SRC/csysv_aa.f(3)

💖 NAME 💖

SRC/csysv_aa.f — yeah bestie, that's the whole name section, she's literally just her filename. Iconic minimalism. This page lives in the Library Functions Manual, and it's about one very specific little Fortran subroutine that lowkey does a LOT. 🦋

---

✨ 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 👑

---

🎀 Function/Subroutine Documentation 🎀

okay so here's the full signature, unchanged, no cap:

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 💅

🌸 Purpose 🌸

So 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. She's solving stuff, that's her whole job. 💜

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. Then the factored form of A is used to solve the system of equations A * X = B. Like, she breaks it apart, then puts it back together to solve it. main character energy fr fr. 🧚

✨ Parameters ✨

• UPLO — UPLO is CHARACTER*1. Which triangle are we working with, bestie?
  • = '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. (zero is allowed, she's chill like that)
• 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. So like, the other half is just vibing, untouched. 🙈
  • 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). Do NOT skip this one, it's a vibe check for your array. ⭐
• 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. Glow-up moment. ✨
• 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. She tells you how much room she really wanted. 💅
• 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. It's giving "just asking, not committing" 🫶
• 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: that INFO > 0 case is a real one — the factorization finishes but the block diagonal matrix D is exactly singular, so no solution for you. Not a crash, just a "girl, there's no answer" moment.

👑 Author 👑

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

Definition at line 160 of file csysv_aa.f.

---

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. (not me, a robot did it 🤖)

---

okay that's the whole page, you ate that 🍓 — this was LAPACK, Version 3.12.0, page SRC/csysv_aa.f(3). go forth and solve some complex symmetric systems, bestie 💖🎀🦋