.Modelica.Math.Special.erfInv

Information

Syntax

Special.erfInv(u);

Description

This function computes the inverse of the error function erf(u) = 2/sqrt(pi)*Integral_0_u exp(-t^2)*dt numerically with a relative precision of about 1e-15. Therefore, u = erf(erfInv(u)). Input argument u must be in the range (otherwise an assertion is raised):

-1 ≤ u ≤ 1

If u = 1, the function returns Modelica.Constants.inf.
If u = -1, 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

  erfInv(0)            // = 0
  erfInv(0.5)          // = 0.4769362762044699
  erfInv(0.999999)     // = 3.458910737275499
  erfInv(0.9999999999) // = 4.572824958544925

See also

erf, erfc, erfcInv.

Interface

function erfInv
  extends Modelica.Icons.Function;
  input Real u "Input argument in the range -1 <= u <= 1";
  output Real y "= inverse of error function";
end erfInv;

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