Crate gramschmidt

Gram Schmidt procedures for Rust and ndarray

This crate implements three different Gram Schmidt procedures in the form of QR decompositions:

• The classical Gram Schmidt procedure, [cgs];
• the modified or stabilized Gram Schmidt procedure, [mgs];
• the reorthogonalized Gram Schmidt procedure, [cgs2].

Structs

Classical

A classical Gram Schmidt factorization. See the Gram Schmidt Wikipedia entry for more information.

Modified

A modified Gram Schmidt factorization, which has a better numerical stability compared to the classical Gram Schmidt procedure. See its Wikipedia entry for more information.

Reorthogonalized

A reorthogonalized Gram Schmidt factorization, also known as CGS2 in the literature. See Giraud et al. for a definition. It performs two successive classical Gram Schmidt procedures, which has a higher performance than modified Gram Schmidt while providing a similar numerical stability.

Enums

Error

Errors that occur during a initialization of a Gram Schmidt factorization.

Traits

GramSchmidt

Functions

cgs

Convenience function that calculates a Classical Gram Schmidt QR factorization, returning a tuple (Q,R).

cgs2

Convenience function that calculates a Reorthogonalized Gram Schmmidt QR factorization (see Giraud et al. for details), returning a tuple (Q,R).

mgs

Convenience function that calculates a Modified Gram Schmidt QR factorization, returning a tuple (Q,R).

Type Aliases

Result