SRC/zsysv_aa.f(3)

💖 SRC/zsysv_aa.f(3) — Library Functions Manual 💖

🌸 NAME 🌸

SRC/zsysv_aa.f

✨ SYNOPSIS ✨

🛠️ Functions/Subroutines

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

ZSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices. slay.

🦋 Function/Subroutine Documentation 🦋

subroutine zsysv_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)

ZSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices. no cap.

🌈 Purpose

Ok bestie, here’s the vibe: ZSYSV computes the solution to a complex system of linear equations

A * X = B,

where A is an N-by-N symmetric matrix and X and B are N-by-NRHS matrices. 💅

Aasen’s algorithm is used to factor A as

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

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is symmetric tridiagonal. The factored form of A is then used to solve the system of equations A * X = B. iconic, honestly. ✨

💅 Parameters

• UPLO — CHARACTER*1
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.
• N — INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0.
• NRHS — INTEGER. The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
• A — COMPLEX*16 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, if INFO = 0, the tridiagonal matrix T and the multipliers used to obtain the factor U or L from the factorization A = U**T*T*U or A = L*T*L**T as computed by ZSYTRF.
• LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• 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).
• B — 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 — INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• WORK — COMPLEX*16 array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — INTEGER. The length of WORK. LWORK >= MAX(1,2*N,3*N-2), and for the best performance, LWORK >= MAX(1,N*NB), where NB is the optimal blocksize for ZSYTRF_AA.
  • 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, 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 zsysv_aa.f.

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This page was generated automatically by Doxygen for LAPACK from the source code. It’s LAPACK Version 3.12.0, bestie — source: SRC/zsysv_aa.f(3). 🫶✨