matrix_algorithms::QRResult< T, M, N > Struct Template Reference

Result of Householder QR decomposition. More...

#include <qr.h>

Collaboration diagram for matrix_algorithms::QRResult< T, M, N >:

Public Member Functions
FusedMatrix< T, M, M >	Q () const
	Extract the full orthogonal factor Q (M×M).
FusedMatrix< T, M, N >	R () const
	Extract the upper-triangular factor R (M×N).
FusedVector< T, M >	apply_Qt (const FusedVector< T, M > &b) const
	Apply Qᵀ to a vector b without forming Q explicitly.

Public Attributes
FusedMatrix< T, M, N >	QR
	Compact Householder + R storage.
FusedVector< T, N >	tau
	Householder scaling factors.

Detailed Description

template<typename T, my_size_t M, my_size_t N>
struct matrix_algorithms::QRResult< T, M, N >

Result of Householder QR decomposition.

Compact storage: R in upper triangle, normalized Householder vectors (leading 1 implicit) below diagonal, tau vector of scaling factors.

Template Parameters

T	Scalar type.
M	Number of rows (M ≥ N).
N	Number of columns.

Member Function Documentation

apply_Qt()

template<typename T , my_size_t M, my_size_t N>

FusedVector< T, M > matrix_algorithms::QRResult< T, M, N >::apply_Qt ( const FusedVector< T, M > &  b ) const

inline

Apply Qᵀ to a vector b without forming Q explicitly.

Computes Qᵀ·b by applying Householder reflections in forward order. Used for least squares: solve R·x = Qᵀ·b.

Parameters

b	Input vector of length M.

Returns

Qᵀ·b.

Q()

template<typename T , my_size_t M, my_size_t N>

FusedMatrix< T, M, M > matrix_algorithms::QRResult< T, M, N >::Q ( ) const

inline

Extract the full orthogonal factor Q (M×M).

Accumulates Householder reflections in reverse order: Q = H₀ · H₁ · … · H_{N−1} where Hⱼ = I − τⱼ · vⱼ · vⱼᵀ.

Here is the call graph for this function:

R()

template<typename T , my_size_t M, my_size_t N>

FusedMatrix< T, M, N > matrix_algorithms::QRResult< T, M, N >::R ( ) const

inline

Extract the upper-triangular factor R (M×N).

R(i,j) = QR(i,j) for i ≤ j, zero below diagonal.

Member Data Documentation

QR

template<typename T , my_size_t M, my_size_t N>

FusedMatrix<T, M, N> matrix_algorithms::QRResult< T, M, N >::QR

Compact Householder + R storage.

tau

template<typename T , my_size_t M, my_size_t N>

FusedVector<T, N> matrix_algorithms::QRResult< T, M, N >::tau

Householder scaling factors.

---

The documentation for this struct was generated from the following file:

• core/include/algorithms/decomposition/qr.h