DPOTRF(3)

💅 DPOTRF(3) — the top-looking block Cholesky, bestie edition ✨

okay so first things first: this page lives in the Library Functions Manual, and its NAME is literally a whole path, no cap:

/home/abuild/rpmbuild/BUILD/lapack-
static-3.12.0-build/lapack-3.12.0/SRC/VARIANTS/cholesky/TOP/dpotrf.f

yes bestie, the name is a file path. that's the whole vibe. it's giving "i am the source file and also the manpage" 💀

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✨ SYNOPSIS ✨

Functions/Subroutines 🫶

• subroutine DPOTRF (uplo, n, a, lda, info) — the DPOTRF VARIANT: top-looking block version of the algorithm, and it's calling Level 3 BLAS. she's fancy like that 💅

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🌸 Function/Subroutine Documentation 🌸

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

DPOTRF VARIANT: top-looking block version of the algorithm, calling Level 3 BLAS. iconic behaviour, honestly 👑

🎀 Purpose:

!>
!> DPOTRF computes the Cholesky factorization of a real symmetric
!> positive definite matrix A.
!>
!> The factorization has the form
!>    A = U**T * U,  if UPLO = 'U', or
!>    A = L  * L**T,  if UPLO = 'L',
!> where U is an upper triangular matrix and L is lower triangular.
!>
!> This is the top-looking block version of the algorithm, calling Level 3 BLAS.
!>
!>

so like, she factorizes your real symmetric positive definite matrix A. that's her whole job and she ate 🔥

🌈 Parameters

• UPLO 🦋

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

• N ⭐

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

• A 💖

!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
!>          N-by-N upper triangular part of A contains the upper
!>          triangular part of the matrix A, and the strictly lower
!>          triangular part of A is not referenced.  If UPLO = 'L', the
!>          leading N-by-N lower triangular part of A contains the lower
!>          triangular part of the matrix A, and the strictly upper
!>          triangular part of A is not referenced.
!>

!>          On exit, if INFO = 0, the factor U or L from the Cholesky
!>          factorization A = U**T*U or A = L*L**T.
!>

ngl bestie, one triangle is all she reads. the other one is literally just sitting there, not referenced, minding her business 🙈

• LDA 🧚

!>          LDA is INTEGER
!>          The leading dimension of the array A.  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, the leading principal minor of order i
!>                is not positive, and the factorization could not be
!>                completed.
!>

lowkey important: INFO > 0 means the leading principal minor of order i is not positive and the factorization could not be completed. that's a real "she said no" moment 😭

👑 Author

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

the whole squad collaborated. main character energy from four institutions at once, fr fr 💜

📅 Date

December 2016

🦋 Definition at line 101 of file dpotrf.f.

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🌟 Author (the meta one) 🌟

Generated automatically by Doxygen for LAPACK from the source code. so nobody hand-wrote this beauty, she was born from the source code itself. automated queen 💅✨

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and that's the whole page, bestie! this was brought to you by LAPACK, Version 3.12.0 🎀 — and the header/footer path vibes were .../VARIANTS/cholesky/TOP/dpotrf.f(3), because of course they were. mwah 💖🫶🌈