SRC/dpstf2.f(3)

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🫶 SRC/dpstf2.f(3) — Library Functions Manual 🫶

🌸 NAME 🌸

SRC/dpstf2.f — that's the name, bestie 💅

✨ SYNOPSIS ✨

💅 Functions/Subroutines 💅

  • subroutine dpstf2 (uplo, n, a, lda, piv, rank, tol, work, info) — DPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix.

🧚 Function/Subroutine Documentation 🧚

🎀 subroutine dpstf2 🎀

subroutine dpstf2 (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)

DPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix.

🔥 Purpose 🔥

okay so DPSTF2 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.

Heads up, bestie: this algorithm does not attempt to check that A is positive semidefinite. This version of the algorithm calls level 2 BLAS. 💀

🌈 Parameters 🌈

💜 UPLO 💜

UPLO is CHARACTER*1 — it specifies 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 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 as above. slay ✨

🍓 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.

🌸 LDA 🌸

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

💖 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 140 of file dpstf2.f.

🤖 Author 🤖

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okay that's the whole page, bestie 💖 this one's from SRC/dpstf2.f(3) and it's LAPACK Version 3.12.0. The footer didn't hand us a date, so no invented date here, periodt. 🫶

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