DataInterpolations.jl
DataInterpolations.jl is a library for performing interpolations of onedimensional 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)
API
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[4] # Gives the 4th value of u
Available Interpolations
In all cases, u
an AbstractVector
of values and t
is an AbstractVector
of timepoints
corresponding to (u,t)
pairs.

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 ordern
. 
QuadraticSpline(u,t)
 A quadratic spline interpolation. 
CubicSpline(u,t)
 A cubic spline interpolation. 
BSplineInterpolation(u,t,d,pVec,knotVec)
 An interpolation Bspline. This is a Bspline which hits each of the data points. The argument choices are:d
 degree of BsplinepVec
 Symbol to Parameters Vector,pVec = :Uniform
for uniform spaced parameters andknotVec = :ArcLen
for parameters generated by chord length method.knotVec
 Symbol to Knot Vector,knotVec = :Uniform
for uniform knot vector,knotVec = :Average
for average spaced knot vector.

BSplineApprox(u,t,d,h,pVec,knotVec)
 A regression Bspline which smooths the fitting curve. The argument choices are the same as theBSplineInterpolation
, with the additional parameterh<length(t)
which is the number of control points to use, with smallerh
indicating more smoothing. 
Loess(u,t,d,α)
 A local least square regression.d
is the degree of the polynomial to use andα
is a smoothing parameter. 
GPInterpolation(u,t,m,k,n=2.0)
 A Gaussian Process interpolation via GaussianProcess.jl. Stochastic: each trajectory is different.m
is mean function.k
is kernel function.n
is log standard deviation of observation noise and defaults to2.0
. Available Mean functions
MeanZero
 Zero mean functionMeanConst
 Constant mean functionMeanLin
 Linear mean functionMeanPoly
 Polynomial mean function
 Available Kernel functions (covariance functions)
Lin
 Linear covariance functionSE
 Squared exponential covariance functionRQ
 Rational quadratic covariance functionMatern
 Matern covariance functionPeriodic
 Periodic covariance functionPoly
 Polnomial covariance functionNoise
 White noise covariance functionConst
 Constant (bias) covariance function
 Available Mean functions

Curvefit(u,t,m,p,alg)
 An interpolation which is done by fitting a usergiven functional formm(t,p)
wherep
is the vector of parameters. The user's inputp
is a an initial value for a leastsquare fitting,alg
is the algorithm choice to use for optimize the cost function (sum of squared deviations) viaOptim.jl
and optimalp
s are used in the interpolation.
Plotting
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:
:linear_interp
:quadratic_interp
:lagrange_interp
:quadratic_spline
:cubic_spline
:loess
By and large, these accept the same keywords as their function counterparts.