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.
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
We can efficiently interpolate onto a vector of new t
values:
t′ = 0.5:1.0:3.5
interp(t′)
Inplace interpolation also works:
u′ = similar(u, length(t′))
interp(u′, t′)
Indexing retrieves 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. 
AkimaInterpolation(u, t)
 Akima spline interpolation provides a smoothing effect and is computationally efficient. 
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 andpVec = :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.
Extension Methods
The follow methods require extra dependencies and will be loaded as package extensions.
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. Requiresusing Optim
.RegularizationSmooth(u,t,d;λ,alg)
 A regularization algorithm (ridge regression) which is done by minimizing an objective function (l2 loss + derivatives of orderd
) integrated in the time span. It is a global method and creates a smooth curve. Requiresusing RegularizationTools
.
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
By and large, these accept the same keywords as their function counterparts.