DSYSV_AA(3)

💅 NAME

okay so this whole page is about the file /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dsysv_aa.f — that's the source file, bestie. It lives in the Library Functions Manual as dsysv_aa.f(3), and yes, the filename is the main character.

✨ SYNOPSIS

🧚 Functions/Subroutines

       subroutine DSYSV_AA (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork,
           info)
            DSYSV_AA computes the solution to system of linear equations A * X
           = B for SY matrices

Like, that's the call shape. DSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices. Periodt.

🎀 Function/Subroutine Documentation

   subroutine DSYSV_AA (character uplo, integer n, integer nrhs, double
       precision, dimension( lda, * ) a, integer lda, integer, dimension( * )
       ipiv, double precision, dimension( ldb, * ) b, integer ldb, double
       precision, dimension( * ) work, integer lwork, integer info)

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

🌸 Purpose

okay so DSYSV — yes, the Purpose text says DSYSV, keep that energy — computes the solution to a real 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.

tiny source-flavor note: the raw file wraps all this in Doxygen !> comment markers. Cute, but the math is the moment.

🍓 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 DOUBLE PRECISION 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 DSYTRF.
• 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 the best performance, LWORK >= MAX(1,N*NB), where NB is the optimal blocksize for DSYTRF_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 — 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 dsysv_aa.f.

🦋 Author

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that's the whole page. The footer stamp is LAPACK, Version 3.12.0, and it points back to /home/abui.../dsysv_aa.f(3) — no separate date printed in that footer, that's just the source/version vibe. 💖✨