/home/abui...sytri_3x.f(3)

💖 CSYTRI_3X — Library Functions Manual 💖

okay so bestie, this page is from the Library Functions Manual and it is literally about /home/abui...sytri_3x.f(3). The vibe? LAPACK, complex symmetric chaos, and one very blocked inverse routine. Let's get into it 💅

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/csytri_3x.f

that's the name line, bestie — yes, it's a whole path 💀 iconic.

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🌸 SYNOPSIS 🌸

🎀 Functions/Subroutines 🎀

• subroutine CSYTRI_3X (uplo, n, a, lda, e, ipiv, work, nb, info) — the callable thing.
  • CSYTRI_3X

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💖 Function/Subroutine Documentation 💖

Here's the full signature, no cap:

subroutine CSYTRI_3X (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) e, integer, dimension( * ) ipiv, complex, dimension( n+nb+1, * ) work, integer nb, integer info)

CSYTRI_3X

🎯 Purpose

CSYTRI_3X computes the inverse of a complex symmetric indefinite matrix A using the factorization computed by CSYTRF_RK or CSYTRF_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.

This is the blocked version of the algorithm, calling Level 3 BLAS. highkey efficient energy 🔥

🧸 Parameters

• UPLO — UPLO is 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 is INTEGER. The order of the matrix A. N >= 0.
• A — A is COMPLEX array, dimension (LDA,N).
  • On entry, diagonal of the block diagonal matrix D and factors U or L as computed by CSYTRF_RK and CSYTRF_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 is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• E — E is COMPLEX 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. not me forgetting that caveat 🙈
• IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by CSYTRF_RK or CSYTRF_BK.
• WORK — WORK is COMPLEX array, dimension (N+NB+1,NB+3).
• NB — NB is INTEGER. Block size.
• 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) = 0; the matrix is singular and its inverse could not be computed. 💀 singular matrix said no ❌

👑 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

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Definition at line 158 of file csytri_3x.f.

🤖 Author

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page, bestie 💋 — LAPACK Version 3.12.0, source page /home/abui...sytri_3x.f(3). The footer doesn't spell out a separate date; that source/version/path combo is the send-off. periodt ✨🫶