scipy.special.erf

scipy.special.erf(z, out=None) = <ufunc 'erf'>

Returns the error function of complex argument.

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

Parameters

xndarray

Input array.

outndarray, optional

Optional output array for the function values

Returns

resscalar or ndarray

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

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()