ZSYTRS_3(3)

💖 ZSYTRS_3(3) — the solve-the-system one 💖

okay so bestie, this page lives at /home/abui.../zsytrs_3.f(3) (yes the path is giving "buried in a build tree" energy, we love her anyway) and it's from the LAPACK Library Functions Manual. Buckle up, it's a Fortran subroutine and she's iconic ✨

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🌸 SYNOPSIS 🌸

Functions/Subroutines:

subroutine ZSYTRS_3 (uplo, n, nrhs, a, lda, e, ipiv, b, ldb, info)
    ZSYTRS_3

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🎀 Function/Subroutine Documentation 🎀

subroutine ZSYTRS_3 (character uplo, integer n, integer nrhs, complex*16,
    dimension( lda, * ) a, integer lda, complex*16, dimension( * ) e,
    integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer
    ldb, integer info)

ZSYTRS_3 💅 (that's her name, that's her whole brand)

✨ Purpose ✨

okay so real talk: ZSYTRS_3 solves a system of linear equations A * X = B with a complex symmetric matrix A, using the factorization computed by ZSYTRF_RK or ZSYTRF_BK:

A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

where U (or L) is a unit upper (or lower) triangular matrix, U**T (or L**T) is the transpose of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. no cap, that's the whole structure 🫶

This algorithm is using Level 3 BLAS. she's fast like that 🔥

💜 Parameters 💜

• UPLO — UPLO is CHARACTER*1. it specifies whether the details of the factorization are stored as an upper or lower triangular matrix, and the vibes differ:
  • = 'U': upper triangular, form is A = P*U*D*(U**T)*(P**T);
  • = 'L': lower triangular, form is A = P*L*D*(L**T)*(P**T).
• N — N is INTEGER. the order of the matrix A. N >= 0. (yes she can be zero, she's valid 💀)
• 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*16 array, dimension (LDA,N). On entry it holds the diagonal of the block diagonal matrix D and the factors U or L as computed by ZSYTRF_RK and ZSYTRF_BK, literally like this:
  • a) ONLY diagonal elements of the symmetric block diagonal matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); (the superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and
  • b) If UPLO = 'U': factor U in the superdiagonal part of A. If UPLO = 'L': factor L in the subdiagonal part of A.
• LDA — LDA is INTEGER. the leading dimension of the array A. LDA >= max(1,N). respect the leading dimension bestie 🙈
• E — E is COMPLEX*16 array, dimension (N). On entry, contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where:
  • If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
  • If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.

NOTE: for a 1-by-1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both UPLO = 'U' or UPLO = 'L' cases. so don't come for her about that slot, it's just vibing 🌸

• IPIV — IPIV is INTEGER array, dimension (N). the details of the interchanges and the block structure of D as determined by ZSYTRF_RK or ZSYTRF_BK. she knows things 👑
• B — B is COMPLEX*16 array, dimension (LDB,NRHS). On entry, the right hand side matrix B. On exit, the solution matrix X. glow-up moment, literally main character energy ✨
• LDB — LDB is INTEGER. the leading dimension of the array B. LDB >= max(1,N).
• INFO — INFO is INTEGER:
  • = 0: successful exit 🎉
  • < 0: if INFO = -i, the i-th argument had an illegal value 😭 (so check your args, bestie, she will clock you)

🦋 Author 🦋

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

🌈 Contributors 🌈

• June 2017, Igor Kozachenko, Computer Science Division, University of California, Berkeley
• September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, School of Mathematics, University of Manchester

⭐ Definition ⭐

Definition at line 163 of file zsytrs_3.f. yes, line 163, we counted 💅

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👑 Author (of this page, not the subroutine) 👑

Generated automatically by Doxygen for LAPACK from the source code. so nobody hand-wrote this one, the robots ate 🤖✨

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okay that's the whole page, no notes, she ate and left no crumbs 🍓🫶

LAPACK — Version 3.12.0 — /home/abui.../zsytrs_3.f(3) — mwah, bye bestie 💖🧚‍♀️🎀