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FitPeaks v1¶
Summary¶
Fit one or multiple peaks in all spectra of a given workspace
Properties¶
Name |
Direction |
Type |
Default |
Description |
|---|---|---|---|---|
InputWorkspace |
Input |
Mandatory |
Name of the input workspace for peak fitting. |
|
OutputWorkspace |
Output |
Mandatory |
Name of the output workspace containing peak centers for fitting offset.The output workspace is point data.Each workspace index corresponds to a spectrum. Each X value ranges from 0 to N-1, where N is the number of peaks to fit. Each Y value is the peak position obtained by peak fitting. Negative value is used for error signals. -1 for data is zero; -2 for maximum value is smaller than specified minimum value.and -3 for non-converged fitting. |
|
StartWorkspaceIndex |
Input |
number |
0 |
Starting workspace index for fit |
StopWorkspaceIndex |
Input |
number |
Optional |
Last workspace index for fit is the smaller of this value and the workspace index of last spectrum. |
PeakCenters |
Input |
dbl list |
List of peak centers to use as initial guess for fit. |
|
PeakCentersWorkspace |
Input |
MatrixWorkspace containing referent peak centers for each spectrum, defined at the same workspace indices. |
||
PeakFunction |
Input |
string |
Gaussian |
Use of a BackToBackExponential profile is only reccomended if the coeficients to calculate A and B are defined in the instrument Parameters.xml file. Allowed values: [‘AsymmetricPearsonVII’, ‘BackToBackExponential’, ‘Bk2BkExpConvPV’, ‘DeltaFunction’, ‘ElasticDiffRotDiscreteCircle’, ‘ElasticDiffSphere’, ‘ElasticIsoRotDiff’, ‘ExamplePeakFunction’, ‘Gaussian’, ‘IkedaCarpenterPV’, ‘Lorentzian’, ‘PearsonIV’, ‘PseudoVoigt’, ‘Voigt’] |
BackgroundType |
Input |
string |
Linear |
Type of Background. Allowed values: [‘Flat’, ‘Linear’, ‘Quadratic’] |
FitWindowBoundaryList |
Input |
dbl list |
List of boundaries of the peak fitting window corresponding to PeakCenters. |
|
FitPeakWindowWorkspace |
Input |
MatrixWorkspace containing peak windows for each peak center in each spectrum, defined at the same workspace indices. |
||
PeakWidthPercent |
Input |
number |
Optional |
The estimated peak width as a percentage of the d-spacing of the center of the peak. Value must be less than 1. |
PeakParameterNames |
Input |
str list |
List of peak parameters’ names |
|
PeakParameterValues |
Input |
dbl list |
List of peak parameters’ value |
|
PeakParameterValueTable |
Input |
Name of the an optional workspace, whose each column corresponds to given peak parameter names, and each row corresponds to a subset of spectra. |
||
FitFromRight |
Input |
boolean |
True |
Flag for the order to fit peaks. If true, peaks are fitted from rightmost;Otherwise peaks are fitted from leftmost. |
Minimizer |
Input |
string |
Levenberg-Marquardt |
Minimizer to use for fitting. Allowed values: [‘BFGS’, ‘Conjugate gradient (Fletcher-Reeves imp.)’, ‘Conjugate gradient (Polak-Ribiere imp.)’, ‘Damped GaussNewton’, ‘FABADA’, ‘Levenberg-Marquardt’, ‘Levenberg-MarquardtMD’, ‘Simplex’, ‘SteepestDescent’, ‘Trust Region’] |
CostFunction |
Input |
string |
Least squares |
Cost functions. Allowed values: [‘Least squares’, ‘Rwp’] |
MaxFitIterations |
Input |
number |
50 |
Maximum number of function fitting iterations. |
FindBackgroundSigma |
Input |
number |
Optional |
Deprecated property. Use MinimumSignalToNoiseRatio instead. |
HighBackground |
Input |
boolean |
True |
Flag whether the input data has high background compared to peak heights. |
PositionTolerance |
Input |
dbl list |
List of tolerance on fitted peak positions against given peak positions.If there is only one value given, then |
|
MinimumPeakHeight |
Input |
number |
0 |
Used for validating peaks before and after fitting. If a peak’s observed/estimated or fitted height is under this value, the peak will be marked as error. |
ConstrainPeakPositions |
Input |
boolean |
True |
If true peak position will be constrained by estimated positions (highest Y value position) and the peak width either estimted by observation or calculate. |
FittedPeaksWorkspace |
Output |
Name of the output matrix workspace with fitted peak. This output workspace has the same dimension as the input workspace.The Y values belonged to peaks to fit are replaced by fitted value. Values of estimated background are used if peak fails to be fit. |
||
OutputPeakParametersWorkspace |
Output |
Mandatory |
Name of table workspace containing all fitted peak parameters. |
|
OutputParameterFitErrorsWorkspace |
Output |
Name of workspace containing all fitted peak parameters’ fitting error.It must be used along with FittedPeaksWorkspace and RawPeakParameters (True) |
||
RawPeakParameters |
Input |
boolean |
True |
false generates table with effective centre/width/height parameters. true generates a table with peak function parameters |
MinimumSignalToNoiseRatio |
Input |
number |
0 |
Used for validating peaks before fitting. If the signal-to-noise ratio is under this value, the peak will be marked as error. This does not apply to peaks for which the noise cannot be estimated. |
MinimumPeakTotalCount |
Input |
number |
Optional |
Used for validating peaks before fitting. If the total peak window Y-value count is under this value, the peak will be excluded from fitting and calibration. |
MinimumSignalToSigmaRatio |
Input |
number |
0 |
Used for validating peaks after fitting. If the signal-to-sigma ratio is under this value, the peak will be excluded from fitting and calibration. |
Description¶
This algorithm fits a set of specified peaks in a set of specified spectra in a MatrixWorkspace,
returning a list of the successfully fitted peaks along with
optional output for fitting information.
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 the following columns,
which reflect the fact that the peak has been fitted to a Gaussian atop
a linear background: spectrum, centre, width, height,
backgroundintercept & backgroundslope.
Assumption¶
It is assumed that the profile parameters of a peak at a given d-spacing, such as the peak width, are correlated between adjacent spectra (in index).
Required pre-knowledge¶
The following information are required.
Assumed position of each peak
Peak profile function
Background type (flat or linear)
Starting values of peak parameters
For better results¶
Peak fit window: this is an option
specified by user
figured out by FindPeakBackground, and peak FWHM estimated from the height and integrated intensity in the window assuming a Gaussian distribution (overwriting the peak profile parameters initialised from the reuslt of the previous spectrum).
if the workspace is in unit dSpacing and \(\Delta d/d\)
Peak position tolerance: there could be three cases for how the peak position tolerance is specified.
specified by user
defined by peak windows
half distance to the neighboring peak (if not (a) and not (b))
whole range of X-axis (if there is one and only one peak in a spectrum)
Description of algorithm¶
For each spectrum, it is assumed that there are N peaks to fit. The fitting starts from either the peak at the smallest X value or the largest X values depending on the user’s input. The first peak will be fit with the starting value provided by the user. except background and peak center, which will be determiend by observation.
Background¶
Linear background is used for fitting peaks. The background parameters will be estimated via observation.
Estimation of values of peak profiles¶
Peak height, center, and FWHM and peak center are estimated by observing the maximum value within peak fit window and calculating the first two moments.
When using peak profiles that do not have a one-to-one mapping between
effective and raw parameters, you may need to supply starting
information for more of the parameters. This can be done by specifying
PeakParameterNames and PeakParameterValues for some or all of
the parameters (e.g. Mixing for a PseudoVoigt) which
will be used for the first peak fit in each spectrum. To supply all
parameters, PeakParameterNames and PeakParameterValueTable can
be used. WARNING Partially specifying peak parameters such as
height and position will be overwritten by observed values.
Subalgorithms used¶
FitPeaks uses the Fit algorithm to fit each single peak.
FitPeaks uses the FindPeakBackground algorithm to estimate the background of each peak.
Inputs¶
The inputs tends to be general enough for various use cases.
Limitations on Partial Spectra¶
For partial spectra peak fitting, the spectra must be consecutive.
Peak positions¶
One of only one of the following will be taken.
-
At each workspace index, a “spectrum” in the form of predicted peak centers is defined.
The workspace index for each spectrum corresponds to the workspace index in the input workspace.
X value is position in d-spacing of each reference peak.
Y value is unused.
Peak centers are stored in
m_peakCenterWorkspace.Spectra can be a subset of all spectra because
FitPeakscan work on partial spectra.
An array of double as the positions of the peaks to fit.
Peak centers are stored in
m_peakCenters
Peaks’ positions must be given in ascending order
Parameter FitFromRight deontes start fits from right most peak rather than left most peak.
Fit Window¶
There are two input parameters that are associated with fitting window.
FitWindowBoundaryList
FitPeakWindowWorkspace
If either of these is defined, then a peak’s range to fit (i.e., x-min and x-max) is confined by this window.
The fit windows must correspond to a peak center. For each peak center, the window list must have a lower and upper bound, meaning each window list must be twice as long as the corresponding center list.
If the windows are specified using FitWindowBoundaryList, then the same set of windows will be used on all spectra to be fit in the workspace. In this case window information will be retrieved from FitWindowBoundaryList. If the windows are specified using FitPeakWindowWorkspace, then at each workspace index to be fit, the x-values must define a list of fit windows to use. In this case window information will be retried from FitPeakWindowWorkspace. If neither is given, but the input workspace is in d-spacing, then instrument resolutions will be used to estimate the peak widths, instead.
Tolerance on Fitting Peaks Positions¶
Tolerance will be always checked!
Uniform tolerance
Non-uniform tolerance
Case 2, 3 and 4
Algorithm Configurations¶
Peak profile starting value will be given as
an array
PeakParameterValuessuch that the starting values are uniform among all spectra.a table (workspace)
PeakParameterValueTablesuch that the starting values are not necessary same among all spectra.
Calculation of starting value of peak profile and background parameters¶
FitPeaks supports estimating peak parameter names as starting values.
Workflow¶
Call FindPeakBackground to estimate the background of peak with a numerical approach.
Some tests have made to show that most time FindPeakBackground failed to do a valid estimation. Therefore this feature is temporarily disabled.
If FindPeakBackground fails, estimate-peak-background will be used for simple approximation.
Estimate the peak parameter, estimate-peak-parameter, by using the estimated peak background obtained in either step 1 or step 2.
Estimate the peak range, which is used to constrain the peak position in fitting, by using the left FWHM and right FWHM from step 3.
Estimate background¶
Estimate-peak-background takes peak fit window for pre-knowledge, and calculate a and b in the linear background function.
The algorithm is 1. Find the left and right N points respectively, average both x and y value 2. Use \((\bar{x}_1, \bar{y}_1)\) and \((\bar{x}_2, \bar{y}_2)\) to calculate a and b in \(y = a\cdot x + b\)
Estimate peak parameters¶
Estimate-peak-parameters requires background parameters being estimated.
Here is the approach to estimate the peak parameters
Remove background.
Find maximum Y value as the observed peak center and peak height \(H_{obs}\).
Check peak height with user-specified minimum height and peak center that must be at least more than 3 data points away from the boundary of fit window.
Find the left and right FWHM by searching \(x_i\) and \(x_{i+1}\) such that \(H_{obs}\) is between \(y_i\) and \(y_{i+1}\).
Estimate peak range¶
Estimate-peak-range requires inputs including expected peak center, fit window and estimated right and left FWHM. It will output the left and right boundary of the peak such that the background can be fit by excluding the peak.
Peak range is defined as \(x_0 \pm 3 \cdot FWHM\), for either left or right half of peak.
Check the number of background points out of peak range at the left and right side respectively. It is required to have at least 3 background points at either side, i.e., \(min(3, \frac{i_{x0} - i_{min}}{6})\) for left side.
Fit peak with high background¶
Step 1¶
Reduce the background by finding a linear function \(B_i = a\cdot x_i + b\), such that \(\sum_i (Y_i - B_i)\) is minimum while any \(Y_i - B_i\) is non-negative.
This approach is good for any background close to linear within the fit window.
Step 2¶
With the background reduced in step 1, it will be more reliable to estimate the peak’s FWHM via observation.
Step 3¶
Fit peak… ………..
Step 3¶
Get the peak range (by estimate-peak-range) and fit the background with FitMultiDomain to fit background.
Step 4¶
Remove the background and fit peak!
Outputs¶
Algorithm FitPeaks is designed for various purposes including but not limited to vanadium peak striping and fitting diamond peaks to calibrate detectors’ positions.
On the other hand, due to the complexity in peak fitting, users prefer to check the fitting results.
Therefore, FitPeaks supports various fexible and informative outputs.
OutputWorkspaces¶
OutputWorkspace¶
It is a MatrixWorkspace containing the peak positions expected and fitted.
The output workspace has N spectra corresponding to the spectra that are specified by user via
StartWorkspaceIndexandStopWorkspaceIndex.These spectra are in order from 0 to N.
If there are m peaks that are required to fit for, then each spectrum in the output workspace has m data points.
In each spectrum, x(i) is the expected position of i-th peak; y(i) is the fitted position of i-th peak; and e(i) is the cost from fitting.
There are several cases that the fitting could fail. A negative peak position y(i) combined with e(i) equal to DBL_MAX denote such failure.
Cause of fitting failure is denoted by different negative value of y(i) - -1: empty spectrum - -2: spectrum with too few counts - -3: peak is low - -4: TODO : find out the answer - -5: TODO : find out the answer
OutputPeakParametersWorkspace¶
It is an output MatrixWorkspace containing function parameters’ fitted values
for all peaks that are specified to fit.
The order of the peaks will be exactly the sequence of peaks as the order of the given positions of peaks.
If user specifies a subset of spectra to fit, this TableWorksapce will only contain function parameters’ value that corresponds to the spectra that are fitted.
OutputParameterFitErrorsWorkspace¶
It is an optional output MatrixWorkspace containing function parameters’ fitting error,
i.e., uncertainties, for all peaks that are specified to fit.
The order of the peaks will be exactly the sequence of peaks as the order of the given positions of peaks.
If user specifies a subset of spectra to fit, this TableWorksapce will only contain function parameters’ uncertainties that corresponds to the spectra that are fitted.
It has one less column than OutputPeakParametersWorkspace, which is chi2.
FittedPeaksWorkspace¶
It is an optional output MatrixWorkspace containing the peaks
calculated from fitting result.
FittingCostWorkspace¶
It is a MatrixWorkspace recording the cost of each peak that is fitted.
It is in the exactly same order as the given positions of peaks to fit.
Its X values store the fitted peak positions and Y values are for \(\chi^2\).
If a peak’s fitting is bad, then the peak position will be its proposed peak position, while its \(\chi^2\) shall be some special value.
FittedPeaksWorkspace¶
It is an optional output MatrixWorkspace.
For each spectrum, in each fit window, the Y values will be replaced by the calculated peak and background value. If fitting is bad, then only background is calculated.
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)
FitPeaks(InputWorkspace='ws', PeakCenters='5.1', FitWindowBoundaryList='0,10', OutputPeakParametersWorkspace='fitted_params',
BackgroundType='Linear', FittedPeaksWorkspace='fitted', OutputWorkspace='peakpositions')
peakposws = mtd['peakpositions']
param_ws = mtd['fitted_params']
row = param_ws.row(0)
# output
print ('Fitted peak position: {0:.5f}'.format(peakposws.readY(0)[0]))
print ("Peak 0 Centre: {0:.5f}, width: {1:.5f}, height: {2:.5f}".format(row["PeakCentre"], row["Sigma"], row["Height"]))
# clean up workspaces
DeleteWorkspace(Workspace='fitted')
DeleteWorkspace(Workspace='fitted_params')
DeleteWorkspace(Workspace='ws')
DeleteWorkspace(Workspace='peakpositions')
Output:
Fitted peak position: 5.00000
Peak 0 Centre: ..., width: ..., height: ...
Example - Fit peaks on high background (vanadium):
# load a 4 spectra workspace
ws = Load("PG3_733.nxs")
van_peak_centers = "0.5044,0.5191,0.5350,0.5526,0.5936,0.6178,0.6453,0.6768,0.7134,0.7566,0.8089,0.8737,0.9571,1.0701,1.2356,1.5133,2.1401"
FitPeaks(InputWorkspace=ws, StartWorkspaceIndex=0, StopWorkspaceIndex=3,PeakCenters=van_peak_centers,
FitFromRight=True,HighBackground=True,
BackgroundType='Quadratic',
PeakWidthPercent=0.008,
OutputWorkspace='PG3_733_peak_positions',OutputPeakParametersWorkspace='PG3_733_peak_params',
FittedPeaksWorkspace='PG3_733_fitted_peaks')
PG3_733_peak_positions = mtd["PG3_733_peak_positions"]
ep0 = PG3_733_peak_positions.readX(0)[-1]
ep1 = PG3_733_peak_positions.readX(0)[-2]
ep2 = PG3_733_peak_positions.readX(0)[-3]
fp0 = PG3_733_peak_positions.readY(0)[-1]
fp1 = PG3_733_peak_positions.readY(0)[-2]
fp2 = PG3_733_peak_positions.readY(0)[-3]
# print data
print ('Spectrum 1: Expected right most 3 peaks at {0:.3f}, {1:.3f}, {2:.3f}'.format(ep0, ep1, ep2))
print ('Spectrum 1: Found right most 3 peaks at {0:.3f}, {1:.3f}, {2:.3f}'.format(fp0, fp1, fp2))
# delete workspaces
DeleteWorkspace(Workspace='PG3_733_peak_positions')
DeleteWorkspace(Workspace='PG3_733_fitted_peaks')
DeleteWorkspace(Workspace='PG3_733_peak_params')
DeleteWorkspace(Workspace='ws')
Output:
Spectrum 1: Expected right most 3 peaks at 2.140, 1.513, 1.236
Spectrum 1: Found right most 3 peaks at 2.149, 1.519, 1.240
Example - Fit back-to-back exponential peaks (Vulcan diamond):
# load data
Load(Filename="vulcan_diamond.nxs", OutputWorkspace="diamond_3peaks")
FitPeaks(InputWorkspace="diamond_3peaks", StartWorkspaceIndex=0, StopWorkspaceIndex=5,
PeakCenters="0.6867, 0.728299, 0.89198, 1.0758",
PeakFunction="BackToBackExponential", BackgroundType="Linear",
FitWindowBoundaryList="0.67, 0.709, 0.71, 0.76, 0.87, 0.92, 1.05, 1.1",
PeakParameterNames="I, A, B, X0, S",
PeakParameterValues="2.5e+06, 5400, 1700, 1.07, 0.000355",
FitFromRight=True,
HighBackground=False,
OutputWorkspace="diamond_peaks_centers",
OutputPeakParametersWorkspace="PeakParametersWS2",
FittedPeaksWorkspace="FittedPeaksWS2")
fitted_peak_pos_ws = mtd['diamond_peaks_centers']
# print result
for ws_index in range(0, 1):
print ('Spectrum {0}:'.format(ws_index+1))
for peak_index in range(2, 4):
exp_pos = fitted_peak_pos_ws.readX(ws_index)[peak_index]
fit_pos = fitted_peak_pos_ws.readY(ws_index)[peak_index]
print ('Expected @ {0:.3f} Fitted @ {1:.3f}'.format(exp_pos, fit_pos))
# clean
DeleteWorkspace(Workspace='diamond_3peaks')
DeleteWorkspace(Workspace='diamond_peaks_centers')
DeleteWorkspace(Workspace='FittedPeaksWS2')
DeleteWorkspace(Workspace='PeakParametersWS2')
Output:
Spectrum 1:
Expected @ 0.892 Fitted @ 0.892
Expected @ 1.076 Fitted @ 1.075
Categories: AlgorithmIndex | Optimization
Source¶
C++ header: FitPeaks.h
C++ source: FitPeaks.cpp