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Return table of counts for each possible unique combination in ``*args``.
When ``len(args) > 1``, the array computed by this function is
often referred to as a *contingency table* [1]_.
The arguments must be sequences with the same length. The second return
value, `count`, is an integer array with ``len(args)`` dimensions. If
`levels` is None, the shape of `count` is ``(n0, n1, ...)``, where ``nk``
is the number of unique elements in ``args[k]``.
Parameters
----------
*args : sequences
A sequence of sequences whose unique aligned elements are to be
counted. The sequences in args must all be the same length.
levels : sequence, optional
If `levels` is given, it must be a sequence that is the same length as
`args`. Each element in `levels` is either a sequence or None. If it
is a sequence, it gives the values in the corresponding sequence in
`args` that are to be counted. If any value in the sequences in `args`
does not occur in the corresponding sequence in `levels`, that value
is ignored and not counted in the returned array `count`. The default
value of `levels` for ``args[i]`` is ``np.unique(args[i])``
sparse : bool, optional
If True, return a sparse matrix. The matrix will be an instance of
the `scipy.sparse.coo_matrix` class. Because SciPy's sparse matrices
must be 2-d, only two input sequences are allowed when `sparse` is
True. Default is False.
Returns
-------
res : CrosstabResult
An object containing the following attributes:
elements : tuple of numpy.ndarrays.
Tuple of length ``len(args)`` containing the arrays of elements
that are counted in `count`. These can be interpreted as the
labels of the corresponding dimensions of `count`. If `levels` was
given, then if ``levels[i]`` is not None, ``elements[i]`` will
hold the values given in ``levels[i]``.
count : numpy.ndarray or scipy.sparse.coo_matrix
Counts of the unique elements in ``zip(*args)``, stored in an
array. Also known as a *contingency table* when ``len(args) > 1``.
See Also
--------
numpy.unique
Notes
-----
.. versionadded:: 1.7.0
References
----------
.. [1] "Contingency table", http://en.wikipedia.org/wiki/Contingency_table
Examples
--------
>>> from scipy.stats.contingency import crosstab
Given the lists `a` and `x`, create a contingency table that counts the
frequencies of the corresponding pairs.
>>> a = ['A', 'B', 'A', 'A', 'B', 'B', 'A', 'A', 'B', 'B']
>>> x = ['X', 'X', 'X', 'Y', 'Z', 'Z', 'Y', 'Y', 'Z', 'Z']
>>> res = crosstab(a, x)
>>> avals, xvals = res.elements
>>> avals
array(['A', 'B'], dtype='<U1')
>>> xvals
array(['X', 'Y', 'Z'], dtype='<U1')
>>> res.count
array([[2, 3, 0],
[1, 0, 4]])
So `('A', 'X')` occurs twice, `('A', 'Y')` occurs three times, etc.
Higher dimensional contingency tables can be created.
>>> p = [0, 0, 0, 0, 1, 1, 1, 0, 0, 1]
>>> res = crosstab(a, x, p)
>>> res.count
array([[[2, 0],
[2, 1],
[0, 0]],
[[1, 0],
[0, 0],
[1, 3]]])
>>> res.count.shape
(2, 3, 2)
The values to be counted can be set by using the `levels` argument.
It allows the elements of interest in each input sequence to be
given explicitly instead finding the unique elements of the sequence.
For example, suppose one of the arguments is an array containing the
answers to a survey question, with integer values 1 to 4. Even if the
value 1 does not occur in the data, we want an entry for it in the table.
>>> q1 = [2, 3, 3, 2, 4, 4, 2, 3, 4, 4, 4, 3, 3, 3, 4] # 1 does not occur.
>>> q2 = [4, 4, 2, 2, 2, 4, 1, 1, 2, 2, 4, 2, 2, 2, 4] # 3 does not occur.
>>> options = [1, 2, 3, 4]
>>> res = crosstab(q1, q2, levels=(options, options))
>>> res.count
array([[0, 0, 0, 0],
[1, 1, 0, 1],
[1, 4, 0, 1],
[0, 3, 0, 3]])
If `levels` is given, but an element of `levels` is None, the unique values
of the corresponding argument are used. For example,
>>> res = crosstab(q1, q2, levels=(None, options))
>>> res.elements
[array([2, 3, 4]), [1, 2, 3, 4]]
>>> res.count
array([[1, 1, 0, 1],
[1, 4, 0, 1],
[0, 3, 0, 3]])
If we want to ignore the pairs where 4 occurs in ``q2``, we can
give just the values [1, 2] to `levels`, and the 4 will be ignored:
>>> res = crosstab(q1, q2, levels=(None, [1, 2]))
>>> res.elements
[array([2, 3, 4]), [1, 2]]
>>> res.count
array([[1, 1],
[1, 4],
[0, 3]])
Finally, let's repeat the first example, but return a sparse matrix:
>>> res = crosstab(a, x, sparse=True)
>>> res.count
<2x3 sparse matrix of type '<class 'numpy.int64'>'
with 4 stored elements in COOrdinate format>
>>> res.count.A
array([[2, 3, 0],
[1, 0, 4]])
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