SRC/dpstrf.f(3)

🌸 NAME 🌸

SRC/dpstrf.f — okay so this page is titled SRC/dpstrf.f(3) and it lives in the Library Functions Manual. It’s all about dpstrf: Cholesky factorization with complete pivoting for a real symmetric positive semidefinite matrix. The main character energy is real. 💅

✨ 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

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. No cap.

🌟 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.

⚠️ Important vibe check: this algorithm does not attempt to check that A is positive semidefinite. This version of the algorithm calls level 3 BLAS.

🎀 Parameters

• UPLO — is CHARACTER*1. Specifies whether the upper or lower triangular part of the symmetric matrix A is stored.
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• N — is INTEGER. The order of the matrix A. N >= 0.
• 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 — is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• PIV — is INTEGER array, dimension (N). PIV is such that the nonzero entries are P( PIV(K), K ) = 1.
• RANK — is INTEGER. The rank of A given by the number of steps the algorithm completed.
• 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 — is DOUBLE PRECISION array, dimension (2*N). Work space.
• 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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Sign-off, bestie: this page says LAPACK Version 3.12.0, and the file/source tag is SRC/dpstrf.f(3). Date check: the footer doesn’t list a date, so I’m not inventing one — we stay factual in this group chat. 💖✨🎀