global X Y xx yy xo dx SlopeThreshold AmpThreshold SmoothWidth FitWidth plotcolor
global PeakLabels PeakID Names Positions maxerror SavedSignal oldAmpThreshold
global logplot P AUTOZERO showpeak valleymode
key=get(gcf,'CurrentCharacter');
if isscalar(key),
ly=length(Y);
switch double(key),
case 29
% Pans down when left arrow pressed.
xo=xo+dx/10;
if xo>ly,xo=ly;end
[xx,yy]=RedrawSignal(X,Y,xo,dx);
case 28
% Pans up when right arrow pressed.
xo=xo-dx/10;
if xo<1,xo=1;end
[xx,yy]=RedrawSignal(X,Y,xo,dx);
case 91
% Nudge down 1 point when [ pressed.
xo=xo-1;
if xo<1,xo=1;end
[xx,yy]=RedrawSignal(X,Y,xo,dx);
case 93
% Nudge up 1 point when ] pressed.
xo=xo+1;
if xo>ly,xo=ly;end
[xx,yy]=RedrawSignal(X,Y,xo,dx);
case 46
% Pans down when < key pressed.
xo=xo+dx/2;
if xo>ly,xo=ly;end
[xx,yy]=RedrawSignal(X,Y,xo,dx);
case 44
% Pans up when > key pressed.
xo=xo-dx/2;
if xo<1,xo=1;end
[xx,yy]=RedrawSignal(X,Y,xo,dx);
case 31
% Zooms out when up arrow pressed.
dx=dx+dx/10;
[xx,yy]=RedrawSignal(X,Y,xo,dx);
case 30
% Zooms in when down arrow pressed.
dx=dx-dx/10;
if dx<2,dx=2;end
[xx,yy]=RedrawSignal(X,Y,xo,dx);
case 47
% Zooms out when / pressed.
dx=dx+ly/50;
[xx,yy]=RedrawSignal(X,Y,xo,dx);
case 39
% Zooms in when ' pressed.
dx=dx-ly/50;
if dx<2,dx=2;end
[xx,yy]=RedrawSignal(X,Y,xo,dx);
case 27 % When 'ESC' key is pressed, resets pan and zoom
xo=length(Y)/2; % Initial Pan setting
dx=length(Y)/4; % Initial Zoom setting
[xx,yy]=RedrawSignal(X,Y,xo,dx);
case 13  % Change plot color when Return (Enter) key pressed
plotcolor=plotcolor+1;
if plotcolor==6, plotcolor=0;end
[xx,yy]=RedrawSignal(X,Y,xo,dx);
case 98
% When 'b' key is pressed, user clicks graph
% to enter background points, then graph re-drawn.
SavedSignal=Y;
oldAmpThreshold=AmpThreshold;
BaselinePoints=input('Number of baseline points to click: ');
if isempty(BaselinePoints),BaselinePoints=8;end
AmpThreshold=input('Amplitude Threshold: ');
if isempty(AmpThreshold),AmpThreshold=oldAmpThreshold;end
% Acquire background points from user mouse clicks
subplot(2,1,2)
title(['Click on ' num2str(BaselinePoints) ' points on the baseline between the peaks.'])
bX=[];bY=[];
for g=1:BaselinePoints;
[clickX,clickY] = ginput(1);
bX(g)=clickX;
bY(g)=clickY;
xlabel(['Baseline point '  num2str(g) ' / ' num2str(BaselinePoints) ])
end
yy=Y;
for k=1:length(bX)-1,
fp=val2ind(X,bX(k)); % First point in segment
lp=val2ind(X,bX(k+1));  % Last point in segment
% Subtract piecewise linear background from Y
yy(fp:lp)=Y(fp:lp)-((bY(k+1)-bY(k))/(bX(k+1)-bX(k))*(X(fp:lp)-bX(k))+bY(k));
end
Y=yy;
[xx,yy]=RedrawSignal(X,Y,xo,dx);
case 103
% When 'g' key is pressed, restores signal background and AmpThreshold.
Y=SavedSignal;
AmpThreshold=oldAmpThreshold;
[xx,yy]=RedrawSignal(X,Y,xo,dx);
case 97
% When 'a' key is pressed, increases "AmpThreshold" by 10%
AmpThreshold=AmpThreshold+.1*AmpThreshold;
[xx,yy]=RedrawSignal(X,Y,xo,dx);
case 122
% When 'z' key is pressed, decreases "AmpThreshold" by 10%
AmpThreshold=AmpThreshold-.1*AmpThreshold;
[xx,yy]=RedrawSignal(X,Y,xo,dx);
case 115 % When 's' key is pressed, increases "SlopeThreshold" by 10%
SlopeThreshold=SlopeThreshold+.1*SlopeThreshold;
[xx,yy]=RedrawSignal(X,Y,xo,dx);
case 120 % When 'x' key is pressed, decreases "SlopeThreshold" by 10%
SlopeThreshold=SlopeThreshold-.1*SlopeThreshold;
[xx,yy]=RedrawSignal(X,Y,xo,dx);
case 100
% When 'd' key is pressed, increases "SmoothWidth" by 1 or 10%
if SmoothWidth>20,
SmoothWidth=round(SmoothWidth+.1.*SmoothWidth);
else
SmoothWidth=SmoothWidth+1;
end
[xx,yy]=RedrawSignal(X,Y,xo,dx);
case 99
% When 'c' key is pressed, decreases "SmoothWidth" by 1 or 10%
if SmoothWidth>20,
SmoothWidth=round(SmoothWidth-.1.*SmoothWidth);
else
SmoothWidth=SmoothWidth-1;
end
if SmoothWidth<1, SmoothWidth=1;end
[xx,yy]=RedrawSignal(X,Y,xo,dx);
case 102
% When 'f' key is pressed, increases "FitWidth" by 1 or 10%
if FitWidth>20,
FitWidth=round(FitWidth+.1.*FitWidth);
else
FitWidth=FitWidth+1;
end
[xx,yy]=RedrawSignal(X,Y,xo,dx);
case 118
% When 'v' key is pressed, decreases "FitWidth" by 1 or 10%
if FitWidth>20,
FitWidth=round(FitWidth-.1.*FitWidth);
else
FitWidth=FitWidth-1;
end
if FitWidth<3, FitWidth=3;end
[xx,yy]=RedrawSignal(X,Y,xo,dx);
case 45
% When '-' key is pressed, invert the signal
Y=-Y;
[xx,yy]=RedrawSignal(X,Y,xo,dx);
disp('Signal was inverted.')
case 48
% When '0' (zero) key is pressed, subtracts minimum from entire signal
% (to remove positive or negative offset).
Y=Y-min(Y);
[xx,yy]=RedrawSignal(X,Y,xo,dx);
disp('Mininum signal set to zero.')
case 114
% When 'r' key is pressed, prints a report listing current
% settings and peak table.
disp('--------------------------------------------------------')
disp(['Amplitude Threshold (AmpT) = ' num2str(AmpThreshold) ] )
disp(['Slope Threshold (SlopeT) = ' num2str(SlopeThreshold) ] )
disp(['Smooth Width (SmoothW) = ' num2str(SmoothWidth) ' points' ] )
disp(['Fit Width (FitW) = ' num2str(FitWidth) ' points' ] )
sizeP=size(P);
NumPeaks=sizeP(1);
window=max(xx)-min(xx);
if AUTOZERO,
disp('Autozero ON')
disp([ 'Window span: ' num2str(window) ]);
else
disp('Autozero OFF')
end
if valleymode,
disp('        Valley#     Position     Height      Width          Area')
else
disp('          Peak#     Position     Height      Width          Area')
end
PP=MeasurePeaks(NumPeaks,X,Y,P,dx,SmoothWidth,FitWidth,AUTOZERO,valleymode);
disp(PP)
case 112
% When 'p' key is pressed, prints out peak table
disp('--------------------------------------------------------')
sizeP=size(P);
NumPeaks=sizeP(1);
window=max(xx)-min(xx);
if AUTOZERO,
disp('Autozero ON')
disp([ 'Window span: ' num2str(window) ' units'])
else
disp('Autozero OFF')
end
if valleymode,
disp('        Valley#     Position     Height      Width          Area')
else
disp('          Peak#     Position     Height      Width          Area')
end
PP=MeasurePeaks(NumPeaks,X,Y,P,dx,SmoothWidth,FitWidth,AUTOZERO,valleymode);
disp(PP)
case 107
% When 'k' key is pressed, prints out table of keyboard commands
disp('KEYBOARD CONTROLS:')
disp(' Pan left and right..........Coarse pan: < and >')
disp('                             Fine pan: left and right cursor arrows')
disp('                             Nudge: [ ] ')
disp(' Zoom in and out.............Coarse zoom: / and "  ')
disp('                             Fine zoom: up and down cursor arrows')
disp(' Resets pan and zoom.........ESC')
disp(' Change plot color...........Enter  (cycles through standard colors)')
disp(' Adjust AmpThreshold.........A,Z (Larger values ignore short peaks)')
disp(' Adjust SmoothWidth..........D,C (Larger values ignore sharp peaks}')
disp(' Baseline correction:        B, enter # points, then click baseline ')
disp(' Restore original signal.....G  to cancel previous background subtraction')
disp(' Invert signal...............-  Invert (negate) the signal (flip + and -)')
disp(' Set minimum to zero.........0  (Zero) Sets minumun signal to zero')
disp(' Toggle log y mode OFF/ON....Y  Plot log Y axis on lower graph')
disp(' Toggle autozero OFF/ON......T  Auto background subtraction on upper graph')
disp(' Toggle valley mode OFF/ON...U  Switch to valley mode')
disp(' Print report................R  prints Peak table and parameters')
disp(' Step through peaks..........Space/Tab  Jumps to next/previous peak')
disp(' Print peak table............P  Peak #, Position, Height, Width, Area')
disp(' Normal peak fit.............N  Fit peaks in upper window with peakfit.m')
disp(' Multiple peak fit...........M  Fit all peaks in signal with peakfit.m')
disp(' Print keyboard commands.....K  prints this list')
disp(' Print findpeaks arguments...Q  prints findpeaks function with arguments')
disp(' Print ipeak arguments.......W  prints ipeak function with all arguments')
disp(' Peak labels ON/OFF..........L  displays peak parameters on upper graph')
disp(' Peak ID ON/OFF..............I  Identifies closest peaks in Names database.')
disp(' Print table of peak IDs.....O  Prints Name, Position, Error, Amplitude')
case 113
% When 'Q' is pressed, prints findpeaks function with arguments
disp(['findpeaks(x,y,'  num2str(SlopeThreshold) ',' num2str(AmpThreshold)  ',' num2str(SmoothWidth)  ',' num2str(FitWidth) ',3)'] )
case 119
% When 'W' is pressed, prints ipeak function with arguments
center=(max(xx)+min(xx))/2;
window=max(xx)-min(xx);
disp(['ipeak(DataMatrix,0,'  num2str(AmpThreshold) ',' num2str(SlopeThreshold)  ',' num2str(SmoothWidth)  ',' num2str(FitWidth) ',' num2str(center) ',' num2str(window) ')'] )
case 105
% When 'I' is pressed, toggles on/off PeakID in upper panel
if PeakID==0,
PeakID=1;
% disp([ 'Loaded "DataTable" from disk. Number of Names:' num2str(length(Positions)) ] )
% disp(['Position range: ' num2str(min(Positions)) '-' num2str(max(Positions)) ] )
else
PeakID=0;
end
[xx,yy]=RedrawSignal(X,Y,xo,dx);
case 108
% When 'L' is pressed, toggles on/off peak labels in upper panel
if PeakLabels==0,
PeakLabels=1;
else
PeakLabels=0;
end
[xx,yy]=RedrawSignal(X,Y,xo,dx);
case 121
% When 'Y' is pressed, toggles on/off log plot mode
if logplot==0,
logplot=1;
else
logplot=0;
end
[xx,yy]=RedrawSignal(X,Y,xo,dx);
case 117
% When 'U' is pressed, toggles valleymode on/off
if valleymode==0,
valleymode=1;
else
valleymode=0;
end
[xx,yy]=RedrawSignal(X,Y,xo,dx);
case 111
% When 'o' is pressed, prints table of identified peaks
if PeakID,
disp('      Name          Position      Error         Amplitude')  %  Print out column lables for table
for n=1:length(P(:,2)),
% m=index of the cloest match in Positions
m=val2ind(Positions,P(n,2));
% Error=difference between detected peak and nearest
% peak in table
Error=abs(P(n,2)-Positions(m));
if Error<maxerror, % Only identify the peaks if the error is less than MaxError
disp([Names(m) Positions(m) Error P(n,3)]); % Print out one line of Positions and Errors table
end % if error
end  % for n
end  % if PeakID

case 110
% When 'N' is pressed, applies peakfit function only to peaks in
% the upper window (up to 6 peaks).
% [xx,yy]=RedrawSignal(X,Y,xo,dx);
sizeP=size(P);
NumPeaksUW=sizeP(1);
if NumPeaksUW>1,
PUW=[]; % PUW=table of peaks in upper window
for peak=1:NumPeaksUW, % NumPeaksUW=number of peaks in upper window
if P(peak,2)>min(xx),
if P(peak,2)<max(xx),
PUW=[PUW;P(peak,:)];
end %  if P(peak,2)<max(xx),
end %  if P(peak,2)>min(xx),
end % for peak=1:length(P),
else
PUW=P;
end
sizePUW=size(PUW);
NumPeaksUW=sizePUW(1);
center=(max(xx)+min(xx))/2;
window=max(xx)-min(xx);
extra=1;
disp('1=Gaussian (default), 2=Lorentzian, 3=logistic, 4=Pearson');
disp('7=Equal-width Lorentzians, 8=exponentionally broadened equal-width Gaussian');
Shape=input('Peak shape (1-8): ');
if isempty(Shape),Shape=1;end
NumTrials=input('Number of trials: ');
if isempty(NumTrials),NumTrials=1;end
if Shape==4||Shape==5||Shape==8,
extra=input('Extra parameter: ');
end % if Shape==4||Shape==5||Shape==8,
if NumTrials>1,disp(['Best of ' num2str(NumTrials) ' trial fits.' ]), end
switch NumPeaksUW
case 1
startvector=[PUW(1,2) PUW(1,4)];
case 2
startvector=[PUW(1,2) PUW(1,4) PUW(2,2) PUW(2,4)];
case 3
startvector=[PUW(1,2) PUW(1,4) PUW(2,2) PUW(2,4) PUW(3,2) PUW(3,4)];
case 4
startvector=[PUW(1,2) PUW(1,4) PUW(2,2) PUW(2,4) PUW(3,2) PUW(3,4) PUW(4,2) PUW(4,4)];
case 5
startvector=[PUW(1,2) PUW(1,4) PUW(2,2) PUW(2,4) PUW(3,2) PUW(3,4) PUW(4,2) PUW(4,4) PUW(5,2) PUW(5,4)];
case 6
startvector=[PUW(1,2) PUW(1,4) PUW(2,2) PUW(2,4) PUW(3,2) PUW(3,4) PUW(4,2) PUW(4,4) PUW(5,2) PUW(5,4) PUW(6,2) PUW(6,4)];
end % switch NumPeaksUW
[FitResults,MeanFitError]=peakfit([xx,yy],center,window,NumPeaksUW,Shape,extra,NumTrials,startvector,AUTOZERO);
switch Shape
case 1
ShapeString='Gaussian';
case 2
ShapeString='Lorentzian';
case 3
ShapeString='logistic';
case 4
ShapeString='Pearson7';
case 5
ShapeString='ExpGaussian';
case 6
ShapeString='Equal width Gaussians';
case 7
ShapeString='Equal width Lorentzians';
case 8
ShapeString='Equal-width ExpGauss.';
otherwise
ShapeString='';
end % switch Shape
disp(['Least-squares fit to ' ShapeString ' peak model' ])
disp(['Fitting Error ' num2str(MeanFitError) '%'])
disp('          Peak#     Position     Height      Width         Area  ')
for peak=1:NumPeaksUW,FitResults(peak,1)=PUW(peak,1);end
disp(FitResults(:,1:5))
case 116
% When 't' key is pressed, toggles AUTOZERO mode
if AUTOZERO,
AUTOZERO=0;
[xx,yy]=RedrawSignal(X,Y,xo,dx);
else
AUTOZERO=1;
[xx,yy]=RedrawSignal(X,Y,xo,dx);
end
case 101
% When 'e' is pressed,
disp('-------------------------------------------------------------')
case 109
% When 'M' is pressed, applies peakfit function to all peaks
AllFitResults=[];
[xx,yy]=RedrawSignal(X,Y,xo,dx);
sizeP=size(P);
NumPeaks=sizeP(1);
if NumPeaks>2,
center=(max(xx)+min(xx))/2;
window=max(xx)-min(xx);
extra=1;
disp('1=Gaussian (default), 2=Lorentzian, 3=logistic, 4=Pearson');
disp('7=Equal-width Lorentzians, 8=exponentionally broadened equal-width Gaussian');
Shape=input('Peak shape (1-8): ');
if isempty(Shape),Shape=1;end
NumTrials=input('Number of trials (1-100): ');
if isempty(NumTrials),NumTrials=1;end
if Shape==4||Shape==5||Shape==8,
extra=input('Extra parameter: ');
end
switch Shape
case 1
ShapeString='Gaussian';
case 2
ShapeString='Lorentzian';
case 3
ShapeString='logistic';
case 4
ShapeString='Pearson7';
case 5
ShapeString='ExpGaussian';
case 6
ShapeString='Equal width Gaussians';
case 7
ShapeString='Equal width Lorentzians';
case 8
ShapeString='Equal-width ExpGauss.';
otherwise
ShapeString='';
end % switch Shape
disp(['Multiple Least-squares fit to ' ShapeString ' peak model' ]);
disp('          Peak#     Position     Height      Width         Area          Error')
for peak=1:NumPeaks-1,
xcenter=P(peak,2);
xrange=8*P(peak,4);
xo=val2ind(X,xcenter);
hirange=val2ind(X,xcenter+xrange./2);
lorange=val2ind(X,xcenter-xrange./2);
dx=(hirange-lorange);
[xx,yy]=RedrawSignal(X,Y,xo,dx);
PP=findpeaks(xx,yy,SlopeThreshold,AmpThreshold,SmoothWidth,FitWidth,3);
sizeP=size(PP);
NumPeaksUW=sizeP(1);% Number of peaks in Upper Window
switch NumPeaksUW
case 1
startvector=[PP(1,2) PP(1,4)];
case 2
startvector=[PP(1,2) PP(1,4) PP(2,2) PP(2,4)];
case 3
startvector=[PP(1,2) PP(1,4) PP(2,2) PP(2,4) PP(3,2) PP(3,4)];
case 4
startvector=[PP(1,2) PP(1,4) PP(2,2) PP(2,4) PP(3,2) PP(3,4) PP(4,2) PP(4,4)];
case 5
startvector=[PP(1,2) PP(1,4) PP(2,2) PP(2,4) PP(3,2) PP(3,4) PP(4,2) PP(4,4) PP(5,2) PP(5,4)];
case 6
startvector=[PP(1,2) PP(1,4) PP(2,2) PP(2,4) PP(3,2) PP(3,4) PP(4,2) PP(4,4) PP(5,2) PP(5,4) PP(6,2) PP(6,4)];
end % switch NumPeaksUW

[FitResults,MeanFitError]=peakfit([xx,yy],center,window,NumPeaksUW,Shape,extra,NumTrials,startvector,0);
% for peak=1:NumPeaks,FitResults(peak,1)=PUW(peak,1);end
for fittrial=1:NumPeaksUW,  % Number of peaks in Upper Window
AllFitResults=[AllFitResults;[val2ind(P(:,2),FitResults(fittrial,2)) FitResults(fittrial,2:5) MeanFitError]];
end % for fittrial
end % peak=1:NumPeaks-1,
% Select the best for for each peak
SortedResults=sortrows(AllFitResults,2); % Sort AllFitResults by position (column 2)
SizeAllFitResults=size(AllFitResults);
NumFits=SizeAllFitResults(1);
BestFits=[];
for FitNumber=1:NumPeaks,
FirstColumn=min(val2ind(SortedResults(:,1),FitNumber));
LastColumn=max(val2ind(SortedResults(:,1),FitNumber));
SelectedSection=SortedResults(FirstColumn:LastColumn,:);
SortedSection=sortrows(SelectedSection,6);
BestRow=SortedSection(1,:);
BestFits=[BestFits;BestRow];
end
disp(BestFits)
else disp('Too few peaks detected; use the Normal curve fit instead.')
end % if  NumPeaks>2,
case 32
% When Spacebar is pressed, jumps to next peak
if valleymode,
P=findvalleys(X,Y,SlopeThreshold,AmpThreshold,SmoothWidth,FitWidth);
else
P=findpeaks(X,Y,SlopeThreshold,AmpThreshold,SmoothWidth,FitWidth,3);
end
sizeP=size(P);
NumPeaks=sizeP(1);
showpeak=showpeak+1;
if showpeak>NumPeaks,showpeak=1;end
center=P(showpeak,2);
xo=val2ind(X,center);
[xx,yy]=RedrawSignal(X,Y,xo,dx);
case 9
% When Tab is pressed, jumps to previous peak
if valleymode,
P=findvalleys(X,Y,SlopeThreshold,AmpThreshold,SmoothWidth,FitWidth,3);
else
P=findpeaks(X,Y,SlopeThreshold,AmpThreshold,SmoothWidth,FitWidth,3);
end
sizeP=size(P);
NumPeaks=sizeP(1);
showpeak=showpeak-1;
if showpeak>NumPeaks,showpeak=1;end
if showpeak<1,showpeak=NumPeaks;end
center=P(showpeak,2);
xo=val2ind(X,center);
[xx,yy]=RedrawSignal(X,Y,xo,dx);
otherwise
UnassignedKey=double(key)
disp('Press k to print out list of keyboard commands')
end % switch double(key),
end % if ischar(key),
% ----------------------------------------------------------------------
function [xx,yy]=RedrawSignal(X,Y,xo,dx)
% Plots the entire signal (X,Y) in the lower half of the plot window and an
% isolated segment (xx,yy) in the upper half, controlled by Pan and Zoom
% keys.
global SlopeThreshold AmpThreshold SmoothWidth FitWidth PeakLabels valleymode
global PeakID Names Positions maxerror P plotcolor logplot AUTOZERO
Startx=round(xo-(dx/2));
Endx=abs(round(xo+(dx/2)-1));
if (Endx-Startx)<SmoothWidth,Endx=Startx+SmoothWidth;end
if Endx>length(Y),Endx=length(Y);end
if Startx<1,Startx=1;end
PlotRange=Startx:Endx;
if (Endx-Startx)<5, PlotRange=xo:xo+5;end
xx=X(PlotRange);
yy=Y(PlotRange);
hold off
% clf
% Plots isolated segment (xx,yy) in the upper half
switch plotcolor
case 0
color='b.';
case 1
color='g.';
case 2
color='r.';
case 3
color='c.';
case 4
color='m.';
case 5
color='k.';
end
% auto-zero operation
if AUTOZERO==1,
X1=min(xx);
X2=max(xx);
Y1=mean(yy(1:length(xx)/20));
Y2=mean(yy((length(xx)-length(xx)/20):length(xx)));
yy=yy-((Y2-Y1)/(X2-X1)*(xx-X1)+Y1);
end % if
figure(1);subplot(2,1,1);plot(xx,yy,color);
hold off
if AUTOZERO==1
if valleymode
title('iPeak 3.9.   Valley mode. Autozero ON.  Press K for keyboard commands')
else
title('iPeak 3.9.   Peak mode.   Autozero ON.  Press K for keyboard commands')
end
else
if valleymode
title('iPeak 3.9.   Valley mode. Autozero OFF.  Press K for keyboard commands')
else
title('iPeak 3.9.   Peak mode.   Autozero OFF.  Press K for keyboard commands')
end
end

axis([X(Startx(1)) X(Endx(1)) min(yy) max(yy)+(max(yy)-min(yy))/10]);
xlabel('Space/Tab: next/previous peak.  Mode: U  Autozero: T   Log/linear: Y  Report: R')

% Bottom half of the figure shows full signal
subplot(2,1,2);cla
switch plotcolor
case 0; color='b';
case 1; color='g';
case 2; color='r';
case 3; color='c';
case 4; color='m';
case 5; color='k';
end
hold off
if logplot,
semilogy(X,abs(Y),color)  % Graph the signal with linear Y axis
else
plot(X,Y,color)  % Graph the signal with linear Y axis
end
if valleymode,
P=findvalleys(X,Y,SlopeThreshold,AmpThreshold,SmoothWidth,FitWidth,3);
else
P=findpeaks(X,Y,SlopeThreshold,AmpThreshold,SmoothWidth,FitWidth,3);
end
title('AmpT: A/Z   SlopeT: S/X   SmoothW: D/C    FitW: F/V   Background: B'  )
if logplot,
ylabel('Log y mode')
xlabel(['    AmpT: ' num2str(AmpThreshold) '     SlopeT: ' num2str(SlopeThreshold) '    SmoothW: ' num2str(SmoothWidth) '    FitW: ' num2str(FitWidth) ])
axis([X(1) X(length(X)) min(abs(Y)) max(Y)]); % Update plot
else
ylabel('Linear mode')
xlabel(['    AmpT: ' num2str(AmpThreshold) '     SlopeT: ' num2str(SlopeThreshold) '    SmoothW: ' num2str(SmoothWidth) '    FitW: ' num2str(FitWidth) ])
axis([X(1) X(length(X)) min(Y) max(Y)]); % Update plot
end
text(P(:,2),P(:,3),num2str(P(:,1)))  % Number the peaks found on the lower graph
hold on
% Mark the zoom range on the full signal with two magenta dotted vertical lines
center=X(round(xo));
checkzero=abs(Y);
checkzero(~checkzero)=NaN; % Find smallest non-zero value
plot([min(xx) min(xx)],[min(checkzero) max(Y)],'m--')
plot([max(xx) max(xx)],[min(checkzero) max(Y)],'m--')
plot([center center],[min(checkzero) max(Y)],'g-')
% Number the peaks found on the upper graph
subplot(2,1,1);
if valleymode,
PP=findvalleys(xx,yy,SlopeThreshold,AmpThreshold,SmoothWidth,FitWidth,3);
else
PP=findpeaks(xx,yy,SlopeThreshold,AmpThreshold,SmoothWidth,FitWidth,3);
end
if PeakLabels,
% Label the peaks on the upper graph with number, position, height, and
% width
% auto-zero operation
if AUTOZERO==1,
X1=min(xx);
X2=max(xx);
Y1=mean(yy(1:length(xx)/20));
Y2=mean(yy((length(xx)-length(xx)/20):length(xx)));
yy=yy-((Y2-Y1)/(X2-X1)*(xx-X1)+Y1);
end % if AUTOZERO
topaxis=axis;
yrange=topaxis(4)-topaxis(3);
pos1=.1*yrange;
pos2=.2*yrange;
pos3=.3*yrange;
pos4=.4*yrange;
text(P(:,2),P(:,3)-pos1,num2str(P(:,1)))
text(PP(:,2),PP(:,3)-pos2,num2str(PP(:,2)))
text(PP(:,2),PP(:,3)-pos3,num2str(PP(:,3)))
text(PP(:,2),PP(:,3)-pos4,num2str(PP(:,4)))
else
topaxis=axis;
yrange=topaxis(4)-topaxis(3);
pos1=.1*yrange;
% Number the peaks on the upper graph
text(P(:,2),P(:,3)-pos1,num2str(P(:,1)))
end
hold on
lyy=min(yy);
uyy=max(yy)+(max(yy)-min(yy))/10;
if lyy<uyy;
axis([X(Startx(1)) X(Endx(1)) lyy uyy ]);
end
center=X(round(xo));
hold on;plot([center center],[lyy uyy],'g-')
% Draw red best-fit line through peak tops in upper windows.
if PP(1)>0, % if any peaks are detected
sizePP=size(PP);
lengthPP=sizePP(1);
for PeakNumber=1:lengthPP,
subplot(2,1,1);
if PeakNumber>lengthPP,PeakNumber=lengthPP;end
n1=round(val2ind(xx,PP(PeakNumber,2))-FitWidth/2);
n2=round(val2ind(xx,PP(PeakNumber,2))+FitWidth/2);
if n1<1, n1=1;end
if n2>length(yy), n2=length(yy);end
PlotRange=n1:n2;
xxx=xx(PlotRange);
yyy=yy(PlotRange);
if valleymode,
[coef,S]=polyfit(xxx,yyy,2);  % Fit parabola to sub-group with centering and scaling
c1=coef(3);c2=coef(2);c3=coef(1);
subplot(2,1,1);
plotspace=linspace(min(xxx),max(xxx));
plot(plotspace,c3*plotspace.^2+c2*plotspace+c1,'r');
else
% Fit parabola to log10 of sub-group
[coef,S,MU]=polyfit(xxx,log(abs(yyy)),2);
c1=coef(3);c2=coef(2);c3=coef(1);
% Compute peak position and height of fitted parabola
PeakX=-((MU(2).*c2/(2*c3))-MU(1));
PeakY=exp(c1-c3*(c2/(2*c3))^2);
MeasuredWidth=norm(MU(2).*2.35482/(sqrt(2)*sqrt(-1*c3)));
subplot(2,1,1);
plotspace=linspace(min(xxx),max(xxx));
plot(plotspace,PeakY.*gaussian(plotspace,PeakX,MeasuredWidth),'r');
end
end   % for PeakNumber
% Place a label in the upper left corner with peak number, position,
% height, and width of the peak closest to the center of the window.
PeakAtCenter=val2ind(P(:,2),center);
% auto-zero operation
if AUTOZERO==1,
X1=min(xx);
X2=max(xx);
Y1=mean(yy(1:length(xx)/20));
Y2=mean(yy((length(xx)-length(xx)/20):length(xx)));
yy=yy-((Y2-Y1)/(X2-X1)*(xx-X1)+Y1);
end % if AUTOZERO
n1=round(val2ind(xx,P(PeakAtCenter,2))-FitWidth/2);
n2=round(val2ind(xx,P(PeakAtCenter,2))+FitWidth/2);
if n1<1, n1=1;end
if n2>length(yy), n2=length(yy);end
FitRange=n1:n2;
xxx=xx(FitRange);
yyy=yy(FitRange);
if valleymode,
[coef]=polyfit(xxx,yyy,2);  % Fit parabola to sub-group with centering and scaling
c1=coef(3);c2=coef(2);c3=coef(1);
PeakX=-c2/(2*c3);
PeakY=(c1-(c2*c2/(4*c3)));
MeasuredWidth=norm(2.35482/(sqrt(2)*sqrt(-1*c3)));
else
% Fit parabola to log10 of sub-group
[coef,S,MU]=polyfit(xxx,log(abs(yyy)),2);
c1=coef(3);c2=coef(2);c3=coef(1);
% Compute peak position and height or fitted parabola
PeakX=-((MU(2).*c2/(2*c3))-MU(1));
PeakY=exp(c1-c3*(c2/(2*c3))^2);
MeasuredWidth=norm(MU(2).*2.35482/(sqrt(2)*sqrt(-1*c3)));
end
startx=min(xx)+(max(xx)-min(xx))./20;
dyy=(max(yy)-min(yy))./10;
starty=max(yy)-dyy;
if valleymode,
text(startx,starty+dyy/2,['Valley ' num2str(PeakAtCenter) ] );
else
text(startx,starty+dyy/2,['Peak ' num2str(PeakAtCenter) ] );
end
topaxis=axis;
yrange=topaxis(4)-topaxis(3);
pos1=.1*yrange;
pos2=.2*yrange;
pos3=.3*yrange;
text(startx,starty+dyy/2-pos1,['Position: ' num2str(PeakX)])
text(startx,starty+dyy/2-pos2,['Height: ' num2str(PeakY)])
text(startx,starty+dyy/2-pos3,['Width: ' num2str(MeasuredWidth)])
% Add peak identification if peak identification mode is ON and
% information provided in arguments 9, 10, and 11.
if PeakID, % If peak identification mode is ON
for n=1:length(PP(:,2)),
%      [PP(n,2) Positionsv(n)]
m=val2ind(Positions,PP(n,2)); % m=index of the cloest match in Positions
Error=abs(PP(n,2)-Positions(m)); % Error=difference between detected peak and nearest peak in table
if Error<maxerror, % Only identify the peaks if the error is less than MaxError
text(PP(n,2),PP(n,3),Names(m)); % Label the graph peaks with element names
end % if error
end  % for n
end  % if PeakID
end  % if any peaks are detected
hold off
sizeP=size(P);
NumPeaks=sizeP(1);
P=MeasurePeaks(NumPeaks,X,Y,P,dx,SmoothWidth,FitWidth,AUTOZERO,valleymode);
%-----------------------------------------------------------------
function PP=MeasurePeaks(NumPeaks,X,Y,P,dx,SmoothWidth,FitWidth,AUTOZERO,valleymode)
PP=zeros(size(P));
for PeakNumber=1:NumPeaks,
center=P(PeakNumber,2);
xo=val2ind(X,center);
Startx=round(xo-(dx/2));
Endx=abs(round(xo+(dx/2)-1));
if (Endx-Startx)<SmoothWidth,Endx=Startx+SmoothWidth;end
if Endx>length(Y),Endx=length(Y);end
if Startx<1,Startx=1;end
PlotRange=Startx:Endx;
if (Endx-Startx)<5, PlotRange=xo:xo+5;end
xx=X(PlotRange);
yy=Y(PlotRange);
if AUTOZERO==1,
X1=min(xx);
X2=max(xx);
Y1=mean(yy(1:length(xx)/20));
Y2=mean(yy((length(xx)-length(xx)/20):length(xx)));
yy=yy-((Y2-Y1)/(X2-X1)*(xx-X1)+Y1);
end % if AUTOZERO
n1=round(val2ind(xx,P(PeakNumber,2))-FitWidth/2);
n2=round(val2ind(xx,P(PeakNumber,2))+FitWidth/2);
if n1<1, n1=1;end
if n2>length(yy), n2=length(yy);end
FitRange=n1:n2;
xxx=xx(FitRange);
yyy=yy(FitRange);
if valleymode,
[coef]=polyfit(xxx,yyy,2);  % Fit parabola to sub-group xxx, yyy
c1=coef(3);c2=coef(2);c3=coef(1);
PeakX=-c2/(2*c3);
PeakY=(c1-(c2*c2/(4*c3)));
MeasuredWidth=norm(2.35482/(sqrt(2)*sqrt(-1*c3)));
EstimatedArea=0;
else
[coef,S,MU]=polyfit(xxx,log(abs(yyy)),2);   % Fit parabola to log10 of sub-group
c1=coef(3);c2=coef(2);c3=coef(1);
% Compute peak position and height or fitted parabola
PeakX=-((MU(2).*c2/(2*c3))-MU(1));
PeakY=exp(c1-c3*(c2/(2*c3))^2);
MeasuredWidth=norm(MU(2).*2.35482/(sqrt(2)*sqrt(-1*c3)));
EstimatedArea=1.0646.*PeakY*MeasuredWidth;
end
PP(PeakNumber,:)=[PeakNumber PeakX PeakY MeasuredWidth EstimatedArea];
end   % for PeakNumber
% ----------------------------------------------------------------------
function P=findpeaks(x,y,SlopeThreshold,AmpThreshold,smoothwidth,peakgroup,smoothtype)
% function P=findpeaks(x,y,SlopeThreshold,AmpThreshold,smoothwidth,peakgroup,smoothtype)
% Function to locate the positive peaks in a noisy x-y time series data
% set.  Detects peaks by looking for downward zero-crossings
% in the first derivative that exceed SlopeThreshold.
% Returns list (P) containing peak number and position,
% height, width, and area of each peak. Arguments "slopeThreshold",
% "ampThreshold" and "smoothwidth" control peak sensitivity.
% Higher values will neglect smaller features. "Smoothwidth" is
% the width of the smooth applied before peak detection; larger
% values ignore narrow peaks. "Peakgroup" is the number points
% around the top part of the peak that are taken for measurement.
% The argument "smoothtype" determines the smooth algorithm:
%   If smoothtype=1, rectangular (sliding-average or boxcar)
%   If smoothtype=2, triangular (2 passes of sliding-average)
%   If smoothtype=3, pseudo-Gaussian (3 passes of sliding-average)
% See http://terpconnect.umd.edu/~toh/spectrum/Smoothing.html and
% http://terpconnect.umd.edu/~toh/spectrum/PeakFindingandMeasurement.htm
% T. C. O'Haver, 1995.  Version 4.1, Last revised September, 2011
if nargin~=7;smoothtype=1;end  % smoothtype=1 if not specified in argument
if smoothtype>3;smoothtype=3;end
if smoothtype<1;smoothtype=1;end
smoothwidth=round(smoothwidth);
peakgroup=round(peakgroup);
d=fastsmooth(deriv(y),smoothwidth,smoothtype);
n=round(peakgroup/2+1);
P=[0 0 0 0 0];
vectorlength=length(y);
peak=1;
AmpTest=AmpThreshold;
for j=smoothwidth:length(y)-smoothwidth,
if sign(d(j)) > sign (d(j+1)), % Detects zero-crossing
if d(j)-d(j+1) > SlopeThreshold*y(j), % if slope of derivative is larger than SlopeThreshold
if y(j) > AmpTest,  % if height of peak is larger than AmpThreshold
xx=zeros(size(peakgroup));yy=zeros(size(peakgroup));
for k=1:peakgroup, % Create sub-group of points near peak
groupindex=j+k-n+2;
if groupindex<1, groupindex=1;end
if groupindex>vectorlength, groupindex=vectorlength;end
xx(k)=x(groupindex);yy(k)=y(groupindex);
end
[coef,S,MU]=polyfit(xx,log(abs(yy)),2);  % Fit parabola to log10 of sub-group with centering and scaling
c1=coef(3);c2=coef(2);c3=coef(1);
PeakX=-((MU(2).*c2/(2*c3))-MU(1));   % Compute peak position and height of fitted parabola
PeakY=exp(c1-c3*(c2/(2*c3))^2);
MeasuredWidth=norm(MU(2).*2.35482/(sqrt(2)*sqrt(-1*c3)));
% if the peak is too narrow for least-squares technique to work
% well, just use the max value of y in the sub-group of points near peak.
if peakgroup<3,
PeakY=max(yy);
pindex=val2ind(yy,PeakY);
PeakX=xx(pindex(1));
end
% Construct matrix P. One row for each peak
% detected, containing the peak number, peak
% position (x-value) and peak height (y-value).
P(peak,:) = [round(peak) PeakX PeakY MeasuredWidth  1.0646.*PeakY*MeasuredWidth];
peak=peak+1;

end
end
end
end
% ----------------------------------------------------------------------
function V=findvalleys(x,y,SlopeThreshold,AmpThreshold,smoothwidth,peakgroup,smoothtype)
% function P=findvalleys(x,y,SlopeThreshold,AmpThreshold,smoothwidth,peakgroup,smoothtype)
% Function to locate the valleys (mimnima) in a noisy x-y time series data
% set.  Detects valleys by looking for upward zero-crossings
% in the first derivative that exceed SlopeThreshold.
% Returns list (V) containing valley number and position,
% depth, and width of each valley. Arguments "slopeThreshold",
% "ampThreshold" and "smoothwidth" control sensitivity.
% Higher values will neglect smaller features. "Smoothwidth" is
% the width of the smooth applied before valley detection; larger
% values ignore narrow features. "Peakgroup" is the number points
% around the bottom part of the valley that are fit to a parabola to
% determine the valley vertex (x and y at lowest point) and width.
% The argument "smoothtype" determines the smooth algorithm:
%   If smoothtype=1, rectangular (sliding-average or boxcar)
%   If smoothtype=2, triangular (2 passes of sliding-average)
%   If smoothtype=3, pseudo-Gaussian (3 passes of sliding-average)
% See http://terpconnect.umd.edu/~toh/spectrum/Smoothing.html and
% http://terpconnect.umd.edu/~toh/spectrum/PeakFindingandMeasurement.htm
% T. C. O'Haver, Version 2.1, September, 2011
if nargin~=7;smoothtype=1;end  % smoothtype=1 if not specified in argument
if smoothtype>3;smoothtype=3;end
if smoothtype<1;smoothtype=1;end
smoothwidth=round(smoothwidth);
peakgroup=round(peakgroup);
d=fastsmooth(deriv(y),smoothwidth,smoothtype);
n=round(peakgroup/2+1);
V=[0 0 0 0 0];
vectorlength=length(y);
peak=1;
AmpTest=AmpThreshold;
for j=smoothwidth:length(y)-smoothwidth,
if sign(d(j)) < sign (d(j+1)), % Detects zero-crossing
if d(j+1)-d(j) > SlopeThreshold*y(j), % if slope of derivative is larger than SlopeThreshold
if y(j) > AmpTest,  % if height of valley is larger than AmpThreshold
xx=zeros(size(peakgroup));yy=zeros(size(peakgroup));
for k=1:peakgroup, % Create sub-group of points near valley
groupindex=j+k-n+1;
if groupindex<1, groupindex=1;end
if groupindex>vectorlength, groupindex=vectorlength;end
xx(k)=x(groupindex);yy(k)=y(groupindex);
end
[coef,S]=polyfit(xx,yy,2);  % Fit parabola to sub-group with centering and scaling
c1=coef(3);c2=coef(2);c3=coef(1);
valleyX=-c2/(2*c3);   % Compute valley position and height of fitted parabola
valleyY=(c1-(c2*c2/(4*c3)));
MeasuredWidth=norm(2.35482/(sqrt(2)*sqrt(-1*c3)));
% if the valley is too narrow for least-squares technique to work
% well, just use the min value of y in the sub-group of points near valley.
if peakgroup<5,
valleyY=min(yy);
pindex=val2ind(yy,valleyY);
valleyX=xx(pindex(1));
end
% Construct matrix P. One row for each valley
% detected, containing the valley number, valley
% position (x-value) and valley depth (y-value).
% Area is not measured for valleys, so put a zero
V(peak,:) = [round(peak) valleyX valleyY MeasuredWidth 0];
peak=peak+1;
end
end
end
end
% ----------------------------------------------------------------------
function d=deriv(a)
% First derivative of vector using 2-point central difference.
%  T. C. O'Haver, 1988.
n=length(a);
d=zeros(size(a));
d(1)=a(2)-a(1);
d(n)=a(n)-a(n-1);
for j = 2:n-1;
d(j)=(a(j+1)-a(j-1)) ./ 2;
end
% ----------------------------------------------------------------------
function SmoothY=fastsmooth(Y,w,type,ends)
% fastsmooth(Y,w,type,ends) smooths vector Y with smooth
%  of width w. Version 2.0, May 2008.
% The argument "type" determines the smooth type:
%   If type=1, rectangular (sliding-average or boxcar)
%   If type=2, triangular (2 passes of sliding-average)
%   If type=3, pseudo-Gaussian (3 passes of sliding-average)
% The argument "ends" controls how the "ends" of the signal
% (the first w/2 points and the last w/2 points) are handled.
%   If ends=0, the ends are zero.  (In this mode the elapsed
%     time is independent of the smooth width). The fastest.
%   If ends=1, the ends are smoothed with progressively
%     smaller smooths the closer to the end. (In this mode the
%     elapsed time increases with increasing smooth widths).
% fastsmooth(Y,w,type) smooths with ends=0.
% fastsmooth(Y,w) smooths with type=1 and ends=0.
% Example:
% fastsmooth([1 1 1 10 10 10 1 1 1 1],3)= [0 1 4 7 10 7 4 1 1 0]
% fastsmooth([1 1 1 10 10 10 1 1 1 1],3,1,1)= [1 1 4 7 10 7 4 1 1 1]
%  T. C. O'Haver, May, 2008.
if nargin==2, ends=0; type=1; end
if nargin==3, ends=0; end
switch type
case 1
SmoothY=sa(Y,w,ends);
case 2
SmoothY=sa(sa(Y,w,ends),w,ends);
case 3
SmoothY=sa(sa(sa(Y,w,ends),w,ends),w,ends);
end

function SmoothY=sa(Y,smoothwidth,ends)
w=round(smoothwidth);
SumPoints=sum(Y(1:w));
s=zeros(size(Y));
halfw=round(w/2);
L=length(Y);
for k=1:L-w,
s(k+halfw-1)=SumPoints;
SumPoints=SumPoints-Y(k);
SumPoints=SumPoints+Y(k+w);
end
s(k+halfw)=sum(Y(L-w+1:L));
SmoothY=s./w;
% Taper the ends of the signal if ends=1.
if ends==1,
startpoint=(smoothwidth + 1)/2;
SmoothY(1)=(Y(1)+Y(2))./2;
for k=2:startpoint,
SmoothY(k)=mean(Y(1:(2*k-1)));
SmoothY(L-k+1)=mean(Y(L-2*k+2:L));
end
SmoothY(L)=(Y(L)+Y(L-1))./2;
end
% ----------------------------------------------------------------------
function [FitResults,LowestError,BestStart,xi,yi]=peakfit(signal,center,window,NumPeaks,peakshape,extra,NumTrials,start,AUTOZERO,fixedwidth)
% Version 2.6: June, 2012. Added fixed-width Gaussian and Lorentzian

global AA xxx PEAKHEIGHTS FIXEDWIDTH

format short g
format compact
warning off all

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
xoffset=center-window/2;
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=1;
case 2
NumPeaks=1;
peakshape=1;
extra=0;
NumTrials=1;
xx=signal;yy=center;
start=calcstart(xx,NumPeaks,xoffset);
AUTOZERO=1;
case 3
NumPeaks=1;
peakshape=1;
extra=0;
NumTrials=1;
start=calcstart(xx,NumPeaks,xoffset);
AUTOZERO=1;
case 4
peakshape=1;
extra=0;
NumTrials=1;
start=calcstart(xx,NumPeaks,xoffset);
AUTOZERO=1;
case 5
extra=0;
NumTrials=1;
start=calcstart(xx,NumPeaks,xoffset);
AUTOZERO=1;
case 6
NumTrials=1;
start=calcstart(xx,NumPeaks,xoffset);
AUTOZERO=1;
case 7
start=calcstart(xx,NumPeaks,xoffset);
AUTOZERO=1;
case 8
AUTOZERO=1;
case 10
FIXEDWIDTH=fixedwidth;
otherwise
end % switch nargin

% Default values for placeholder zeros
if NumTrials==0;NumTrials=1;end
if peakshape==0;peakshape=1;end
if NumPeaks==0;NumPeaks=1;end
if start==0;start=calcstart(xx,NumPeaks,xoffset);end
if FIXEDWIDTH==0, FIXEDWIDTH=length(xx)/10;end

% Remove linear baseline from data segment if AUTOZERO==1
X1=min(xx);
X2=max(xx);
bkgsize=round(length(xx)/10);
if bkgsize<2,bkgsize=2;end
if AUTOZERO==1, % linear autozero operation
Y1=mean(yy(1:bkgsize));
Y2=mean(yy((length(xx)-bkgsize):length(xx)));
yy=yy-((Y2-Y1)/(X2-X1)*(xx-X1)+Y1);
end % if
lxx=length(xx);
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;
switch NumPeaks
case 1
newstart(1)=start(1)-xoffset;
case 2
newstart(1)=start(1)-xoffset;
newstart(3)=start(3)-xoffset;
case 3
newstart(1)=start(1)-xoffset;
newstart(3)=start(3)-xoffset;
newstart(5)=start(5)-xoffset;
case 4
newstart(1)=start(1)-xoffset;
newstart(3)=start(3)-xoffset;
newstart(5)=start(5)-xoffset;
newstart(7)=start(7)-xoffset;
case 5
newstart(1)=start(1)-xoffset;
newstart(3)=start(3)-xoffset;
newstart(5)=start(5)-xoffset;
newstart(7)=start(7)-xoffset;
newstart(9)=start(9)-xoffset;
case 6
newstart(1)=start(1)-xoffset;
newstart(3)=start(3)-xoffset;
newstart(5)=start(5)-xoffset;
newstart(7)=start(7)-xoffset;
newstart(9)=start(9)-xoffset;
newstart(11)=start(11)-xoffset;
otherwise
end % switch NumPeaks

% Perform peak fitting for selected peak shape using fminsearch function
options = optimset('TolX',.00001,'Display','off' );
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,
% disp(['Trial number ' num2str(k) ] ) % optionally prints the current trial number as progress indicator
switch peakshape
case 1
TrialParameters=fminsearch(@fitgaussian,newstart,options,xx,yy);
ShapeString='Gaussian';
case 2
TrialParameters=fminsearch(@fitlorentzian,newstart,options,xx,yy);
ShapeString='Lorentzian';
case 3
TrialParameters=fminsearch(@fitlogistic,newstart,options,xx,yy);
ShapeString='Logistic';
case 4
TrialParameters=fminsearch(@fitpearson,newstart,options,xx,yy,extra);
ShapeString='Pearson';
case 5
zxx=[zeros(size(xx)) xx zeros(size(xx)) ];
zyy=[zeros(size(yy)) yy zeros(size(yy)) ];
TrialParameters=fminsearch(@fitexpgaussian,newstart,options,zxx,zyy,-extra);
ShapeString='ExpGaussian';
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(@fitewgaussian,cwnewstart,options,xx,yy);
ShapeString='Equal width Gaussians';
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(@fitlorentziancw,cwnewstart,options,xx,yy);
ShapeString='Equal width Lorentzians';
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(@fitexpewgaussian,cwnewstart,options,xx,yy,-extra);
ShapeString='Exp. equal width Gaussians';
case 9
TrialParameters=fminsearch(@fitexppulse,newstart,options,xx,yy);
ShapeString='Exponential Pulse';
case 10
TrialParameters=fminsearch(@fitsigmoid,newstart,options,xx,yy);
ShapeString='Sigmoid';
case 11
fixedstart=[];
for pc=1:NumPeaks,
fixedstart(pc)=min(xx)+pc.*(max(xx)-min(xx))./(NumPeaks+1);
end
TrialParameters=fminsearch(@FitFWGaussian,fixedstart,options,xx,yy);
ShapeString='Fixed-width Gaussian';
case 12
fixedstart=[];
for pc=1:NumPeaks,
fixedstart(pc)=min(xx)+pc.*(max(xx)-min(xx))./(NumPeaks+1);
end
TrialParameters=fminsearch(@FitFWLorentzian,fixedstart,options,xx,yy);
ShapeString='Fixed-width Lorentzian';
otherwise
end % switch peakshape

% Construct model from Trial parameters
A=zeros(NumPeaks,n);
for m=1:NumPeaks,
switch peakshape
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,:)=sigmoid(xx,TrialParameters(2*m-1),TrialParameters(2*m));
case 11
A(m,:)=gaussian(xx,TrialParameters(m),FIXEDWIDTH);
case 12
A(m,:)=lorentzian(xx,TrialParameters(m),FIXEDWIDTH);
otherwise
end % switch
switch NumPeaks % adds random variation to non-linear parameters
case 1
newstart=[newstart(1)*(1+randn/50) newstart(2)*(1+randn/10)];
case 2
newstart=[newstart(1)*(1+randn/50) newstart(2)*(1+randn/10) newstart(3)*(1+randn/50) newstart(4)*(1+randn/10)];
case 3
newstart=[newstart(1)*(1+randn/50) newstart(2)*(1+randn/10) newstart(3)*(1+randn/50) newstart(4)*(1+randn/10) newstart(5)*(1+randn/50) newstart(6)*(1+randn/10)];
case 4
newstart=[newstart(1)*(1+randn/50) newstart(2)*(1+randn/10) newstart(3)*(1+randn/50) newstart(4)*(1+randn/10) newstart(5)*(1+randn/50) newstart(6)*(1+randn/10)  newstart(7)*(1+randn/50) newstart(8)*(1+randn/10)];
case 5
newstart=[newstart(1)*(1+randn/50) newstart(2)*(1+randn/10) newstart(3)*(1+randn/50) newstart(4)*(1+randn/10) newstart(5)*(1+randn/50) newstart(6)*(1+randn/10)  newstart(7)*(1+randn/50) newstart(8)*(1+randn/10)  newstart(9)*(1+randn/50) newstart(10)*(1+randn/10)];
otherwise
end % switch NumPeaks
end % for
% Multiplies each row by the corresponding amplitude and adds them up
model=PEAKHEIGHTS'*A;

% 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(PEAKHEIGHTS)>0,  % 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=PEAKHEIGHTS; % 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,100);
xxx=linspace(min(xx),max(xx));
for m=1:NumPeaks,
switch peakshape
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,:)=sigmoid(xxx,FitParameters(2*m-1),FitParameters(2*m));
case 11
AA(m,:)=gaussian(xxx,FitParameters(m),FIXEDWIDTH);
case 12
AA(m,:)=lorentzian(xxx,FitParameters(m),FIXEDWIDTH);
otherwise
end % switch
end % for

% 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;
else
mmodel=height*AA;
end
% Top half of the figure shows original signal and the fitted model.
subplot(2,1,1);plot(xx+xoffset,yy,'b.'); % Plot the original signal in blue dots
hold on
for m=1:NumPeaks,
plot(xxx+xoffset,height(m)*AA(m,:),'g')  % 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

% Mark starting peak positions with vertical dashed lines
for marker=1:NumPeaks,
markx=BestStart((2*marker)-1);
subplot(2,1,1);plot([markx+xoffset markx+xoffset],[0 max(yy)],'m--')
end % for
plot(xxx+xoffset,mmodel,'r');  % Plot the total model (sum of component peaks) in red lines
hold off;
axis([min(xx)+xoffset max(xx)+xoffset min(yy) max(yy)]);
switch AUTOZERO,
case 0
title('Peakfit 2.6. Autozero OFF.')
case 1
title('Peakfit 2.6. Linear autozero.')
case 2
end
if peakshape==4||peakshape==5||peakshape==8, % Shapes with Extra factor
xlabel(['Peaks = ' num2str(NumPeaks) '     Shape = ' ShapeString '     Error = ' num2str(round(100*LowestError)/100) '%    Extra = ' num2str(extra) ] )
else
xlabel(['Peaks = ' num2str(NumPeaks) '     Shape = ' ShapeString '     Error = ' num2str(round(100*LowestError)/100) '%' ] )
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')

% 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==6||peakshape==7||peakshape==8, % equal-width peak models
FitResults=[[round(m) FitParameters(m)+xoffset height(m) abs(FitParameters(NumPeaks+1)) area(m)]];
else
if peakshape==11||peakshape==12,
FitResults=[[round(m) FitParameters(m)+xoffset height(m) FIXEDWIDTH 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==6||peakshape==7||peakshape==8, % equal-width peak models
FitResults=[FitResults ; [round(m) FitParameters(m)+xoffset height(m) abs(FitParameters(NumPeaks+1)) area(m)]];
else
if peakshape==11||peakshape==12,
FitResults=[FitResults ; [round(m) FitParameters(m)+xoffset height(m) FIXEDWIDTH 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

% Display Fit Results on upper graph
subplot(2,1,1);
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==9||peakshape==10,
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
% ----------------------------------------------------------------------
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/5];
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
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
PEAKHEIGHTS = abs(A\y');
z = A*PEAKHEIGHTS;
err = norm(z-y');
% ----------------------------------------------------------------------
function err = fitewgaussian(lambda,t,y)
% Fitting function for a Gaussian band signal with equal peak widths.
global PEAKHEIGHTS
numpeaks=round(length(lambda)-1);
A = zeros(length(t),numpeaks);
for j = 1:numpeaks,
A(:,j) = gaussian(t,lambda(j),lambda(numpeaks+1))';
end
PEAKHEIGHTS = abs(A\y');
z = A*PEAKHEIGHTS;
err = norm(z-y');
% ----------------------------------------------------------------------
function err = FitFWGaussian(lambda,t,y)
%	Fitting function for a fixed width Gaussian
global PEAKHEIGHTS FIXEDWIDTH
numpeaks=round(length(lambda));
A = zeros(length(t),numpeaks);
for j = 1:numpeaks,
A(:,j) = gaussian(t,lambda(j),FIXEDWIDTH)';
end
PEAKHEIGHTS = abs(A\y');
z = A*PEAKHEIGHTS;
err = norm(z-y');
% ----------------------------------------------------------------------
function err = FitFWLorentzian(lambda,t,y)
%	Fitting function for a fixed width Gaussian
global PEAKHEIGHTS FIXEDWIDTH
numpeaks=round(length(lambda));
A = zeros(length(t),numpeaks);
for j = 1:numpeaks,
A(:,j) = lorentzian(t,lambda(j),FIXEDWIDTH)';
end
PEAKHEIGHTS = abs(A\y');
z = A*PEAKHEIGHTS;
err = norm(z-y');
% ----------------------------------------------------------------------
function err = fitlorentziancw(lambda,t,y)
% Fitting function for a Lorentzian band signal with equal peak widths.
global PEAKHEIGHTS
numpeaks=round(length(lambda)-1);
A = zeros(length(t),numpeaks);
for j = 1:numpeaks,
A(:,j) = lorentzian(t,lambda(j),lambda(numpeaks+1))';
end
PEAKHEIGHTS = abs(A\y');
z = A*PEAKHEIGHTS;
err = norm(z-y');
% ----------------------------------------------------------------------
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)./(0.6005612.*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
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
PEAKHEIGHTS = A\y';
z = A*PEAKHEIGHTS;
err = norm(z-y');
% ----------------------------------------------------------------------
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
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
PEAKHEIGHTS = A\y';
z = A*PEAKHEIGHTS;
err = norm(z-y');
% ----------------------------------------------------------------------
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 = fitlognormal(lambda,t,y)
%	Fitting function for lognormal, lambda(1)=position, lambda(2)=width
%	between the data and the values computed by the current
%	function of lambda.  Fitlognormal assumes a lognormal function
%  T. C. O'Haver, May 2006
global PEAKHEIGHTS
A = zeros(length(t),round(length(lambda)/2));
for j = 1:length(lambda)/2,
A(:,j) = lognormal(t,lambda(2*j-1),lambda(2*j))';
end
PEAKHEIGHTS = A\y';
z = A*PEAKHEIGHTS;
err = norm(z-y');
% ----------------------------------------------------------------------
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 = 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
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
PEAKHEIGHTS = A\y';
z = A*PEAKHEIGHTS;
err = norm(z-y');
% ----------------------------------------------------------------------
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
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
PEAKHEIGHTS = A\y';
z = A*PEAKHEIGHTS;
err = norm(z-y');
% ----------------------------------------------------------------------
function err = fitexpewgaussian(lambda,t,y,timeconstant)
% Fitting function for exponentially-broadened Gaussian bands with equal peak widths.
global PEAKHEIGHTS
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
PEAKHEIGHTS = abs(A\y');
z = A*PEAKHEIGHTS;
err = norm(z-y');
% ----------------------------------------------------------------------
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)./(0.6005612.*wid)) .^2);
% ----------------------------------------------------------------------
% ExpBroaden(y,t) convolutes y by an exponential decay of time constant t
% by multiplying Fourier transforms and inverse transforming the result.
ly=length(y);
ey=[zeros(size(y));y;zeros(size(y))];
fy=fft(ey);
a=exp(-(1:length(fy))./t);
fa=fft(a);
fy1=fy.*fa';
ybz=real(ifft(fy1))./sum(a);
yb=ybz(ly+2:length(ybz)-ly+1);
% ----------------------------------------------------------------------
function err = fitexppulse(tau,x,y)
% Iterative fit of the sum of exponental pulses
% of the form Height.*exp(-tau1.*x).*(1-exp(-tau2.*x)))
global PEAKHEIGHTS
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
PEAKHEIGHTS =abs(A\y');
z = A*PEAKHEIGHTS;
err = norm(z-y');
% ----------------------------------------------------------------------
function g = exppulse(x,t1,t2)
% Exponential pulse of the form
% Height.*exp(-tau1.*x).*(1-exp(-tau2.*x)))
e=(x-t1)./t2;
p = 4*exp(-e).*(1-exp(-e));
p=p .* [p>0];
g = p';
% ----------------------------------------------------------------------
function err = fitsigmoid(tau,x,y)
% Fitting function for iterative fit to the sum of
% sigmiods of the form Height./(1 + exp((t1 - t)/t2))
global PEAKHEIGHTS
A = zeros(length(x),round(length(tau)/2));
for j = 1:length(tau)/2,
A(:,j) = sigmoid(x,tau(2*j-1),tau(2*j));
end
PEAKHEIGHTS = A\y';
z = A*PEAKHEIGHTS;
err = norm(z-y');
% ----------------------------------------------------------------------
function g=sigmoid(x,t1,t2)
g=1./(1 + exp((t1 - x)./t2))';
```