SPSTRF(3)

💖 SPSTRF(3) 💖

okay bestie, this is SPSTRF(3) from the Library Functions Manual — and it's giving “Cholesky factorization with complete pivoting” main character energy, honestly iconic 💅✨

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🌸 NAME 🌸

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

That’s the file this page is about, bestie 🫶

🦋 SYNOPSIS 🦋

✨ Functions/Subroutines ✨

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

👑 Function/Subroutine Documentation 👑

subroutine SPSTRF (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)

SPSTRF computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix. No cap, that’s the whole assignment 🔥

🎀 Purpose 🎀

SPSTRF 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. That’s the vibe: it is not doing that check, bestie 😭

🌸 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.
• 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 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.
• 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 spstrf.f.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole page, bestie 🫶 footer sign-off: LAPACK Version 3.12.0, source /home/abui...RC/spstrf.f(3) — no date is printed on this page, so I’m not inventing one 🙈💜