SRC/spotrf2.f(3)

📦
version 3.12.1 · 7 versions
, in arch rolling

💖 NAME 💖

SRC/spotrf2.f — that's the page name, bestie. 💅

This is the Library Functions Manual page for it, and okay so we're about to get into a recursive Cholesky factorization moment. ✨

✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

  • recursive subroutine spotrf2 (uplo, n, a, lda, info) — SPOTRF2

🌸 Function/Subroutine Documentation 🌸

recursive subroutine spotrf2 (character uplo, integer n, real, dimension(
     lda, * ) a, integer lda, integer info)

SPOTRF2

🦋 Purpose 🦋

SPOTRF2 computes the Cholesky factorization of a real symmetric positive definite matrix A using the recursive algorithm. 🫶

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. iconic triangular behavior, no cap. 💜

This is the recursive version of the algorithm. It divides the matrix into four submatrices:

       [  A11 | A12  ]  where A11 is n1 by n1 and A22 is n2 by n2
   A = [ -----|----- ]  with n1 = n/2
       [  A21 | A22  ]       n2 = n-n1

The subroutine calls itself to factor A11. Update and scale A21 or A12, update A22 then call itself to factor A22. recursion ate, fr fr. 🔥

💅 Parameters 💅

  • UPLO — is CHARACTER*1. = 'U': upper triangle of A is stored; = 'L': lower triangle of A is stored. 🎀
  • N — is INTEGER. The order of the matrix A. N >= 0. ✨
  • A — is REAL 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 — is INTEGER. The leading dimension of the array A. LDA >= max(1,N). 💫
  • 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. 😭

🌈 Author 🌈

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

Definition at line 105 of file spotrf2.f.

🌸 Author 🌸

Generated automatically by Doxygen for LAPACK from the source code.

💖 That's the whole page, bestie — LAPACK Version 3.12.0, page source SRC/spotrf2.f(3), and the footer doesn't print a date, so I'm not inventing one. Mwah! 🎀

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