SRC/strtri.f(3)

💅 SRC/strtri.f — like, the actual manual page, bestie

okay so this is a page from the LAPACK library manual (that's the big serious linear-algebra one, yes she's iconic) and today's main character is strtri. buckle up 🎀

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✨ NAME ✨

SRC/strtri.f — no cap, that's literally it, that's the name 💖

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🦋 SYNOPSIS 🦋

Functions/Subroutines

• subroutine strtri (uplo, diag, n, a, lda, info) — the one and only STRTRI 👑

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🌸 Function/Subroutine Documentation 🌸

subroutine strtri (character uplo, character diag, integer n, real,
     dimension( lda, * ) a, integer lda, integer info)

STRTRI — say her name, say it loud 📣

💜 Purpose

ok so here's the tea, straight from the source:

!>
!> STRTRI computes the inverse of a real upper or lower triangular
!> matrix A.
!>
!> This is the Level 3 BLAS version of the algorithm.
!>

so yeah — she inverts a real triangular matrix for you, upper or lower, your call. and she's the Level 3 BLAS version of the algorithm, which is lowkey a flex. slay ✨

🍓 Parameters

UPLO

!>          UPLO is CHARACTER*1
!>          = 'U':  A is upper triangular;
!>          = 'L':  A is lower triangular.
!>

the vibe check for which triangle we're doing 🔼

• 'U' → A is upper triangular ⬆️
• 'L' → A is lower triangular ⬇️

DIAG

!>          DIAG is CHARACTER*1
!>          = 'N':  A is non-unit triangular;
!>          = 'U':  A is unit triangular.
!>

this one decides whether the diagonal is doing its own thing or just being a bunch of ones 🫶

• 'N' → A is non-unit triangular (diagonal is real, she's got range)
• 'U' → A is unit triangular (diagonal is all 1s, no thoughts head empty)

N

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

the order of the matrix A, bestie. and reminder: N >= 0 — negative N is not the move, don't even try it 💀

A

!>          A is REAL array, dimension (LDA,N)
!>          On entry, the triangular matrix A.  If UPLO = 'U', the
!>          leading N-by-N upper triangular part of the array A contains
!>          the upper triangular matrix, and the strictly lower
!>          triangular part of A is not referenced.  If UPLO = 'L', the
!>          leading N-by-N lower triangular part of the array A contains
!>          the lower triangular matrix, and the strictly upper
!>          triangular part of A is not referenced.  If DIAG = 'U', the
!>          diagonal elements of A are also not referenced and are
!>          assumed to be 1.
!>          On exit, the (triangular) inverse of the original matrix, in
!>          the same storage format.
!>

ok this is the big one, the main character herself 💅 A is a REAL array, dimension (LDA,N).

• on entry: it's your triangular matrix A.
  • if UPLO = 'U' → the leading N-by-N upper triangular part of the array holds the upper triangular matrix, and the strictly lower triangular part of A is not referenced (she's not looking at it, she's not thinking about it 🙈).
  • if UPLO = 'L' → the leading N-by-N lower triangular part holds the lower triangular matrix, and the strictly upper triangular part of A is not referenced.
  • if DIAG = 'U' → the diagonal elements of A are also not referenced and are assumed to be 1.
• on exit: the (triangular) inverse of the original matrix, in the same storage format. she did the glow-up in place, obsessed 😭✨

LDA

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

the leading dimension of the array A. rule of the house: LDA >= max(1,N) 📏

INFO

!>          INFO is INTEGER
!>          = 0: successful exit
!>          < 0: if INFO = -i, the i-th argument had an illegal value
!>          > 0: if INFO = i, A(i,i) is exactly zero.  The triangular
!>               matrix is singular and its inverse can not be computed.
!>

the little status report at the end 🫡

• = 0 → successful exit, we ate 🎉
• < 0 → if INFO = -i, the i-th argument had an illegal value (somebody typed something goofy 😬)
• > 0 → if INFO = i, A(i,i) is exactly zero. the triangular matrix is singular and its inverse can not be computed. periodt, there's no coming back from that 💀

ngl the INFO > 0 case is the dramatic one — singular matrix means no inverse exists, so don't go acting surprised when it bails on you.

👑 Author

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

the whole collective behind the icon, fr fr 🫶

Definition at line 108 of file strtri.f. — for the girlies who need receipts 🔍

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🌈 Author (the meta one)

Generated automatically by Doxygen for LAPACK from the source code. (yes, the docs have docs, it's giving main character energy all the way down 🧚)

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and that's the whole page, bestie — every flag, every parameter, every exit code, nothing skipped 💖

catch you in the next manpage — this one's from LAPACK, Version 3.12.0, page SRC/strtri.f(3). mwah 💋✨🌸