205 lines
7.2 KiB
Python
205 lines
7.2 KiB
Python
import numpy as np
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from scipy.sparse import coo_matrix
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from scipy._lib._bunch import _make_tuple_bunch
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CrosstabResult = _make_tuple_bunch(
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"CrosstabResult", ["elements", "count"]
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)
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def crosstab(*args, levels=None, sparse=False):
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"""
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Return table of counts for each possible unique combination in ``*args``.
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When ``len(args) > 1``, the array computed by this function is
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often referred to as a *contingency table* [1]_.
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The arguments must be sequences with the same length. The second return
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value, `count`, is an integer array with ``len(args)`` dimensions. If
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`levels` is None, the shape of `count` is ``(n0, n1, ...)``, where ``nk``
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is the number of unique elements in ``args[k]``.
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Parameters
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----------
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*args : sequences
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A sequence of sequences whose unique aligned elements are to be
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counted. The sequences in args must all be the same length.
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levels : sequence, optional
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If `levels` is given, it must be a sequence that is the same length as
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`args`. Each element in `levels` is either a sequence or None. If it
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is a sequence, it gives the values in the corresponding sequence in
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`args` that are to be counted. If any value in the sequences in `args`
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does not occur in the corresponding sequence in `levels`, that value
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is ignored and not counted in the returned array `count`. The default
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value of `levels` for ``args[i]`` is ``np.unique(args[i])``
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sparse : bool, optional
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If True, return a sparse matrix. The matrix will be an instance of
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the `scipy.sparse.coo_matrix` class. Because SciPy's sparse matrices
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must be 2-d, only two input sequences are allowed when `sparse` is
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True. Default is False.
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Returns
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-------
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res : CrosstabResult
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An object containing the following attributes:
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elements : tuple of numpy.ndarrays.
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Tuple of length ``len(args)`` containing the arrays of elements
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that are counted in `count`. These can be interpreted as the
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labels of the corresponding dimensions of `count`. If `levels` was
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given, then if ``levels[i]`` is not None, ``elements[i]`` will
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hold the values given in ``levels[i]``.
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count : numpy.ndarray or scipy.sparse.coo_matrix
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Counts of the unique elements in ``zip(*args)``, stored in an
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array. Also known as a *contingency table* when ``len(args) > 1``.
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See Also
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--------
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numpy.unique
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Notes
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-----
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.. versionadded:: 1.7.0
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References
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----------
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.. [1] "Contingency table", http://en.wikipedia.org/wiki/Contingency_table
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Examples
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--------
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>>> from scipy.stats.contingency import crosstab
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Given the lists `a` and `x`, create a contingency table that counts the
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frequencies of the corresponding pairs.
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>>> a = ['A', 'B', 'A', 'A', 'B', 'B', 'A', 'A', 'B', 'B']
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>>> x = ['X', 'X', 'X', 'Y', 'Z', 'Z', 'Y', 'Y', 'Z', 'Z']
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>>> res = crosstab(a, x)
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>>> avals, xvals = res.elements
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>>> avals
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array(['A', 'B'], dtype='<U1')
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>>> xvals
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array(['X', 'Y', 'Z'], dtype='<U1')
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>>> res.count
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array([[2, 3, 0],
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[1, 0, 4]])
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So `('A', 'X')` occurs twice, `('A', 'Y')` occurs three times, etc.
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Higher dimensional contingency tables can be created.
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>>> p = [0, 0, 0, 0, 1, 1, 1, 0, 0, 1]
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>>> res = crosstab(a, x, p)
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>>> res.count
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array([[[2, 0],
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[2, 1],
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[0, 0]],
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[[1, 0],
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[0, 0],
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[1, 3]]])
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>>> res.count.shape
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(2, 3, 2)
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The values to be counted can be set by using the `levels` argument.
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It allows the elements of interest in each input sequence to be
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given explicitly instead finding the unique elements of the sequence.
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For example, suppose one of the arguments is an array containing the
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answers to a survey question, with integer values 1 to 4. Even if the
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value 1 does not occur in the data, we want an entry for it in the table.
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>>> q1 = [2, 3, 3, 2, 4, 4, 2, 3, 4, 4, 4, 3, 3, 3, 4] # 1 does not occur.
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>>> q2 = [4, 4, 2, 2, 2, 4, 1, 1, 2, 2, 4, 2, 2, 2, 4] # 3 does not occur.
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>>> options = [1, 2, 3, 4]
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>>> res = crosstab(q1, q2, levels=(options, options))
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>>> res.count
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array([[0, 0, 0, 0],
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[1, 1, 0, 1],
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[1, 4, 0, 1],
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[0, 3, 0, 3]])
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If `levels` is given, but an element of `levels` is None, the unique values
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of the corresponding argument are used. For example,
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>>> res = crosstab(q1, q2, levels=(None, options))
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>>> res.elements
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[array([2, 3, 4]), [1, 2, 3, 4]]
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>>> res.count
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array([[1, 1, 0, 1],
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[1, 4, 0, 1],
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[0, 3, 0, 3]])
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If we want to ignore the pairs where 4 occurs in ``q2``, we can
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give just the values [1, 2] to `levels`, and the 4 will be ignored:
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>>> res = crosstab(q1, q2, levels=(None, [1, 2]))
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>>> res.elements
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[array([2, 3, 4]), [1, 2]]
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>>> res.count
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array([[1, 1],
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[1, 4],
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[0, 3]])
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Finally, let's repeat the first example, but return a sparse matrix:
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>>> res = crosstab(a, x, sparse=True)
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>>> res.count
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<2x3 sparse matrix of type '<class 'numpy.int64'>'
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with 4 stored elements in COOrdinate format>
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>>> res.count.A
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array([[2, 3, 0],
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[1, 0, 4]])
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"""
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nargs = len(args)
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if nargs == 0:
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raise TypeError("At least one input sequence is required.")
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len0 = len(args[0])
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if not all(len(a) == len0 for a in args[1:]):
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raise ValueError("All input sequences must have the same length.")
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if sparse and nargs != 2:
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raise ValueError("When `sparse` is True, only two input sequences "
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"are allowed.")
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if levels is None:
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# Call np.unique with return_inverse=True on each argument.
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actual_levels, indices = zip(*[np.unique(a, return_inverse=True)
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for a in args])
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else:
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# `levels` is not None...
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if len(levels) != nargs:
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raise ValueError('len(levels) must equal the number of input '
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'sequences')
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args = [np.asarray(arg) for arg in args]
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mask = np.zeros((nargs, len0), dtype=np.bool_)
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inv = np.zeros((nargs, len0), dtype=np.intp)
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actual_levels = []
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for k, (levels_list, arg) in enumerate(zip(levels, args)):
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if levels_list is None:
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levels_list, inv[k, :] = np.unique(arg, return_inverse=True)
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mask[k, :] = True
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else:
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q = arg == np.asarray(levels_list).reshape(-1, 1)
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mask[k, :] = np.any(q, axis=0)
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qnz = q.T.nonzero()
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inv[k, qnz[0]] = qnz[1]
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actual_levels.append(levels_list)
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mask_all = mask.all(axis=0)
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indices = tuple(inv[:, mask_all])
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if sparse:
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count = coo_matrix((np.ones(len(indices[0]), dtype=int),
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(indices[0], indices[1])))
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count.sum_duplicates()
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else:
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shape = [len(u) for u in actual_levels]
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count = np.zeros(shape, dtype=int)
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np.add.at(count, indices, 1)
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return CrosstabResult(actual_levels, count)
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