.

Parameters
----------
x : (N,) array_like
    A sequence of values to be binned along the first dimension.
y : (N,) array_like
    A sequence of values to be binned along the second dimension.
values : (N,) array_like or list of (N,) array_like
    The data on which the statistic will be computed.  This must be
    the same shape as `x`, or a list of sequences - each with the same
    shape as `x`.  If `values` is such a list, the statistic will be
    computed on each independently.
statistic : string or callable, optional
    The statistic to compute (default is 'mean').
    The following statistics are available:

      * 'mean' : compute the mean of values for points within each bin.
        Empty bins will be represented by NaN.
      * 'std' : compute the standard deviation within each bin. This
        is implicitly calculated with ddof=0.
      * 'median' : compute the median of values for points within each
        bin. Empty bins will be represented by NaN.
      * 'count' : compute the count of points within each bin.  This is
        identical to an unweighted histogram.  `values` array is not
        referenced.
      * 'sum' : compute the sum of values for points within each bin.
        This is identical to a weighted histogram.
      * 'min' : compute the minimum of values for points within each bin.
        Empty bins will be represented by NaN.
      * 'max' : compute the maximum of values for point within each bin.
        Empty bins will be represented by NaN.
      * function : a user-defined function which takes a 1D array of
        values, and outputs a single numerical statistic. This function
        will be called on the values in each bin.  Empty bins will be
        represented by function([]), or NaN if this returns an error.

bins : int or [int, int] or array_like or [array, array], optional
    The bin specification:

      * the number of bins for the two dimensions (nx = ny = bins),
      * the number of bins in each dimension (nx, ny = bins),
      * the bin edges for the two dimensions (x_edge = y_edge = bins),
      * the bin edges in each dimension (x_edge, y_edge = bins).

    If the bin edges are specified, the number of bins will be,
    (nx = len(x_edge)-1, ny = len(y_edge)-1).

range : (2,2) array_like, optional
    The leftmost and rightmost edges of the bins along each dimension
    (if not specified explicitly in the `bins` parameters):
    [[xmin, xmax], [ymin, ymax]]. All values outside of this range will be
    considered outliers and not tallied in the histogram.
expand_binnumbers : bool, optional
    'False' (default): the returned `binnumber` is a shape (N,) array of
    linearized bin indices.
    'True': the returned `binnumber` is 'unraveled' into a shape (2,N)
    ndarray, where each row gives the bin numbers in the corresponding
    dimension.
    See the `binnumber` returned value, and the `Examples` section.

    .. versionadded:: 0.17.0

Returns
-------
statistic : (nx, ny) ndarray
    The values of the selected statistic in each two-dimensional bin.
x_edge : (nx + 1) ndarray
    The bin edges along the first dimension.
y_edge : (ny + 1) ndarray
    The bin edges along the second dimension.
binnumber : (N,) array of ints or (2,N) ndarray of ints
    This assigns to each element of `sample` an integer that represents the
    bin in which this observation falls.  The representation depends on the
    `expand_binnumbers` argument.  See `Notes` for details.


See Also
--------
numpy.digitize, numpy.histogram2d, binned_statistic, binned_statistic_dd

Notes
-----
Binedges:
All but the last (righthand-most) bin is half-open.  In other words, if
`bins` is ``[1, 2, 3, 4]``, then the first bin is ``[1, 2)`` (including 1,
but excluding 2) and the second ``[2, 3)``.  The last bin, however, is
``[3, 4]``, which *includes* 4.

`binnumber`:
This returned argument assigns to each element of `sample` an integer that
represents the bin in which it belongs.  The representation depends on the
`expand_binnumbers` argument. If 'False' (default): The returned
`binnumber` is a shape (N,) array of linearized indices mapping each
element of `sample` to its corresponding bin (using row-major ordering).
Note that the returned linearized bin indices are used for an array with
extra bins on the outer binedges to capture values outside of the defined
bin bounds.
If 'True': The returned `binnumber` is a shape (2,N) ndarray where
each row indicates bin placements for each dimension respectively.  In each
dimension, a binnumber of `i` means the corresponding value is between
(D_edge[i-1], D_edge[i]), where 'D' is either 'x' or 'y'.

.. versionadded:: 0.11.0

Examples
--------
>>> from scipy import stats

Calculate the counts with explicit bin-edges:

>>> x = [0.1, 0.1, 0.1, 0.6]
>>> y = [2.1, 2.6, 2.1, 2.1]
>>> binx = [0.0, 0.5, 1.0]
>>> biny = [2.0, 2.5, 3.0]
>>> ret = stats.binned_statistic_2d(x, y, None, 'count', bins=[binx, biny])
>>> ret.statistic
array([[2., 1.],
       [1., 0.]])

The bin in which each sample is placed is given by the `binnumber`
returned parameter.  By default, these are the linearized bin indices:

>>> ret.binnumber
array([5, 6, 5, 9])

The bin indices can also be expanded into separate entries for each
dimension using the `expand_binnumbers` parameter:

>>> ret = stats.binned_statistic_2d(x, y, None, 'count', bins=[binx, biny],
...                                 expand_binnumbers=True)
>>> ret.binnumber
array([[1, 1, 1, 2],
       [1, 2, 1, 1]])

Which shows that the first three elements belong in the xbin 1, and the
fourth into xbin 2; and so on for y.

r