DPSTRF(3)

💖 DPSTRF(3) — Library Functions Manual 💖

okay bestie, welcome to the dpstrf.f(3) page from the Library Functions Manual. This is the LAPACK routine for the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix. It's giving linear algebra main character energy, and we are seated. 🪑✨

🌸 NAME 🌸

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

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

subroutine DPSTRF (uplo, n, a, lda, piv, rank, tol, work, info)

DPSTRF computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix.

🫶 Function/Subroutine Documentation 🫶

subroutine DPSTRF (character uplo, integer n, double precision, dimension(
     lda, * ) a, integer lda, integer, dimension( n ) piv, integer rank,
     double precision tol, double precision, dimension( 2*n ) work, integer
     info)

DPSTRF computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix.

💅 Purpose 💅

!>
!> DPSTRF computes the Cholesky factorization with complete
!> pivoting of a real symmetric positive semidefinite matrix A.
!>
!> The factorization has the form
!>    P**T * A * P = U**T * U ,  if UPLO = 'U',
!>    P**T * A * P = L  * L**T,  if UPLO = 'L',
!> where U is an upper triangular matrix and L is lower triangular, and
!> P is stored as vector PIV.
!>
!> This algorithm does not attempt to check that A is positive
!> semidefinite. This version of the algorithm calls level 3 BLAS.
!>

So like, it factors A with pivoting, but it is not out here checking that A is positive semidefinite for you. Level 3 BLAS is doing the heavy lifting. 💪

🍓 Parameters 🍓

UPLO

UPLO is CHARACTER*1 — tells us whether the upper or lower triangular part of the symmetric matrix A is stored.

• 'U': Upper triangular
• 'L': Lower triangular

N

N is INTEGER — the order of 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 as above.

LDA

LDA is INTEGER — the leading dimension of the array A. LDA >= max(1,N).

PIV

PIV is INTEGER array, dimension (N) — PIV is such that the nonzero entries are P( PIV(K), K ) = 1.

RANK

RANK is INTEGER — the rank of A, given by the number of steps the algorithm completed.

TOL

TOL is DOUBLE PRECISION — user defined tolerance. If TOL < 0, then N*U*MAX( A(K,K) ) will be used. The algorithm terminates at the (K-1)st step if the pivot <= TOL.

WORK

WORK is DOUBLE PRECISION array, dimension (2*N) — work space.

INFO

INFO is INTEGER

• < 0: If INFO = -K, the K-th argument had an illegal value,
• = 0: algorithm completed successfully, and
• > 0: the matrix A is either rank deficient with computed rank as returned in RANK, or is not positive semidefinite. See Section 7 of LAPACK Working Note #161 for further information.

🦋 Author 🦋

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

Definition at line 141 of file dpstrf.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole page, bestie 💖 — no cap. It's from LAPACK Version 3.12.0, and the footer path is /home/abui...RC/dpstrf.f(3). Go forth and factor something cute! 🎀✨