www.gusucode.com > 峰值搜索源码程序 > 峰值搜索源码程序/PeakFinder/findpeaksE.m
function P=findpeaksE(x,y,SlopeThreshold,AmpThreshold,smoothwidth,peakgroup,smoothtype)
% function
% P=findpeaksE(x,y,SlopeThreshold,AmpThreshold,smoothwidth,peakgroup,smootht
% ype) 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 matrix (P) containing
% peak number and position, height, width, area, and percent fitting error
% 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 5.3, Last revised December, 2014
% Example 1: x=[0:.01:50];y=cos(x);P=findpeaksE(x,y,0,-1,5,5)
% Example 2: x=[0:.01:2];y=humps(x);P=findpeaksE(x,y,0,-.01,5,5)
% Example 3:
% x=[0:.01:5];y=x.*sin(x.^2).^2+.1*whitenoise(x);
% P=findpeaksE(x,y,.0001,1,15,10)
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 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+1;
if groupindex<1, groupindex=1;end
if groupindex>vectorlength, groupindex=vectorlength;end
xx(k)=rmnan(x(groupindex));yy(k)=rmnan(y(groupindex));
end
[Height, Position, Width]=gaussfit(xx,yy);
PeakX=real(Position); % Compute peak position and height of fitted parabola
PeakY=real(Height);
MeasuredWidth=real(Width);
residual=yy-PeakY*gaussian(xx,PeakX,MeasuredWidth);
Error=100.*abs(stdev(residual)./PeakY);
% 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).
if isnan(PeakX) || isnan(PeakY) || PeakY<AmpThreshold,
else
P(peak,:) = [round(peak) PeakX PeakY MeasuredWidth 1.0646.*PeakY*MeasuredWidth Error];
peak=peak+1;
end
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 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 a=rmnan(a)
% Removes NaNs and Infs from vectors, replacing with nearest real numbers.
% Example:
% >> v=[1 2 3 4 Inf 6 7 Inf 9];
% >> rmnan(v)
% ans =
% 1 2 3 4 4 6 7 7 9
la=length(a);
if isnan(a(1)) || isinf(a(1)),a(1)=0;end
for point=1:la,
if isnan(a(point)) || isinf(a(point)),
a(point)=a(point-1);
end
end
% ----------------------------------------------------------------------
function y=smoothnegs(y)
% Replaces zeros and negative points with 2 passes of 3-point average
ly=length(y);
if min(y)<=0,
if y(1)<=0,y(1)=y(1)+y(2)+y(3)./3;end
for pnt=2:ly-1,
if y(pnt)<=0,y(pnt)=y(pnt-1)+y(pnt)+y(pnt+1)./3;end
end
if y(ly)<=0,y(ly)=y(ly-2)+y(ly-1)+y(ly)./3;end
end
if min(y)<=0,
if y(1)<=0,y(1)=y(1)+y(2)+y(3)./3;end
for pnt=2:ly-1,
if y(pnt)<=0,y(pnt)=y(pnt-1)+y(pnt)+y(pnt+1)./3;end
end
if y(ly)<=0,y(ly)=y(ly-2)+y(ly-1)+y(ly)./3;end
end
% ----------------------------------------------------------------------
function [Height, Position, Width]=gaussfit(x,y)
% Converts y-axis to a log scale, fits a parabola
% (quadratic) to the (x,ln(y)) data, then calculates
% the position, width, and height of the
% Gaussian from the three coefficients of the
% quadratic fit. This is accurate only if the data have
% no baseline offset (that is, trends to zero far off the
% peak) and if there are no zeros or negative values in y.
%
% Example 1: Simplest Gaussian data set
% [Height, Position, Width]=gaussfit([1 2 3],[1 2 1])
% returns Height = 2, Position = 2, Width = 2
%
% Example 2: best fit to synthetic noisy Gaussian
% x=50:150;y=100.*gaussian(x,100,100)+10.*randn(size(x));
% [Height,Position,Width]=gaussfit(x,y)
% returns [Height,Position,Width] clustered around 100,100,100.
%
% Example 3: plots data set as points and best-fit Gaussian as line
% x=[1 2 3 4 5];y=[1 2 2.5 2 1];
% [Height,Position,Width]=gaussfit(x,y);
% plot(x,y,'o',linspace(0,8),Height.*gaussian(linspace(0,8),Position,Width))
% Copyright (c) 2012, Thomas C. O'Haver
maxy=max(y);
for p=1:length(y),
if y(p)<(maxy/100),y(p)=maxy/100;end
end % for p=1:length(y),
z=log(y);
coef=polyfit(x,z,2);
a=coef(3);
b=coef(2);
c=coef(1);
Height=exp(a-c*(b/(2*c))^2);
Position=-b/(2*c);
Width=2.35482/(sqrt(2)*sqrt(-c));
function stddev=stdev(a)
% Octave and Matlab compatible standard deviation function
sa=size(a);
reshape(a,1,length(a));
if sa(1)>sa(2),
stddev=std(a);
else
stddev=(std(a'));
end;