SRC/cpotrf2.f(3)

🌸 SRC/cpotrf2.f(3) 🌸

okay bestie, this page comes straight from the Library Functions Manual, and it’s all about one recursive little icon: cpotrf2. Let’s get into it 💅

💖 NAME 💖

SRC/cpotrf2.f

✨ SYNOPSIS ✨

Functions/Subroutines

• recursive subroutine cpotrf2 (uplo, n, a, lda, info)
  • CPOTRF2

🫶 Function/Subroutine Documentation 🫶

recursive subroutine cpotrf2 (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer info)

CPOTRF2

🎯 Purpose 🎯

okay so CPOTRF2 computes the Cholesky factorization of a Hermitian positive definite matrix A using the recursive algorithm. No cap.

The factorization has the form:

A = U**H * U,  if UPLO = 'U', or
A = L  * L**H,  if UPLO = 'L',

where U is an upper triangular matrix and L is lower triangular.

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 calls itself to factor A22. It’s giving recursion main character energy 😭

🌈 Parameters 🌈

• UPLO — character selector for which triangle is stored 🦋
  • UPLO is CHARACTER*1
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.
• N — the order of the matrix, lowkey important 💫
  • N is INTEGER
  • The order of the matrix A. N >= 0.
• A — the matrix itself, and she’s COMPLEX 🫶
  • A is COMPLEX array, dimension (LDA,N)
  • On entry, the Hermitian 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**H*U or A = L*L**H.
• LDA — leading dimension, keep it legal bestie 💅
  • LDA is INTEGER
  • The leading dimension of the array A. LDA >= max(1,N).
• INFO — the exit-status tea ☕
  • 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 cpotrf2.f.

👑 Author 👑

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