function?V=findvalleys（xySlopeThresholdAmpThresholdsmoothwidthpeakgroupsmoothtype）
%?function?P=findvalleys（xySlopeThresholdAmpThresholdsmoothwidthpeakgroupsmoothtype）
%?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?3.1?June?2013
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）smoothwidthsmoothtype）;
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））?????????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
????????????????[coefSMU]=polyfit（xxyy2）;??%?Fit?parabola?to?sub-group?with?centering?and?scaling
????????????????c1=coef（3）;c2=coef（2）;c3=coef（1）;
????????????????valleyX=-（（MU（2）.*c2/（2*c3））-MU（1））;????%?Compute?valley?position?and?height?of?fitted?parabola
????????????????valleyY=（c1-（c2*c2/（4*c3）））;
????????????????MeasuredWidth=norm（MU（2）.*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
????????????????????valley