numpy.i0 — NumPy v1.13 Manual (original) (raw)
Modified Bessel function of the first kind, order 0.
Usually denoted 
. 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. |
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| Returns: | out : ndarray, shape = x.shape, dtype = x.dtype The modified Bessel function evaluated at each of the elements of x. |
| Raises: | TypeError: array cannot be safely cast to required type If argument consists exclusively of int dtypes. |
Notes
We use the algorithm published by Clenshaw [R32] and referenced by Abramowitz and Stegun [R33], 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 [R34] as having a peak of 5.8e-16 with an rms of 1.4e-16 (n = 30000).
References
| [R32] | (1, 2) C. W. Clenshaw, “Chebyshev series for mathematical functions”, in_National Physical Laboratory Mathematical Tables_, vol. 5, London: Her Majesty’s Stationery Office, 1962. |
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| [R33] | (1, 2) M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 10th printing, New York: Dover, 1964, pp. 379.http://www.math.sfu.ca/~cbm/aands/page_379.htm |
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| [R34] | (1, 2) http://kobesearch.cpan.org/htdocs/Math-Cephes/Math/Cephes.html |
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Examples
np.i0([0.]) array(1.0) np.i0([0., 1. + 2j]) array([ 1.00000000+0.j , 0.18785373+0.64616944j])