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import scipy.special as spspecial
from ..arithmetic.utils import arithmetic_operand
from ..utils import infer_dtype, implement_scipy
from .core import TensorSpecialUnaryOp, _register_special_op
@_register_special_op
@arithmetic_operand(sparse_mode="unary")
class TensorErf(TensorSpecialUnaryOp):
_func_name = "erf"
[docs]@implement_scipy(spspecial.erf)
@infer_dtype(spspecial.erf)
def erf(x, out=None, where=None, **kwargs):
"""
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 : Tensor
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
--------
>>> 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()
"""
op = TensorErf(**kwargs)
return op(x, out=out, where=where)