ZHESV_AA(3)

📦 version 3.12.0, in opensuse-leap 16.0

💖 ZHESV_AA(3) 💖

okay so this is the Library Functions Manual page for ZHESV_AA(3) — manual name folded in near the top like a lil sticker 🎀. It’s giving very serious LAPACK business, but make it cute.

✨ NAME ✨

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

That’s the source file this page is about, no cap. The page title is ZHESV_AA(3).

🌸 SYNOPSIS 🌸

🧚 Functions/Subroutines 🧚

subroutine ZHESV_AA (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork,
     info)

And the one-liner: ZHESV_AA computes the solution to system of linear equations A * X = B for HE matrices. Periodt 💅

🦋 Function/Subroutine Documentation 🦋

💜 subroutine ZHESV_AA 💜

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

ZHESV_AA computes the solution to system of linear equations A * X = B for HE matrices. Same energy as the synopsis because that is literally the description ✨

🎀 Purpose 🎀

Here’s the whole purpose, bestie, with the math kept EXACT:

ZHESV_AA 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 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 tridiagonal. The factored form of A is then used to solve the system of equations A * X = B.

Highkey a whole journey, but it slays 😭

💅 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 number of linear equations, i.e., 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, if INFO = 0, the tridiagonal matrix T and the multipliers used to obtain the factor U or L from the factorization A = U**H*T*U or A = L*T*L**H as computed by ZHETRF_AA.

LDA

LDA is INTEGER.

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

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).

B

B is COMPLEX*16 array, dimension (LDB,NRHS).

On entry, the N-by-NRHS right hand side matrix B.

On exit, if INFO = 0, the N-by-NRHS solution matrix X.

LDB

LDB is INTEGER.

The leading dimension of the array B. LDB >= max(1,N).

WORK

WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)).

On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER.

The length of WORK. LWORK >= MAX(1,2*N,3*N-2), and for best performance LWORK >= max(1,N*NB), where NB is the optimal blocksize for ZHETRF.

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, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, so the solution could not be computed.

👑 Author 👑

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

Definition at line 160 of file zhesv_aa.f.

🌈 Author 🌈

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okay that’s the entire page, bestie 🫶 — it’s from LAPACK, Version 3.12.0, and the footer path is /home/abui.../zhesv_aa.f(3). Mwah 💋

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