/home/abui.../zpotrf2.f(3)

💅 NAME 💅

Okay so this page is from the Library Functions Manual, and its header is /home/abui.../zpotrf2.f(3) — consider that title line folded in, bestie ✨.

The actual name/path is:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zpotrf2.f

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✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

• recursive subroutine ZPOTRF2 (uplo, n, a, lda, info) — ZPOTRF2

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🫶 Function/Subroutine Documentation 🫶

recursive subroutine ZPOTRF2 (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer info)

ZPOTRF2

🎀 Purpose: 🎀

ZPOTRF2 computes the Cholesky factorization of a Hermitian positive definite matrix A using the recursive algorithm. Iconic linear algebra behavior, 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 call itself to factor A22. Recursion really said “main character energy” 😭🔥.

🧚 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 COMPLEX*16 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 — 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.

Bestie, that INFO > 0 case is important: 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 zpotrf2.f.

🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole page, bestie 💖 — from LAPACK, Version 3.12.0, and the path is /home/abui.../zpotrf2.f(3). Byeeee 🦋