SRC/clahef_aa.f(3)

✨ SRC/clahef_aa.f(3) ✨

okay so this is a page from the Library Functions Manual bestie, and it's literally all about one little Fortran subroutine that does Big Math. buckle up 💖

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🌸 NAME 🌸

SRC/clahef_aa.f — that's the file, that's the vibe, main character energy fr fr

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🎀 SYNOPSIS 🎀

Functions/Subroutines

ok so there's exactly one icon here and she's serving:

• subroutine clahef_aa (uplo, j1, m, nb, a, lda, ipiv, h, ldh, work) — the one and only, CLAHEF_AA herself 👑

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💅 Function/Subroutine Documentation 💅

here's the full signature, no cap, copied exactly:

subroutine clahef_aa (character uplo, integer j1, integer m, integer nb,
    complex, dimension( lda, * ) a, integer lda, integer, dimension( * )
    ipiv, complex, dimension( ldh, * ) h, integer ldh, complex, dimension( *
    ) work)

CLAHEF_AA — spelled out, all caps, iconic.

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🔥 Purpose 🔥

ok so what does she DO. CLAHEF_AA factorizes a panel of a complex hermitian matrix A using the Aasen's algorithm. the panel is a set of NB rows of A when UPLO is U, or a set of NB columns when UPLO is L. slay 🫶

and like, to factorize the panel, Aasen's algorithm needs the last row (or column) of the previous panel. so the first row, or column, of A is set to be the first row, or column, of an identity matrix — which is what gets used to factorize the first panel. cute little bootstrap moment honestly 💖

the resulting J-th row of U, or J-th column of L, is stored in the (J-1)-th row, or column, of A (without the unit diagonals), while the diagonal and subdiagonal of A are overwritten by those of T. yes, overwritten. that's just how she rolls 💀

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🌈 Parameters 🌈

• UPLO — UPLO is CHARACTER*1
  • = 'U': upper triangle of A is stored
  • = 'L': lower triangle of A is stored
• J1 — J1 is INTEGER
  • the location of the first row, or column, of the panel within the submatrix of A, passed to this routine. e.g. when called by CHETRF_AA, for the first panel, J1 is 1, while for the remaining panels, J1 is 2. iykyk
• M — M is INTEGER
  • the dimension of the submatrix. M >= 0. (zero is allowed bestie, she's flexible)
• NB — NB is INTEGER
  • the dimension of the panel to be facotorized 💅 yes we're keeping the typo energy, she's doing her best
• A — A is COMPLEX array, dimension (LDA,M) for the first panel, while dimension (LDA,M+1) for the remaining panels
  • on entry, A contains the last row, or column, of the previous panel, and the trailing submatrix of A to be factorized — except for the first panel, only the panel is passed
  • on exit, the leading panel is factorized. she ATE 🔥
• LDA — LDA is INTEGER
  • the leading dimension of the array A. LDA >= max(1,N).
• IPIV — IPIV is INTEGER array, dimension (N)
  • details of the row and column interchanges: the row and column k were interchanged with the row and column IPIV(k). receipts 🧾
• H — H is COMPLEX workspace, dimension (LDH,NB)
• LDH — LDH is INTEGER
  • the leading dimension of the workspace H. LDH >= max(1,M).
• WORK — WORK is COMPLEX workspace, dimension (M).

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👑 Author 👑

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

the whole squad showed up, we love a collab 🫶✨

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⭐ Definition at line 142 of file clahef_aa.f. ⭐

literally line 142, go look, she's right there 📍

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🦋 Author 🦋

generated automatically by Doxygen for LAPACK from the source code. not a human, just a very diligent little robot doing her thing 🤖💜

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💀 reminder bestie: A, IPIV, and the diagonal/subdiagonal situation all get overwritten, so don't come crying if your matrix doesn't look the same after. that's the whole point, no cap.

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ok that's the whole page!! mwah 💋 this was SRC/clahef_aa.f(3) from LAPACK, Version 3.12.0 — see you in the next man page, bestie, periodt 🎀✨🦋