SRC/spstrf.f(3)

🎀 NAME 🎀

SRC/spstrf.f — that’s the file, 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. Periodt. 🔥

💖 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. Yup, that’s the whole vibe 👑

🌸 Purpose

Okay so SPSTRF computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix A. No cap.

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. Iconic linear algebra behavior, honestly ✨

🚨 Real talk, bestie: 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 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 — 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 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 — is REAL 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 140 of file spstrf.f.

🌈 Author 🌈

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That’s the whole page, bestie — footer energy is LAPACK, Version 3.12.0, SRC/spstrf.f(3) 🫶🎀