Cubic spline approximation (smoothing) in Rust
csaps is a crate for univariate, multivariate and n-dimensional grid data approximation using cubic smoothing splines.
The package can be useful in practical engineering tasks for data approximation and smoothing.
Univariate data auto-smoothing
use ndarray::{array, Array1};use csaps::CubicSmoothingSpline;fn main() {let x = vec![1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0];let y = vec![2.3, 3.5, 3.3, 1.2, 4.5, 6.2, 5.6, 7.2, 1.5];let spline = CubicSmoothingSpline::new(&x, &y).make().unwrap();let xi = Array1::linspace(1., 9., 30);let yi = spline.evaluate(&xi).unwrap();println!("{}", xi);println!("{}", yi);}
Multivariate data smoothing with weights and specified smoothing parameter
use ndarray::{array, Array1};use csaps::CubicSmoothingSpline;fn main() {let x = array![1., 2., 3., 4.];let y = array![[1., 2., 3., 4.],[5., 6., 7., 8.]];let w = array![1., 0.7, 0.5, 1.];let spline = CubicSmoothingSpline::new(&x, &y).with_weights(&w).with_smooth(0.8).make().unwrap();let xi = Array1::linspace(1., 4., 10);let yi = spline.evaluate(&xi).unwrap();println!("{}", xi);println!("{}", yi);}
2-d grid (surface) data smoothing
use ndarray::array;use csaps::GridCubicSmoothingSpline;fn main() {let x0 = array![1.0, 2.0, 3.0, 4.0];let x1 = array![1.0, 2.0, 3.0, 4.0];let x = vec![x0.view(), x1.view()];let y = array![[0.5, 1.2, 3.4, 2.5],[1.5, 2.2, 4.4, 3.5],[2.5, 3.2, 5.4, 4.5],[3.5, 4.2, 6.4, 5.5],];let yi = GridCubicSmoothingSpline::new(&x, &y).with_smooth_fill(0.5).make().unwrap().evaluate(&x).unwrap();println!("xi: {:?}", xi);println!("yi: {}", yi);}
Currently, the performance of computation of smoothing splines might be very low for a large data.
The algorithm of sparse matrices mutliplication in sprs crate is not optimized for large diagonal
matrices which causes a poor performance of computation of smoothing splines.
See issue for details.
The crate implementation is based on ndarray and
sprs crates and has been inspired by Fortran routine SMOOTH from PGS
(originally written by Carl de Boor).
The implementation of the algorithm in other languages: