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

💅 NAME 💅

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zsytri_3x.f

okay so bestie, this is a page from the Library Functions Manual, and the whole entire vibe is: one (1) Fortran file, deep in the LAPACK source tree, living its best life at SRC/zsytri_3x.f. That's it. That's the name. Path and everything, no cap. 🎀

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✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

• subroutine ZSYTRI_3X (uplo, n, a, lda, e, ipiv, work, nb, info) — literally the whole point of this page, she's the icon, she's the moment: ZSYTRI_3X.

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🦋 Function/Subroutine Documentation 🦋

👑 the signature, verbatim, don't touch

subroutine ZSYTRI_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)

ZSYTRI_3X 🫶

💜 Purpose:

!> ZSYTRI_3X 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. !> !> This is the blocked version of the algorithm, calling Level 3 BLAS. !>

so like. she inverts a complex symmetric indefinite matrix A, using the factorization that ZSYTRF_RK or ZSYTRF_BK already did the hard work for. blocked version, Level 3 BLAS, main character energy fr fr. 💅

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🍓 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. !>

a single character, bestie. picks a side: 'U' = upper triangle of A is stored, 'L' = lower triangle of A is stored. choose wisely, it's giving fork in the road. 🌸

N

!> N is INTEGER !> The order of the matrix A. N >= 0. !>

N is INTEGER — the order of the matrix A. N >= 0. zero is allowed, she's flexible like that. ✨

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 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. !>

A is COMPLEX*16 array, dimension (LDA,N). on entry she's carrying two things:

• a) ONLY the diagonal elements of the symmetric block diagonal matrix D, on the diagonal of A, like D(k,k) = A(k,k) — and the superdiagonal (or subdiagonal) elements of D should be provided on entry in array E, okay? not here. E. noted. 🙈
• b) if UPLO = 'U': factor U lives in the superdiagonal part of A. if UPLO = 'L': factor L lives in the subdiagonal part of A.

on exit, if INFO = 0, you get 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.

don't ask her about the other triangle, she literally does not look at it. 💀

LDA

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

LDA is INTEGER — the leading dimension of the array A. LDA >= max(1,N). periodt. 👑

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 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. !>

E is COMPLEX*16 array, dimension (N). on entry she holds 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, and E(1) is not referenced;
• if UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, and E(N) is 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 the UPLO = 'U' or UPLO = 'L' cases. she said what she said. 🧚

IPIV

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

IPIV is INTEGER array, dimension (N) — all the deets on the interchanges and the block structure of D, exactly as determined by ZSYTRF_RK or ZSYTRF_BK. she doesn't decide these, she just receives them. 💅

WORK

!> WORK is COMPLEX*16 array, dimension (N+NB+1,NB+3). !>

WORK is COMPLEX*16 array, dimension (N+NB+1,NB+3). that's the workspace, that's the whole description, she's not elaborate, she's just big. 🫶

NB

!> NB is INTEGER !> Block size. !>

NB is INTEGER — block size. short king. 🎀

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. !>

INFO is INTEGER, the vibe check of the whole operation:

• = 0: successful exit. slay. ✨
• < 0: if INFO = -i, the i-th argument had an illegal value. read your args, bestie, i'm begging. 😭
• > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its inverse could not be computed. that's a no. the inverse is simply not happening. 💀

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🌈 Author 🌈

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

four whole institutions, all of them showing up for this one subroutine. iconic. 👑

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💖 Contributors: 💖

!> !> June 2017, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !>

June 2017, Igor Kozachenko, Computer Science Division, University of California, Berkeley. the way that's so specific, we love a credited contributor. 🦋

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⭐ Definition at line 158 of file zsytri_3x.f. ⭐

like yes, line 158, she's located, she's findable, go look. 💜

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🌸 Author 🌸

Generated automatically by Doxygen for LAPACK from the source code. so nobody hand-wrote this, a robot did it, and honestly? she ate. 🤖✨

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sign-off time, bestie 🎀 — this whole page came to you courtesy of LAPACK, Version 3.12.0, and yeah, the file is still /home/abui...sytri_3x.f(3) in case you forgot where you were. mwah. 💋