ZGETRF(3)

✨ ZGETRF(3) ✨

okay bestie, gather round, we're doing a LAPACK deep-dive 💅 this one lives in the Library Functions Manual, and the actual file it's documenting is:

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

yes that's a whole path, no i will not be shortening it, the path is iconic and we respect it 🫶

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🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine ZGETRF (m, n, a, lda, ipiv, info)

ZGETRF — that's the main character, that's her name 💖

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🦋 Function/Subroutine Documentation 🦋

subroutine ZGETRF (integer m, integer n, complex*16, dimension( lda, * ) a,
    integer lda, integer, dimension( * ) ipiv, integer info)

ZGETRF 😌✨

🎀 Purpose 🎀

!> !> ZGETRF computes an LU factorization of a general M-by-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). !> !> This is the right-looking Level 3 BLAS version of the algorithm. !>

so literally what it does is take your general M-by-N matrix A and factorize it as A = P * L * U using partial pivoting with row interchanges, no cap 🔥 P is a permutation matrix, L is lower triangular with unit diagonal elements (lower trapezoidal if m > n, she contains multitudes), and U is upper triangular (upper trapezoidal if m < n). and the whole thing is the right-looking Level 3 BLAS version of the algorithm — highkey the fast one, we love her 💅

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🌈 Parameters 🌈

• M — integer, and it's the number of rows of the matrix A. must satisfy M >= 0. zero rows? valid. slay.

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

• N — integer, the number of columns of the matrix A. must satisfy N >= 0. same energy.

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

• A — COMPLEX*16 array, dimension (LDA,N). on entry it's the M-by-N matrix you want factored, and on exit it holds the factors L and U from the factorization A = P*L*U. caveat bestie: the unit diagonal elements of L are not stored — they're implied, we don't waste memory on ones 🙈

!>          A is COMPLEX*16 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 — integer, the leading dimension of the array A. must satisfy LDA >= max(1,M). periodt.

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

• IPIV — 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). that's the receipts of every swap, keep them 🎀

!>          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 — integer, the vibe check on how it went:
  • = 0: successful exit, we ate 💅
  • < 0: if INFO = -i, the i-th argument had an illegal value — you passed something cursed 😭
  • > 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. not a drill, that's undefined-behaviour-adjacent behaviour, be careful fr fr 💀

!>          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.

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👑 Author 👑

the legends themselves:

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

💜 Definition 💜

at line 107 of file zgetrf.f. iykyk 📍

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⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code 🤖 (yes the robots wrote the docs, we still stan)

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and that's the whole page bestie 🧚💖 brought to you by LAPACK, Version 3.12.0, straight out of /home/abui...RC/zgetrf.f(3) — go factorize something gorgeous today 🌸🦋💅