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ProcessBackground v1¶

Summary ¶

ProcessBackground provides some tools to process powder diffraction pattern’s background in order to help Le Bail Fit.

Properties ¶

Name	Direction	Type	Default	Description
InputWorkspace	Input	Workspace2D	Mandatory	Name of the output workspace containing the processed background.
WorkspaceIndex	Input	number	0	Workspace index for the input workspaces.
OutputWorkspace	Output	Workspace2D		Output workspace containing processed background
Options	Input	string	RemovePeaks	Name of the functionality realized by this algorithm. Allowed values: [‘SelectBackgroundPoints’, ‘RemovePeaks’, ‘DeleteRegion’, ‘AddRegion’]
LowerBound	Input	number	Optional	Lower boundary of the data to have background processed.
UpperBound	Input	number	Optional	Upper boundary of the data to have background processed.
ReferenceWorkspace	Input	Workspace2D		Name of the workspace containing the data required by function AddRegion.
BackgroundType	Input	string	Polynomial	Type of the background. Options include Polynomial and Chebyshev. Allowed values: [‘Polynomial’, ‘Chebyshev’]
SelectionMode	Input	string	N/A	If choise is UserFunction, background will be selected by an input background function. Otherwise, background function will be fitted from user’s input data points. Allowed values: [‘N/A’, ‘FitGivenDataPoints’, ‘UserFunction’]
BackgroundOrder	Input	number	0	Order of polynomial or chebyshev background.
BackgroundPoints	Input	dbl list		Vector of doubles, each of which is the X-axis value of the background point selected by user.
BackgroundTableWorkspace	Input	TableWorkspace		Name of the table workspace containing background parameters for mode SelectBackgroundPoints.
BackgroundPointSelectMode	Input	string	All Background Points	Mode to select background points. Allowed values: [‘All Background Points’, ‘Input Background Points Only’]
NoiseTolerance	Input	number	1	Tolerance of noise range.
NegativeNoiseTolerance	Input	number	Optional	Tolerance of noise range for negative number.
UserBackgroundWorkspace	Output	Workspace2D		Output workspace containing fitted background from points specified by users.
OutputBackgroundParameterWorkspace	Output	TableWorkspace		Output parameter table workspace containing the background fitting result.
OutputBackgroundType	Input	string	Polynomial	Type of background to fit with selected background points. Allowed values: [‘Polynomial’, ‘Chebyshev’]
OutputBackgroundOrder	Input	number	6	Order of background to fit with selected background points.
BraggPeakTableWorkspace	Input	TableWorkspace		Name of table workspace containing peaks’ parameters.
NumberOfFWHM	Input	number	1	Number of FWHM to as the peak region to have peak removed.

Description ¶

The algorithm ProcessBackground() provides several functions for user to process background to prepare Le Bail Fit.

There are a few functional options for user to choose.

SelectBackgroundPoints: selecting background points from diffraction data. Usually the output will be used to fit background;
RemovePeaks: removing peaks from a given MatrixWorks from diffraction data;

This feature is designed to select many background points with user’s simple input. User is required to select only a few background points in the middle of two adjacent peaks. Algorithm will fit these few points (BackgroundPoints) to a background function of specified type.

The purpose of this option is to select as many background data points as possible for future background function fitting.

Prior information can be given by two modes. Property ‘SelectionMode’ determines which modes to use. One (1)is from a list of X-values specified by users via property “BackgroundPoints”. The other (2) is through a (background) function, whose type is specified by property “BackgroundType” and values are given via input table workspace “BackgroundTableWorkspace”.

Select background points from given X-values ¶

Here is how it works. Assume that the \(X^{(u)}\) is the list of x values specified by users.

Create a data set (X, Y, E) from input workspace, where \(X_i\) is the nearest value to \(X^{(u)}_i\);
Fit the background function against the data set (X, Y, E);
Select the data points, which are within a certain range above and below the fitted background function;
The last step is to fit background function against the selected background points

Select background points from given function ¶

In this approach, the difference from the other apporach is to use the user given background function to select data points within a range other than fitting the background function from given data points in the other approach. Thus, it is just the last step of previous approach.

Output workspaces ¶

OutputWorkspace: It contains 3 spectra.
- spectrum 0: the selected background data points;
- spectrum 1: the fitted background function against the selected data points;
- spectrum 2: the difference of sepctrum 0 and 1
OutputBackgroundParameterWorkspace: A table workspace containing the fitted parameter values including \(\chi^2\).
UserBackgroundWorkspace: a MatrixWorkspace to visualize by user.
- spectrum 0: background function (either given by user or fit from given data points) that is used to select background points;
- spectrum 1: diffraction data with background (spectrum 0) removed;
- spectrum 2: upper boundary on data points to be selected for spectrum 1;
- spectrum 3: lower boundary on data points to be selected for spectrum 1

Algorithm properties ¶

Besides the common algorithm properties, below is the list of properties specific to this function option.

Inputs:
- LowerBoundary
- UpperBoundary
- BackgroundType
- SelectionMode
- BackgroundOrder and BackgroundPoints / BackgroundTableWorkspace
- NoiseTolerance
- NegativeNoiseTolerance
- OutputBackgroundType
- OutputBackgroundOrder
Outputs:
- OutputBackgroundParameterWorkspace
- UserBackgroundWorkspace

A suggested workflow ¶

Here is a good example to select background points from a powder diffraction pattern by calling ProcessBackground() in a self-consistent manner.

Select a set of background points (X values only), which can roughly describes the background, manually;
Call ProcessBackground with Option=’SelectBackgroundPoints’ and SelectionMode=’UserSpecifyBackground’. A good choice for background function to enter is 6-th order polynomial;
Plot spectra 2 to 4 in UserBackgroundWorkspace to check whether ‘Tolerance’ is proper or not. If not then reset the tolerance and run ProcessBackground again with previous setup;
Fit OutputWorkspace (the selected background) with a background function;
Call ProcessBackground with Option=’SelectBackgroundPoints’ and SelectionMode=’UserFunction’. Set the background parameter workspace as the output parameter table workspace obtained in the last step;
Repeat step 4 and 5 for a few times until the background plot by fitted background function from selected background points is close enough to real background.

Simple Remove Peaks ¶

This algorithm is to remove peaks and output the backgrounds, which can be used to fit an artibrary background function after calling this algorithm.

It is assumed that the all peaks have been fitted reasonably well. Then by removing the peaks within range \(X_i^{(0)} \pm FWHM\), and save the rest data points, which are very likely backgrounds, to an output workspace.

Required and optional algorithm properties ¶

Besides the common algorithm properties, below is the list of properties specific to this function option.

Inputs:
- BraggPeakTableWorkspace
- NumberOfFWHM
Outputs:
- UserBackgroundWorkspace: a dummy output for not raising trouble with python script

Add Region ¶

Replace a region, which is defined by ‘LowerBoundary’ and ‘UpperBoundary’, in a workspace from another reference workspace.

Required and optional algorithm properties ¶

Inputs
- LowerBoundary (required)
- UpperBoundary (required)
- ReferenceWorkspace (required)

Delete Region ¶

Removed a specified region, which is defined by ‘LowerBoundary’ and ‘UpperBoundary’, from the input workspace.

Required and optional algorithm properties ¶

Inputs
- LowerBoundary (required)
- UpperBoundary (required)

Usage ¶

Example - Select background from a powgen data:

LoadAscii(Filename=r'PG3_15035-3.dat', OutputWorkspace='PG3_15035-3',Unit='TOF')

outputs = ProcessBackground(InputWorkspace='PG3_15035-3', WorkspaceIndex = 0, Options='SelectBackgroundPoints',
      LowerBound='9726',UpperBound='119000', BackgroundType = 'Polynomial',  BackgroundOrder = 6,
      SelectionMode='FitGivenDataPoints', BackgroundPointSelectMode = "All Background Points",
      BackgroundPoints='10082,10591,11154,12615,13690,13715,15073,16893,17764,19628,21318,24192,35350,44212,50900,60000,69900,79000',
      NoiseTolerance = 0.10,
      OutputWorkspace='PG3_15035-3_BkgdPts', OutputBackgroundType = "Polynomial", OutputBackgroundOrder = 6,
      OutputBackgroundParameterWorkspace = "OutBackgroundParameters", UserBackgroundWorkspace="UserTheory")

tbws = outputs[2]

print("Number of output workspace = {}, Number of selected background points = {}".format(len(outputs), len(outputs[0].readX(0))))
print("Fitted background function: A0 = {:.5e}, A1 = {:.5e}, A2 = {:.5e} ...".format(tbws.cell(1, 1), tbws.cell(2, 1), tbws.cell(3,1)))

Output:

Number of output workspace = 3, Number of selected background points = 4944
Fitted background function: A0 = 5.43859e-01, A1 = -5.20674e-05, A2 = 2.84119e-09 ...

Example - Add Region:

import math
import random

vecx = []
vecy1 = []
vecy2 = []
vece = []

x0 = 0.0
dx = 0.01

random.seed(1)
for i in range(1000):
  x = x0 + float(i) * dx
  vecx.append(x)
  y = (random.random() - 0.5) * 2.0 + 2.0 + math.exp(-(x-4.0)**2/0.1)
  e = math.sqrt(y)
  vecy1.append(y)
  vecy2.append(-y)
  vece.append(e)

ws1 = CreateWorkspace(DataX = vecx, DataY = vecy1, DataE = vece, NSpec = 1)
ws2 = CreateWorkspace(DataX = vecx, DataY = vecy2, DataE = vece, NSpec = 1)

outputs = ProcessBackground(InputWorkspace=ws1, WorkspaceIndex=0, OutputWorkspace="ws12", Options="AddRegion",
      LowerBound = 3.0, UpperBound = 5.0, ReferenceWorkspace = ws2)

for i in [200, 400, 450, 500, 700]:
    print("X = {0:.5f}, Input Y[{1}] = {2:.5f}, Reference Y[{1}] = {3:.5f}, Output Y[{1}] = {4:.5f}".format(
           vecx[i], i, ws1.readY(0)[i], ws2.readY(0)[i], outputs[0].readY(0)[i]))

Output:

X = 2.00000, Input Y[200] = 1.65069, Reference Y[200] = -1.65069, Output Y[200] = 1.65069
X = 4.00000, Input Y[400] = 3.81388, Reference Y[400] = -3.81388, Output Y[400] = -3.81388
X = 4.50000, Input Y[450] = 2.68751, Reference Y[450] = -2.68751, Output Y[450] = -2.68751
X = 5.00000, Input Y[500] = 2.00611, Reference Y[500] = -2.00611, Output Y[500] = 1.71367
X = 7.00000, Input Y[700] = 1.12037, Reference Y[700] = -1.12037, Output Y[700] = 2.87033

Example - Delete Region:

import math
import random

vecx = []
vecy = []
vece = []

x0 = 0.0
dx = 0.01

random.seed(1)
for i in range(1000):
  x = x0 + float(i) * dx
  vecx.append(x)
  y = (random.random() - 0.5) * 2.0 + 2.0 + math.exp(-(x-4.0)**2/0.1)
  e = math.sqrt(y)
  vecy.append(y)
  vece.append(e)

ws1 = CreateWorkspace(DataX = vecx, DataY = vecy, DataE = vece, NSpec = 1)

outputs = ProcessBackground(InputWorkspace=ws1, WorkspaceIndex=0, OutputWorkspace="ws2", Options="DeleteRegion",
      LowerBound = 3.0, UpperBound = 5.0)

print("Input has {} data points; Output has {} data points.".format(len(ws1.readX(0)), len(outputs[0].readX(0))))

Output:

Input has 1000 data points; Output has 799 data points.

Example - Remove peaks:

import math
import random

vecx = []
vecy = []
vece = []
numpts = 1000
x0 = 0
dx = 0.01

random.seed(1)
for i in range(1000):
  x = float(i)*dx
  y = 5 + (random.random() - 1)*2. + 10*math.exp( -(x-2.0)**2/0.1**2 ) + 20*math.exp( -(x-7.5)**2/0.05**2 )
  e = math.sqrt(y)
  vecx.append(x)
  vecy.append(y)
  vece.append(e)

ws = CreateWorkspace(DataX = vecx, DataY = vecy, DataE = vece, NSpec = 1)
peaktb = CreateEmptyTableWorkspace()
peaktb.addColumn("double", "TOF_h")
peaktb.addColumn("double", "FWHM")
peaktb.addRow([2.0, 0.3])
peaktb.addRow([7.40, 0.13])

outputs = ProcessBackground(InputWorkspace=ws, WorkspaceIndex=0, OutputWorkspace="background",
    Options="RemovePeaks", BraggPeakTableWorkspace=peaktb, NumberOfFWHM=3)

Fit(Function='name=Polynomial,n=1,A0=0.0,A1=0.0', InputWorkspace='background',  CreateOutput=True, StartX=0, EndX=9.9900000000000002,
    OutputNormalisedCovarianceMatrix='background_NormalisedCovarianceMatrix', OutputParameters='background_Parameters', OutputWorkspace='background_Workspace')

outparws = mtd["background_Parameters"]
print("Input workspace has {} data points; Output workspace has {} data points.".format(len(ws.readX(0)), len(outputs[0].readX(0))))
print("Fitted background parameters: A0 = {:.5e}, A1 = {:.5e}, Chi-square = {:.5f}".format(outparws.cell(0, 1), outparws.cell(1,1), outparws.cell(2,1)))

Output:

Input workspace has 1000 data points; Output workspace has 741 data points.
Fitted background parameters: A0 = 3.90254e+00, A1 = 1.09284e-02, Chi-square = 0.08237

Categories: AlgorithmIndex | Diffraction\Utility

Source ¶

C++ header: ProcessBackground.h

C++ source: ProcessBackground.cpp