numpy.histogram

numpy.histogram(a, bins=10, range=None, normed=False, weights=None, density=None)

Compute the histogram of a set of data.

Parameters :

a : array_like

Input data. The histogram is computed over the flattened array.

bins : int or sequence of scalars, optional

If bins is an int, it defines the number of equal-width bins in the given range (10, by default). If bins is a sequence, it defines the bin edges, including the rightmost edge, allowing for non-uniform bin widths.

range : (float, float), optional

The lower and upper range of the bins. If not provided, range is simply (a.min(), a.max()). Values outside the range are ignored.

normed : bool, optional

This keyword is deprecated in Numpy 1.6 due to confusing/buggy behavior. It will be removed in Numpy 2.0. Use the density keyword instead. If False, the result will contain the number of samples in each bin. If True, the result is the value of the probability density function at the bin, normalized such that the integral over the range is 1. Note that this latter behavior is known to be buggy with unequal bin widths; use density instead.

weights : array_like, optional

An array of weights, of the same shape as a. Each value in a only contributes its associated weight towards the bin count (instead of 1). If normed is True, the weights are normalized, so that the integral of the density over the range remains 1

density : bool, optional

If False, the result will contain the number of samples in each bin. If True, the result is the value of the probability density function at the bin, normalized such that the integral over the range is 1. Note that the sum of the histogram values will not be equal to 1 unless bins of unity width are chosen; it is not a probability mass function. Overrides the normed keyword if given.

Returns :

hist : array

The values of the histogram. See normed and weights for a description of the possible semantics.

bin_edges : array of dtype float

Return the bin edges (length(hist)+1).

See also

histogramdd, bincount, searchsorted, digitize

Notes

All but the last (righthand-most) bin is half-open. 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.

Examples

>>> np.histogram([1, 2, 1], bins=[0, 1, 2, 3])
(array([0, 2, 1]), array([0, 1, 2, 3]))
>>> np.histogram(np.arange(4), bins=np.arange(5), density=True)
(array([ 0.25,  0.25,  0.25,  0.25]), array([0, 1, 2, 3, 4]))
>>> np.histogram([[1, 2, 1], [1, 0, 1]], bins=[0,1,2,3])
(array([1, 4, 1]), array([0, 1, 2, 3]))

>>> a = np.arange(5)
>>> hist, bin_edges = np.histogram(a, density=True)
>>> hist
array([ 0.5,  0. ,  0.5,  0. ,  0. ,  0.5,  0. ,  0.5,  0. ,  0.5])
>>> hist.sum()
2.4999999999999996
>>> np.sum(hist*np.diff(bin_edges))
1.0