Skip to content

# bnels/Splines.jl

A B-Spline interpolation package for Julia
Julia Fetching latest commit…
Cannot retrieve the latest commit at this time.
Type Name Latest commit message Commit time
Failed to load latest commit information. doc src test .gitignore LICENSE.md README.md

# Splines.jl

A B-Spline interpolation package for Julia

## Getting Started

You can install the Splines module in Julia

```Pkg.checkout("git@github.com:bnels/Splines.jl.git")
Pkg.build("Splines")```

You can update the package using the usual

`Pkg.update()`

Now you're ready to start using Splines!

## Basics

Splines.jl uses B-Splines as a basis for constructing Spline interpolations. This is all under the hood, so for basic spline manipulations, you only need to provide a knot sequence, function values at knots, and what order of spline you would like to use (e.g. 4th order splines are piecewise cubic).

```using Splines

ts = [linspace(-10,10,50);] # knot sequence
vs = cos(ts) # signal values at knots
m = 4 # cubic splines

S = Spline(vs, ts, m)```

You can now treat your spline as a function, and can evaluate it at any point, or a vector of points

```using PyPlot

xs = [linspace(-10,10,150);]
ys = S(xs)
plot(xs, ys)``` ## Beyond the Basics

### Derivatives

You can take derivatives of your spline interpolation by adding an extra argument to your Spline function call

```using Splines
using PyPlot

ts = [linspace(-10.,10.,50);] # knot sequence
vs = cos(ts) # values at knots
m = 6 # spline order

S = Spline(vs, ts, m)

xs = [linspace(-6,6,150);] # points to evaluate splines at

plot(xs, S(xs), "blue")
plot(xs, S(xs, 1), "red")
plot(xs, S(xs, 2), "green")``` Note that the number of derivatives you can take is limited by the order of spline you are using, and that you will begin to lose accuracy at the endpoints of your knot sequence as you increase derivatives

### Arithmetic Operations

Splines support muliplication and division by scalars.

```# still using the Spline on cosine input
plot(xs, S(xs), "blue")
plot(xs, 2*S(xs), "red")
plot(xs, S(xs)/2, "green")``` You can also add two splines together. The resulting spline will be on the union of their knot sequences.

`S = S1 + S2`

### Hilbert Transforms

You can also take the Hilbert transform of splines. This is useful for the EMD algorithm (e.g. EMD.jl) and signal processing. You can tell a Spline to return its Hilbert transform by setting its third argument to a boolean true.

```plot(xs, S(xs), "blue") # cos(x)
plot(xs, S(xs, 0, true), "red") # should be sin(x)``` You can also take derivatives of the Hilbert transform by setting the second argument to an integer other than 0.

You can’t perform that action at this time.