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I have been looking at some spike detection code, I use some that I developed, but I was wondering if there were better ideas. So I have been trying a few. This code - from yesterday - intrigued me until I looked at it and decided the basic algorithm is not really good,

```
PeakDetect = 0
filteredY = 0.0
filteredY(1:lag+1) = y(1:lag+1)
avgFilter = 0.0
avgFilter(lag+1) = mean(y(1:2*lag+1))
stdFilter = 0.0
stdFilter(lag+1) = std(y(1:2*lag+1))
write(*,100)1,lag + 1,2*lag+1, avgFilter(lag+1), stdFilter(lag+1)
100 Format(3(i6," "),2(F10.5," "))
if (stdFilter(lag+1)/avgFilter(lag+1)>0.1) then ! If the coefficient of variation exceeds 10%, the signal is too uneven at the start, possibly because of a peak.
write(unit=*,fmt=1001)
1001 format(1X,'Warning: Peak detection might have failed, as there may be a peak at the edge of the frequency range.',/)
end if
```

as it assumes that if we determine the average over a length and the standard deviation - then if the coefficient of variation is more than 10% you have a spike at the beginning.

Whereas a set of numbers with mean close to zero will trip this every time.

Interesting problem.

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The concept for the code is ok, somewhat, it is the implementation that is suspect. The coder does a look ahead and determines an average and stdev about a set of numbers centered on the value of interest, but in the code, the coder sets the forward values to zero.

Interesting.

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```
function PeakDetect(y,lag,threshold, influence)
implicit none
! Declaring part
real, dimension(:), intent(in) :: y
real, dimension(size(y)) :: filteredY, avgFilter, stdFilter, PD, PeakDetect
integer :: lag, ii
real :: threshold, influence
!real mean
!real std
! Executing part
PD = 0.0
filteredY = Y
filteredY(1:lag+1) = y(1:lag+1)
avgFilter = 0.0
avgFilter(lag+1) = mean(y(1:2*lag+1))
stdFilter = 0.0
stdFilter(lag+1) = std(y(1:2*lag+1))
write(*,100)1,y(1)*1000.0,1,2*lag+1, avgFilter(lag+1), stdFilter(lag+1),0, 1
100 Format((i6," "),F10.5," ", 2(i6," "),4(F10.5," "))
if (stdFilter(lag+1)/avgFilter(lag+1)>0.1) then ! If the coefficient of variation exceeds 10%, the signal is too uneven at the start, possibly because of a peak.
write(unit=*,fmt=1001)
1001 format(1X,'Warning: Peak detection might have failed, as there may be a peak at the edge of the frequency range.',/)
end if
do ii = lag+2, (size(y)-1)
if (abs(y(ii) - avgFilter(ii-1)) > threshold * stdFilter(ii-1)) then
! Find only the largest outstanding value which is only the one greater than its predecessor and its successor
write(*,*)ii,(y(ii)-avgFilter(ii-1)),y(ii)-y(ii-1),y(ii)-y(ii+1)
if (y(ii) > avgFilter(ii-1) .AND. y(ii) > y(ii-1) .AND. y(ii) > y(ii+1)) then
PD(ii) = 1
write(*,*)"here"
end if
filteredY(ii) = influence * y(ii) + (1 - influence) * filteredY(ii-1)
else
filteredY(ii) = y(ii)
end if
! Modified with respect to the original code. Mean and standard deviation are calculted symmetrically around the current point
avgFilter(ii) = mean(filteredY(ii-lag:ii+lag))
stdFilter(ii) = std(filteredY(ii-lag:ii+lag))
write(*,100)ii,y(ii)*1000.0,ii-lag,ii+lag, avgFilter(ii)*1000.0, stdFilter(ii)*1000.0,PD(ii),(y(ii)-avgFilter(ii))/stdFilter(ii)
end do
PeakDetect = PD
end function PeakDetect
```

So the function is called PeakDetect, in the original code, the coder set values of PeakDetect(i) = 1.0, but when you do a debug, the PeakDetect array does not turn up in the autos, and the values array returned are all zero, but if I create an array PD, and do PeakDetect = PD just before the return it works normally and I can see PD in the autos.

Is this normal behaviour. At least now I am getting peaks, just to many.

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The interesting challenge with modern bulk data is you start to pick up the things that are non-Gaussian, this picture shows a typical sample. The pattern repeats at 512 -- binary system, and you can see the non- Gaussian at about 100 into the 512 segment. Often the problem with non-Gaussian is the distribution is not symmetric and has a much broader range than the Gaussian stuff. But the Gaussian stuff gives you a nice smooth middle set.

The trick is determining the Gaussian from non-Gaussian. And now fixing the rather common filter above for more difficult data.

The challenge is not having to much of the big data, you can use extreme techniques the problem is people want the benefits of big data without the waiting time. ie how long does it take paint to dry, no do not stick your finger in the wet paint to test it.

Interesting fun.

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This is a topic for which a lot of algorithms have been thought of. I have myself implemented a few, based on the available literature, though not (yet) in Fortran.

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This is a problem in that each of the 512 points in a segment is drawn from an individual probability distribution that is being driven by a distinct and separate linearly independent equation and so the results are not at all Gaussian and so using means and std is a real challenge, not over the long term, if you have 5 million data sets it is not hard, but people want an answer in 2 to 4 minutes, each 512 is 8 seconds, so we have from 14 to 28 data sets.

The interesting problem is to confirm that the current method is the best.

Fortran is missing many things, unfortunately, but that is its beauty it is stable.

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This algorithm has some potential, but I am tired of having to plot the results in Excel, so I am fixing a BMP generator program in Fortran to draw simple plots of the results.

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```
subroutine circle(rgb, iA, jA, iB,jB,m1, m2, m3)
implicit none
integer iA, iB, m1,m2,m3, jA, jB, i, j, iC, jC,m4,m5,m6,iD,jD
character*1 rgb(3,ihpixf,jvpixf) ! RGB pixel data array
real iAA, iBB, jAA, jBB, iCC, jCC,iA1, jA1, delI, delJ, lenG, lenH
iAA = real(iA)
iBB = real(iB)
jAA = real(jA)
jBB = real(jB)
lenH = (abs(jBB - jAA))/2.0
iCC = (iAA+iBB)/2.0
jCC = (jAA+jBB)/2.0
iC = int(iCC)
jC = int(jCC)
iD = iB - iA
jD = jB - jA
if(id .ne. jD) then
stop "Not a circle"
endif
do 110 j = jA, jB
do 120 i = iA, iB
if(j .eq. jA .and. i .eq. iC) then
write(*,*)i,j
rgb(1,i,j) = char(m1)
rgb(2,i,j) = char(m2)
rgb(3,i,j) = char(m3)
else if(j .gt. jA .and. j .lt. jC .and. i .eq. iC) then
write(*,*)i,j
rgb(1,i,j) = char(m1)
rgb(2,i,j) = char(m2)
rgb(3,i,j) = char(m3)
elseif(j .eq. jC) then
write(*,*)"here I am ", i,j,iC,jC
rgb(1,i,j) = char(m1)
rgb(2,i,j) = char(m2)
rgb(3,i,j) = char(m3)
else if(j .gt. jC .and. j .lt. jB .and. i .eq. iC) then
write(*,*)i,j
rgb(1,i,j) = char(m1)
rgb(2,i,j) = char(m2)
rgb(3,i,j) = char(m3)
elseif(j .eq. jb.and. i .eq. iC) then
write(*,*)i,j
rgb(1,i,j) = char(m1)
rgb(2,i,j) = char(m2)
rgb(3,i,j) = char(m3)
else
write(*,*)i,j
iA1 = real(i)
jA1 = real(j)
delI = abs(iA1 - iC)
delJ = abs(jA1 - jC)
lenG = sqrt(delI*delI + delJ*delJ)
if(lenG .gt. lenH) then
if(lenH .gt. 0.9 * lenG) then
rgb(1,i,j) = char(m1)
rgb(2,i,j) = char(155)
rgb(3,i,j) = char(155)
write(*,*)"Drawn A"
else
write(*,*)"Not drawn A"
endif
else
write(*,*)"Drawn"
rgb(1,i,j) = char(m1)
rgb(2,i,j) = char(m2)
rgb(3,i,j) = char(m3)
endif
endif
120 end do
110 end do
return
end subroutine
```

The interesting part is drawing a pixelated circle, do you think it would be better to create a flag that is set in the if statements and then have a small routine for the rgb setting or how I have got it? Not sure which would be faster.

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