SRC/chesv_aa.f(3)

💖 NAME 💖

SRC/chesv_aa.f — that’s the page, bestie, and it’s from the Library Functions Manual. Iconic.

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🌸 SYNOPSIS 🌸

🧚 Functions/Subroutines 🧚

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

CHESV_AA computes the solution to system of linear equations A * X = B for HE matrices. No cap, that’s the whole vibe.

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🦋 Function/Subroutine Documentation 🦋

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

CHESV_AA computes the solution to system of linear equations A * X = B for HE matrices. Main character subroutine energy fr fr.

🍓 Purpose 🍓

Okay so CHESV_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. <sparkle>Literally the setup.</sparkle>

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. That’s the whole arc.

🎀 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 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 CHETRF_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 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 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 CHETRF. 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.

Heads up bestie: the INFO > 0 case means the factorization finished but D(i,i) is exactly zero, so the block diagonal matrix D is exactly singular and the solution could not be computed. Not a slay, just a fact.

👑 Author 👑

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

Definition at line 160 of file chesv_aa.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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LAPACK Version 3.12.0 — SRC/chesv_aa.f(3) — and that’s the cute little sign-off, mwah 💋 bye bestie, go solve those systems.