maxframe.tensor.i0#

maxframe.tensor.i0(x, **kwargs)[source]#

Modified Bessel function of the first kind, order 0.

Usually denoted \(I_0\). This function does broadcast, but will not “up-cast” int dtype arguments unless accompanied by at least one float or complex dtype argument (see Raises below).

Parameters:: x (array_like, dtype float or complex) – Argument of the Bessel function.
Returns:: out – The modified Bessel function evaluated at each of the elements of x.
Return type:: Tensor, shape = x.shape, dtype = x.dtype
Raises:: TypeError – array cannot be safely cast to required type: If argument consists exclusively of int dtypes.

See also

scipy.special.iv, scipy.special.ive

Notes

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

Examples

>>> import maxframe.tensor as mt

>>> mt.i0([0.]).execute()
array([1.])
>>> mt.i0([0., 1. + 2j]).execute()
array([ 1.00000000+0.j        ,  0.18785373+0.64616944j])

maxframe.tensor.i0#

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