scipy.special.erf#
- scipy.special.erf(z, out=None) = <ufunc 'erf'>#
- Returns the error function of complex argument. - It is defined as - 2/sqrt(pi)*integral(exp(-t**2), t=0..z).- Parameters:
- xndarray
- Input array. 
- outndarray, optional
- Optional output array for the function values 
 
- Returns:
- resscalar or ndarray
- The values of the error function at the given points x. 
 
 - Notes - The cumulative of the unit normal distribution is given by - Phi(z) = 1/2[1 + erf(z/sqrt(2))].- erfhas experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable- SCIPY_ARRAY_API=1and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.- Library - CPU - GPU - NumPy - ✅ - n/a - CuPy - n/a - ✅ - PyTorch - ✅ - ✅ - JAX - ✅ - ✅ - Dask - ✅ - n/a - See Support for the array API standard for more information. - References [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 - >>> import numpy as np >>> 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() 