numpy.dual

module documentation
(source)

Deprecated since version 1.20.

This module is deprecated. Instead of importing functions from numpy.dual, the functions should be imported directly from NumPy or SciPy.

Aliases for functions which may be accelerated by SciPy.

SciPy can be built to use accelerated or otherwise improved libraries for FFTs, linear algebra, and special functions. This module allows developers to transparently support these accelerated functions when SciPy is available but still support users who have only installed NumPy.

Function i0 Modified Bessel function of the first kind, order 0.
Function register_func Undocumented
Function restore_all Undocumented
Function restore_func Undocumented
Variable _restore_dict Undocumented
@array_function_dispatch(_i0_dispatcher)
def i0(x): (source)

Modified Bessel function of the first kind, order 0.

Usually denoted I0.

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

>>> np.i0(0.)
array(1.0)
>>> np.i0([0, 1, 2, 3])
array([1.        , 1.26606588, 2.2795853 , 4.88079259])
Parameters
x:array_like of floatArgument of the Bessel function.
Returns
ndarray, shape = x.shape, dtype = floatout - The modified Bessel function evaluated at each of the elements of x.
def register_func(name, func): (source)

Undocumented

def restore_all(): (source)

Undocumented

def restore_func(name): (source)

Undocumented

_restore_dict: dict = (source)

Undocumented