Module smartcore::linalg::qr

QR factorization that factors a matrix into a product of an orthogonal matrix and an upper triangular matrix.

QR Decomposition

Any real square matrix \(A \in R^{n \times n}\) can be decomposed as a product of an orthogonal matrix \(Q\) and an upper triangular matrix \(R\):

\[A = QR\]

Example:

use smartcore::linalg::naive::dense_matrix::*;
use smartcore::linalg::qr::*;

let A = DenseMatrix::from_2d_array(&[
                &[0.9, 0.4, 0.7],
                &[0.4, 0.5, 0.3],
                &[0.7, 0.3, 0.8]
        ]);

let qr = A.qr().unwrap();
let orthogonal: DenseMatrix<f64> = qr.Q();
let triangular: DenseMatrix<f64> = qr.R();

References:

• "No bullshit guide to linear algebra", Ivan Savov, 2016, 7.6 Matrix decompositions
• "Numerical Recipes: The Art of Scientific Computing", Press W.H., Teukolsky S.A., Vetterling W.T, Flannery B.P, 3rd ed., 2.10 QR Decomposition

Structs

QR	Results of QR decomposition.

Traits

QRDecomposableMatrix

Trait that implements QR decomposition routine for any matrix.