ZLAHEF(3)

💅 ZLAHEF — the man page, but make it a group chat

okay so bestie, real talk: this page is zlahef.f(3) — that's the zlahef.f source file, manual section 3 (library functions, the good section ✨). The full path is literally:

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

No cap, that's the whole NAME section. The actual tea is down below 👇

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✨ SYNOPSIS ✨

Functions/Subroutines 🦋

• subroutine ZLAHEF (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info) — ZLAHEF computes a partial factorization of a complex Hermitian indefinite matrix using the Bunch-Kaufman diagonal pivoting method. It's the blocked algorithm, calling Level 3 BLAS. Iconic behaviour fr.

subroutine ZLAHEF (character uplo, integer n, integer nb, integer kb,
    complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * )
    ipiv, complex*16, dimension( ldw, * ) w, integer ldw, integer info)

ZLAHEF computes a partial factorization of a complex Hermitian indefinite matrix using the Bunch-Kaufman diagonal pivoting method. Blocked algorithm, calling Level 3 BLAS. She's efficient, she's structured, she's giving main character energy 👑

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🫶 Function/Subroutine Documentation 🫶

Purpose 💖

!> ZLAHEF computes a partial factorization of a complex Hermitian !> matrix A using the Bunch-Kaufman diagonal pivoting method. The !> partial factorization has the form: ! !> A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = 'U', or: !> ( 0 U22 ) ( 0 D ) ( U12H U22H ) ! !> A = ( L11 0 ) ( D 0 ) ( L11H L21H ) if UPLO = 'L' !> ( L21 I ) ( 0 A22 ) ( 0 I ) ! !> where the order of D is at most NB. The actual order is returned in !> the argument KB, and is either NB or NB-1, or N if N <= NB. !> Note that U**H denotes the conjugate transpose of U. ! !> ZLAHEF is an auxiliary routine called by ZHETRF. It uses blocked code !> (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or !> A22 (if UPLO = 'L').

so like — D has order at most NB, the actual order comes back in KB, and it's either NB or NB-1, or N if N <= NB. Also remember U**H is the conjugate transpose of U, iykyk 💅

And she's an auxiliary routine, called by ZHETRF. She uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or A22 (if UPLO = 'L'). Team player energy 🫶

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Parameters 🎀

UPLO

!> UPLO is CHARACTER*1 !> Specifies whether the upper or lower triangular part of the !> Hermitian matrix A is stored: !> = 'U': Upper triangular !> = 'L': Lower triangular

• 'U' → upper triangular 💫
• 'L' → lower triangular 🌸

pick one bestie, that's the vibe check

N

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

The order of the matrix A, and she must be N >= 0. Negative N is not the moment 🙈

NB

!> NB is INTEGER !> The maximum number of columns of the matrix A that should be !> factored. NB should be at least 2 to allow for 2-by-2 pivot !> blocks.

Max number of columns of A that should be factored. NB should be at least 2 so 2-by-2 pivot blocks can actually happen — don't skimp on her 🍓

KB

!> KB is INTEGER !> The number of columns of A that were actually factored. !> KB is either NB-1 or NB, or N if N <= NB.

The number of columns of A that were actually factored. KB is either NB-1 or NB, or N if N <= NB. She tells you what really happened, no cap ✨

A

!> A is COMPLEX*16 array, dimension (LDA,N) !> On entry, the Hermitian matrix A. If UPLO = 'U', the leading !> n-by-n upper triangular part of A contains the upper !> triangular part of the matrix A, and the strictly lower !> triangular part of A is not referenced. If UPLO = 'L', the !> leading n-by-n lower triangular part of A contains the lower !> triangular part of the matrix A, and the strictly upper !> triangular part of A is not referenced. !> On exit, A contains details of the partial factorization.

COMPLEX*16 array, dimension (LDA,N).

On entry: the Hermitian matrix A.

• If UPLO = 'U', the leading n-by-n upper triangular part of A holds the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced.
• If UPLO = 'L', the leading n-by-n lower triangular part of A holds the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.

On exit: A contains details of the partial factorization 👑

LDA

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

Leading dimension of array A. Must be LDA >= max(1,N). Respect her boundaries 💅

IPIV

!> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D. ! !> If UPLO = 'U': !> Only the last KB elements of IPIV are set. ! !> If IPIV(k) > 0, then rows and columns k and IPIV(k) were !> interchanged and D(k,k) is a 1-by-1 diagonal block. ! !> If IPIV(k) = IPIV(k-1) < 0, then rows and columns !> k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) !> is a 2-by-2 diagonal block. ! !> If UPLO = 'L': !> Only the first KB elements of IPIV are set. ! !> If IPIV(k) > 0, then rows and columns k and IPIV(k) were !> interchanged and D(k,k) is a 1-by-1 diagonal block. ! !> If IPIV(k) = IPIV(k+1) < 0, then rows and columns !> k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) !> is a 2-by-2 diagonal block.

INTEGER array, dimension (N). Holds the details of the interchanges and the block structure of D. This is the gossip column of the routine ngl.

If UPLO = 'U': only the last KB elements of IPIV are set.

• If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 diagonal block.
• If IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) were interchanged, and D(k-1:k,k-1:k) is a 2-by-2 diagonal block.

If UPLO = 'L': only the first KB elements of IPIV are set.

• If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 diagonal block.
• If IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were interchanged, and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

see the pattern? k-1 going up, k+1 going down. symmetry slay 🦋

W

!> W is COMPLEX*16 array, dimension (LDW,NB)

COMPLEX*16 array, dimension (LDW,NB). That's it, that's the whole description. mysterious queen 💜

LDW

!> LDW is INTEGER !> The leading dimension of the array W. LDW >= max(1,N).

Leading dimension of array W. Must be LDW >= max(1,N). same rule, W edition ✨

INFO

!> INFO is INTEGER !> = 0: successful exit !> > 0: if INFO = k, D(k,k) is exactly zero. The factorization !> has been completed, but the block diagonal matrix D is !> exactly singular.

INTEGER. The vibe report:

• = 0: successful exit 🎉
• > 0: if INFO = k, then D(k,k) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular 💀

⚠️ okay so that INFO > 0 case is not a crash — the work finished! It's just that D is exactly singular. Read the value, don't ignore it, bestie 😭

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Author 👑

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

the whole squad, credited properly 🫶

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Contributors 🌈

!> December 2016, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley

December 2016, Igor Kozachenko, Computer Science Division, University of California, Berkeley. giving credit where credit is due, periodt 💅

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Definition at line 176 of file zlahef.f 📍

That's where she lives. line 176. no further questions 🎀

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📜 Author (the Doxygen one) 📜

Generated automatically by Doxygen for LAPACK from the source code.

like, the whole page was auto-generated, she didn't even write this herself. queen behaviour honestly 🤖✨

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and that's the page bestie!! 💖 big sign-off energy: this is LAPACK, Version 3.12.0, and the footer also shows the path /home/abui...RC/zlahef.f(3) — truncated path, same file, same zlahef.f manual page we've been stanning this whole time. go forth and factorize your Hermitian indefinite matrix, you absolute icon 👑🦋💜