SRC/ssytrf_aa.f(3)

💅 SRC/ssytrf_aa.f(3) — or, the LAPACK library functions manual page that lives rent-free in my head

okay so bestie, this is SRC/ssytrf_aa.f(3), straight out of the LAPACK library functions manual. she's a Fortran source file, she's a subroutine doc page, and she's lowkey iconic. let's get into it 🎀

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✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine ssytrf_aa (uplo, n, a, lda, ipiv, work, lwork, info) — the one and only SSYTRF_AA 💫

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🦋 Function/Subroutine Documentation 🦋

subroutine ssytrf_aa (character uplo, integer n, real, dimension( lda, * )
    a, integer lda, integer, dimension( * ) ipiv, real, dimension( * ) work,
    integer lwork, integer info)

SSYTRF_AA — that's her name, that's her whole brand 👑

🌸 Purpose 🌸

okay so here's the tea, and I need you to focus bestie:

SSYTRF_AA computes the factorization of a real symmetric matrix A using the Aasen's algorithm. the form of the factorization is:

A = U**T*T*U  or  A = L*T*L**T

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is a symmetric tridiagonal matrix. 🫶

and listen — this is the blocked version of the algorithm, calling Level 3 BLAS. highkey the upgraded glow-up version, not the scrappy little unblocked one. periodt.

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💖 Parameters 💖

grab a snack, we're going through all of them, no skipping 💅

UPLO

• UPLO is CHARACTER*1
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.

pick your fighter, bestie — only the triangle you name gets any attention 🎀

N

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

zero is legal, don't come for her. ✨

A

• A is REAL array, dimension (LDA,N)
  • On entry, the symmetric 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, the tridiagonal matrix is stored in the diagonals and the subdiagonals of A just below (or above) the diagonals, and L is stored below (or above) the subdiagonals, when UPLO is 'L' (or 'U').

she goes in as one thing and comes out as a whole different vibe. main character transformation arc, literally. 🦋

LDA

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

yes the max(1,...) is there for the N = 0 girlies, she's got you. 💜

IPIV

• IPIV is INTEGER array, dimension (N)
  • On exit, it contains the details of the interchanges, i.e., the row and column k of A were interchanged with the row and column IPIV(k).

the receipts of who swapped with whom 📋✨

WORK

• WORK is REAL array, dimension (MAX(1,LWORK))
  • On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

she's not just a scratch pad, she's a messenger. 🕊️

LWORK

• LWORK is INTEGER
  • The length of WORK.
  • LWORK >= 1, if N <= 1, and LWORK >= 2*N, otherwise.
  • For optimum performance LWORK >= N*(1+NB), where NB is the optimal blocksize, returned by ILAENV.
  • If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

ngl, LWORK = -1 is the "just tell me how much room you need, I'm not committing yet" option. she'll answer you, no judgment, and XERBLA won't come yelling. 🙈

INFO

• INFO is INTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value.

okay so < 0 means somebody fumbled an input — and INFO will straight up tell you which argument. read the number, fix the argument, try again. you got this. 💀➡️🔥

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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 collaborative effort. 🫶

Definition at line 133 of file ssytrf_aa.f.

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🌈 Author (again, yes really) 🌈

Generated automatically by Doxygen for LAPACK from the source code. she wasn't hand-written, she was manifested by a doc generator. no cap. ⭐

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okay that's the whole page bestie, you're officially fluent in ssytrf_aa. go factor some symmetric matrices with Aasen's algorithm and slay. 💅✨

LAPACK — Version 3.12.0 — SRC/ssytrf_aa.f(3) — mwah, sending you off with a little bow on top 🎀💖