scipy.special.erfinv#

scipy.special.erfinv(y, out=None) = <ufunc 'erfinv'>#

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:

yndarray: Argument at which to evaluate. Domain: [-1, 1]
outndarray, optional: Optional output array for the function values

Returns:

erfinvscalar 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()

../../_images/scipy-special-erfinv-1.png