Struct nalgebra::linalg::ColPivQR

pub struct ColPivQR<N: ComplexField, R: DimMin<C>, C: Dim> where
    DefaultAllocator: Allocator<N, R, C> + Allocator<N, DimMinimum<R, C>> + Allocator<(usize, usize), DimMinimum<R, C>>,  { /* fields omitted */ }

The QR decomposition (with column pivoting) of a general matrix.

Implementations

impl<N: ComplexField, R: DimMin<C>, C: Dim> ColPivQR<N, R, C> where
    DefaultAllocator: Allocator<N, R, C> + Allocator<N, R> + Allocator<N, DimMinimum<R, C>> + Allocator<(usize, usize), DimMinimum<R, C>>, 

pub fn new(matrix: MatrixMN<N, R, C>) -> Self

Computes the ColPivQR decomposition using householder reflections.

pub fn r(&self) -> MatrixMN<N, DimMinimum<R, C>, C> where
    DefaultAllocator: Allocator<N, DimMinimum<R, C>, C>, 

Retrieves the upper trapezoidal submatrix R of this decomposition.

pub fn unpack_r(self) -> MatrixMN<N, DimMinimum<R, C>, C> where
    DefaultAllocator: Reallocator<N, R, C, DimMinimum<R, C>, C>, 

Retrieves the upper trapezoidal submatrix R of this decomposition.

This is usually faster than r but consumes self.

pub fn q(&self) -> MatrixMN<N, R, DimMinimum<R, C>> where
    DefaultAllocator: Allocator<N, R, DimMinimum<R, C>>, 

Computes the orthogonal matrix Q of this decomposition.

pub fn p(&self) -> &PermutationSequence<DimMinimum<R, C>>

Retrieves the column permutation of this decomposition.

pub fn unpack(
    self
) -> (MatrixMN<N, R, DimMinimum<R, C>>, MatrixMN<N, DimMinimum<R, C>, C>, PermutationSequence<DimMinimum<R, C>>) where
    DimMinimum<R, C>: DimMin<C, Output = DimMinimum<R, C>>,
    DefaultAllocator: Allocator<N, R, DimMinimum<R, C>> + Reallocator<N, R, C, DimMinimum<R, C>, C> + Allocator<(usize, usize), DimMinimum<R, C>>, 

Unpacks this decomposition into its two matrix factors.

pub fn q_tr_mul<R2: Dim, C2: Dim, S2>(&self, rhs: &mut Matrix<N, R2, C2, S2>) where
    S2: StorageMut<N, R2, C2>, 

Multiplies the provided matrix by the transpose of the Q matrix of this decomposition.

impl<N: ComplexField, D: DimMin<D, Output = D>> ColPivQR<N, D, D> where
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D> + Allocator<(usize, usize), DimMinimum<D, D>>, 

pub fn solve<R2: Dim, C2: Dim, S2>(
    &self,
    b: &Matrix<N, R2, C2, S2>
) -> Option<MatrixMN<N, R2, C2>> where
    S2: StorageMut<N, R2, C2>,
    ShapeConstraint: SameNumberOfRows<R2, D>,
    DefaultAllocator: Allocator<N, R2, C2>, 

Solves the linear system self * x = b, where x is the unknown to be determined.

Returns None if self is not invertible.

pub fn solve_mut<R2: Dim, C2: Dim, S2>(
    &self,
    b: &mut Matrix<N, R2, C2, S2>
) -> bool where
    S2: StorageMut<N, R2, C2>,
    ShapeConstraint: SameNumberOfRows<R2, D>, 

Solves the linear system self * x = b, where x is the unknown to be determined.

If the decomposed matrix is not invertible, this returns false and its input b is overwritten with garbage.

pub fn try_inverse(&self) -> Option<MatrixN<N, D>>

Computes the inverse of the decomposed matrix.

Returns None if the decomposed matrix is not invertible.

pub fn is_invertible(&self) -> bool

Indicates if the decomposed matrix is invertible.

pub fn determinant(&self) -> N

Computes the determinant of the decomposed matrix.

Trait Implementations

impl<N: Clone + ComplexField, R: Clone + DimMin<C>, C: Clone + Dim> Clone for ColPivQR<N, R, C> where
    DefaultAllocator: Allocator<N, R, C> + Allocator<N, DimMinimum<R, C>> + Allocator<(usize, usize), DimMinimum<R, C>>, 

fn clone(&self) -> ColPivQR<N, R, C>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<N: ComplexField, R: DimMin<C>, C: Dim> Copy for ColPivQR<N, R, C> where
    DefaultAllocator: Allocator<N, R, C> + Allocator<N, DimMinimum<R, C>> + Allocator<(usize, usize), DimMinimum<R, C>>,
    MatrixMN<N, R, C>: Copy,
    PermutationSequence<DimMinimum<R, C>>: Copy,
    VectorN<N, DimMinimum<R, C>>: Copy, 

impl<N: Debug + ComplexField, R: Debug + DimMin<C>, C: Debug + Dim> Debug for ColPivQR<N, R, C> where
    DefaultAllocator: Allocator<N, R, C> + Allocator<N, DimMinimum<R, C>> + Allocator<(usize, usize), DimMinimum<R, C>>, 

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

Formats the value using the given formatter.