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¶
Abramowitz & Stegun, section 7.1, equations 7.1.9, 7.1.23, and 7.1.29
Main author Paul Godfrey
Small changes by Peter J. Acklam