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Module « numpy.matlib »

Fonction i0 - module numpy.matlib

Signature de la fonction i0

def i0(x) 

Description

help(numpy.matlib.i0)

Modified Bessel function of the first kind, order 0.

Usually denoted :math:`I_0`.

Parameters
----------
x : array_like of float
    Argument of the Bessel function.

Returns
-------
out : ndarray, shape = x.shape, dtype = float
    The modified Bessel function evaluated at each of the elements of `x`.

See Also
--------
scipy.special.i0, scipy.special.iv, scipy.special.ive

Notes
-----
The scipy implementation is recommended over this function: it is a
proper ufunc written in C, and more than an order of magnitude faster.

We use the algorithm published by Clenshaw [1]_ and referenced by
Abramowitz and Stegun [2]_, for which the function domain is
partitioned into the two intervals [0,8] and (8,inf), and Chebyshev
polynomial expansions are employed in each interval. Relative error on
the domain [0,30] using IEEE arithmetic is documented [3]_ as having a
peak of 5.8e-16 with an rms of 1.4e-16 (n = 30000).

References
----------
.. [1] C. W. Clenshaw, "Chebyshev series for mathematical functions", in
       *National Physical Laboratory Mathematical Tables*, vol. 5, London:
       Her Majesty's Stationery Office, 1962.
.. [2] M. Abramowitz and I. A. Stegun, *Handbook of Mathematical
       Functions*, 10th printing, New York: Dover, 1964, pp. 379.
       https://personal.math.ubc.ca/~cbm/aands/page_379.htm
.. [3] https://metacpan.org/pod/distribution/Math-Cephes/lib/Math/Cephes.pod#i0:-Modified-Bessel-function-of-order-zero

Examples
--------
>>> import numpy as np
>>> np.i0(0.)
array(1.0)
>>> np.i0([0, 1, 2, 3])
array([1.        , 1.26606588, 2.2795853 , 4.88079259])

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