Condition number estimation in Rust

This crate implements the matrix 1-norm estimator by [Higham and Tisseur] (Algorithm 2.4 on page 7 (1190)) in the linked PDF.

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

Todo

Right now, this crate only returns the 1-norm, and further allocates anew on every call to normest1. It does not currently yield the vectors necessary to calculate the actual condition number. This isn't hard to do, but needs to be implemented... Outstanding are:

• [ ] Return vectors required for calculating the 1-norm;
• [x] Create a struct holding the necessary temporaries to repeatedly call normest1 without extra allocation.
• [ ] Implement extra tests to mimic the numerical experiments in [Higham and Tisseur].
• [ ] Make some nice docs.

Example usage

The example below generates a random matrix a and estimates its 1-norm. On average, this gives pretty good results. Of course, there are some matrices where this algorithm severely underestimates the actual 1-norm. See [Higham and Tisseur] for more.

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].

``rust extern crate openblas_src; // Need to declareopenblas_src` (or some other BLAS provider) explicitly to link to a BLAS library.

use ndarray::{ prelude::*, Zip, }; use ndarrayrand::RandomExt; use rand::{ SeedableRng, }; use rand::distributions::StandardNormal; use randxoshiro::Xoshiro256Plus;

fn main() { let t = 2; let n = 100; let itmax = 5;

let mut rng = Xoshiro256Plus::seed_from_u64(1234);
let distribution = StandardNormal;

let mut a = Array::random_using((n, n), distribution, &mut rng);
a.mapv_inplace(|x| 1.0/x);

let estimated = condest::normest1(&a, t, itmax);
let expected = {
    let (layout, a_slice) = if let Some(a_slice) = a.as_slice() {
        (cblas::Layout::RowMajor, a_slice)
    } else if let Some(a_slice) = a.as_slice_memory_order() {
        (cblas::Layout::ColumnMajor, a_slice)
    } else {
        panic!("Matrix not contiguous!")
    };

    unsafe {
        lapacke::dlange(
        layout,
        b'1',
        n as i32,
        n as i32,
        a_slice,
        n as i32,
    )}
};

assert_eq!(estimated, expected);

} ```