SRC/dsytrf_aa_2stage.f(3)

💖 SRC/dsytrf_aa_2stage.f(3) 💖

This page is from the Library Functions Manual — yes bestie, it's a whole manual page for SRC/dsytrf_aa_2stage.f(3), and it's lowkey iconic. It's all about DSYTRF_AA_2STAGE and Aasen's algorithm, so grab a boba 🧋 and let's get into it.

🌸 NAME 🌸

SRC/dsytrf_aa_2stage.f

✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine dsytrf_aa_2stage (uplo, n, a, lda, tb, ltb, ipiv, ipiv2, work, lwork, info) — DSYTRF_AA_2STAGE

🦋 Function/Subroutine Documentation 🦋

okay so the whole main-character subroutine is right here:

subroutine dsytrf_aa_2stage (character uplo, integer n, double precision,
    dimension( lda, * ) a, integer lda, double precision, dimension( * ) tb,
    integer ltb, integer, dimension( * ) ipiv, integer, dimension( * )
    ipiv2, double precision, dimension( * ) work, integer lwork, integer
    info)
    DSYTRF_AA_2STAGE

💡 Purpose 💡

DSYTRF_AA_2STAGE computes the factorization of a real 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 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. Slay ✨.

🎀 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 DOUBLE PRECISION 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, 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).
• TB — TB is DOUBLE PRECISION array, dimension (MAX(1,LTB)). On exit, details of the LU factorization of the band matrix.
• 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 IPIV2(k).
• WORK — WORK is DOUBLE PRECISION 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.

👑 Author 👑

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

Definition at line 158 of file dsytrf_aa_2stage.f.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

---

Okay bestie, that's the whole page 💅. Signing off with LAPACK Version 3.12.0 and SRC/dsytrf_aa_2stage.f(3) — generated automatically by Doxygen for LAPACK from the source code, and yes, it ate. 💖✨