Struct ColPivQr

pub struct ColPivQr<E>
where
    E: Entity,
{
    factors: Mat<E>,
    householder: Mat<E>,
    col_perm: Vec<usize>,
    col_perm_inv: Vec<usize>,
}

QR decomposition with column pivoting.

Fields

factors: Mat<E>

householder: Mat<E>

col_perm: Vec<usize>

col_perm_inv: Vec<usize>

Implementations

impl<E> ColPivQr<E>

where E: ComplexField,

pub fn new<ViewE>(matrix: MatRef<'_, ViewE>) -> ColPivQr<E>

where ViewE: Conjugate<Canonical = E>,

Returns the QR decomposition of the input matrix with column pivoting.

The factorization is such that $AP^\top = QR$, where $R$ is upper trapezoidal, $Q$ is unitary, and $P$ is a permutation matrix.

pub fn col_permutation(&self) -> PermRef<'_, usize>

Returns the column permutation matrix $P$ of the QR decomposition.

pub fn compute_r(&self) -> Mat<E>

Returns the factor $R$ of the QR decomposition.

pub fn compute_q(&self) -> Mat<E>

Returns the factor $Q$ of the QR decomposition.

pub fn compute_thin_r(&self) -> Mat<E>

Returns the top $r$ rows of the factor $R$ of the QR decomposition, where $r = \min(\text{nrows}(A), \text{ncols}(A))$.

pub fn compute_thin_q(&self) -> Mat<E>

Returns the leftmost $r$ columns of the factor $R$ of the QR decomposition, where $r = \min(\text{nrows}(A), \text{ncols}(A))$.

Trait Implementations

impl<E> Debug for ColPivQr<E>

where E: Debug + Entity,

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

Formats the value using the given formatter.

impl<E> SolverCore<E> for ColPivQr<E>

where E: ComplexField,

fn reconstruct(&self) -> Mat<E>

Reconstructs the original matrix using the decomposition.

fn inverse(&self) -> Mat<E>

Computes the inverse of the original matrix using the decomposition.

impl<E> SpSolverCore<E> for ColPivQr<E>

where E: ComplexField,

fn nrows(&self) -> usize

Returns the number of rows of the matrix used to construct this decomposition.

fn ncols(&self) -> usize

Returns the number of columns of the matrix used to construct this decomposition.

impl<E> SolverLstsqCore<E> for ColPivQr<E>

where E: ComplexField,

impl<E> SpSolverLstsqCore<E> for ColPivQr<E>

where E: ComplexField,