SRC/spstf2.f(3)

💖 SRC/spstf2.f(3) — Library Functions Manual 💖

okay bestie, welcome to the SRC/spstf2.f(3) page from the Library Functions Manual ✨ this is the manual for a Fortran subroutine that factors a real symmetric positive semidefinite matrix with complete pivoting, and it is lowkey iconic.

🦋 NAME 🦋

SRC/spstf2.f

✨ 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.

🌸 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. That’s the main character energy of this whole page, fr fr.

🎯 Purpose 🎯

okay so here’s the tea: 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.

⚠️ Important caveat, 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, A is 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.

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💜 That’s the whole manual, bestie! The footer vibe is LAPACK Version 3.12.0 and SRC/spstf2.f(3). Periodt. 💅✨