SRC/zhesv_aa_2stage.f(3)

💖 SRC/zhesv_aa_2stage.f(3) 💖

okay so welcome to the SRC/zhesv_aa_2stage.f(3) page from the Library Functions Manual — yes bestie, we're deep in the LAPACK function docs now 💅 This one is all about the routine ZHESV_AA_2STAGE, and ngl she has main character energy. Stay for the parameters, they're lowkey iconic.

🌸 NAME 🌸

SRC/zhesv_aa_2stage.f — that's the name, bestie. No notes, fr fr.

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

subroutine zhesv_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2,
    b, ldb, work, lwork, info)

This subroutine ZHESV_AA_2STAGE computes the solution to system of linear equations A * X = B for HE matrices. That's the whole vibe. 💖

🌟 Function/Subroutine Documentation 🌟

subroutine zhesv_aa_2stage (character uplo, integer n, integer nrhs,
    complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( *
    ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * )
    ipiv2, complex*16, dimension( ldb, * ) b, integer ldb, complex*16,
    dimension( * ) work, integer lwork, integer info)

This routine ZHESV_AA_2STAGE computes the solution to system of linear equations A * X = B for HE matrices.

🎀 Purpose 🎀

Okay so the purpose is a whole moment:

ZHESV_AA_2STAGE computes the solution to a complex system of linear equations:

A * X = B,

where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS matrices. 💖

Aasen's 2-stage algorithm is used to factor A as:

A = U**H * T * U,  if UPLO = 'U', or
A = L * T * L**H,  if UPLO = 'L',

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is Hermitian and band. The matrix T is then LU-factored with partial pivoting. The factored form of A is then used to solve the system of equations A * X = B.

This is the blocked version of the algorithm, calling Level 3 BLAS. Periodt. 🔥

💅 Parameters 💅

Now the cast of characters, bestie. Vibe check: every single one is accounted for:

• 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.
• NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
• A — A is 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 — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• TB — TB is COMPLEX*16 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). Yep, the original says IPIV(k) here — I'm not editing the lore, bestie 💀
• B — B is COMPLEX*16 array, dimension (LDB,NRHS). On entry, the right hand side matrix B. On exit, the solution matrix X.
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• WORK — WORK is COMPLEX*16 workspace of size (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal 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 185 of file zhesv_aa_2stage.f.

🌈 Author 🌈

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