.BuildingSystems.Utilities.Math.Functions.smoothInterpolation

Information

For xSup₁ ≤ x ≤ xSup_n, where n is the size of the support points xSup, which must be strictly monotonically increasing, this function interpolates using cubic hermite spline. For x outside this interval, the function linearly extrapolates.

If n=2, linear interpolation is used an if n=1, the function value y¹ is returned.

Note that if xSup and ySup only depend on parameters or constants, and therefore will not change during the simulation, it is more efficient to first call BuildingSystems.Utilities.Math.Functions.splineDerivatives to find the derivatives, and then call BuildingSystems.Utilities.Math.Functions.interpolate to perform the interpolation. This way the derivatives only need to be computed once upon initialisation, not at each step during the simulation. See the example implemented in BuildingSystems.Utilities.Math.Functions.Examples.Interpolate.

In contrast to the function Modelica.Math.Vectors.interpolate which provides linear interpolation, this function does not trigger events.

For how to use this function, see BuildingSystems.Utilities.Math.Functions.Examples.SmoothInterpolation.

Interface

function smoothInterpolation
  extends Modelica.Icons.Function;
  input Real x "Abscissa value";
  input Real xSup[:] "Support points (strictly increasing)";
  input Real ySup[size(xSup, 1)] "Function values at xSup";
  input Boolean ensureMonotonicity = isMonotonic(ySup, strict = false) "Set to true to ensure monotonicity of the cubic hermite";
  output Real yInt "Interpolated ordinate value";
end smoothInterpolation;

Revisions

• October 1, 2015, by Michael Wetter:
  First implementation.