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Module « numpy.matlib »

Fonction histogram_bin_edges - module numpy.matlib

Signature de la fonction histogram_bin_edges

def histogram_bin_edges(a, bins=10, range=None, weights=None) 

Description

help(numpy.matlib.histogram_bin_edges)

Function to calculate only the edges of the bins used by the `histogram`
function.

Parameters
----------
a : array_like
    Input data. The histogram is computed over the flattened array.
bins : int or sequence of scalars or str, 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.

    If `bins` is a string from the list below, `histogram_bin_edges` will
    use the method chosen to calculate the optimal bin width and
    consequently the number of bins (see the Notes section for more detail
    on the estimators) from the data that falls within the requested range.
    While the bin width will be optimal for the actual data
    in the range, the number of bins will be computed to fill the
    entire range, including the empty portions. For visualisation,
    using the 'auto' option is suggested. Weighted data is not
    supported for automated bin size selection.

    'auto'
        Minimum bin width between the 'sturges' and 'fd' estimators.
        Provides good all-around performance.

    'fd' (Freedman Diaconis Estimator)
        Robust (resilient to outliers) estimator that takes into
        account data variability and data size.

    'doane'
        An improved version of Sturges' estimator that works better
        with non-normal datasets.

    'scott'
        Less robust estimator that takes into account data variability
        and data size.

    'stone'
        Estimator based on leave-one-out cross-validation estimate of
        the integrated squared error. Can be regarded as a generalization
        of Scott's rule.

    'rice'
        Estimator does not take variability into account, only data
        size. Commonly overestimates number of bins required.

    'sturges'
        R's default method, only accounts for data size. Only
        optimal for gaussian data and underestimates number of bins
        for large non-gaussian datasets.

    'sqrt'
        Square root (of data size) estimator, used by Excel and
        other programs for its speed and simplicity.

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. The first element of the range must be less than or
    equal to the second. `range` affects the automatic bin
    computation as well. While bin width is computed to be optimal
    based on the actual data within `range`, the bin count will fill
    the entire range including portions containing no data.

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). This is currently not used by any of the bin estimators,
    but may be in the future.

Returns
-------
bin_edges : array of dtype float
    The edges to pass into `histogram`

See Also
--------
histogram

Notes
-----
The methods to estimate the optimal number of bins are well founded
in literature, and are inspired by the choices R provides for
histogram visualisation. Note that having the number of bins
proportional to :math:`n^{1/3}` is asymptotically optimal, which is
why it appears in most estimators. These are simply plug-in methods
that give good starting points for number of bins. In the equations
below, :math:`h` is the binwidth and :math:`n_h` is the number of
bins. All estimators that compute bin counts are recast to bin width
using the `ptp` of the data. The final bin count is obtained from
``np.round(np.ceil(range / h))``. The final bin width is often less
than what is returned by the estimators below.

'auto' (minimum bin width of the 'sturges' and 'fd' estimators)
    A compromise to get a good value. For small datasets the Sturges
    value will usually be chosen, while larger datasets will usually
    default to FD.  Avoids the overly conservative behaviour of FD
    and Sturges for small and large datasets respectively.
    Switchover point is usually :math:`a.size \approx 1000`.

'fd' (Freedman Diaconis Estimator)
    .. math:: h = 2 \frac{IQR}{n^{1/3}}

    The binwidth is proportional to the interquartile range (IQR)
    and inversely proportional to cube root of a.size. Can be too
    conservative for small datasets, but is quite good for large
    datasets. The IQR is very robust to outliers.

'scott'
    .. math:: h = \sigma \sqrt[3]{\frac{24 \sqrt{\pi}}{n}}

    The binwidth is proportional to the standard deviation of the
    data and inversely proportional to cube root of ``x.size``. Can
    be too conservative for small datasets, but is quite good for
    large datasets. The standard deviation is not very robust to
    outliers. Values are very similar to the Freedman-Diaconis
    estimator in the absence of outliers.

'rice'
    .. math:: n_h = 2n^{1/3}

    The number of bins is only proportional to cube root of
    ``a.size``. It tends to overestimate the number of bins and it
    does not take into account data variability.

'sturges'
    .. math:: n_h = \log _{2}(n) + 1

    The number of bins is the base 2 log of ``a.size``.  This
    estimator assumes normality of data and is too conservative for
    larger, non-normal datasets. This is the default method in R's
    ``hist`` method.

'doane'
    .. math:: n_h = 1 + \log_{2}(n) +
                    \log_{2}\left(1 + \frac{|g_1|}{\sigma_{g_1}}\right)

        g_1 = mean\left[\left(\frac{x - \mu}{\sigma}\right)^3\right]

        \sigma_{g_1} = \sqrt{\frac{6(n - 2)}{(n + 1)(n + 3)}}

    An improved version of Sturges' formula that produces better
    estimates for non-normal datasets. This estimator attempts to
    account for the skew of the data.

'sqrt'
    .. math:: n_h = \sqrt n

    The simplest and fastest estimator. Only takes into account the
    data size.

Additionally, if the data is of integer dtype, then the binwidth will never
be less than 1.

Examples
--------
>>> import numpy as np
>>> arr = np.array([0, 0, 0, 1, 2, 3, 3, 4, 5])
>>> np.histogram_bin_edges(arr, bins='auto', range=(0, 1))
array([0.  , 0.25, 0.5 , 0.75, 1.  ])
>>> np.histogram_bin_edges(arr, bins=2)
array([0. , 2.5, 5. ])

For consistency with histogram, an array of pre-computed bins is
passed through unmodified:

>>> np.histogram_bin_edges(arr, [1, 2])
array([1, 2])

This function allows one set of bins to be computed, and reused across
multiple histograms:

>>> shared_bins = np.histogram_bin_edges(arr, bins='auto')
>>> shared_bins
array([0., 1., 2., 3., 4., 5.])

>>> group_id = np.array([0, 1, 1, 0, 1, 1, 0, 1, 1])
>>> hist_0, _ = np.histogram(arr[group_id == 0], bins=shared_bins)
>>> hist_1, _ = np.histogram(arr[group_id == 1], bins=shared_bins)

>>> hist_0; hist_1
array([1, 1, 0, 1, 0])
array([2, 0, 1, 1, 2])

Which gives more easily comparable results than using separate bins for
each histogram:

>>> hist_0, bins_0 = np.histogram(arr[group_id == 0], bins='auto')
>>> hist_1, bins_1 = np.histogram(arr[group_id == 1], bins='auto')
>>> hist_0; hist_1
array([1, 1, 1])
array([2, 1, 1, 2])
>>> bins_0; bins_1
array([0., 1., 2., 3.])
array([0.  , 1.25, 2.5 , 3.75, 5.  ])

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