Slice Description

Similarly to Data Description, the slice descriptions are just dictionaries that indicate how the program should produce multi-dimensional slices. For ease of use in scripts, we can generate a function that returns a list of dictionaries.

import numpy as np
from matplotlib.colors import LogNorm

def define_data_slices(extra=''):
    dsl=[]

    # Add single LE slice
    description={'QDimension0':'1,0,0',
                 'QDimension1':'0,1,0',
                 'QDimension2':'0,0,1',
                 'Dimension0Name':'QDimension2',
                 'Dimension0Binning':'-2.5,0.025,2.5',
                 'Dimension1Name':'DeltaE',
                 'Dimension1Binning':'-0.5,0.025,3.25',
                 'Dimension2Name':'QDimension0',
                 'Dimension2Binning':'-0.2,0.2',
                 'Dimension3Name':'QDimension1',
                 'Dimension3Binning':'-2,2',
                  #'SymmetryOperations':'x,y,z;-x,y,z;x,y,-z;-x,y,-z',
                 'ConvertToChi':False,
                 'Plot_parameters':{'norm':LogNorm()},
                 'Axes_parameters':{'xrange':None,'yrange':None,
                                    'xtitle':None, 'ytitle':None,
                                    'title':'CNCS slice',
                                    'aspect_ratio':None,
                                    'tight_axes':True,
                                    'grid':True},
                 'Name':'LE_slice_ K=[-2,2]'+extra}
    dsl.append(description)

    # Add KL slices at different energies in a loop
    for E in np.arange(0,2,0.5):
        dE=0.05
        description={'QDimension0':'1,0,0',
                     'QDimension1':'0,1,0',
                     'QDimension2':'0,0,1',
                     'Dimension0Name':'QDimension1',
                     'Dimension0Binning':'-2.,0.025,2.',
                     'Dimension1Name':'QDimension2',
                     'Dimension1Binning':'-2.5,0.025,2.5',
                     'Dimension2Name':'QDimension0',
                     'Dimension2Binning':'-0.2,0.2',
                     'Dimension3Name':'DeltaE',
                     'Dimension3Binning':f'{E-dE},{E+dE}',
                     'SymmetryOperations':'x,y,z;-x,y,z;x,y,-z;-x,y,-z',
                     'ConvertToChi':False,
                     'Plot_parameters':{'norm':LogNorm(vmin=1e-4,vmax=1e-1)},
                     'Axes_parameters':{'xrange':None,'yrange':None,
                                        'xtitle':None, 'ytitle':None,
                                        'title':f'CNCS E=[{E-dE},{E+dE}]meV',
                                        'aspect_ratio':None,
                                        'tight_axes':True,
                                        'grid':True},
                     'Name':f'KL_slice_{E:.1f}meV'+extra}
        dsl.append(description)

    return dsl

For first time users of this software, a recommended approach would be to copy the block between lines 6-30 for each of the slices. Don’t forget to append the slice description to the list.

Note that the program is using the MDNorm algorithm to generate slices, so most of the parameters in the slice descriptions are just properties of the algorithm.

Name

Each slice needs to have a unique name. In the example above, the function returning the list of slice description contains an extra parameter. This is to allow to use the same function to describe slices out of different datasets. For example, one can call

sd_5K = define_data_slices(extra='_T=5K')
sd_1K = define_data_slices(extra='_T=1K')

Reciprocal space geometry parameters

QDimension0, QDimension1, QDimension2

These represent three 3D vectors that define the projection axes. If not defined, these are set by default to [1,0,0], [0,1,0], [0,0,1], corresponding to projections along the [H,0,0], [0,K,0], [0,0,L] axes. Note that this projections must not be co-planar, but they don’t have to be orthogonal.

Dimension0Name, Dimension1Name, …

These parameters specify the dimension of the ouput multidimensional histogram workspace. Allowed values are QDimension0, QDimension1, QDimension2, DeltaE, and any of the names in the AdditionalDimensions parameters. By default the first three are QDimension0, QDimension1, QDimension2. There needs to be exactly one Name for every dimension in the MDE workspace.

So if one would like to generate a two dimensional slice, with the horizontal axis being [0,K,0] and the vertical axis along the energy transfer, they would need to choose QDimension1 for Dimension0Name, DeltaE for Dimension1Name, with the remaining dimension names being QDimension0 and QDimension2.

Dimension0Binning, Dimension1Binning, …

For each of the dimensions in the output workspace one must choose a binning. These parameters are strings, containing one, two, or three numbers, with the following meaning:

three numbers - minimum value, step, maximum value
two numbers - minimum value, maximum value (data is integrated between these limits)
one number - step. This is similar to the three number option, but the program will decide the minimum and maximum values.
empty string - completely integrate the corresponding dimension

For example, a 2D slice in the [0, K, L] plane around the elastic line will be defined by

   'Dimension0Name':'QDimension1',
   'Dimension0Binning':'-2.,0.025,2.',
   'Dimension1Name':'QDimension2',
   'Dimension1Binning':'-2.5,0.025,2.5',
   'Dimension2Name':'QDimension0',
   'Dimension2Binning':'-0.2,0.2',
   'Dimension3Name':'DeltaE',
   'Dimension3Binning':'-.1,.1',

A 1D cut along the energy transfer, with a step of 0.1 meV, going through [2,1,0] Bragg peak, would look similar to this:

   'Dimension0Name':'DeltaE',
   'Dimension0Binning':'0.1',
   'Dimension1Name':'QDimension0',
   'Dimension1Binning':'1.9,2.1',
   'Dimension2Name':'QDimension1',
   'Dimension2Binning':'0.9,1.1',
   'Dimension3Name':'QDimension2',
   'Dimension3Binning':'-.1,.1',

SymmetryOperations

To increase statistics, one might use symmetry operations. This parameter is a string that contain one of the following:

list of symmetry operations. Different symmetry operations are separated by semicolon. For example, 'x,y,z;x,-y,z;-x,y,z;-x,-y,z'.
a string describing the space group.
a string describing the point group.

Notes:

applying a symmetry operation is not folding the data
if one is looking to add symmetrized data and the original one, don’t forget to add the identity operation x,y,z.
the time to produce a slice increases proportionally with the number of symmetry operations.
point and space groups are case and space sensitive. To get a list of possible space and point groups run the code below in Mantid:

from mantid.geometry import SpaceGroupFactory
from mantid.geometry import PointGroupFactory

print('Point groups')
print('; '.join([pgs for pgs in PointGroupFactory.getAllPointGroupSymbols()]))
print('Space groups')
print('; '.join([sgs for sgs in SpaceGroupFactory.getAllSpaceGroupSymbols()]))

As part of the experimental reduction, an important step is plotting of the cuts and slices of the data. While it is not necessary to fill in these parameters (plotting can be done independently of this software), sometimes it’s convenient to to store the settings for given figures. This program uses matplotlib and the Mantid extensions to it.

Axes_parameters

This is a dictionary of key-value pairs that are related to the axis objects in matplotlib. Not all features are supported.

title - a tring that contains the title of the plot
grid - if True it will show the grid
xrange, yrange - list with two elements to control the extents of x and y axes
xtitle, ytitle - strings to override the default axes titles
aspect_ratio - ‘auto’, ‘equal’, or a float. See set_aspect
tight_axes - the tight parameter for matplotlib.axes.Axes.autoscale

Plot_parameters

For one dimensional data, the plot_slice function uses the matplotlib errorbar function, while for two dimensional plots it uses the pcolormesh. Any key-value pairs in the Plot_parameters are passed to the corresponding matplotlib function.

Other parameters

ConvertToChi

If set to True, this parameter will change the plots to dynamic susceptibility χ’’. The temperature is taken from the data description. See AppliedDetailedBalanceMD algorithm in Mantid.

Smoothing

If a number is given, the histogram will be smoothed using a Gaussian kernel with the given FWHM (in units of histogram bins).