numpy.quantile

numpy.quantile(a, q, axis=None, out=None, overwrite_input=False, interpolation='linear', keepdims=False)

Compute the q-th quantile of the data along the specified axis.

New in version 1.15.0.

Parameters:

a : array_like

Input array or object that can be converted to an array.

q : array_like of float

Quantile or sequence of quantiles to compute, which must be between 0 and 1 inclusive.

axis : {int, tuple of int, None}, optional

Axis or axes along which the quantiles are computed. The default is to compute the quantile(s) along a flattened version of the array.

out : ndarray, optional

Alternative output array in which to place the result. It must have the same shape and buffer length as the expected output, but the type (of the output) will be cast if necessary.

overwrite_input : bool, optional

If True, then allow the input array a to be modified by intermediate calculations, to save memory. In this case, the contents of the input a after this function completes is undefined.

interpolation : {‘linear’, ‘lower’, ‘higher’, ‘midpoint’, ‘nearest’}

This optional parameter specifies the interpolation method to use when the desired quantile lies between two data points i < j:

• linear: i + (j - i) * fraction, where fraction is the fractional part of the index surrounded by i and j.
• lower: i.
• higher: j.
• nearest: i or j, whichever is nearest.
• midpoint: (i + j) / 2.

keepdims : bool, optional

If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original array a.

Returns:

quantile : scalar or ndarray

If q is a single quantile and axis=None, then the result is a scalar. If multiple quantiles are given, first axis of the result corresponds to the quantiles. The other axes are the axes that remain after the reduction of a. If the input contains integers or floats smaller than float64, the output data-type is float64. Otherwise, the output data-type is the same as that of the input. If out is specified, that array is returned instead.

See also

mean

percentile

equivalent to quantile, but with q in the range [0, 100].

median

equivalent to quantile(..., 0.5)

nanquantile

Notes

Given a vector V of length N, the q-th quantile of V is the value q of the way from the minimum to the maximum in a sorted copy of V. The values and distances of the two nearest neighbors as well as the interpolation parameter will determine the quantile if the normalized ranking does not match the location of q exactly. This function is the same as the median if q=0.5, the same as the minimum if q=0.0 and the same as the maximum if q=1.0.

Examples

>>> a = np.array([[10, 7, 4], [3, 2, 1]])
>>> a
array([[10,  7,  4],
       [ 3,  2,  1]])
>>> np.quantile(a, 0.5)
3.5
>>> np.quantile(a, 0.5, axis=0)
array([6.5, 4.5, 2.5])
>>> np.quantile(a, 0.5, axis=1)
array([7.,  2.])
>>> np.quantile(a, 0.5, axis=1, keepdims=True)
array([[7.],
       [2.]])
>>> m = np.quantile(a, 0.5, axis=0)
>>> out = np.zeros_like(m)
>>> np.quantile(a, 0.5, axis=0, out=out)
array([6.5, 4.5, 2.5])
>>> m
array([6.5, 4.5, 2.5])
>>> b = a.copy()
>>> np.quantile(b, 0.5, axis=1, overwrite_input=True)
array([7.,  2.])
>>> assert not np.all(a == b)