num::QRResult Struct Reference

Result of a QR factorization: A = Q * R. More...

#include <qr.hpp>

Public Attributes
Matrix	Q
	mxm orthogonal
Matrix	R
	mxn upper triangular

Detailed Description

Result of a QR factorization: A = Q * R.

Q is an mxm orthogonal matrix (Q^T * Q = I). R is an mxn upper triangular matrix (entries below the diagonal are zero).

For an overdetermined system (m > n), the least-squares solution minimises ||A*x - b||_2 and is obtained by back-substituting into R[:n,:n] * x = (Q^T*b)[:n]. The residual norm is ||(Q^T*b)[n:]||_2.

Definition at line 18 of file qr.hpp.

Member Data Documentation

Q

Matrix num::QRResult::Q

mxm orthogonal

Definition at line 19 of file qr.hpp.

Referenced by num::qr_solve(), and num::svd_truncated().

R

Matrix num::QRResult::R

mxn upper triangular

Definition at line 20 of file qr.hpp.

Referenced by num::qr_solve().

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

• /home/runner/work/numerics/numerics/include/linalg/factorization/qr.hpp