/home/abui.../dgetrf2.f(3)

💖 NAME 💖

okay bestie, this is the dgetrf2.f(3) page from the Library Functions Manual. The title line up top is basically /home/abui.../dgetrf2.f(3), and the full NAME entry is the source path, literally:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dgetrf2.f

It's giving “LAPACK source file who got her own manpage” energy, and honestly? obsessed. 🎀

✨ SYNOPSIS ✨

Functions/Subroutines

• recursive subroutine DGETRF2 (m, n, a, lda, ipiv, info) — this is the main character: DGETRF2. 💅

🎀 Function/Subroutine Documentation 🎀

Here's the full signature, exactly as the page shows it:

recursive subroutine DGETRF2 (integer m, integer n, double precision,
    dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv,
    integer info)

DGETRF2

Purpose 🧚

okay so DGETRF2 computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges. Slay. ✨

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). Triangular icon behavior, no cap. 💅

This is the recursive version of the algorithm. It divides the matrix into four submatrices:

       [  A11 | A12  ]  where A11 is n1 by n1 and A22 is n2 by n2
A =    [ -----|----- ]  with n1 = min(m,n)/2
       [  A21 | A22  ]       n2 = n-n1

Then the subroutine calls itself to factor:

                                       [ A11 ]
The subroutine calls itself to factor [ --- ],
                                       [ A12 ]
                 [ A12 ]
do the swaps on [ --- ], solve A12, update A22,
                 [ A22 ]

then calls itself to factor A22 and do the swaps on A21. Recursive queen behavior, fr fr. 🌀

Parameters 💖

• M

M is INTEGER The number of rows of the matrix A. M >= 0.

• N

N is INTEGER The number of columns of the matrix A. N >= 0.

• A

A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the M-by-N matrix to be factored. On exit, the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored.

• LDA

LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).

• IPIV

IPIV is INTEGER array, dimension (min(M,N)) The pivot indices; for 1 <= i <= min(M,N), row i of the matrix was interchanged with row IPIV(i).

• INFO

INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations.

Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 112 of file dgetrf2.f.

Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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Cute sign-off time: this page is LAPACK Version 3.12.0, and the footer path is /home/abui.../dgetrf2.f(3). That's the whole manual-page moment — stay slay, bestie! 🌈💜