Indexing#

Indexing a BaseSignal provides a powerful, convenient and Pythonic way to access and modify its data. In HyperSpy indexing is achieved using isig and inav, which allow the navigation and signal dimensions to be indexed independently. The idea is essentially to specify a subset of the data based on its position in the array and it is therefore essential to know the convention adopted for specifying that position, which is described here.

Those new to Python may find indexing a somewhat esoteric concept but once mastered it is one of the most powerful features of Python based code and greatly simplifies many common tasks. HyperSpy’s Signal indexing is similar to numpy array indexing and those new to Python are encouraged to read the associated numpy documentation on the subject.

Key features of indexing in HyperSpy are as follows (note that some of these features differ from numpy):

  • HyperSpy indexing does:

    • Allow independent indexing of signal and navigation dimensions

    • Support indexing with decimal numbers.

    • Support indexing with units.

    • Support indexing with relative coordinates i.e. ‘rel0.5’

    • Use the image order for indexing i.e. [x, y, z,…] (HyperSpy) vs […, z, y, x] (numpy)

  • HyperSpy indexing does not:

    • Support indexing using arrays.

    • Allow the addition of new axes using the newaxis object.

The examples below illustrate a range of common indexing tasks.

First consider indexing a single spectrum, which has only one signal dimension (and no navigation dimensions) so we use isig:

>>> s = hs.signals.Signal1D(np.arange(10))
>>> s
<Signal1D, title: , dimensions: (|10)>
>>> s.data
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> s.isig[0]
<Signal1D, title: , dimensions: (|1)>
>>> s.isig[0].data
array([0])
>>> s.isig[9].data
array([9])
>>> s.isig[-1].data
array([9])
>>> s.isig[:5]
<Signal1D, title: , dimensions: (|5)>
>>> s.isig[:5].data
array([0, 1, 2, 3, 4])
>>> s.isig[5::-1]
<Signal1D, title: , dimensions: (|6)>
>>> s.isig[5::-1]
<Signal1D, title: , dimensions: (|6)>
>>> s.isig[5::2]
<Signal1D, title: , dimensions: (|3)>
>>> s.isig[5::2].data
array([5, 7, 9])

Unlike numpy, HyperSpy supports indexing using decimal numbers or strings (containing a decimal number and units), in which case HyperSpy indexes using the axis scales instead of the indices. Additionally, one can index using relative coordinates, for example 'rel0.5' to index the middle of the axis.

>>> s = hs.signals.Signal1D(np.arange(10))
>>> s
<Signal1D, title: , dimensions: (|10)>
>>> s.data
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> s.axes_manager[0].scale = 0.5
>>> s.axes_manager[0].axis
array([0. , 0.5, 1. , 1.5, 2. , 2.5, 3. , 3.5, 4. , 4.5])
>>> s.isig[0.5:4.].data
array([1, 2, 3, 4, 5, 6, 7])
>>> s.isig[0.5:4].data
array([1, 2, 3])
>>> s.isig[0.5:4:2].data
array([1, 3])
>>> s.axes_manager[0].units = 'µm'
>>> s.isig[:'2000 nm'].data
array([0, 1, 2, 3])
>>> s.isig[:'rel0.5'].data
array([0, 1, 2, 3])

Importantly the original BaseSignal and its “indexed self” share their data and, therefore, modifying the value of the data in one modifies the same value in the other. Note also that in the example below s.data is used to access the data as a numpy array directly and this array is then indexed using numpy indexing.

>>> s = hs.signals.Signal1D(np.arange(10))
>>> s
<Signal1D, title: , dimensions: (|10)>
>>> s.data
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> si = s.isig[::2]
>>> si.data
array([0, 2, 4, 6, 8])
>>> si.data[:] = 10
>>> si.data
array([10, 10, 10, 10, 10])
>>> s.data
array([10,  1, 10,  3, 10,  5, 10,  7, 10,  9])
>>> s.data[:] = 0
>>> si.data
array([0, 0, 0, 0, 0])

Of course it is also possible to use the same syntax to index multidimensional data treating navigation axes using inav and signal axes using isig.

>>> s = hs.signals.Signal1D(np.arange(2*3*4).reshape((2,3,4)))
>>> s
<Signal1D, title: , dimensions: (3, 2|4)>
>>> s.data 
array([[[ 0,  1,  2,  3],
    [ 4,  5,  6,  7],
    [ 8,  9, 10, 11]],

   [[12, 13, 14, 15],
    [16, 17, 18, 19],
    [20, 21, 22, 23]]])
>>> s.axes_manager[0].name = 'x'
>>> s.axes_manager[1].name = 'y'
>>> s.axes_manager[2].name = 't'
>>> s.axes_manager.signal_axes
(<t axis, size: 4>,)
>>> s.axes_manager.navigation_axes
(<x axis, size: 3, index: 0>, <y axis, size: 2, index: 0>)
>>> s.inav[0,0].data
array([0, 1, 2, 3])
>>> s.inav[0,0].axes_manager
<Axes manager, axes: (|4)>
            Name |   size |  index |  offset |   scale |  units
================ | ====== | ====== | ======= | ======= | ======
---------------- | ------ | ------ | ------- | ------- | ------
               t |      4 |      0 |       0 |       1 | <undefined>
>>> s.inav[0,0].isig[::-1].data
array([3, 2, 1, 0])
>>> s.isig[0]
<BaseSignal, title: , dimensions: (3, 2|)>
>>> s.isig[0].axes_manager
<Axes manager, axes: (3, 2|)>
            Name |   size |  index |  offset |   scale |  units
================ | ====== | ====== | ======= | ======= | ======
               x |      3 |      0 |       0 |       1 | <undefined>
               y |      2 |      0 |       0 |       1 | <undefined>
---------------- | ------ | ------ | ------- | ------- | ------
>>> s.isig[0].data
array([[ 0,  4,  8],
   [12, 16, 20]])

Independent indexation of the signal and navigation dimensions is demonstrated further in the following:

>>> s = hs.signals.Signal1D(np.arange(2*3*4).reshape((2,3,4)))
>>> s
<Signal1D, title: , dimensions: (3, 2|4)>
>>> s.data 
array([[[ 0,  1,  2,  3],
    [ 4,  5,  6,  7],
    [ 8,  9, 10, 11]],

   [[12, 13, 14, 15],
    [16, 17, 18, 19],
    [20, 21, 22, 23]]])
>>> s.axes_manager[0].name = 'x'
>>> s.axes_manager[1].name = 'y'
>>> s.axes_manager[2].name = 't'
>>> s.axes_manager.signal_axes
(<t axis, size: 4>,)
>>> s.axes_manager.navigation_axes
(<x axis, size: 3, index: 0>, <y axis, size: 2, index: 0>)
>>> s.inav[0,0].data
array([0, 1, 2, 3])
>>> s.inav[0,0].axes_manager
<Axes manager, axes: (|4)>
            Name |   size |  index |  offset |   scale |  units
================ | ====== | ====== | ======= | ======= | ======
---------------- | ------ | ------ | ------- | ------- | ------
               t |      4 |      0 |       0 |       1 | <undefined>
>>> s.isig[0]
<BaseSignal, title: , dimensions: (3, 2|)>
>>> s.isig[0].axes_manager
<Axes manager, axes: (3, 2|)>
            Name |   size |  index |  offset |   scale |  units
================ | ====== | ====== | ======= | ======= | ======
               x |      3 |      0 |       0 |       1 | <undefined>
               y |      2 |      0 |       0 |       1 | <undefined>
---------------- | ------ | ------ | ------- | ------- | ------
>>> s.isig[0].data
array([[ 0,  4,  8],
   [12, 16, 20]])

The same syntax can be used to set the data values in signal and navigation dimensions respectively:

>>> s = hs.signals.Signal1D(np.arange(2*3*4).reshape((2,3,4)))
>>> s
<Signal1D, title: , dimensions: (3, 2|4)>
>>> s.data 
array([[[ 0,  1,  2,  3],
    [ 4,  5,  6,  7],
    [ 8,  9, 10, 11]],

   [[12, 13, 14, 15],
    [16, 17, 18, 19],
    [20, 21, 22, 23]]])
>>> s.inav[0,0].data
array([0, 1, 2, 3])
>>> s.inav[0,0] = 1
>>> s.inav[0,0].data
array([1, 1, 1, 1])
>>> s.inav[0,0] = s.inav[1,1]
>>> s.inav[0,0].data
array([16, 17, 18, 19])
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