code: def binned_statistic_dd(
      sample,
      values,
      statistic="mean",
      bins=10,
      range=None,
      expand_binnumbers=False,
      binned_statistic_result=None,
  ):
      """
      Compute a multidimensional binned statistic for a set of data.
  
      This is a generalization of a histogramdd 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 within each bin.
  
      Parameters
      ----------
      sample : array_like
          Data to histogram passed as a sequence of N arrays of length D, or
          as an (N,D) array.
      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 `sample`, or a list of sequences - each with the
          same shape as `sample`.  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.
            * '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.
            * 'std' : compute the standard deviation within each bin. This
              is implicitly calculated with ddof=0. If the number of values
              within a given bin is 0 or 1, the computed standard deviation value
              will be 0 for the bin.
            * '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 : sequence or positive int, optional
          The bin specification must be in one of the following forms:
  
            * A sequence of arrays describing the bin edges along each dimension.
            * The number of bins for each dimension (nx, ny, ... = bins).
            * The number of bins for all dimensions (nx = ny = ... = bins).
      range : sequence, optional
          A sequence of lower and upper bin edges to be used if the edges are
          not given explicitly in `bins`. Defaults to the minimum and maximum
          values along each dimension.
      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 (D,N)
          ndarray, where each row gives the bin numbers in the corresponding
          dimension.
          See the `binnumber` returned value, and the `Examples` section of
          `binned_statistic_2d`.
      binned_statistic_result : binnedStatisticddResult
          Result of a previous call to the function in order to reuse bin edges
          and bin numbers with new values and/or a different statistic.
          To reuse bin numbers, `expand_binnumbers` must have been set to False
          (the default)
  
          .. versionadded:: 0.17.0
  
      Returns
      -------
      statistic : ndarray, shape(nx1, nx2, nx3,...)
          The values of the selected statistic in each two-dimensional bin.
      bin_edges : list of ndarrays
          A list of D arrays describing the (nxi + 1) bin edges for each
          dimension.
      binnumber : (N,) array of ints or (D,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.histogramdd, binned_statistic, binned_statistic_2d
  
      Notes
      -----
      Binedges:
      All but the last (righthand-most) bin is half-open in each dimension.  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).
      If 'True': The returned `binnumber` is a shape (D,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
      (bin_edges[D][i-1], bin_edges[D][i]), for each dimension 'D'.
  
      .. versionadded:: 0.11.0
  
      Examples
      --------
      >>> from scipy import stats
      >>> import matplotlib.pyplot as plt
      >>> from mpl_toolkits.mplot3d import Axes3D
  
      Take an array of 600 (x, y) coordinates as an example.
      `binned_statistic_dd` can handle arrays of higher dimension `D`. But a plot
      of dimension `D+1` is required.
  
      >>> mu = np.array([0., 1.])
      >>> sigma = np.array([[1., -0.5],[-0.5, 1.5]])
      >>> multinormal = stats.multivariate_normal(mu, sigma)
      >>> data = multinormal.rvs(size=600, random_state=235412)
      >>> data.shape
      (600, 2)
  
      Create bins and count how many arrays fall in each bin:
  
      >>> N = 60
      >>> x = np.linspace(-3, 3, N)
      >>> y = np.linspace(-3, 4, N)
      >>> ret = stats.binned_statistic_dd(data, np.arange(600), bins=[x, y],
      ...                                 statistic='count')
      >>> bincounts = ret.statistic
  
      Set the volume and the location of bars:
  
      >>> dx = x[1] - x[0]
      >>> dy = y[1] - y[0]
      >>> x, y = np.meshgrid(x[:-1]+dx/2, y[:-1]+dy/2)
      >>> z = 0
  
      >>> bincounts = bincounts.ravel()
      >>> x = x.ravel()
      >>> y = y.ravel()
  
      >>> fig = plt.figure()
      >>> ax = fig.add_subplot(111, projection='3d')
      >>> with np.errstate(divide='ignore'):   # silence random axes3d warning
      ...     ax.bar3d(x, y, z, dx, dy, bincounts)
  
      Reuse bin numbers and bin edges with new values:
  
      >>> ret2 = stats.binned_statistic_dd(data, -np.arange(600),
      ...                                  binned_statistic_result=ret,
      ...                                  statistic='mean')
      """
      known_stats = [
          "mean",
          "median",
          "count",
          "sum",
          "std",
          "min",
          "max",
      ]
      if not callable(statistic) and statistic not in known_stats:
          raise ValueError("invalid statistic %r" % (statistic,))
  
      try:
          bins = index(bins)
      except TypeError:
          # bins is not an integer
          pass
      # If bins was an integer-like object, now it is an actual Python int.
  
      # NOTE: for _bin_edges(), see e.g. gh-11365
      if isinstance(bins, int) and not np.isfinite(sample).all():
          raise ValueError("%r contains non-finite values." % (sample,))
  
      # `Ndim` is the number of dimensions (e.g. `2` for `binned_statistic_2d`)
      # `Dlen` is the length of elements along each dimension.
      # This code is based on np.histogramdd
      try:
          # `sample` is an ND-array.
          Dlen, Ndim = sample.shape
      except (AttributeError, ValueError):
          # `sample` is a sequence of 1D arrays.
          sample = np.atleast_2d(sample).T
          Dlen, Ndim = sample.shape
  
      # Store initial shape of `values` to preserve it in the output
      values = np.asarray(values)
      input_shape = list(values.shape)
      # Make sure that `values` is 2D to iterate over rows
      values = np.atleast_2d(values)
      Vdim, Vlen = values.shape
  
      # Make sure `values` match `sample`
      if statistic != "count" and Vlen != Dlen:
          raise AttributeError(
              "The number of `values` elements must match the "
              "length of each `sample` dimension."
          )
  
      try:
          M = len(bins)
          if M != Ndim:
              raise AttributeError(
                  "The dimension of bins must be equal "
                  "to the dimension of the sample x."
              )
      except TypeError:
          bins = Ndim * [bins]
  
      if binned_statistic_result is None:
          nbin, edges, dedges = _bin_edges(sample, bins, range)
          binnumbers = _bin_numbers(sample, nbin, edges, dedges)
      else:
          edges = binned_statistic_result.bin_edges
          nbin = np.array(
              [len(edges[i]) + 1 for i in builtins.range(Ndim)]
          )
          # +1 for outlier bins
          dedges = [np.diff(edges[i]) for i in builtins.range(Ndim)]
          binnumbers = binned_statistic_result.binnumber
  
      result = np.empty([Vdim, nbin.prod()], float)
  
      if statistic == "mean":
          result.fill(np.nan)
          flatcount = np.bincount(binnumbers, None)
          a = flatcount.nonzero()
          for vv in builtins.range(Vdim):
              flatsum = np.bincount(binnumbers, values[vv])
              result[vv, a] = flatsum[a] / flatcount[a]
      elif statistic == "std":
          result.fill(0)
          _calc_binned_statistic(
              Vdim, binnumbers, result, values, np.std
          )
      elif statistic == "count":
          result.fill(0)
          flatcount = np.bincount(binnumbers, None)
          a = np.arange(len(flatcount))
          result[:, a] = flatcount[np.newaxis, :]
      elif statistic == "sum":
          result.fill(0)
          for vv in builtins.range(Vdim):
              flatsum = np.bincount(binnumbers, values[vv])
              a = np.arange(len(flatsum))
              result[vv, a] = flatsum
      elif statistic == "median":
          result.fill(np.nan)
          _calc_binned_statistic(
              Vdim, binnumbers, result, values, np.median
          )
      elif statistic == "min":
          result.fill(np.nan)
          _calc_binned_statistic(
              Vdim, binnumbers, result, values, np.min
          )
      elif statistic == "max":
          result.fill(np.nan)
          _calc_binned_statistic(
              Vdim, binnumbers, result, values, np.max
          )
      elif callable(statistic):
          with np.errstate(
              invalid="ignore"
          ), suppress_warnings() as sup:
              sup.filter(RuntimeWarning)
              try:
                  null = statistic([])
              except Exception:
                  null = np.nan
          result.fill(null)
          _calc_binned_statistic(
              Vdim,
              binnumbers,
              result,
              values,
              statistic,
              is_callable=True,
          )
  
      # Shape into a proper matrix
      result = result.reshape(np.append(Vdim, nbin))
  
      # Remove outliers (indices 0 and -1 for each bin-dimension).
      core = tuple([slice(None)] + Ndim * [slice(1, -1)])
      result = result[core]
  
      # Unravel binnumbers into an ndarray, each row the bins for each dimension
      if expand_binnumbers and Ndim > 1:
          binnumbers = np.asarray(np.unravel_index(binnumbers, nbin))
  
      if np.any(result.shape[1:] != nbin - 2):
          raise RuntimeError("Internal Shape Error")
  
      # Reshape to have output (`result`) match input (`values`) shape
      result = result.reshape(input_shape[:-1] + list(nbin - 2))
  
      return BinnedStatisticddResult(result, edges, binnumbers)
  
file_path: catboost/contrib/python/scipy/py3/scipy/stats/_binned_statistic.py
imports: import builtins
  import numpy
  from numpy.testing import suppress_warnings
  from operator import index
  from collections import namedtuple
label_desc: Use image node_id 3 for calling a global function with example usage: binned_statistic_dd(sample, values, statistic, bins, range, expand_binnumbers, binned_statistic_result) and returns: BinnedStatisticddResult