A wrapper for the interpolation methods of DataInterpolations.jl.

Wraps the methods in such a way that they are callable as f(u,t) to create and return an interpolation of u over t. The first argument of the constructor always defines the interpolation method, all following arguments will be used in the interpolation.

The additional keyword crop = false indicates to discard the first and last element of the time series.


# Create the wrapper struct
itp_method = InterpolationMethod(QuadraticSpline)
# Create a callable interpolation
itp = itp_method(u,t)
# Return u[2]
collocate_data(data, tpoints)
collocate_data(data, tpoints, kernel; crop, kwargs...)

Unified interface for collocation techniques. The input can either be a CollocationKernel (see list below) or a wrapped InterpolationMethod from DataInterpolations.jl.

Computes a non-parametrically smoothed estimate of u' and u given the data, where each column is a snapshot of the timeseries at tpoints[i].


u′,u,t = collocate_data(data,tpoints,kernel=SigmoidKernel())
u′,u,t = collocate_data(data,tpoints,tpoints_sample,interp,args...)
u′,u,t = collocate_data(data,tpoints,interp)

Collocation Kernels

See this paper for more information.

  • EpanechnikovKernel
  • UniformKernel
  • TriangularKernel
  • QuarticKernel
  • TriweightKernel
  • TricubeKernel
  • GaussianKernel
  • CosineKernel
  • LogisticKernel
  • SigmoidKernel
  • SilvermanKernel

Interpolation Methods

See DataInterpolations.jl for more information.

  • ConstantInterpolation
  • LinearInterpolation
  • QuadraticInterpolation
  • LagrangeInterpolation
  • QuadraticSpline
  • CubicSpline
  • BSplineInterpolation
  • BSplineApprox
  • Curvefit