Struct rulinalg::matrix::decomposition::ThinQR

pub struct ThinQR<T> {
    pub q1: Matrix<T>,
    pub r1: Matrix<T>,
}

The result of computing a thin (or reduced) QR decomposition.

Let A denote the m x n matrix given by A = QR. Then Q is an m x m orthogonal matrix, and R is an m x n upper trapezoidal matrix.

If m > n, we may write

A = QR = [ Q1 Q2 ] [ R1 ] = Q1 R1
                   [  0 ]

where Q1 is an m x n matrix with orthogonal columns, and R1 is an n x n upper triangular matrix. For some applications, the remaining (m - n) columns of the full Q matrix are not needed, in which case the thin QR decomposition is substantially cheaper if m >> n.

If m <= n, then the thin QR decomposition coincides with the usual decomposition. See QR for details.

To actually compute the QR decomposition, see Householder QR.

Fields

q1: Matrix<T>

The matrix Q1 in the decomposition A = Q1 R1.

r1: Matrix<T>

The upper-triangular matrix R1 in the decomposition A = Q1 R1.

Trait Implementations

impl<T: Clone> Clone for ThinQR<T>

fn clone(&self) -> ThinQR<T>

Returns a copy of the value.

const fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<T: Debug> Debug for ThinQR<T>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.