qr.hpp

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/// @file qr.hpp
/// @brief QR factorization via Householder reflections.
#pragma once
 
#include "core/matrix.hpp"
#include "core/policy.hpp"
 
namespace num {
 
/// @brief QR factorization \f$A=QR\f$.
struct QRResult {
    Matrix Q;
    Matrix R;
};
 
/// @brief Factor \f$A\in\mathbb{R}^{m\times n}\f$ as \f$A=QR\f$.
QRResult qr(const Matrix& A, Backend backend = lapack_backend);
 
/// @brief Solve \f$\min_x \|Ax-b\|_2\f$.
void qr_solve(const QRResult& f, const Vector& b, Vector& x);
 
} // namespace num