komm.gaussian_q

Computes the Gaussian Q-function. It is given by $$ \mathrm{Q}(x) = \frac{1}{\sqrt{2\pi}} \int_x^\infty \mathrm{e}^{-u^2/2} \, \mathrm{d}u. $$ This corresponds to the complementary cumulative distribution function of the standard gaussian distribution. For more details, see Wikipedia: Q-function.

Parameters:

• x (ArrayLike) –

  The input to the function. Should be a float or array of floats.

Returns:

• y (NDArray[floating] | floating) –

  The value $y = \mathrm{Q}(x)$.

Examples:

>>> komm.gaussian_q(0.0)
np.float64(0.5)

>>> komm.gaussian_q([[-1.0], [0.0], [1.0]])
array([[0.84134475],
       [0.5       ],
       [0.15865525]])