#matrix #exponential #linalg #ndarray #expm

expm

An implementation of the expm matrix exponential function by Higham and Al-Mohy, 2009

2 releases

0.1.1 Jan 22, 2019
0.1.0 Jan 22, 2019

#4 in #exponential

MIT/Apache

31KB
568 lines

Matrix exponentiation in Rust

This crate contains expm, an implementation of Algorithm 6.1 by Al-Mohy, Higham in the Rust programming language. It calculates the exponential of a matrix. See the linked paper for more information.

It uses the excellent rust-ndarray crate for matrix storage.

Example usage

The example below calculates the exponential of the unit matrix.

Important: You need to explicitly link to a BLAS + LAPACK provider such as openblas_src. See the explanations given at the blas-lapack-rs organization.

extern crate openblas_src;
use approx::assert_ulps_eq;
#[test]
fn exp_of_unit() {
    let n = 5;
    let a = ndarray::Array2::eye(n);
    let mut b = unsafe { ndarray::Array2::<f64>::uninitialized((n, n)) };

    crate::expm(&a, &mut b);

    for &elem in &b.diag() {
        assert_ulps_eq!(elem, 1f64.exp(), max_ulps=1);
    }
}

TODO

Care was taken to implement the algorithm with performance in mind. As such, no extra allocations after the initial setup of the Expm struct are done, and Expm can be reused to repeatedly calculate the exponential of matrices with the same dimension.

However, profiling the code might reveal ways to improve it.

  • Profile code and optimize;
  • Write more tests to verify the goodness of the algorithm for difficult matrices;
  • Tune the parameters t and itmax when calculating the 1-norms (right now, t=2, itmax=5, which is what Scipy and Matlab are doing);
  • Ensure that the compiler performs const propagation when calculating the Padé coefficients;
  • Test the Padé coefficient against their hard-coded results;
  • Evaluate, whether the unsafe blocks are really necessary in all instances or could be removed.

Dependencies

~5MB
~153K SLoC