SRC/zhetrf_aa_2stage.f(3)

📦
version 3.12.1 · 4 versions
, in arch rolling

🌸 NAME 🌸

SRC/zhetrf_aa_2stage.f — from the LAPACK Library Functions Manual, bestie. This is the page for the ZHETRF_AA_2STAGE routine, and it's giving serious linear algebra main character energy. 💅

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine zhetrf_aa_2stage (uplo, n, a, lda, tb, ltb, ipiv, ipiv2,
           work, lwork, info)

ZHETRF_AA_2STAGE — yes, that's the whole vibe. 🫶

💖 Function/Subroutine Documentation 💖

subroutine zhetrf_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)

ZHETRF_AA_2STAGE

🎀 Purpose 🎀

Okay so ZHETRF_AA_2STAGE computes the factorization of a double hermitian matrix A using Aasen's algorithm. The form of the factorization is:

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

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is a hermitian band matrix with the bandwidth of NB. And listen: 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. Literally 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. Simple as that, bestie. ✨

A

A is COMPLEX*16 array, dimension (LDA,N).

On entry, it's 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). Respect the leading dimension, periodt. 💅

TB

TB is COMPLEX*16 array, dimension (MAX(1,LTB)).

On exit, it holds details of the LU factorization of the band matrix. Obsessed with this for TB, honestly. 🎀

LTB

LTB is INTEGER.

The size of the array TB. LTB >= MAX(1,4*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). Yep, the page says IPIV(k) right there, so that's what we're keeping. 💀

WORK

WORK is COMPLEX*16 workspace of size (MAX(1,LWORK)). 🧚

LWORK

LWORK is INTEGER.

The size of WORK. LWORK >= MAX(1,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, that's the failure case — take note. 👑

🫶 Author 🫶

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

Definition at line 158 of file zhetrf_aa_2stage.f. 🌈

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code. ⭐

💖 okay that's the whole page — LAPACK Version 3.12.0, SRC/zhetrf_aa_2stage.f(3), from the Library Functions Manual. No date is printed on this footer, so I'm not inventing one, bestie. Bye! 💖

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