SSYTRF_AA_2STAGE(3)

✨ NAME ✨

Okay so bestie, we’re on the ssytrf_aa_2stage.f(3) page of the Library Functions Manual, and the file being documented is literally this absolute path right here:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/ssytrf_aa_2stage.f

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🌸 SYNOPSIS 🌸

💅 Functions/Subroutines 💅

• subroutine SSYTRF_AA_2STAGE (uplo, n, a, lda, tb, ltb, ipiv, ipiv2, work, lwork, info) — the icon itself, SSYTRF_AA_2STAGE, with all those arguments lined up like a group chat roll call.

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💖 Function/Subroutine Documentation 💖

The full signature, copied exactly, because we do not play with source-code spelling around here:

   subroutine SSYTRF_AA_2STAGE (character uplo, integer n, real, dimension(
       lda, * ) a, integer lda, real, dimension( * ) tb, integer ltb, integer,
       dimension( * ) ipiv, integer, dimension( * ) ipiv2, real, dimension( * )
       work, integer lwork, integer info)

And yes, the name is SSYTRF_AA_2STAGE again. Documentation said “say it again for the people in the back,” and honestly? slay.

🌈 Purpose 🌈

Bestie, listen: SSYTRF_AA_2STAGE computes the factorization of a real symmetric matrix A using 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 band matrix with the bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is LU factorized with partial pivoting).

This is the blocked version of the algorithm, calling Level 3 BLAS. Highkey iconic behavior.

🎀 Parameters 🎀

• UPLO — UPLO is CHARACTER*1. It’s giving “which triangle are we keeping?” energy: = 'U': upper triangle of A is stored; = 'L': lower triangle of A is stored.
• N — N is INTEGER, the order of the matrix A. Constraint: N >= 0.
• A — A is a REAL array, dimension (LDA,N). On entry, it’s 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, L is stored below (or above) the subdiagonal blocks, when UPLO is 'L' (or 'U'). Not me checking both triangles like a paranoid bestie.

• LDA — LDA is INTEGER, the leading dimension of the array A. Constraint: LDA >= max(1,N).
• TB — TB is a REAL array, dimension (LTB). On exit, it contains details of the LU factorization of the band matrix.
• LTB — LTB is INTEGER, the size of the array TB. Constraint: LTB >= 4*N, internally used to select NB such that LTB >= (3*NB+1)*N.

If LTB = -1, then a workspace query is assumed; the routine only calculates the optimal size of LTB, returns this value as the first entry of TB, and no error message related to LTB is issued by XERBLA. Workspace-query era, we love to see it.

• IPIV — IPIV is an 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).
• IPIV2 — IPIV2 is an INTEGER array, dimension (N). On exit, it contains the details of the interchanges, i.e., the row and column k of T were interchanged with the row and column IPIV(k). Yes, the source says IPIV(k) right there; we’re keeping it exactly as written, no cap.
• WORK — WORK is a REAL workspace of size LWORK.
• LWORK — LWORK is INTEGER, the size of WORK. Constraint: LWORK >= N, internally used to select NB such that LWORK >= N*NB.

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. Another workspace query? We stay querying.

• INFO — INFO is INTEGER. The vibe check goes like this:
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value.
  • > 0: if INFO = i, band LU factorization failed on i-th column

👑 Author 👑

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

Definition at line 158 of file ssytrf_aa_2stage.f. Noted, bookmarked, timestamped in my brain.

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💫 Author 💫

Generated automatically by Doxygen for LAPACK from the source code. Automation ate, honestly.

Mwah 💋 — this was LAPACK Version 3.12.0, page path /home/abui...aa_2stage.f(3), and yes bestie, that’s the cute little footer sign-off.