P=findpeaks(x,y,SlopeThreshold,AmpThreshold,smoothwidth,peakgroup)

function P=findpeaks(x,y,SlopeThreshold,AmpThreshold,smoothwidth,peakgroup)
% function P=findpeaks(x,y,SlopeThreshold,AmpThreshold,smoothwidth,peakgroup)
% Function to locate the positive peaks in a noisy x-y 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, and width of each peak. SlopeThreshold,
% AmpThreshold, and smoothwidth control sensitivity
% Higher values will neglect smaller features. Peakgroup
% is the number of points around the "top part" of the peak.
% T. C. O'Haver, 1995.  Version 2  Last revised Oct 27, 2006
smoothwidth=round(smoothwidth);
peakgroup=round(peakgroup);
d=fastsmooth(deriv(y),smoothwidth);
n=round(peakgroup/2+1);
P=[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
          for k=1:peakgroup, % Create sub-group of points near peak
              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,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).*2.35703/(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<7,
             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];
          peak=peak+1;
        end
      end
   end
end

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 ([e-mail]) 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);