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