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Module « scipy.special »

Fonction erfinv - module scipy.special

Signature de la fonction erfinv

def erfinv(*args, **kwargs) 

Description

help(scipy.special.erfinv)

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

erfinv(y, out=None)

Inverse of the error function.

Computes the inverse of the error function.

In the complex domain, there is no unique complex number w satisfying
erf(w)=z. This indicates a true inverse function would be multivalued.
When the domain restricts to the real, -1 < x < 1, there is a unique real
number satisfying erf(erfinv(x)) = x.

Parameters
----------
y : ndarray
    Argument at which to evaluate. Domain: [-1, 1]
out : ndarray, optional
    Optional output array for the function values

Returns
-------
erfinv : scalar or ndarray
    The inverse of erf of y, element-wise

See Also
--------
erf : Error function of a complex argument
erfc : Complementary error function, ``1 - erf(x)``
erfcinv : Inverse of the complementary error function

Notes
-----
This function wraps the ``erf_inv`` routine from the
Boost Math C++ library [1]_.

References
----------
.. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.

Examples
--------
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from scipy.special import erfinv, erf

>>> erfinv(0.5)
0.4769362762044699

>>> y = np.linspace(-1.0, 1.0, num=9)
>>> x = erfinv(y)
>>> x
array([       -inf, -0.81341985, -0.47693628, -0.22531206,  0.        ,
        0.22531206,  0.47693628,  0.81341985,         inf])

Verify that ``erf(erfinv(y))`` is ``y``.

>>> erf(x)
array([-1.  , -0.75, -0.5 , -0.25,  0.  ,  0.25,  0.5 ,  0.75,  1.  ])

Plot the function:

>>> y = np.linspace(-1, 1, 200)
>>> fig, ax = plt.subplots()
>>> ax.plot(y, erfinv(y))
>>> ax.grid(True)
>>> ax.set_xlabel('y')
>>> ax.set_title('erfinv(y)')
>>> plt.show()

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