3.12

FindPeaks v1

../_images/FindPeaks-v1_dlg.png

FindPeaks dialog.

Summary

Searches for peaks in a dataset.

Properties

Name Direction Type Default Description
InputWorkspace Input MatrixWorkspace Mandatory Name of the workspace to search
WorkspaceIndex Input number Optional If set, only this spectrum will be searched for peaks (otherwise all are)
FWHM Input number 7 Estimated number of points covered by the fwhm of a peak (default 7)
Tolerance Input number 4 A measure of the strictness desired in meeting the condition on peak candidates, Mariscotti recommends 2 (default 4)
PeakPositions Input dbl list   Optional: enter a comma-separated list of the expected X-position of the centre of the peaks. Only peaks near these positions will be fitted.
FitWindows Input dbl list   Optional: enter a comma-separated list of the expected X-position of windows to fit. The number of values must be exactly double the number of specified peaks.
PeakFunction Input string Gaussian Allowed values: [‘BackToBackExponential’, ‘Bk2BkExpConvPV’, ‘DeltaFunction’, ‘ElasticDiffRotDiscreteCircle’, ‘ElasticDiffSphere’, ‘ElasticIsoRotDiff’, ‘ExamplePeakFunction’, ‘Gaussian’, ‘IkedaCarpenterPV’, ‘Lorentzian’, ‘PseudoVoigt’, ‘Voigt’]
BackgroundType Input string Linear Type of Background. Allowed values: [‘Flat’, ‘Linear’, ‘Quadratic’]
HighBackground Input boolean True Relatively weak peak in high background
MinGuessedPeakWidth Input number 2 Minimum guessed peak width for fit. It is in unit of number of pixels.
MaxGuessedPeakWidth Input number 10 Maximum guessed peak width for fit. It is in unit of number of pixels.
GuessedPeakWidthStep Input number 2 Step of guessed peak width. It is in unit of number of pixels.
PeakPositionTolerance Input number Optional Tolerance on the found peaks’ positions against the input peak positions. Non-positive value indicates that this option is turned off.
PeaksList Output TableWorkspace Mandatory The name of the TableWorkspace in which to store the list of peaks found
RawPeakParameters Input boolean False false generates table with effective centre/width/height parameters. true generates a table with peak function parameters
MinimumPeakHeight Input number 2.22507385851e-308 Minimum allowed peak height.
MinimumPeakHeightObs Input number 0 Least value of the maximum observed Y value of a peak within specified region. If any peak’s maximum observed Y value is smaller, then this peak will not be fit. It is designed for EventWorkspace with integer counts.
CostFunction Input string Chi-Square Cost functions. Allowed values: [‘Chi-Square’, ‘Rwp’]
Minimizer Input string Levenberg-MarquardtMD Minimizer to use for fitting. Minimizers available are “Levenberg-Marquardt”, “Simplex”,”Conjugate gradient (Fletcher-Reeves imp.)”, “Conjugate gradient (Polak-Ribiere imp.)”, “BFGS”, and “Levenberg-MarquardtMD”. Allowed values: [‘BFGS’, ‘Conjugate gradient (Fletcher-Reeves imp.)’, ‘Conjugate gradient (Polak-Ribiere imp.)’, ‘Damped GaussNewton’, ‘FABADA’, ‘Levenberg-Marquardt’, ‘Levenberg-MarquardtMD’, ‘Simplex’, ‘SteepestDescent’, ‘Trust Region’]
StartFromObservedPeakCentre Input boolean True Use observed value as the starting value of peak centre.

Description

This algorithm searches the specified spectra in a workspace for peaks, returning a list of the found and successfully fitted peaks. The search algorithm is described in full in reference [1]. In summary: the second difference of each spectrum is computed and smoothed. This smoothed data is then searched for patterns consistent with the presence of a peak. The list of candidate peaks found is passed to a fitting routine and those that are successfully fitted are kept and returned in the output workspace (and logged at information level). The output TableWorkspace contains columns, which reflect the fact that the peak has been fitted to a peak function atop a background: spectrum, centre, width, height, backgroundintercept and backgroundslope. Setting RawPeakParameters=True will give the actual peak fit parameters rather than this abstraction.

Subalgorithms used

FindPeaks uses the SmoothData v1 algorithm to, well, smooth the data - a necessary step to identify peaks in statistically fluctuating data. The Fit v1 algorithm is used to fit candidate peaks.

Treating weak peaks vs. high background

FindPeaks uses a more complicated approach to fit peaks if HighBackground is flagged. In this case, FindPeak will fit the background first, and then do a Gaussian fit the peak with the fitted background removed. This procedure will be repeated for a couple of times with different guessed peak widths. And the parameters of the best result is selected. The last step is to fit the peak with a combo function including background and Gaussian by using the previously recorded best background and peak parameters as the starting values.

Criteria To Validate Peaks Found

FindPeaks finds peaks by fitting a Guassian with background to a certain range in the input histogram. Fit v1 may not give a correct result even if chi^2 is used as criteria alone. Thus some other criteria are provided as options to validate the result

  1. Peak position. If peak positions are given, and trustful, then the fitted peak position must be within a short distance to the give one.
  2. Peak height. In the certain number of trial, peak height can be used to select the best fit among various starting sigma values.

Fit Window

If FitWindows is defined, then a peak’s range to fit (i.e., x-min and x-max) is confined by this window.

If FitWindows is defined, starting peak centres are NOT user’s input, but found by highest value within peak window. (Is this correct???)

Estimation of peak’s background and range

If FindPeaksBackground fails, then it is necessary to estimate a rough peak range and background according to observed data.

  1. Assume the local background (within the given fitting window) is close to linear;
  2. Take the first 3 and last 3 data points to calcualte the linear background;
  3. Remove background (rougly) and calcualte peak’s height, width, and centre;
  4. If the peak centre (starting value) uses observed value, then set peakcentre to that value. Otherwise, set it to given value;
  5. Get the bin indexes of xmin, xmax and peakcentre;
  6. Calcualte peak range, i.e., left and right boundary;
  7. If any peak boundary exceeds or too close to the boundary, there will be 2 methods to solve this issue;
    1. If peak centre is restricted to given value, then the peak range will be from 1/6 to 5/6 of the given data points;
    2. If peak centre is set to observed value, then the 3 leftmost data points will be used for background.

See also

The peak shape functions and background functions for details on the various functions. The documentation for minimizers.

References

  1. M.A.Mariscotti, A method for automatic identification of peaks in the presence of background and its application to spectrum analysis , NIM 50 (1967) 309

Usage

Example - Find a single peak:

ws = CreateSampleWorkspace(Function="User Defined", UserDefinedFunction="name=LinearBackground, \
   A0=0.3;name=Gaussian, PeakCentre=5, Height=10, Sigma=0.7", NumBanks=1, BankPixelWidth=1, XMin=0, XMax=10, BinWidth=0.1)

table = FindPeaks(InputWorkspace='ws', FWHM='20')

row = table.row(0)

print("Peak 1 {Centre: %.3f, width: %.3f, height: %.3f }" % ( row["centre"],  row["width"], row["height"]))

Output:

Peak 1 {Centre: 5.050, width: 1.648, height: 10.000 }

Categories: Algorithms | Optimization\PeakFinding

Source

C++ source: FindPeaks.cpp (last modified: 2018-02-22)

C++ header: FindPeaks.h (last modified: 2018-02-22)