SRC/chetrf_aa_2stage.f(3)

💖 NAME 💖

Okay so bestie, this page is SRC/chetrf_aa_2stage.f(3) from the Library Functions Manual, and the actual file it's documenting is SRC/chetrf_aa_2stage.f. It's giving linear-algebra main character energy, and we're keeping every single detail. Periodt. ✨

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✨ SYNOPSIS ✨

🌈 Functions/Subroutines 🌈

       subroutine chetrf_aa_2stage (uplo, n, a, lda, tb, ltb, ipiv, ipiv2,
           work, lwork, info)
           CHETRF_AA_2STAGE

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💅 Function/Subroutine Documentation 💅

🎀 CHETRF_AA_2STAGE 🎀

   subroutine chetrf_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)
       CHETRF_AA_2STAGE

🦋 Purpose 🦋

CHETRF_AA_2STAGE computes the factorization of a real hermitian 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 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. Lowkey iconic. 🔥

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🌸 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').

🦋 LDA

LDA is INTEGER

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

🍓 TB

TB is COMPLEX 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 IPIV(k).

🧚 WORK

WORK is COMPLEX 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

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🌟 Author 🌟

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

Definition at line 158 of file chetrf_aa_2stage.f.

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🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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And that's the whole iconic page, bestie 💅 — auto-generated by Doxygen for LAPACK from the source code, LAPACK Version 3.12.0, and it's SRC/chetrf_aa_2stage.f(3). Slay and happy factorizing! 🎀✨