Module « scipy.special »

Fonction erf - module scipy.special

Signature de la fonction erf

Description

erf.__doc__

erf(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

erf(z)

Returns the error function of complex argument.

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

Parameters
----------
x : ndarray
    Input array.

Returns
-------
res : 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()