dpnp.scipy.special.erf

dpnp.scipy.special.erf(x, out=None)

Calculates the Gauss error function of a given input array.

It is defined as \(\frac{2}{\sqrt{\pi}} \int_{0}^{z} e^{-t^2} \, dt\).

For full documentation refer to scipy.special.erf.

Parameters:

• x ({dpnp.ndarray, usm_ndarray}) -- Input array, expected to have a real-valued floating-point data type.

• out ({dpnp.ndarray, usm_ndarray}, optional) -- Optional output array for the function values.

Returns:

out -- The values of the error function at the given points x.

Return type:

dpnp.ndarray

See also

dpnp.scipy.special.erfc

Complementary error function.

dpnp.scipy.special.erfinv

Inverse of the error function.

dpnp.scipy.special.erfcinv

Inverse of the complementary error function.

dpnp.scipy.special.erfcx

Scaled complementary error function.

dpnp.scipy.special.erfi

Imaginary error function.

Notes

The cumulative of the unit normal distribution is given by

\[\Phi(z) = \frac{1}{2} \left[ 1 + \operatorname{erf} \left( \frac{z}{\sqrt{2}} \right) \right]\]

Examples

>>> import dpnp as np
>>> x = np.linspace(-3, 3, num=5)
>>> np.scipy.special.erf(x)
array([[-0.99997791, -0.96610515,  0.        ,  0.96610515,  0.99997791])