# numpy.digitize

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

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

  right | order of bins | returned index i satisfies
  --- | --- | ---
  `False` | increasing | `bins[i-1] <= x < bins[i]`
  `True` | increasing | `bins[i-1] < x <= bins[i]`
  `False` | decreasing | `bins[i-1] > x >= bins[i]`
  `True` | decreasing | `bins[i-1] >= x > bins[i]`

  If values in x are beyond the bounds of bins, 0 or `len(bins)` is returned as appropriate.

  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:
    indices 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`, `searchsorted`

  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.

  For monotonically _increasing_ bins, the following are equivalent:

      np.digitize(x, bins, right=True)
      np.searchsorted(bins, x, side='left')

  Note that as the order of the arguments are reversed, the side must be too. The `searchsorted` call is marginally faster, as it does not do any monotonicity checks. Perhaps more importantly, it supports all dtypes.

  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])