CLAHEF(3)

💜 CLAHEF(3) — like, the whole vibe

okay so real quick before we dive in: this is a page from the Library Functions Manual, and the file it lives in is /home/abui...RC/clahef.f(3). yes the path is giving truncated-build-directory energy, we love that for us 💅

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/clahef.f — that's the whole name, bestie. it's a mouthful, it's iconic, it's literally just the source file path. 🎀

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🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine CLAHEF (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)

CLAHEF computes a partial factorization of a complex Hermitian indefinite matrix using the Bunch-Kaufman diagonal pivoting method (blocked algorithm, calling Level 3 BLAS).

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🦋 Function/Subroutine Documentation 🦋

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

CLAHEF computes a partial factorization of a complex Hermitian indefinite matrix using the Bunch-Kaufman diagonal pivoting method (blocked algorithm, calling Level 3 BLAS).

🧚 Purpose

ok so picture this — CLAHEF 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  ) ( U12**H U22**H )

A  =  ( L11  0 ) (  D   0  ) ( L11**H L21**H )  if UPLO = 'L'
      ( L21  I ) (  0  A22 ) (  0      I     )

where the order of D is at most NB. the actual order gets handed back to you in the argument KB, and it's either NB or NB-1, or N if N <= NB. also quick note, U**H means the conjugate transpose of U — iykyk 💫

CLAHEF is an auxiliary routine called by CHETRF. it uses blocked code (calling Level 3 BLAS, fancy) to update the submatrix A11 (if UPLO = 'U') or A22 (if UPLO = 'L'). ✨

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🎀 Parameters 🎀

UPLO

UPLO is CHARACTER*1 — it specifies whether the upper or lower triangular part of the Hermitian matrix A is stored:

• = 'U': upper triangular
• = 'L': lower triangular

N

N is INTEGER — the order of the matrix A. N >= 0. 🫶

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. (like, genuinely, at least 2. don't skip that.)

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.

A

A is COMPLEX array, dimension (LDA,N).

On entry, it's 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. main character transformation, honestly 👑

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 interchanges and the block structure of D. this one's got layers, so:

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.

W

W is COMPLEX array, dimension (LDW,NB).

LDW

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

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. 😭 (completed but singular is such a specific heartbreak)

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👑 Author

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

💜 Contributors

November 2013, Igor Kozachenko, Computer Science Division, University of California, Berkeley.

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⭐ Definition at line 176 of file clahef.f.

Author

Generated automatically by Doxygen for LAPACK from the source code. (not a human, just a little documentation goblin doing its thing 🧚)

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and that's the whole page bestie! this one's brought to you by LAPACK, Version 3.12.0, living at /home/abui...RC/clahef.f(3) — slay, go factor something Hermitian 💖✨🦋🌸