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# CalculateMuonAsymmetry v1¶

## Summary¶

This algorithm calculates the asymmetry for a transverse field.

## Properties¶

Name

Direction

Type

Default

Description

NormalizationTable

Input

TableWorkspace

Name of the table containing the normalizations for the asymmetries.

UnNormalizedWorkspaceList

Input

str list

Mandatory

An ordered list of workspaces (to get the initial values for the normalizations).

ReNormalizedWorkspaceList

Input

str list

Mandatory

An ordered list of workspaces (to get the initial values for the normalizations).

OutputFitWorkspace

Input

string

fit

The name of the output fit workspace.

StartX

Input

number

0.1

The lower limit for calculating the asymmetry (an X value).

EndX

Input

number

15

The upper limit for calculating the asymmetry (an X value).

Exclude

Input

dbl list

A list of pairs of real numbers, defining the regions to exclude from the fit for all spectra.

InputFunction

Input

Function

Mandatory

The fitting function to be converted.

Minimizer

Input

string

Levenberg-MarquardtMD

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’]

MaxIterations

Input

number

500

Stop after this number of iterations if a good fit is not found

OutputStatus

Output

string

ChiSquared

Output

number

OutputFunction

Output

Function

The fitting function after fit.

EnableDoublePulse

Input

boolean

False

Controls whether to perform a double pulse or single pulse fit.

PulseOffset

Input

number

0

The time offset between the two pulses

FirstPulseWeight

Input

number

0.5

Weighting of first pulse (w_1).The second pulse weighting (w_1) is set as w_2 = 1 - w_1.

## Description¶

This algorithm calculates the asymmetry from the first muon spectra in a workspace. in a workspace will be corrected.

The formula for calculating the asymmetry (from counts) is given by:

$\textrm{NewData} = (\textrm{OldData}\times e^\frac{t}{\tau})/(F N_0) - 1.0,$

where $$\tau$$ is the muon lifetime (2.1969811e-6 seconds), $$F$$ is the number of good frames and $$N_0$$ is a fitted normalisation constant. The normalisation is calculated by fitting to the normalised counts which is given by

$\textrm{normalisedCounts}=(\textrm{OldData}\times e^\frac{t}{\tau})/F$

and the fitting function is given by

$N_0[1+f(t)]$

and the renormalized data is transformed via the equation:

$\textrm{NewData} = (\textrm{NormalisedCounts}/(N_0) - 1.0.$

## Usage¶

Example - Calculating Asymmetry: This example is for calculating the Asymmetry for a single data set.

import math
import numpy as np

def makeData(name,norm):
xData=np.linspace(start=0,stop=10,num=200)
yData=np.sin(5.2*xData)
result = (1-yData )*norm
ws= CreateWorkspace(DataX=xData, DataY=result,OutputWorkspace=name)
return ws

#create a normalisation table
tab = CreateEmptyTableWorkspace()

ws= makeData("a",2.30)
ws2= makeData("b",1.10)

myFunc='name=GausOsc,$domains=i,Frequency=5.;' TFFunc = ConvertFitFunctionForMuonTFAsymmetry(InputFunction=myFunc,NormalizationTable=tab,WorkspaceList=["a"],Mode="Construct") CalculateMuonAsymmetry(NormalizationTable=tab, unNormalizedWorkspaceList=["a"], ReNormalizedWorkspaceList=["b"], InputFunction= str(TFFunc), OutputFitWorkspace="fit_result",StartX=0.1,EndX=9.9) print("Normalization constant for b: {0:.2f}".format(tab.column(0)[1]))  Output: Normalization constant for b: 2.30  Example - Calculating Asymmetry For multiple data sets: This example is for calculating the Asymmetry for multuiple data sets. import math import numpy as np def makeData(name,norm): xData=np.linspace(start=0,stop=10,num=200) yData=np.sin(5.2*xData) result = (1-yData )*norm ws= CreateWorkspace(DataX=xData, DataY=result,OutputWorkspace=name) return ws #create a normalisation table tab = CreateEmptyTableWorkspace() tab.addColumn('double', 'norm') tab.addColumn('str', 'name') tab.addColumn('str', 'method') tab.addRow([11.,"a","Estimate"]) tab.addRow([22.,"b","Estimate"]) tab.addRow([22.,"c","Estimate"]) tab.addRow([22.,"d","Estimate"]) #create original function and workspace myFunc='name=GausOsc,$domains=i,Frequency=5.;'
myFunc2='name=GausOsc,\$domains=i,Frequency=5.;'
multiFunc='composite=MultiDomainFunction,NumDeriv=1;'+myFunc+myFunc2+'ties=(f0.Frequency=f1.Frequency)'

ws= makeData("a",2.30)
ws2= makeData("b",1.10)
ws3= makeData("c",4.1)
ws4= makeData("d",2.0)

TFFunc = ConvertFitFunctionForMuonTFAsymmetry(InputFunction=multiFunc, NormalizationTable=tab,
WorkspaceList=["a","c"], Mode="Construct")

CalculateMuonAsymmetry(NormalizationTable=tab, unNormalizedWorkspaceList=["a","c"],
ReNormalizedWorkspaceList=["b","d"], InputFunction= str(TFFunc),
OutputFitWorkspace="fit_result",StartX=0.1,EndX=9.9)

print("Normalization constant for b: {0:.2f}".format(tab.column(0)[1]))
print("Normalization constant for d: {0:.2f}".format(tab.column(0)[3]))


Output:

Normalization constant for b: 2.30
Normalization constant for d: 4.10


Example - Calculating Asymmetry for double pulse data:

import math
import numpy as np

delta = 0.33
x = np.linspace(0.,15.,100)
x_offset = np.linspace(delta/2, 15. + delta/2, 100)
x_offset_neg = np.linspace(-delta/2, 15. - delta/2, 100)

testFunction = GausOsc(Frequency = 1.5, A=0.22)
y1 = testFunction(x_offset_neg)
y2 = testFunction(x_offset)
N0 = 6.38
y = N0 * (1 + y1/2+y2/2)
y_norm = y1/2+y2/2
unnormalised_workspace = CreateWorkspace(x,y)
ws_to_normalise = CreateWorkspace(x,y)
ws_correctly_normalised = CreateWorkspace(x,y_norm)

innerFunction = FunctionFactory.createInitialized('name=GausOsc,A=0.20,Sigma=0.2,Frequency=1.0,Phi=0')
tf_function = ConvertFitFunctionForMuonTFAsymmetry(InputFunction=innerFunction, WorkspaceList=['ws_to_normalise'])

CalculateMuonAsymmetry(MaxIterations=100, EnableDoublePulse=True, PulseOffset=delta, UnNormalizedWorkspaceList='unnormalised_workspace', ReNormalizedWorkspaceList='ws_to_normalise',
OutputFitWorkspace='DoublePulseFit', StartX=0, InputFunction=str(tf_function), Minimizer='Levenberg-Marquardt')

double_parameter_workspace = AnalysisDataService.retrieve('DoublePulseFit_Parameters')
values_column = double_parameter_workspace.column(1)

print("Normalization constant is: {0:.2f}".format(values_column[0]))


Output:

Normalization constant is: 6.38


Categories: AlgorithmIndex | Muon