DataInterpolations.jl is a library for performing interpolations of one-dimensional data. By "data interpolations" we mean techniques for interpolating possibly noisy data, and thus some methods are mixtures of regressions with interpolations (i.e. do not hit the data points exactly, smoothing out the lines). This library can be used to fill in intermediate data points in applications like timeseries data.
Tutorial / Demonstration
A tutorial is included and can be found at this page. To run the tutorial yourself locally, use the following Weave commands:
using Weave, DataInterpolations weave(joinpath(dirname(pathof(DataInterpolations)), "../Example", "DataInterpolations.jmd"), out_path=:doc)
All interpolation objects act as functions. Thus for example, using an interpolation looks like:
u = rand(5) t = 0:4 interp = LinearInterpolation(u,t) interp(3.5) # Gives the linear interpolation value at t=3.5
The indexing retreives the underlying values:
interp # Gives the 4th value of u
In all cases,
AbstractVector of values and
t is an
AbstractVector of timepoints
ConstantInterpolation(u,t)- A piecewise constant interpolation.
LinearInterpolation(u,t)- A linear interpolation.
QuadraticInterpolation(u,t)- A quadratic interpolation.
LagrangeInterpolation(u,t,n)- A Lagrange interpolation of order
QuadraticSpline(u,t)- A quadratic spline interpolation.
CubicSpline(u,t)- A cubic spline interpolation.
BSplineInterpolation(u,t,d,pVec,knotVec)- An interpolation B-spline. This is a B-spline which hits each of the data points. The argument choices are:
d- degree of B-spline
pVec- Symbol to Parameters Vector,
pVec = :Uniformfor uniform spaced parameters and
knotVec = :ArcLenfor parameters generated by chord length method.
knotVec- Symbol to Knot Vector,
knotVec = :Uniformfor uniform knot vector,
knotVec = :Averagefor average spaced knot vector.
BSplineApprox(u,t,d,h,pVec,knotVec)- A regression B-spline which smooths the fitting curve. The argument choices are the same as the
BSplineInterpolation, with the additional parameter
h<length(t)which is the number of control points to use, with smaller
hindicating more smoothing.
Loess(u,t,d,α)- A local least square regression.
dis the degree of the polynomial to use and
αis a smoothing parameter.
GPInterpolation(u,t,m,k,n=-2.0)- A Gaussian Process interpolation via GaussianProcess.jl. Stochastic: each trajectory is different.
mis mean function.
kis kernel function.
nis log standard deviation of observation noise and defaults to
- Available Mean functions
MeanZero- Zero mean function
MeanConst- Constant mean function
MeanLin- Linear mean function
MeanPoly- Polynomial mean function
- Available Kernel functions (covariance functions)
Lin- Linear covariance function
SE- Squared exponential covariance function
RQ- Rational quadratic covariance function
Matern- Matern covariance function
Periodic- Periodic covariance function
Poly- Polnomial covariance function
Noise- White noise covariance function
Const- Constant (bias) covariance function
- Available Mean functions
Curvefit(u,t,m,p,alg)- An interpolation which is done by fitting a user-given functional form
pis the vector of parameters. The user's input
pis a an initial value for a least-square fitting,
algis the algorithm choice to use for optimize the cost function (sum of squared deviations) via
ps are used in the interpolation.
DataInterpolations.jl is tied into the Plots.jl ecosystem, by way of RecipesBase.
Any interpolation can be plotted using the
plot command (or any other), since they have type recipes associated with them.
For convenience, and to allow keyword arguments to propagate properly, DataInterpolations.jl also defines several series types, corresponding to different interpolations.
The series types defined are:
By and large, these accept the same keywords as their function counterparts.