SRC/dpotri.f(3)

💅 SRC/dpotri.f — from the LAPACK manual, bestie

okay so this is a page straight outta the LAPACK Library Functions Manual ✨ and it's all about one little subroutine that un-does a Cholesky factorization. yes. we're inverting a matrix. it's giving math girlboss and honestly? obsessed 🎀

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🌸 NAME 🌸

SRC/dpotri.f — the file where our main character lives 🫶

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✨ SYNOPSIS ✨

🦋 Functions/Subroutines

• subroutine dpotri (uplo, n, a, lda, info) — the one, the only, DPOTRI 💖

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💜 Function/Subroutine Documentation 💜

subroutine dpotri (character uplo, integer n, double precision, dimension(
    lda, * ) a, integer lda, integer info)

so this is DPOTRI, the icon, the moment, the legend 👑

🧚 Purpose:

!> !> DPOTRI 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 DPOTRF. !>

lowkey what this means: DPOTRI computes the inverse of a real symmetric positive definite matrix A, and it does that using the Cholesky factorization A = U**T*U or A = L*L**T — the one that DPOTRF already computed for you. so like, DPOTRF did the hard part, and DPOTRI finishes the job. team work makes the dream work fr fr 🌈

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💖 Parameters 💖

💅 UPLO

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

UPLO is CHARACTER*1 and it's basically the vibe selector 😌

• = 'U' → the upper triangle of A is stored
• = 'L' → the lower triangle of A is stored

pick your fighter bestie, but only one ⭐

🌸 N

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

N is an INTEGER — it's the order of the matrix A, and it must satisfy N >= 0. respect the constraint or don't come 💀

🎀 A

!> A is DOUBLE PRECISION 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 !> DPOTRF. !> On exit, the upper or lower triangle of the (symmetric) !> inverse of A, overwriting the input factor U or L. !>

A is a DOUBLE PRECISION array, dimension (LDA,N), and it has a whole glow-up arc ✨

• on entry → it holds the triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, exactly as computed by DPOTRF
• on exit → it holds the upper or lower triangle of the (symmetric) inverse of A, and it overwrites the input factor U or L

so yeah, your factor is gone, replaced by the inverse. not me destroying the evidence 🙈

🦋 LDA

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

LDA is an INTEGER — the leading dimension of the array A, and it has to be LDA >= max(1,N). no cap, max(1,N) is the floor 🫶

🔥 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 it's the vibe check at the end 👑

• = 0 → successful exit, we ate 💅
• < 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 💀

so like, if INFO > 0 the inverse literally could not be computed. that's not a warning to ignore, bestie — the answer does not exist 🚨

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👑 Author 👑

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

the whole squad showed up, we love a collab 🌈

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⭐ Definition at line 94 of file dpotri.f. ⭐

literally line 94, go look, iykyk 👀

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🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code. not a human, just a very efficient little robot doing its thing 🤖✨

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and that's the page!! 💖 this was LAPACK, Version 3.12.0, dated SRC/dpotri.f(3) — mwah, slay, periodt 🫶🎀