jax.scipy.special.erf

jax.scipy.special.erf(x)[source]

Returns the error function of complex argument.

LAX-backend implementation of erf(). Original docstring below.

erf(x, /, out=None, *, where=True, casting=’same_kind’, order=’K’, dtype=None, subok=True[, signature, extobj])

erf(z)

It is defined as 2/sqrt(pi)*integral(exp(-t**2), t=0..z).

Parameters

x (ndarray) – Input array.

Returns

res – The values of the error function at the given points x.

Return type

ndarray

See also

erfc(), erfinv(), erfcinv(), wofz(), erfcx(), erfi()

Notes

The cumulative of the unit normal distribution is given by Phi(z) = 1/2[1 + erf(z/sqrt(2))].

References

1

https://en.wikipedia.org/wiki/Error_function

2

Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972. http://www.math.sfu.ca/~cbm/aands/page_297.htm

3

Steven G. Johnson, Faddeeva W function implementation. http://ab-initio.mit.edu/Faddeeva

Examples

>>> from scipy import special
>>> import matplotlib.pyplot as plt
>>> x = np.linspace(-3, 3)
>>> plt.plot(x, special.erf(x))
>>> plt.xlabel('$x$')
>>> plt.ylabel('$erf(x)$')
>>> plt.show()