SRC/ssytri_rook.f(3)

💅 SRC/ssytri_rook.f — the LAPACK library manual, bestie edition ✨

okay so this page is literally from the LAPACK Library Functions Manual, and it's all about one iconic little subroutine. buckle up 🎀

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🌸 NAME 🌸

SRC/ssytri_rook.f — that's it, that's the name, she's lowkey mysterious like that 💅

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✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine ssytri_rook (uplo, n, a, lda, ipiv, work, info) — this is SSYTRI_ROOK, the main character 👑

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🦋 Function/Subroutine Documentation 🦋

subroutine ssytri_rook (character uplo, integer n, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension( * ) work, integer info)

SSYTRI_ROOK — say it with me, she's the inverse-finder 🫶

💖 Purpose:

!>
!> SSYTRI_ROOK computes the inverse of a real symmetric
!> matrix A using the factorization A = U*D*U**T or A = L*D*L**T
!> computed by SSYTRF_ROOK.
!>

so basically: hand her a real symmetric matrix A plus the factorization A = U*D*U**T or A = L*D*L**T that SSYTRF_ROOK already cooked up, and she gives you the inverse. no cap, that's the whole gig 🔥

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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 triangular, form is A = U*D*U**T;
!>          = 'L':  Lower triangular, form is A = L*D*L**T.
!>

it's a CHARACTER*1 that tells her whether the factorization details are chilling in an upper or lower triangular matrix. pick your fighter: 'U' for upper triangular (form is A = U*D*U**T), or 'L' for lower triangular (form is A = L*D*L**T). choose wisely bestie 💀

N

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

an INTEGER, the order of the matrix A. and she has standards: N >= 0 ✨

A

!>          A is REAL array, dimension (LDA,N)
!>          On entry, the block diagonal matrix D and the multipliers
!>          used to obtain the factor U or L as computed by SSYTRF_ROOK.
!>
!>          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 REAL array, dimension (LDA,N) and honestly she goes through a whole glow-up here:

• on entry she's holding the block diagonal matrix D and the multipliers used to obtain the factor U or L, exactly as computed by SSYTRF_ROOK.
• on exit, if INFO = 0, she's serving 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. respect the boundaries, periodt 🙈

LDA

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

an INTEGER, the leading dimension of the array A. the vibe check here is LDA >= max(1,N) 💅

IPIV

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

an INTEGER array, dimension (N) — it's carrying the details of the interchanges and the block structure of D, as determined by SSYTRF_ROOK. she's got receipts 📋

WORK

!>          WORK is REAL array, dimension (N)
!>

a REAL array, dimension (N). she works hard but she's just workspace, ngl 🫶

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.
!>

an INTEGER, the report card 📝

• = 0: successful exit, we ate 🍓
• < 0: if INFO = -i, the i-th argument had an illegal value — not cute, someone misbehaved
• > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its inverse could not be computed. so sorry bestie, no inverse today 😭

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👑 Author 👑

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

four whole institutions, the collab we deserved 🌟

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🧚 Contributors: 🧚

!>
!>   April 2012, Igor Kozachenko,
!>                  Computer Science Division,
!>                  University of California, Berkeley
!>
!>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
!>                  School of Mathematics,
!>                  University of Manchester
!>
!>

• April 2012 — Igor Kozachenko, Computer Science Division, University of California, Berkeley
• September 2007 — Sven Hammarling, Nicholas J. Higham, Craig Lucas, School of Mathematics, University of Manchester

a whole friend group of mathematicians carried this, we stan 🫶

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💜 Definition at line 128 of file ssytri_rook.f. 💜

that's where she lives, line 128, iconic address ngl 🏠

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⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code. the robots did the paperwork, we just vibe 🤖✨

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heads up bestie: INFO > 0 means D(i,i) = 0 — the matrix is singular and the inverse could not be computed. that's not a "try again" moment, that's a "the math said no" moment 💀

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and that's the whole page, fr fr 💖 this gem came to you from LAPACK, Version 3.12.0, dated with all the love — go inverse something iconic, mwah 🎀🌈💅