functionsmoothTransition

Twice continuously differentiable transition between the regions

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

Information

This function is used by Buildings.Utilities.Math.Functions.inverseXRegularized to provide a twice continuously differentiable transition between the different regions. The code has been implemented in a function as this allows to implement the function Buildings.Utilities.Math.Functions.inverseXRegularized in such a way that Dymola inlines it. However, this function will not be inlined as its body is too large.

Implementation

For efficiency, the polynomial coefficients a, b, c, d, e, f and the inverse of the smoothing parameter deltaInv are exposed as arguments to this function. Also, derivatives are provided in Buildings.Utilities.Math.Functions.BaseClasses.der_smoothTransition and in Buildings.Utilities.Math.Functions.BaseClasses.der_2__smoothTransition.

Inputs

TypeNameDefaultDescription
RealxAbscissa value
RealdeltaAbscissa value below which approximation occurs
RealdeltaInv1/deltaInverse value of delta
Reala-15*deltaInvPolynomial coefficient
Realb119*deltaInv^2Polynomial coefficient
Realc-361*deltaInv^3Polynomial coefficient
Reald534*deltaInv^4Polynomial coefficient
Reale-380*deltaInv^5Polynomial coefficient
Realf104*deltaInv^6Polynomial coefficient

Outputs

TypeNameDefaultDescription
RealyFunction value

Revisions

  • September 12, 2018, by David Blum:
    Change if-statement to if-expression. For issue #1019.
  • August 11, 2015, by Michael Wetter:
    First implementation.