.Modelica_Noise.Math.Special.erfcInv

Information

Syntax

Special.erfInv(u);

Description

This function computes the inverse of the complementary error function erfc(u) = 1 - erf(u) with a relative precision of about 1e-15. Therefore, u = erfc(erfcInv(u)) and erfcInv(u) = erfInv(1 - u). Input argument u must be in the range (otherwise an assertion is raised):

0 ≤ u ≤ 2

If u = 2, the function returns -Modelica.Constants.inf.
If u = 0, the function returns Modelica.Constants.inf
The implementation utilizes the formulation of the Boost library (erf_inv.hpp, developed by John Maddock).
Plot of the function:

For more details, see Wikipedia.

Example

  erfcInv(1)         // = 0
  erfcInv(0.5)       // = 0.4769362762044699
  erfInv(1.999999)   // = -3.4589107372909473

See also

erf, erfc, erfInv.

Interface

function erfcInv
  input Real u "Input argument";
  output Real y "erfcInv(u)";
end erfcInv;

Revisions

Date	Description
June 22, 2015	Initial version implemented by A. Klöckner, F. v.d. Linden, D. Zimmer, M. Otter. DLR Institute of System Dynamics and Control