# Collocation

DataDrivenDiffEq.InterpolationMethodType

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.

Example

# Create the wrapper struct
# Create a callable interpolation
itp = itp_method(u,t)
# Return u[2]
itp(t[2])
source
DataDrivenDiffEq.collocate_dataFunction
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].

Examples

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

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

Interpolation Methods