CSYSV_AA(3)

💖 CSYSV_AA(3) 💖

bestie, this is CSYSV_AA(3) from the Library Functions Manual, and it’s a LAPACK routine that is lowkey doing the most with complex symmetric systems. we love a math icon ✨

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🌸 NAME 🌸

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

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✨ SYNOPSIS ✨

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

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🦋 Function/Subroutine Documentation 🦋

subroutine CSYSV_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)

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

🌟 Purpose 🌟

okay so the main-character job here is: CSYSV 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. genuinely iconic behavior. 🫶

🎀 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 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 CSYTRF.
• 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(2*N, 3*N-2), and for the best performance, LWORK >= max(1,N*NB), where NB is the optimal blocksize for CSYTRF_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.

bestie, that INFO > 0 case is not a slay moment — the factorization finished but the block diagonal matrix D is exactly singular, so the solution could not be computed. do not ignore that. 😭

👑 Author 👑

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

Definition at line 160 of file csysv_aa.f.

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💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. yes, Doxygen really did that. 🧚

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mwah 💖 this page comes from LAPACK Version 3.12.0, with the page path /home/abui.../csysv_aa.f(3). There’s no date listed in the footer, so I’m not inventing one — bye bestie! 🫶