# scipy.stats.binned_statistic_2d

scipy.stats.binned_statistic_2d(x, y, values, statistic='mean', bins=10, range=None, expand_binnumbers=False)

  Compute a bidimensional binned statistic for one or more sets of data.

  This is a generalization of a histogram2d function. A histogram divides the space into bins, and returns the count of the number of points in each bin. This function allows the computation of the sum, mean, median, or other statistic of the values (or set of values) within each bin.

  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.

      New in version 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’.

  New in version 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.