dpotrf.f(3)

🎀 dpotrf.f — LAPACK’s right-looking block Cholesky bestie 🎀

okay so this is dpotrf.f, straight out of the LAPACK fam, and she is very good at one specific job: Cholesky factorization, but make it right-looking block algorithm energy 💅

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✨ NAME ✨

dpotrf.f

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✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

• subroutine dpotrf (UPLO, N, A, LDA, INFO) — DPOTRF VARIANT: right looking block version of the algorithm, calling Level 3 BLAS. no cap, that’s the whole vibe 🫶

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💖 Function/Subroutine Documentation 💖

🦋 subroutine dpotrf (character UPLO, integer N, double precision, dimension( lda, * ) A, integer LDA, integer INFO) 🦋

DPOTRF VARIANT: right looking block version of the algorithm, calling Level 3 BLAS.

🌟 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 right looking block version of the algorithm, calling Level 3 BLAS. she said “right looking” and “Level 3 BLAS” and meant both, periodt ✨

🎀 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.

• 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 minor of order i is not positive definite, and the factorization could not be completed.

bestie, that INFO > 0 case is the “the factorization could not be completed” one — very real, no sugarcoating, the matrix was not giving positive definite 💀

👑 Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🗓️ Date:

December 2016

📍 Definition at line 102 of file VARIANTS/cholesky/RL/dpotrf.f.

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🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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and that’s the page, mwah 💖 Version 3.8.0 — Tue Nov 14 2017 — dpotrf.f(3), signed off with LAPACK sparkle and a little Doxygen-generated bow 🎀✨