CSYTRF_AA_2STAGE(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 CSYTRF_AA_2STAGE(3) 💅

okay bestie, welcome to the LAPACK Library Functions Manual page for CSYTRF_AA_2STAGE. this is the group-chat recap of a complex symmetric matrix factorization routine, and yes it is giving main-character linear algebra energy ✨

🌸 NAME 🌸

the NAME line is literally this source path, no cap:

/home/abuild/rpmbuild/BUILD/lapack-
static-3.12.0-build/lapack-3.12.0/SRC/csytrf_aa_2stage.f

🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine CSYTRF_AA_2STAGE (uplo, n, a, lda, tb, ltb, ipiv, ipiv2,
    work, lwork, info)
    CSYTRF_AA_2STAGE

✨ Function/Subroutine Documentation ✨

here's the typed-out glow-up of the signature, bestie:

subroutine CSYTRF_AA_2STAGE (character uplo, integer n, complex, dimension(
    lda, * ) a, integer lda, complex, dimension( * ) tb, integer ltb,
    integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex,
    dimension( * ) work, integer lwork, integer info)
CSYTRF_AA_2STAGE

🎀 Purpose 🎀

okay so CSYTRF_AA_2STAGE 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 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 🔥

🍓 Parameters 🍓

UPLO

UPLO is CHARACTER*1.

  • = '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.

A

A is COMPLEX 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'). slay 💅

LDA

LDA is INTEGER.

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

TB

TB is COMPLEX array, dimension (LTB).

on exit, details of the LU factorization of the band matrix.

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.

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).

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).

WORK

WORK is COMPLEX workspace of size LWORK.

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.
bestie the INFO > 0 case is the “the band LU factorization said no” moment, so keep an eye on it 😭

👑 Author 👑

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

Definition at line 158 of file csytrf_aa_2stage.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

okay that's the whole page 💖 source/version/date sign-off: this is from LAPACK, Version 3.12.0, and the footer source path is /home/abui...aa_2stage.f(3). the footer doesn't show a separate date, so i’m not inventing one — mwah! 🫶✨

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