CHESV_AA(3)

💖 CHESV_AA(3) 💖

okay so bestie, welcome to the manual page for this icon, live from /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/chesv_aa.f — yes that's the whole path, she's got main character energy and a long address, we respect it 🫶

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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 🔥

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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 ✨

🎀 Purpose 🎀

!>

!> 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.

!>

!> 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.

!>

ngl the vibe check here is: Aasen's algorithm does the factorization, then that factored form gets used to solve A * X = B. That's it, that's the plot 💅

💜 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: if INFO > 0, the factorization did finish but D(i,i) is exactly zero, so the block diagonal matrix D is exactly singular and the solution could not be computed. no cap, that's a whole mood killer.

👑 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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