SRC/zpotrf2.f(3)

💖 SRC/zpotrf2.f 💖

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🌸 NAME 🌸

SRC/zpotrf2.f — that’s the name, no cap. 💅

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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)

recursive subroutine zpotrf2 (character uplo, integer n, complex*16,
       dimension( lda, * ) a, integer lda, integer info)

ZPOTRF2 — say it with me, bestie. 👑

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🦋 Purpose 🦋

Okay so ZPOTRF2 computes the Cholesky factorization of a Hermitian positive definite matrix A using the recursive algorithm. Obsessed with a recursive queen. 💖

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? In this economy? She ate. 💅

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🌟 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.

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💜 Author 💜

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

Definition at line 105 of file zpotrf2.f.

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🌈 Author 🌈

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