SRC/zsytrf_aa_2stage.f(3)

✨ SRC/zsytrf_aa_2stage.f(3) ✨

okay so bestie, welcome to the Library Functions Manual moment for SRC/zsytrf_aa_2stage.f — yes, the title is also the filename, iconic. no cap, this page is where ZSYTRF_AA_2STAGE gets its whole main-character energy, and we are keeping every single detail. 💅

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🌸 NAME 🌸

SRC/zsytrf_aa_2stage.f — that's the name, bestie. literally the file, living its best life. 🦋

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

Here's the subroutine vibe check. Save this exact signature, okay?

       subroutine zsytrf_aa_2stage (uplo, n, a, lda, tb, ltb, ipiv, ipiv2,
           work, lwork, info)
           ZSYTRF_AA_2STAGE

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💅 Function/Subroutine Documentation 💅

The full signature with types and dimensions is giving very precise, very slay:

       subroutine zsytrf_aa_2stage (character uplo, integer n, complex*16,
           dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tb,
           integer ltb, integer, dimension( * ) ipiv, integer, dimension( * )
           ipiv2, complex*16, dimension( * ) work, integer lwork, integer info)
           ZSYTRF_AA_2STAGE

🎀 Purpose 🎀

Okay so ZSYTRF_AA_2STAGE computes the factorization of a complex 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 complex 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. yes bestie, blocked, Level 3 BLAS, main character behavior. 🔥

🍓 Parameters 🍓

🌸 UPLO 🌸

UPLO is CHARACTER*1. It's the triangle selector, iykyk:

• = 'U': Upper triangle of A is stored;
• = 'L': Lower triangle of A is stored.

🌸 N 🌸

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

🌸 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, L is stored below (or above) the subdiagonal blocks, when UPLO is 'L' (or 'U'). 🦋

🌸 LDA 🌸

LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N). no cap, respect the leading dimension. 💅

🌸 TB 🌸

TB is COMPLEX*16 array, dimension (LTB). On exit, details of the LU factorization of the band matrix. that's the tea. 🍵

🌸 LTB 🌸

LTB is INTEGER. The size of the array TB. 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. very demure, very workspace-query. ✨

🌸 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). okay pivot bookkeeping queen. 👑

🌸 IPIV2 🌸

IPIV2 is 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, it says IPIV(k) here — keeping it exactly as the page says, bestie. 🫶

🌸 WORK 🌸

WORK is COMPLEX*16 workspace of size LWORK. that's the workspace, bestie. 💖

🌸 LWORK 🌸

LWORK is INTEGER. The size of WORK. 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. 🔥

🌸 INFO 🌸

INFO is INTEGER:

• = 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 zsytrf_aa_2stage.f.

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🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code. (yes bestie, the robots wrote this one. be nice to Doxygen.) 🤖💜

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okay that's the whole page, bestie. 💖 Footer shoutout: LAPACK Version 3.12.0 and SRC/zsytrf_aa_2stage.f(3) — and no date is listed in this footer, so no cap, don't come for me. 💅✨