.. algorithm::

.. summary::

.. relatedalgorithms::

.. properties::

If the NormalizationIn property is greater than zero, the algorithm will apply the user defined normalization to the data instead of calculating an estimate.

Description
-----------

This algorithm estimates the asymmetry from the specified muon
spectra. By default, all of the spectra
in a workspace will be corrected.

The formula for estimating the asymmetry is given by:

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

where :math:`\tau` is the muon lifetime (2.1969811e-6 seconds), :math:`F` is the number of good frames and :math:`N_0` is a
fitted normalization constant. The normalization is given by

.. math:: N_0= \frac{\Delta t\sum_j(\textrm{OldData}_j)}{\tau F \left( \exp(-\frac{t_0}{\tau})-\exp(-\frac{t_N}{\tau})\right)  },

where the summation only includes the data with times bewtween :math:`t_0` and :math:`t_N` and :math:`\Delta t` is the time step.

Usage
-----

**Example - Removing exponential decay:**

.. testcode:: ExSimple

   import math
   import numpy as np

   tab = CreateEmptyTableWorkspace()
   tab.addColumn('double', 'norm')
   tab.addColumn('str', 'name')
   tab.addColumn('str', 'method')

   y = [100, 150, 50, 10, 5]
   x = [1,2,3,4,5,6]
   input = CreateWorkspace(x,y)
   run = input.getRun()
   run.addProperty("goodfrm","10","None",True)
   output,unnorm=EstimateMuonAsymmetryFromCounts(InputWorkspace=input,spectra=0,NormalizationTable=tab,StartX=1,EndX=5,OutputUnNormData=True)
   print("Asymmetry   :  {}".format(['{0:.2f}'.format(value) for value in output.readY(0)]))
   print("Unnormalized:  {}".format(['{0:.2f}'.format(value) for value in unnorm.readY(0)]))
   print("Normalization constant: {0:.2f}".format(tab.column(0)[0]))

Output:

.. testoutput:: ExSimple

   Asymmetry   :  ['-0.31', '0.64', '-0.14', '-0.73', '-0.79']
   Unnormalized:  ['19.79', '46.80', '24.59', '7.75', '6.11']
   Normalization constant: 28.56

**Example - Setting the normalization:**

.. testcode:: ExNorm

   import math
   import numpy as np

   tab = CreateEmptyTableWorkspace()
   tab.addColumn('double', 'norm')
   tab.addColumn('str', 'name')
   tab.addColumn('str', 'method')

   y = [100, 150, 50, 10, 5]
   x = [1,2,3,4,5,6]
   input = CreateWorkspace(x,y)
   run = input.getRun()
   run.addProperty("goodfrm","10","None",True)

   output=EstimateMuonAsymmetryFromCounts(InputWorkspace=input,spectra=0,NormalizationTable=tab,StartX=1,EndX=5,NormalizationIn=20.0)

   print("Asymmetry:  {}".format(['{0:.2f}'.format(value) for value in output.readY(0)]))
   print("Normalization constant: {0:.2f}".format(tab.column(0)[0]))

Output:

.. testoutput:: ExNorm

   Asymmetry:  ['-0.01', '1.34', '0.23', '-0.61', '-0.69']
   Normalization constant: 20.00

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