#qr #gramschmidt #cgs #mgs #cgs2

gramschmidt

Classical, Modified, Reorthogonalized Gram Schmidt Orthogonalization and QR decompostion

4 releases (2 breaking)

✓ Uses Rust 2018 edition

0.6.0 Aug 12, 2019
0.5.0 Mar 12, 2019
0.4.1 Mar 13, 2018
0.4.0 Jan 22, 2018

#41 in Science

43 downloads per month

MIT license

37KB
641 lines

Gram Schmidt Orthonormalizatoin

Orthogonalization and QR decomposition of matrices in the Rust programming language and rust-ndarray.

This crate provides the following methods:

  • Classical Gram Schmidt, cgs,
  • Modified Gram Schmidt, mgs,
  • Classical Gram Schmidt with Reorthogonalization, cgs2.

Usage

// Import openblas_src or another blas source to have the linker find all symbols.
extern crate openblas_src;

use gramschmidt::{
    GramSchmidt,
    Reorthogonalized,
    Result,
};
use ndarray::arr2;

fn main() -> Result<()> {
    let small_matrix = arr2(
        &[[2.0, 0.5, 0.0, 0.0],
          [0.0, 0.3, 0.0, 0.0],
          [0.0, 1.0, 0.7, 0.0],
          [0.0, 0.0, 0.0, 3.0]]
    );
    let mut cgs2 = Reorthogonalized::from_matrix(&small_matrix)?;
    cgs2.compute(&small_matrix)?;
    assert!(small_matrix.all_close(&cgs2.q().dot(cgs2.r()), 1e-14));
    Ok(())
}

Recent versions

  • 0.6.0: Fixed the dimensions of the triangular matrix R:
    • the previous version was technically large enough to hold all values, but the matrix dimensions were still off.
    • added an example of how to factorize the Lauchli matrix with the different algorithms.
  • 0.5.0: Refactored the library and updated for edition 2018
    • the Gram Schmidt factorizations are now all implemented via the GramSchmidt trait;
    • introduce some error handling;
    • provide convenience functions cgs, cgs2, and mgs.
  • 0.4.1: Fixed doc tests and expanded + simplified tests.
  • 0.4.0: Major rework of the library structure:
    • The algorithms are now configured via structs, the traits are dropped.
    • Provide the structs ClassicalGramSchmidt, ModifiedGramSchmidt, and ReorthogonalizedGramSchmidt (known as cgs, mgs, and cgs2 in the literature, respectively);
    • cgs and cgs2 are implemented using blas routines (major speedup!);
    • All routines are now able to handle column-major (Fortran-) and row-major (C-) order of the input matrices;
    • Remove parallel code.
  • 0.3.1: Update to blas 0.16 and do not specify a default backend (so that the user can set it).
  • 0.3.0: Update to ndarray 0.10, ndarray-parallel 0.5
  • 0.2.1: Added a parallelized algorithm using rayon
  • 0.2.0: Update to ndarray 0.9

Dependencies

~1.5MB
~30K SLoC