SPOTRI(3)

💖 NAME 💖

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

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

that's it, that's the name, she's got a long one and she's not sorry 💅

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✨ SYNOPSIS ✨

🫶 Functions/Subroutines

• subroutine SPOTRI (uplo, n, a, lda, info) — SPOTRI. that's the whole vibe. moving on ✨

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👑 Function/Subroutine Documentation 👑

🌸 subroutine SPOTRI (character uplo, integer n, real, dimension( lda, * ) a, integer lda, integer info)

SPOTRI. yes bestie, we're back, it's her again 💖

💜 Purpose:

!>
!> SPOTRI computes the inverse of a real symmetric positive definite
!> matrix A using the Cholesky factorization A = U**T*U or A = L*L**T
!> computed by SPOTRF.
!>

so like — SPOTRI takes your real symmetric positive definite matrix A, and she un-does it. it's giving inverse era 🔥. the way she does it is by riding on the Cholesky factorization that SPOTRF already computed, so you gotta do your homework first, no skipping steps 🎀

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🦋 Parameters 🦋

🌈 UPLO

!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>

it's a single character, bestie, CHARACTER*1. 'U' means the upper triangle of A is the one being stored, 'L' means it's the lower triangle. pick your fighter, no cap 💀

⭐ N

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

N is an INTEGER and it's the order of the matrix A, and she must be N >= 0. zero is fine, negative is a whole red flag 🙈

🍓 A

!>          A is REAL array, dimension (LDA,N)
!>          On entry, the triangular factor U or L from the Cholesky
!>          factorization A = U**T*U or A = L*L**T, as computed by
!>          SPOTRF.
!>          On exit, the upper or lower triangle of the (symmetric)
!>          inverse of A, overwriting the input factor U or L.
!>

A is a REAL array, dimension (LDA,N), and she is the main character in every sense 👑. on entry she's holding the triangular factor U or L from that Cholesky factorization A = U**T*U or A = L*L**T, as computed by SPOTRF. on exit she's been fully transformed — now she holds the upper or lower triangle of the (symmetric) inverse of A, and yes, she overwrote the input factor U or L to do it. glow-up AND a sacrifice, iconic 😭

🧚 LDA

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

LDA is an INTEGER, she's the leading dimension of the array A, and the rule is LDA >= max(1,N). respect the bounds or perish 💅

🔥 INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>          > 0:  if INFO = i, the (i,i) element of the factor U or L is
!>                zero, and the inverse could not be computed.
!>

INFO is an INTEGER and she's the vibe check at the end, so listen up:

• = 0 — successful exit, we ate, no crumbs ✨
• < 0 — if INFO = -i, then the i-th argument had an illegal value. someone did not read the assignment 😭
• > 0 — if INFO = i, the (i,i) element of the factor U or L is zero, and the inverse could not be computed. that's a wrap, bestie, she literally cannot 💀

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🎀 Author 🎀

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

look at this group project fr fr, four whole institutions and they all showed up 🫶

Definition at line 94 of file spotri.f. — that's where the lore lives, line 94, write it down 🦋

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🌸 Author (the second one, yes really) 🌸

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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okay that's the whole page bestie, go forth and invert your symmetric positive definite matrices responsibly 💖✨

LAPACK, Version 3.12.0, dated /home/abui...RC/spotri.f(3) — mwah, catch you on the next manpage, love u, bye 🎀🦋