Triangular Factorization (trf)

trf (defined in namespace flens::lapack) computes an \(LU\) factorization of a general \(m \times n\) matrix \(A\) using partial pivoting with row interchanges.

The factorization has the form

\[ A = P L U \]

where \(P\) is a permutation matrix, \(L\) is lower triangular with unit diagonal elements (lower trapezoidal if \(m > n\)), and \(U\) is upper triangular (upper trapezoidal if \(m < n\)).

Interface

template <typename MA, typename VPIV>
    typename RestrictTo<IsGeMatrix<MA>::value
                     && IsIntegerDenseVector<VPIV>::value,
             typename RemoveRef<MA>::Type::IndexType>::Type
    trf(MA &&A, VPIV &&piv);

A	`(input/output) real or complex valued GeMatrix` On entry, the \(m \times n\) matrix to be factored. On exit, the factors \(L\) and \(U\) from the factorization \(A = PLU\). The unit diagonal elements of \(L\) are not stored.
piv	`(output) integer valued DenseVector` The pivot indices. For \(1 \leq i \leq \min\{m, n\}\), row \(i\) of the matrix was interchanged with row \(piv_i\).

Notes

Example: lapack-getrf.
This is the right-looking Level 3 BLAS version of the algorithm.
trf is a port of dgetrf and zgetrf. Also this documentation is taken from there.