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