mars.tensor.special.
erf
Returns the error function of complex argument.
It is defined as 2/sqrt(pi)*integral(exp(-t**2), t=0..z).
2/sqrt(pi)*integral(exp(-t**2), t=0..z)
x (Tensor) – Input tensor.
res – The values of the error function at the given points x.
Tensor
See also
erfc, erfinv, erfcinv, wofz, erfcx, erfi
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))].
Phi(z) = 1/2[1 + erf(z/sqrt(2))]
References
https://en.wikipedia.org/wiki/Error_function
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
Steven G. Johnson, Faddeeva W function implementation. http://ab-initio.mit.edu/Faddeeva
Examples
>>> import mars.tensor as mt >>> from mars.tensor import special >>> import matplotlib.pyplot as plt >>> x = mt.linspace(-3, 3) >>> plt.plot(x, special.erf(x)) >>> plt.xlabel('$x$') >>> plt.ylabel('$erf(x)$') >>> plt.show()