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# numpy.digitize

`numpy.``digitize`(x, bins, right=False)

  Return the indices of the bins to which each value in input array belongs.

  Each index `i` returned is such that `bins[i-1] <= x < bins[i]` if bins is monotonically increasing, or `bins[i-1] > x >= bins[i]` if bins is monotonically decreasing. If values in x are beyond the bounds of bins, 0 or `len(bins)` is returned as appropriate. If right is True, then the right bin is closed so that the index `i` is such that `bins[i-1] < x <= bins[i]` or bins[i-1] >= x > bins[i]`` if bins is monotonically increasing or decreasing, respectively.

  Parameters: | x : array_like Input array to be binned. Prior to Numpy 1.10.0, this array had to be 1-dimensional, but can now have any shape. bins : array_like Array of bins. It has to be 1-dimensional and monotonic. right : bool, optional Indicating whether the intervals include the right or the left bin edge. Default behavior is (right==False) indicating that the interval does not include the right edge. The left bin end is open in this case, i.e., bins[i-1] <= x < bins[i] is the default behavior for monotonically increasing bins.
  Returns: | out : ndarray of ints Output array of indices, of same shape as x.
  Raises: | ValueError If bins is not monotonic. TypeError If the type of the input is complex.

  See also

  `bincount`, `histogram`, `unique`

  Notes

  If values in x are such that they fall outside the bin range, attempting to index bins with the indices that `digitize` returns will result in an IndexError.

  New in version 1.10.0.

  np.digitize is implemented in terms of np.searchsorted. This means that a binary search is used to bin the values, which scales much better for larger number of bins than the previous linear search. It also removes the requirement for the input array to be 1-dimensional.

  Examples

      >>> x = np.array([0.2, 6.4, 3.0, 1.6])
      >>> bins = np.array([0.0, 1.0, 2.5, 4.0, 10.0])
      >>> inds = np.digitize(x, bins)
      >>> inds
      array([1, 4, 3, 2])
      >>> for n in range(x.size):
      ...   print bins[inds[n]-1], "<=", x[n], "<", bins[inds[n]]
      ...
      0.0 <= 0.2 < 1.0
      4.0 <= 6.4 < 10.0
      2.5 <= 3.0 < 4.0
      1.0 <= 1.6 < 2.5

      >>> x = np.array([1.2, 10.0, 12.4, 15.5, 20.])
      >>> bins = np.array([0, 5, 10, 15, 20])
      >>> np.digitize(x,bins,right=True)
      array([1, 2, 3, 4, 4])
      >>> np.digitize(x,bins,right=False)
      array([1, 3, 3, 4, 5])