/home/abui...hetri_3x.f(3)

👑 NAME

okay so bestie, this whole page is about one file, and its full government name is literally:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zhetri_3x.f

that's a LAPACK man page, section 3 (library functions), and it's the home of one very specific little icon: ZHETRI_3X. she inverts stuff. she's blocked. she's level 3 BLAS. periodt. 💅

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✨ SYNOPSIS ✨

🫶 Functions/Subroutines

• subroutine ZHETRI_3X (uplo, n, a, lda, e, ipiv, work, nb, info) — that's her. that's the whole girl. ZHETRI_3X.

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🦋 Function/Subroutine Documentation 🦋

subroutine ZHETRI_3X (character uplo, integer n, complex*16, dimension( lda,
* ) a, integer lda, complex*16, dimension( * ) e, integer, dimension( *
) ipiv, complex*16, dimension( n+nb+1, * ) work, integer nb, integer
info)

ZHETRI_3X 💖

🎀 Purpose:

okay so here's the tea, straight from the source, no cap:

!> ZHETRI_3X computes the inverse of a complex Hermitian indefinite
!> matrix A using the factorization computed by ZHETRF_RK or ZHETRF_BK:
!>
!>     A = P*U*D*(U**H)*(P**T) or A = P*L*D*(L**H)*(P**T),
!>
!> where U (or L) is unit upper (or lower) triangular matrix,
!> U**H (or L**H) is the conjugate of U (or L), P is a permutation
!> matrix, P**T is the transpose of P, and D is Hermitian 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.
!>

so like — she takes a complex Hermitian indefinite matrix A, grabs the factorization that ZHETRF_RK or ZHETRF_BK already did, and flips it into an inverse. she's the blocked version of the algorithm and she calls Level 3 BLAS, which is her main character energy tbh 🔥

🌸 Parameters 🌸

• UPLO — UPLO is CHARACTER*1. tells us whether the factorization details are stored as an upper or lower triangular matrix. the options are literally:
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.
• N — N is INTEGER. the order of the matrix A. and N >= 0, okay? non-negotiable. ⭐
• A — A is COMPLEX*16 array, dimension (LDA,N). on entry, she wants the diagonal of the block diagonal matrix D plus the factors U or L exactly as computed by ZHETRF_RK and ZHETRF_BK:
  • a) ONLY diagonal elements of the Hermitian block diagonal matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); — and the superdiagonal (or subdiagonal) elements of D should be provided on entry in array E, got it? 🫶
  • 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, you get the Hermitian 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. and LDA >= max(1,N) fr fr.
• E — E is COMPLEX*16 array, dimension (N). on entry she holds the superdiagonal (or subdiagonal) elements of the Hermitian 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. — so like, don't come for her about E(k), she's simply not looking at it 💀

• IPIV — IPIV is INTEGER array, dimension (N). the details of the interchanges and the block structure of D, as determined by ZHETRF_RK or ZHETRF_BK. iykyk.
• WORK — WORK is COMPLEX*16 array, dimension (N+NB+1,NB+3). that's her workspace, she needs room to be great ✨
• NB — NB is INTEGER. block size. iconic, no notes.
• INFO — INFO is INTEGER, and this is the vibe check at the end:
  • = 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. — yeah that's the 😭 case, the matrix is singular and the inverse is simply not happening.

💜 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
!>
!>

shoutout Igor, June 2017, Computer Science Division, University of California, Berkeley 🫡

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Definition at line 158 of file zhetri_3x.f. — that's where she lives, bestie. line 158. 🏠

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⭐ Author

Generated automatically by Doxygen for LAPACK from the source code. — not me writing this by hand, the robots did it, and honestly? they ate. 🤖💅

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LAPACK — Version 3.12.0 🦋 that's the version, and the file tag is /home/abui...hetri_3x.f(3), and that's the whole page!! mwah, go invert something Hermitian, ily 💖🎀