The syntax is:
a[start:stop] # items start through stop-1
a[start:] # items start through the rest of the array
a[:stop] # items from the beginning through stop-1
a[:] # a copy of the whole array
There is also the step value, which can be used with any of the above:
a[start:stop:step] # start through not past stop, by step
The key point to remember is that the :stop value represents the first value that is not in the selected slice. So, the difference between stop and start is the number of elements selected (if step is 1, the default).
The other feature is that start or stop may be a negative number, which means it counts from the end of the array instead of the beginning. So:
a[-1] # last item in the array
a[-2:] # last two items in the array
a[:-2] # everything except the last two items
Similarly, step may be a negative number:
a[::-1] # all items in the array, reversed
a[1::-1] # the first two items, reversed
a[:-3:-1] # the last two items, reversed
a[-3::-1] # everything except the last two items, reversed
Python is kind to the programmer if there are fewer items than you ask for. For example, if you ask for a[:-2] and a only contains one element, you get an empty list instead of an error. Sometimes you would prefer the error, so you have to be aware that this may happen.
Relationship with the slice object
A slice object can represent a slicing operation, i.e.:
a[start:stop:step]
is equivalent to:
a[slice(start, stop, step)]
Slice objects also behave slightly differently depending on the number of arguments, similar to range(), i.e. both slice(stop) and slice(start, stop[, step]) are supported.
To skip specifying a given argument, one might use None, so that e.g. a[start:] is equivalent to a[slice(start, None)] or a[::-1] is equivalent to a[slice(None, None, -1)].
While the :-based notation is very helpful for simple slicing, the explicit use of slice() objects simplifies the programmatic generation of slicing.
Videos
The syntax is:
a[start:stop] # items start through stop-1
a[start:] # items start through the rest of the array
a[:stop] # items from the beginning through stop-1
a[:] # a copy of the whole array
There is also the step value, which can be used with any of the above:
a[start:stop:step] # start through not past stop, by step
The key point to remember is that the :stop value represents the first value that is not in the selected slice. So, the difference between stop and start is the number of elements selected (if step is 1, the default).
The other feature is that start or stop may be a negative number, which means it counts from the end of the array instead of the beginning. So:
a[-1] # last item in the array
a[-2:] # last two items in the array
a[:-2] # everything except the last two items
Similarly, step may be a negative number:
a[::-1] # all items in the array, reversed
a[1::-1] # the first two items, reversed
a[:-3:-1] # the last two items, reversed
a[-3::-1] # everything except the last two items, reversed
Python is kind to the programmer if there are fewer items than you ask for. For example, if you ask for a[:-2] and a only contains one element, you get an empty list instead of an error. Sometimes you would prefer the error, so you have to be aware that this may happen.
Relationship with the slice object
A slice object can represent a slicing operation, i.e.:
a[start:stop:step]
is equivalent to:
a[slice(start, stop, step)]
Slice objects also behave slightly differently depending on the number of arguments, similar to range(), i.e. both slice(stop) and slice(start, stop[, step]) are supported.
To skip specifying a given argument, one might use None, so that e.g. a[start:] is equivalent to a[slice(start, None)] or a[::-1] is equivalent to a[slice(None, None, -1)].
While the :-based notation is very helpful for simple slicing, the explicit use of slice() objects simplifies the programmatic generation of slicing.
The Python tutorial talks about it (scroll down a bit until you get to the part about slicing).
The ASCII art diagram is helpful too for remembering how slices work:
+---+---+---+---+---+---+
| P | y | t | h | o | n |
+---+---+---+---+---+---+
0 1 2 3 4 5
-6 -5 -4 -3 -2 -1
One way to remember how slices work is to think of the indices as pointing between characters, with the left edge of the first character numbered 0. Then the right edge of the last character of a string of n characters has index n.
Ellipsis is used mainly by the numeric python extension, which adds a multidimensional array type. Since there are more than one dimensions, slicing becomes more complex than just a start and stop index; it is useful to be able to slice in multiple dimensions as well. eg, given a 4x4 array, the top left area would be defined by the slice "[:2,:2]"
>>> a
array([[ 1, 2, 3, 4],
[ 5, 6, 7, 8],
[ 9, 10, 11, 12],
[13, 14, 15, 16]])
>>> a[:2,:2] # top left
array([[1, 2],
[5, 6]])
Ellipsis is used here to indicate a placeholder for the rest of the array dimensions not specified. Think of it as indicating the full slice [:] for dimensions not specified, so
for a 3d array, a[...,0] is the same as a[:,:,0] and for 4d, a[:,:,:,0].
Note that the actual Ellipsis literal (...) is not usable outside the slice syntax in python2, though there is a builtin Ellipsis object. This is what is meant by "The conversion of an ellipsis slice item is the built-in Ellipsis object." ie. "a[...]" is effectively sugar for "a[Ellipsis]". In python3, ... denotes Ellipsis anywhere, so you can write:
>>> ...
Ellipsis
If you're not using numpy, you can pretty much ignore all mention of Ellipsis. None of the builtin types use it, so really all you have to care about is that lists get passed a single slice object, that contains "start","stop" and "step" members. ie:
l[start:stop:step] # proper_slice syntax from the docs you quote.
is equivalent to calling:
l.__getitem__(slice(start, stop, step))
Defining simple test class that just prints what is being passed:
>>> class TestGetitem(object):
... def __getitem__(self, item):
... print type(item), item
...
>>> t = TestGetitem()
Expression example:
>>> t[1]
<type 'int'> 1
>>> t[3-2]
<type 'int'> 1
>>> t['test']
<type 'str'> test
>>> t[t]
<class '__main__.TestGetitem'> <__main__.TestGetitem object at 0xb7e9bc4c>
Slice example:
>>> t[1:2]
<type 'slice'> slice(1, 2, None)
>>> t[1:'this':t]
<type 'slice'> slice(1, 'this', <__main__.TestGetitem object at 0xb7e9bc4c>)
Ellipsis example:
>>> t[...]
<type 'ellipsis'> Ellipsis
Tuple with ellipsis and slice:
>>> t[...,1:]
<type 'tuple'> (Ellipsis, slice(1, None, None))