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()