naginterfaces.library.specfun.erfc_​complex_​vector

naginterfaces.library.specfun.erfc_complex_vector(z)[source]

erfc_complex_vector computes values of the function , for an array of complex values .

For full information please refer to the NAG Library document for s15dr

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/s/s15drf.html

Parameters
zcomplex, array-like, shape

The argument of the function, for .

Returns
fcomplex, ndarray, shape

, the function values.

ivalidint, ndarray, shape

contains the error code for , for .

No error.

Real part of result overflows.

Imaginary part of result overflows.

Both real and imaginary part of result overflows.

Result has less than half precision.

Result has no precision.

Raises
NagValueError
(errno )

On entry, .

Constraint: .

Warns
NagAlgorithmicWarning
(errno )

On entry, at least one value of produced a result with reduced accuracy.

Check for more information.

Notes

erfc_complex_vector computes values of the function , for , where is the complementary error function

for complex . The method used is that in Gautschi (1970) for in the first quadrant of the complex plane, and is extended for in other quadrants via the relations and . Following advice in Gautschi (1970) and van der Laan and Temme (1984), the code in Gautschi (1969) has been adapted to work in various precisions up to decimal places. The real part of is sometimes known as the Voigt function.

References

Gautschi, W, 1969, Algorithm 363: Complex error function, Comm. ACM (12), 635

Gautschi, W, 1970, Efficient computation of the complex error function, SIAM J. Numer. Anal. (7), 187–198

van der Laan, C G and Temme, N M, 1984, Calculation of special functions: the gamma function, the exponential integrals and error-like functions, CWI Tract 10, Centre for Mathematics and Computer Science, Amsterdam