.. algorithm::

.. summary::

.. relatedalgorithms::

.. properties::

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

This algorithm extracts horizontal or vertical profiles from a MatrixWorkspace. The profile is returned as a single histogram workspace. :ref:`Ragged workspaces <Ragged_Workspace>` are not supported.

The orientation of the profile is selected by the *Direction* property. By default, the line runs over the entire workspace. The length can be optionally limited by specifying the *Start* and/or the *End* properties. A region over which the profile is calculated is given by *HalfWidth*. The width is rounded to full bins so that partial bins are included entirely.

Special values can be completely ignored by the *IgnoreNans* and *IgnoreInfs* properties. If a segment of the line contains special values only, it will be set to NaN.

By default, the profile is calculated as an average over the line width. This behavior can be changed by the *Mode* property. The choices are:

'Average'
    Average the values. This is the default.

'Sum'
    Sum the values, weighting them by :math:`n / n_{tot}` where :math:`n` is the number of summed data points (excluding special values if *IgnoreNans* or *IgnoreInfs* is set) and :math:`n_{tot}` is the total number of data points (including special values).

Profiles over distributions
---------------------------

Horizontal profiles over distribution data (Y divided by bin width) will be distributions as well.

However, vertical profiles over distribution data will be non-distributions, albeit the data is normalized by the profile width. To remove the normalization, it is possible to multiply the data by the total width of included bins. This information is contained in the vertical axis:

.. code-block:: python

    # line is a workspace created by LineProfile
    axis = line.getAxis(1)
    height = axis.getMax() - axis.getMin()
    Ys = line.dataY(0)
    Ys *= height
    Es = line.dataE(0)
    Es *= height

Usage
-----

**Example - Horizontal line profile**

.. testcode:: HorizontalLineProfileExample

    import numpy

    ws = CreateSampleWorkspace(
        Function='Quasielastic Tunnelling',
        NumBanks=1
    )

    # Horizontal profile over spectra 5-10
    horProfile = LineProfile(
        InputWorkspace=ws,
        Centre=7.5,
        HalfWidth=2.5,
        Start=3000,
        End=13000
    )

    indexMax = numpy.argmax(horProfile.readY(0))
    epp = horProfile.readX(0)[indexMax]
    print('Elastic peak at {}'.format(epp))

Output:

.. testoutput:: HorizontalLineProfileExample

    Elastic peak at 10000.0

**Example - Vertical line profile**

.. testcode:: VerticalLineProfile

    import numpy

    ws = CreateSampleWorkspace(
        Function='Quasielastic Tunnelling',
        NumBanks=1
    )

    wsInTheta = ConvertSpectrumAxis(
        InputWorkspace=ws,
        Target='Theta'
    )

    # Verical cuts.

    tofs = numpy.arange(3000, 7000, 500)
    cutWSs = list()
    for tof in tofs:
        cutWS = LineProfile(
            InputWorkspace=wsInTheta,
            OutputWorkspace='cut-at-{}-us'.format(tof),
            Direction='Vertical',
            Centre=float(tof),
            HalfWidth=250.0,
            Start=0.5,  # Degrees
            End=0.9
        )
        cutWSs.append(cutWS)

    for cut in cutWSs:
        # Vertical axis holds the TOF bin edges of the cut
        axis = cut.getAxis(1)
        tofStart = axis.getValue(0)
        tofEnd = axis.getValue(1)
        # Notice the overlapping TOFs. This is because partial bins are
        # included in their entirety.
        print('Average intensity between {} and {} microsec: {:.03}'.format(
            tofStart, tofEnd, cut.readY(0)[0]))

Output:

.. testoutput:: VerticalLineProfile

    Average intensity between 2600.0 and 3400.0 microsec: 0.1
    Average intensity between 3200.0 and 3800.0 microsec: 0.1
    Average intensity between 3600.0 and 4400.0 microsec: 0.164
    Average intensity between 4200.0 and 4800.0 microsec: 0.1
    Average intensity between 4600.0 and 5400.0 microsec: 0.1
    Average intensity between 5200.0 and 5800.0 microsec: 0.1
    Average intensity between 5600.0 and 6400.0 microsec: 0.227
    Average intensity between 6200.0 and 6800.0 microsec: 0.1

**Example - The 'Sum' mode**

.. testcode:: SumMode

    import numpy

    ws = CreateSampleWorkspace(
        Function='Quasielastic Tunnelling',
        NumBanks=1
    )

    wsInTheta = ConvertSpectrumAxis(
        InputWorkspace=ws,
        Target='Theta'
    )

    # Lets assign NaNs to the lower left and upper right corners
    # of the workspace.
    for iVert in range(wsInTheta.getNumberHistograms()):
        for iHor in range(wsInTheta.blocksize()):
            if iVert + iHor < 60:
                ys = wsInTheta.dataY(iVert)
                ys[iHor] = numpy.nan
            elif iVert + iHor > 120:
                ys = wsInTheta.dataY(iVert)
                ys[iHor] = numpy.nan

    centre = 0.6
    width = 0.05
    sumCutWS = LineProfile(wsInTheta, centre, width, Mode='Sum')

    # When no NaNs are present both modes give the same result.
    iElastic = sumCutWS.blocksize() // 2
    y = sumCutWS.readY(0)[iElastic]
    e = sumCutWS.readE(0)[iElastic]
    print('Sum profile at elastic peak: {:.8f} +/- {:.10f}'.format(y, e))

    # The weighting is apparent when the profile crosses some
    # special values.
    iEdge = sumCutWS.blocksize() // 6
    y = sumCutWS.readY(0)[iEdge]
    e = sumCutWS.readE(0)[iEdge]
    print('Sum profile near NaNs: {:.11f} +/- {:.11f}'.format(y, e))

.. testoutput:: SumMode

    Sum profile at elastic peak: 103.45916358 +/- 10.1714877761
    Sum profile near NaNs: 1.60000001019 +/- 2.52982213619

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