functionsmoothInterpolation

Interpolate using a cubic Hermite spline with linear extrapolation for a vector xSup[], ySup[] and independent variable x

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

Information

For xSup1 ≤ x ≤ xSupn, 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 Buildings.Utilities.Math.Functions.splineDerivatives to find the derivatives, and then call Buildings.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 Buildings.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 Buildings.Utilities.Math.Functions.Examples.SmoothInterpolation.

Inputs

TypeNameDefaultDescription
RealxAbscissa value
Real[:]xSupSupport points (strictly increasing)
Real[size(xSup, 1)]ySupFunction values at xSup
BooleanensureMonotonicityisMonotonic(ySup, strict = false)Set to true to ensure monotonicity of the cubic hermite

Outputs

TypeNameDefaultDescription
RealyIntInterpolated ordinate value

Revisions

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