SRC/csytrf_aa.f(3)

💖 SRC/csytrf_aa.f 💖

okay bestie, so this page lives in the LAPACK manual, and it's literally all about csytrf_aa — like, the whole page. no cap. let's get into it 🫶

---

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

• subroutine csytrf_aa (uplo, n, a, lda, ipiv, work, lwork, info) — and that's the one and only CSYTRF_AA, our main character 👑

---

🌸 Function/Subroutine Documentation 🌸

💅 the actual signature 💅

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

CSYTRF_AA — say it with me 💜

⭐ Purpose ⭐

bestie, here's the tea: CSYTRF_AA computes the factorization of a complex 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 complex symmetric tridiagonal matrix. iconic behavior fr fr ✨

this is the blocked version of the algorithm, calling Level 3 BLAS. we love an efficient queen 🔥

🦋 Parameters 🦋

• UPLO

UPLO is CHARACTER*1 — pick your vibe:

• = 'U': the upper triangle of A is stored;
• = 'L': the lower triangle of A is stored.

• N

N is INTEGER — the order of the matrix A. constraint: N >= 0 🌈

• A

A is COMPLEX 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'). the glow-up is real 💅

• LDA

LDA is INTEGER — the leading dimension of the array A. constraint: LDA >= max(1,N) 📏

• 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). she's swapping things around, we stan 🔄

• WORK

WORK is COMPLEX array, dimension (MAX(1,LWORK))

on exit, if INFO = 0, WORK(1) returns the optimal LWORK. noted 📝

• LWORK

LWORK is INTEGER — the length of WORK. constraint: LWORK >= MAX(1,2*N). for optimum performance LWORK >= N*(1+NB), where NB is the optimal blocksize. go big or go home bestie 💪

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. very demure, very mindful 🎀

• INFO

INFO is INTEGER

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

ngl bestie, that < 0 case means somebody fed her a bad argument — she will tell you exactly which one via INFO = -i. no mystery, no drama, just receipts.

👑 Author 👑

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

Definition at line 131 of file csytrf_aa.f. 🎯

---

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. iykyk 🤖✨

---

and that's the whole page bestie! LAPACK, Version 3.12.0, dated with the source — mwah 💋🫶