.. algorithm::

.. summary::

.. relatedalgorithms::

.. properties::

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

This algorithm sums the Y values of histograms given by
*InputWorkspaceIndexSet* into a single single histogram. The summation is done
using the method proposed by Cubitt et al. [#CUBITT]_ This involves a
projection to an arbitrary reference angle, :math:`2\theta_R`, with a
"virtual" wavelength, :math:`\lambda_v`. This is the wavelength the neutron
would have had if it had arrived at :math:`2\theta_R` with the same momentum
transfer (:math:`Q`).

Counts are considered to be spread evenly over the input pixel, and the
top-left and bottom-right corner of the pixel are projected onto
:math:`2\theta_R` giving a range in :math:`\lambda_v` to project onto. Counts
are shared out proportionally into the output bins that overlap this range, and
the projected counts from all pixels are summed into the appropriate output
bins.

The input workspace should have wavelength as the X units as well as an instrument.

To produce a reflectivity, the input workspace has to be the reflected beam
workspace where each histogram is individually divided by the summed (in
lambda) direct beam data.

Usage
-----

**Example - basic usage with reflectometry-like data**

.. plot::
   :include-source:

   import numpy as np
   from mantid.simpleapi import *
   import matplotlib.pyplot as plt

   # Direct beam
   noBackground = 'name=LinearBackground, A0=0'
   direct = CreateSampleWorkspace(
       Function='User Defined',
       UserDefinedFunction=noBackground,
       NumBanks=1,
       XUnit='Wavelength',
       XMin=0., XMax=20., BinWidth=1.)
   # Move the detector such that the beam is right at its center.
   MoveInstrumentComponent(
       Workspace=direct,
       ComponentName='bank1',
       X=-0.008 * 4.5, Y= -0.008 * 4.5, Z=0.)
   # Fill intensity for pixels in the beam
   for i in [44, 45, 54, 55]:
       direct.dataY(i).fill(1.)
       direct.dataE(i).fill(0.1)
   # Group detectors to form a 'line detector'. The line is vertical in this case.
   groupingPattern=''
   for row in range(10):
       for column in range(10):
           groupingPattern = groupingPattern + str(column * 10 + row)
           if column < 9:
               groupingPattern = groupingPattern + '+'
       if row < 9:
           groupingPattern = groupingPattern + ','
   direct = GroupDetectors(
       InputWorkspace=direct,
       GroupingPattern=groupingPattern,
       Behaviour='Sum')

   #Reflected beam
   reflected = CreateSampleWorkspace(
       Function='User Defined',
       UserDefinedFunction=noBackground,
       NumBanks=1,
       XUnit='Wavelength',
       XMin=0., XMax=20., BinWidth=1.)
   # Move the detector. This reflectometer moves vertically.
   MoveInstrumentComponent(
       Workspace=reflected,
       ComponentName='bank1',
       X=-0.008 * 4.5, Y= 0.008 * 4, Z=0.)
   # Create some fake reflected beam data.
   Xs = reflected.readX(0)
   Xs = (Xs[1:] + Xs[:-1]) / 2  # Bin edges -> points
   decay = np.exp(-(Xs - 4.) / 3.)
   span = decay < 1.
   for i in [44, 45, 54, 55]:
       Ys = reflected.dataY(i)
       Ys.fill(1.)
       Ys[span] = decay[span]
   reflected = GroupDetectors(
       InputWorkspace=reflected,
       GroupingPattern=groupingPattern,
       Behaviour='Sum')

   # Now we have somewhat realistic data.
   # Sum the direct beam (in lambda).
   direct=SumSpectra(direct, ListOfWorkspaceIndices=[4, 5])
   # Calculate (sum in Q) the reflectivity.
   reflected /= direct
   reflectivity = ReflectometrySumInQ(
       InputWorkspace=reflected,
       InputWorkspaceIndexSet=[4, 5],
       BeamCentre=4)

   reflectivity = CropWorkspace(
       reflectivity,
       XMin=0.1, XMax=19.)

   fig, axes = plt.subplots(subplot_kw={'projection': 'mantid'})
   axes.plot(reflectivity)
   axes.set_ylabel('"Reflectivity"')
   # Uncomment to show the plot window.
   #fig.show()
   mtd.clear()

References
----------

.. [#CUBITT] Cubitt et al., *J. Appl. Crystallogr.*, **6** 2006 (2015)
             `doi: 10.1107/S1600576715019500 <http://dx.doi.org/10.1107/S1600576715019500>`_

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