SRC/dpotrf2.f(3)

✨ NAME ✨

SRC/dpotrf2.f — okay bestie, this page is from the Library Functions Manual, and it's all about SRC/dpotrf2.f. 💅

🌸 SYNOPSIS 🌸

Functions/Subroutines

• recursive subroutine dpotrf2 (uplo, n, a, lda, info) — DPOTRF2 (yes, she’s recursive).

recursive subroutine dpotrf2 (uplo, n, a, lda, info)

💖 Function/Subroutine Documentation 💖

🫶 recursive subroutine dpotrf2 (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, integer info)

DPOTRF2 is here, and she’s ready to factor. Let’s go. 🦋

Purpose

DPOTRF2 computes the Cholesky factorization of a real symmetric positive definite matrix A using the recursive algorithm. It’s giving recursion, and honestly? iconic.

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 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. Recursion-ception, no cap. 🌀

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 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 dpotrf2.f.

🌈 Author 🌈

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💋 mwah — this page is SRC/dpotrf2.f(3) from LAPACK Version 3.12.0. That’s the source/version combo, bestie; now go factor something positive definite. 🎀