SRC/cpstrf.f(3)

✨ SRC/cpstrf.f(3) ✨

okay bestie, welcome to the Library Functions Manual entry for SRC/cpstrf.f — it's giving tiny file, huge math energy, and we're obsessed 💖

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🎀 NAME 🎀

SRC/cpstrf.f — minimal, iconic, periodt 💅

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🌈 SYNOPSIS 🌈

🦋 Functions/Subroutines 🦋

Quick vibe check, iykyk:

subroutine cpstrf (uplo, n, a, lda, piv, rank, tol, work, info)
    CPSTRF computes the Cholesky factorization with complete pivoting of
    complex Hermitian positive semidefinite matrix.

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🧚 Function/Subroutine Documentation 🧚

ngl, the signature is long but she's literally just doing her job 🫶

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

CPSTRF computes the Cholesky factorization with complete pivoting of complex Hermitian positive semidefinite matrix.

🌟 Purpose: 🌟

okay so here's the whole point, bestie: CPSTRF computes the Cholesky factorization with complete pivoting of a complex Hermitian positive semidefinite matrix A. 💖

The factorization has the form

P**T * A * P = U**H * U ,  if UPLO = 'U',
P**T * A * P = L  * L**H,  if UPLO = 'L',

where U is an upper triangular matrix and L is lower triangular, and P is stored as vector PIV.

🚨 no cap, 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 💖

bestie, every parameter matters, fr fr. Here's the full list:

• UPLO — 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 — N is INTEGER. The order of the matrix A. N >= 0.
• A — A is COMPLEX 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 👑

the way that multiple universities and NAG Ltd. are on the credits — highkey iconic 🌈

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 141 of file cpstrf.f.

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🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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xoxo, your LAPACK bestie 💖 — footer stamp: LAPACK Version 3.12.0, SRC/cpstrf.f(3) (no date on this one, just vibes) 🫶