SciPy

numpy.percentile

numpy.percentile(a, q, axis=None, out=None, overwrite_input=False, interpolation='linear')[source]

Compute the qth percentile of the data along the specified axis.

Returns the qth percentile of the array elements.

Parameters :

a : array_like

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

q : float in range of [0,100] (or sequence of floats)

Percentile to compute which must be between 0 and 100 inclusive.

axis : int, optional

Axis along which the percentiles are computed. The default (None) is to compute the percentiles 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 use of memory of input array a for calculations. The input array will be modified by the call to percentile. This will save memory when you do not need to preserve the contents of the input array. In this case you should not make any assumptions about the content of the passed in array a after this function completes – treat it as undefined. Default is False. Note that, if the a input is not already an array this parameter will have no effect, a will be converted to an array internally regardless of the value of this parameter.

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 and 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.

New in version 1.9.0.

Returns :

percentile : scalar or ndarray

If a single percentile q is given and axis=None a scalar is returned. If multiple percentiles q are given an array holding the result is returned. The results are listed in the first axis. (If out is specified, in which case that array is returned instead). If the input contains integers, or floats of smaller precision than 64, then the output data-type is float64. Otherwise, the output data-type is the same as that of the input.

See also

mean, median

Notes

Given a vector V of length N, the qth percentile of V is the qth ranked value in a sorted copy of V. The values and distances of the two nearest neighbors as well as the interpolation parameter will determine the percentile if the normalized ranking does not match q exactly. This function is the same as the median if q=50, the same as the minimum if q=0``and the same as the maximum if ``q=100.

Examples

>>> a = np.array([[10, 7, 4], [3, 2, 1]])
>>> a
array([[10,  7,  4],
       [ 3,  2,  1]])
>>> np.percentile(a, 50)
array([ 3.5])
>>> np.percentile(a, 50, axis=0)
array([[ 6.5,  4.5,  2.5]])
>>> np.percentile(a, 50, axis=1)
array([[ 7.],
       [ 2.]])
>>> m = np.percentile(a, 50, axis=0)
>>> out = np.zeros_like(m)
>>> np.percentile(a, 50, axis=0, out=m)
array([[ 6.5,  4.5,  2.5]])
>>> m
array([[ 6.5,  4.5,  2.5]])
>>> b = a.copy()
>>> np.percentile(b, 50, axis=1, overwrite_input=True)
array([[ 7.],
       [ 2.]])
>>> assert not np.all(a==b)
>>> b = a.copy()
>>> np.percentile(b, 50, axis=None, overwrite_input=True)
array([ 3.5])

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