functionerfcInv

Inverse complementary error function: u = erfc(erfcInv(u))

Extends from Modelica.Icons.Function (Icon for functions).

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.

Inputs

TypeNameDefaultDescription
RealuInput argument

Outputs

TypeNameDefaultDescription
RealyerfcInv(u)

Revisions

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