SPSTF2(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 NAME 💅

okay so bestie, this is the manual page for spstf2.f(3) — yes, the SPSTF2 routine — and we're in the Library Functions Manual. The source file is literally /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/spstf2.f. Slay.

✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

subroutine SPSTF2 (uplo, n, a, lda, piv, rank, tol, work, info)

SPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix. Periodt.

💖 Function/Subroutine Documentation 💖

subroutine SPSTF2 (character uplo, integer n, real, dimension( lda, * ) a,
     integer lda, integer, dimension( n ) piv, integer rank, real tol, real,
     dimension( 2*n ) work, integer info)

SPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix. No cap.

🎯 Purpose 🎯

SPSTF2 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.

⚠️ lowkey important, 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 REAL 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.

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 REAL. 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 REAL 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 spstf2.f.

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

okay that's the whole page, bestie 🫶. Signed with LAPACK Version 3.12.0 energy, source /home/abui...RC/spstf2.f(3), and the date slot is empty on this page — no date to report, ngl. Periodt. 💅✨

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