SRC/cgetrf2.f(3)

💅 SRC/cgetrf2.f 💅

okay so bestie, welcome to the Library Functions Manual — this page is SRC/cgetrf2.f, and it's giving recursive Fortran subroutine energy. Let's get into it. ✨

🌸 NAME 🌸

SRC/cgetrf2.f — that's the page name, and the star of the show is CGETRF2. 🎀

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

• recursive subroutine cgetrf2 (m, n, a, lda, ipiv, info) — CGETRF2.

🦋 Function/Subroutine Documentation 🦋

👑 CGETRF2

recursive subroutine cgetrf2 (integer m, integer n, complex, dimension( lda,
* ) a, integer lda, integer, dimension( * ) ipiv, integer info)

💖 Purpose 💖

CGETRF2 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). Iconic. 👑

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

                                      [ 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.

bestie, this is recursion doing its main character thing — it calls itself, does swaps, solves A12, updates A22, then calls itself again for A22 and does the swaps on A21. periodt. 💫

🌈 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 COMPLEX 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.

okay so that > 0 case is the dramatic one: the factorization finished, but U is singular, and using it to solve a system is a division-by-zero situation. not cute. 💀

👑 Author 👑

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 112 of file cgetrf2.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole page, bestie. Footer energy: LAPACK Version 3.12.0, page SRC/cgetrf2.f(3). mwah 💋✨