ZSYTRI_3(3)

okay bestie, welcome to the zsytri_3.f(3) page from the Library Functions Manual — we’re folding that header info in right here so it doesn’t get lonely ✨

🌸 NAME 🌸

the NAME section is literally this path, no extra lore, no cap:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zsytri_3.f

✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

• subroutine ZSYTRI_3 (uplo, n, a, lda, e, ipiv, work, lwork, info) — ZSYTRI_3

💅 Function/Subroutine Documentation 💅

here’s the full signature from the docs, copied exactly because we do not mess with source code vibes:

subroutine ZSYTRI_3 (character uplo, integer n, complex*16, dimension( lda,
     * ) a, integer lda, complex*16, dimension( * ) e, integer, dimension( *
     ) ipiv, complex*16, dimension( * ) work, integer lwork, integer info)

ZSYTRI_3 — main character energy 🔥

🧮 Purpose 🧮

okay so ZSYTRI_3 computes the inverse of a complex symmetric indefinite 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 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.

ZSYTRI_3 sets the leading dimension of the workspace before calling ZSYTRI_3X that actually computes the inverse. This is the blocked version of the algorithm, calling Level 3 BLAS. iconic behavior fr fr 💅

🎀 Parameters 🎀

💖 UPLO 💖

• UPLO — CHARACTER*1. Specifies whether the details of the factorization are stored as an upper or lower triangular matrix.
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.

🌼 N 🌼

• N — INTEGER. The order of the matrix A. N >= 0.

🦋 A 🦋

• A — COMPLEX*16 array, dimension (LDA,N).
  • On entry, diagonal of the block diagonal matrix D and factors U or L as computed by ZSYTRF_RK and ZSYTRF_BK:
    • a) ONLY diagonal elements of the symmetric block diagonal matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); (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.
  • On exit, if INFO = 0, the symmetric inverse of the original matrix.
    • If UPLO = 'U': the upper triangular part of the inverse is formed and the part of A below the diagonal is not referenced;
    • If UPLO = 'L': the lower triangular part of the inverse is formed and the part of A above the diagonal is not referenced.

🍓 LDA 🍓

• LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N).

🌈 E 🌈

• E — 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 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.

🧚 IPIV 🧚

• IPIV — INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by ZSYTRF_RK or ZSYTRF_BK.

👑 WORK 👑

• WORK — COMPLEX*16 array, dimension (N+NB+1)*(NB+3). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

🔥 LWORK 🔥

• LWORK — INTEGER. The length of WORK. LWORK >= (N+NB+1)*(NB+3).
  • If LDWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of 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.

yes bestie, the source literally says LDWORK = -1 here, and it really says “optimal size of the optimal size” — we copy it exactly, no editing the source 💀

⭐ INFO ⭐

• INFO — INTEGER.
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its inverse could not be computed.

👑 Author 👑

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

🌈 Contributors 🌈

the contributor block, vibes and all:

November 2017,  Igor Kozachenko,
                Computer Science Division,
                University of California, Berkeley

📌 Definition at line 📌

Definition at line 168 of file zsytri_3.f.

🤖 Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole page, bestie! cute little sign-off: LAPACK Version 3.12.0, /home/abui.../zsytri_3.f(3). byeee 🫶✨