erfcplx, erfccplx#

Purpose#

Computes the Gaussian error function (erfcplx()) and its complement (erfccplx()) for complex inputs.

Format#

f_cplx = erfcplx(z)#
f_cplx = erfccplx(z)#
Parameters:

z (NxK complex matrix) – The complex inputs used to compute the Gaussian error function or its complement. \(z > 0\)

Returns:

f_cplx (NxK complex matrix) – the Gaussian error function (erfcplx()) or the complement of the Gaussian error function (erfccplx()).

Examples#

The Gaussian error function of a complex matrix#

// Real component of x
x_real = 1;

// Imaginary component of x
x_imag = -2;

// Form complex x matrix
x_cplx = complex(x_real, x_imag);

// Find Gaussian error function
f_cplx = erfcplx(x_cplx);

After this:

f_cplx = -0.537 +    5.049i

The complement of the Gaussian error function of a complex matrix#

f_ccplx = erfccplx(x_cplx);

Now

f_ccplx = 1.537 -    5.049i

Which is equal to:

1 - f_cplx;

Remarks#

Accuracy is better than 12 significant digits.

References#

  1. Abramowitz & Stegun, section 7.1, equations 7.1.9, 7.1.23, and 7.1.29

  2. Main author Paul Godfrey

  3. Small changes by Peter J. Acklam