BSplineKit.jl

KO | EN

gitlite — search

#python #typescript #llm #golang #linux #docker #java #windows #awesome #cli #security #pytorch #mcp #open-source

(★ 67)

A collection of B-spline tools in Julia

BSplineKit.jl Latest Version Download

Download Latest Version (.zip)

// repository documentation

Was this content helpful?

★ 0 (0 ratings)

# BSplineKit.jl

[![Stable](https://img.shields.io/badge/docs-stable-blue.svg)](https://jipolanco.github.io/BSplineKit.jl/stable/)
[![Dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://jipolanco.github.io/BSplineKit.jl/dev/)
[![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.5150350.svg)](https://doi.org/10.5281/zenodo.5150350)

[![Build Status](https://github.com/jipolanco/BSplineKit.jl/workflows/CI/badge.svg)](https://github.com/jipolanco/BSplineKit.jl/actions)
[![Coverage](https://codecov.io/gh/jipolanco/BSplineKit.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/jipolanco/BSplineKit.jl)

Tools for B-spline based Galerkin and collocation methods in Julia.

## Features

This package provides:

- B-spline bases of arbitrary order on uniform and non-uniform grids;

- evaluation of splines and their derivatives and integrals;

- spline interpolations, smoothing splines and function approximation;

- periodic splines;

- basis recombination, for generating bases satisfying homogeneous boundary
  conditions using linear combinations of B-splines.
  Supported boundary conditions include Dirichlet, Neumann, Robin, and
  generalisations of these;

- banded Galerkin and collocation matrices for solving differential equations,
  using B-spline and recombined bases;

- efficient "banded" 3D arrays as an extension of banded matrices.
  These can store 3D tensors associated to quadratic terms in Galerkin methods.

## Example usage

The following is a very brief overview of some of the functionality provided
by this package.

- Interpolate discrete data using cubic splines (B-spline order `k = 4`):

```julia
  xdata = (0:10).^2  # points don't need to be uniformly distributed
  ydata = rand(length(xdata))
  itp = interpolate(xdata, ydata, BSplineOrder(4))
  itp(12.3)  # interpolation can be evaluated at any intermediate point
  ```

- Create B-spline basis of order `k = 6` (polynomial degree 5) from a given
  set of breakpoints:

```julia
  breaks = log2.(1:16)  # breakpoints don't need to be uniformly distributed either
  B = BSplineBasis(BSplineOrder(6), breaks)
  ```

- Approximate known function by a spline in a previously constructed basis:

```julia
  f(x) = exp(-x) * sin(x)
  fapprox = approximate(f, B)
  f(2.3), fapprox(2.3)  # (0.07476354233090601, 0.0747642348243861)
  ```

- Create derived basis satisfying homogeneous [Robin boundary
  conditions](https://en.wikipedia.org/wiki/Robin_boundary_condition) on the
  two boundaries:

```julia
  bc = Derivative(0) + 3Derivative(1)
  R = RecombinedBSplineBasis(B, bc)  # satisfies u ∓ 3u' = 0 on the left/right boundary
  ```

- Construct [mass matrix](https://en.wikipedia.org/wiki/Mass_matrix) and
  [stiffness matrix](https://en.wikipedia.org/wiki/Stiffness_matrix) for
  the Galerkin method in the recombined basis:

```julia
  # By default, M and L are Hermitian banded matrices
  M = galerkin_matrix(R)
  L = galerkin_matrix(R, (Derivative(1), Derivative(1)))
  ```

- Construct banded 3D tensor associated to non-linear term of the [Burgers
  equation](https://en.wikipedia.org/wiki/Burgers%27_equation):

```julia
  T = galerkin_tensor(R, (Derivative(0), Derivative(1), Derivative(0)))
  ```

See the [heat equation
example](https://jipolanco.github.io/BSplineKit.jl/stable/generated/heat/) in
the docs for the use of these tools to solve partial differential equations.

## References

- C. de Boor, *A Practical Guide to Splines*. New York: Springer-Verlag, 1978.

- J. P. Boyd, *Chebyshev and Fourier Spectral Methods*, Second Edition.
  Mineola, N.Y: Dover Publications, 2001.

- O. Botella and K. Shariff, *B-spline Methods in Fluid Dynamics*, Int. J. Comput.
  Fluid Dyn. 17, 133 (2003).

BSplineKit.jl

BSplineKit.jl Latest Version Download

Today's picks

Was this content helpful?

Recent Feedback

BSplineKit.jl

BSplineKit.jl Latest Version Download

Today's picks

Was this content helpful?

Recent Feedback

Download README