mars.tensor.special.erf#

mars.tensor.special.erf(x, out=None, where=None, **kwargs)[source]#

Returns the error function of complex argument.

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

Parameters: x (Tensor) – Input tensor.
Returns: res – The values of the error function at the given points x.
Return type: Tensor

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

>>> 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()