ZHETRF_AA_2STAGE(3)

Hey bestie 💖 welcome to the Library Functions Manual page for ZHETRF_AA_2STAGE(3) — it's giving big LAPACK energy, and we're gonna go through every single detail together, no cap. ✨

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zhetrf_aa_2stage.f

That's the source file path, periodt. The NAME section really said “here's the file, bestie.” 💅

🦋 SYNOPSIS 🦋

✨ Functions/Subroutines ✨

subroutine ZHETRF_AA_2STAGE (uplo, n, a, lda, tb, ltb, ipiv, ipiv2,
    work, lwork, info)

And the name is ZHETRF_AA_2STAGE — iconic, no notes. 🫶

💖 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 again, because the docs love a little repetition. 🎀

🌟 Purpose 🌟

Okay so ZHETRF_AA_2STAGE computes the factorization of a double hermitian matrix A using the 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 (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 — CHARACTER*1; 'U': upper triangle of A is stored; 'L': lower triangle of A is stored.
• N — INTEGER; the order of the matrix A. N >= 0.
• A — 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 — INTEGER; the leading dimension of the array A. LDA >= max(1,N).
• TB — COMPLEX*16 array, dimension (LTB). On exit, details of the LU factorization of the band matrix.
• LTB — 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 — 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 — 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 — COMPLEX*16 workspace of size LWORK.
• LWORK — 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 — 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 zhetrf_aa_2stage.f.

👑 Author 👑

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