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

Okay bestie, this is /home/abui...lahef_aa.f(3) from the Library Functions Manual — we're doing LAPACK subroutine lore today and it's honestly iconic. ✨

🌸 NAME 🌸

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

✨ SYNOPSIS ✨

Functions/Subroutines

       subroutine ZLAHEF_AA (uplo, j1, m, nb, a, lda, ipiv, h, ldh, work)

ZLAHEF_AA

💖 Function/Subroutine Documentation 💖

🫶 subroutine ZLAHEF_AA

   subroutine ZLAHEF_AA (character uplo, integer j1, integer m, integer nb,
       complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * )
       ipiv, complex*16, dimension( ldh, * ) h, integer ldh, complex*16,
       dimension( * ) work)

ZLAHEF_AA

💡 Purpose:

Bestie, the source block literally starts with DLAHEF_AA even though this is ZLAHEF_AA — I'm keeping that exact spelling because we do not edit the source vibes. 💀

DLAHEF_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.

To factorize the panel, Aasen's algorithm needs the last row, or column, of the previous panel. The first row, or column, of A is set to be the first row, or column, of an identity matrix, and that's what gets used to factorize the first panel.

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.

🧾 Parameters

• UPLO — UPLO is CHARACTER*1
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.
• J1 — J1 is INTEGER. This is where the first row, or column, of the panel sits inside the submatrix of A that's passed to this routine. For example, when called by ZHETRF_AA, the first panel has J1 as 1, while the remaining panels have J1 as 2.
• M — M is INTEGER, and it's the dimension of the submatrix. M >= 0.
• NB — NB is INTEGER, and it's the dimension of the panel to be facotorized. Yes, that's the exact spelling in the source — leaving it exactly as-is, bestie. ✨
• A — A is COMPLEX*16 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.
• LDA — LDA is INTEGER, the leading dimension of the array A. LDA >= max(1,N). (Yep, it says N right there in the source — copying exactly. 💅)
• IPIV — IPIV is INTEGER array, dimension (N). It holds the details of the row and column interchanges: the row and column k were interchanged with the row and column IPIV(k).
• H — H is COMPLEX*16 workspace, dimension (LDH,NB).
• LDH — LDH is INTEGER, the leading dimension of the workspace H. LDH >= max(1,M).
• WORK — WORK is COMPLEX*16 workspace, dimension (M).

👑 Author

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

Definition at line 142 of file zlahef_aa.f.

👑 Author

Generated automatically by Doxygen for LAPACK from the source code.

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💖 Cute sign-off: source/version from the footer is LAPACK, Version 3.12.0, on page /home/abui...lahef_aa.f(3). The original footer doesn't show a date, so no date is invented here — periodt. 🌈👑