SRC/zhetri_3.f(3)

💅 SRC/zhetri_3.f — from the LAPACK Library Functions Manual, bestie

okay so picture this: a whole manual page for SRC/zhetri_3.f, and it's lowkey iconic. it lives in the LAPACK Library Functions Manual section, and honestly it ate. let's get into it 🫶

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✨ NAME ✨

SRC/zhetri_3.f — that's the file, that's the name, no notes 💅

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🎀 SYNOPSIS 🎀

Functions/Subroutines

• subroutine zhetri_3 (uplo, n, a, lda, e, ipiv, work, lwork, info) — literally the whole vibe. this is ZHETRI_3.

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🌸 Function/Subroutine Documentation 🌸

subroutine zhetri_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)

ZHETRI_3

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🦋 Purpose 🦋

okay so what does it DO. ZHETRI_3 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.

and like — ZHETRI_3 sets the leading dimension of the workspace before calling ZHETRI_3X that actually computes the inverse. this is the blocked version of the algorithm, calling Level 3 BLAS. she's doing the prep work so the next routine can slay ✨

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🌈 Parameters 🌈

UPLO

UPLO is CHARACTER*1. it 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. it's The order of the matrix A. N >= 0.

A

A is COMPLEX*16 array, dimension (LDA,N). on entry, diagonal of the block diagonal matrix D and factors U or L 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); (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 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. it's The leading dimension of the array A. LDA >= max(1,N).

E

E is COMPLEX*16 array, dimension (N). on entry, contains 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 don't come for her about it, she literally doesn't look 👀

IPIV

IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by ZHETRF_RK or ZHETRF_BK.

WORK

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

LWORK

LWORK is 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, it really does say "the optimal size of the optimal size of the WORK array" — we don't edit the original, we respect the original 🫶

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.

fr fr, watch out for that > 0 case — singular matrix means the inverse could NOT be computed. no cap, it's just not happening 😭

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👑 Author 👑

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

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🧚 Contributors 🧚

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

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⭐ Definition ⭐

Definition at line 168 of file zhetri_3.f.

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💜 Author (the meta one) 💜

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

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okay that's the whole page, you're welcome, go forth and invert those complex Hermitian indefinite matrices responsibly 🎀

LAPACK — Version 3.12.0 — SRC/zhetri_3.f(3)

mwah 💋 see u in the next manpage bestie