scipy.special.erfcx#

scipy.special.erfcx(x, out=None) = <ufunc 'erfcx'>#

Scaled complementary error function.

The scaled complementary error function is defined as

\[\operatorname{erfcx}(x) = e^{x^2} \operatorname{erfc}(x)\]

Parameters:

xarray_like: Real or complex valued argument
outndarray, optional: Optional output array for the function results

Returns:

scalar or ndarray: Values of the scaled complementary error function

See also

erf, erfc, erfi, dawsn, wofz

Notes

Added in version 0.12.0.

Array API Standard Support

erfcx has support for Python Array API Standard compatible backends in addition to NumPy. 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

For the NumPy backend, this function supports all NumPy ufunc keyword arguments. Other backends may support out, but none of the other ufunc kwargs. out is typically supported for CuPy and PyTorch, but not currently in cases where SciPy relies on a generic Array API implementation or, for PyTorch on CPU, falls back to the NumPy backend. out is never supported for JAX because JAX arrays are immutable. erfcx does not currently support out for the PyTorch backend.

See Support for the array API standard for more information.

References

[1]

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.erfcx(x))
>>> plt.xlabel('$x$')
>>> plt.ylabel('$erfcx(x)$')
>>> plt.show()