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

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

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

fn main() -> Result<()> { let smallmatrix = 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::frommatrix(&smallmatrix)?; cgs2.compute(&smallmatrix)?; assert!(smallmatrix.allclose(&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