CHPCON(3)

🦋 CHPCON — chpcon.f(3) 🦋

ok so real talk, bestie, this is a page from the Library Functions Manual for /home/abui...RC/chpcon.f(3) and it's literally the docs for one single BLAS/LAPACK girlie named CHPCON. she estimates condition numbers. that's her whole thing. 💅

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/chpcon.f — yeah that's the whole path, no cap, that's how this manual page names itself 💀

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🎀 SYNOPSIS 🎀

Functions/Subroutines

• subroutine CHPCON (uplo, n, ap, ipiv, anorm, rcond, work, info) — CHPCON 💖

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🌸 Function/Subroutine Documentation 🌸

subroutine CHPCON (character uplo, integer n, complex, dimension( * ) ap,
    integer, dimension( * ) ipiv, real anorm, real rcond, complex,
    dimension( * ) work, integer info)

CHPCON 👑

💜 Purpose:

!>
!> CHPCON estimates the reciprocal of the condition number of a complex
!> Hermitian packed matrix A using the factorization A = U*D*U**H or
!> A = L*D*L**H computed by CHPTRF.
!>
!> An estimate is obtained for norm(inv(A)), and the reciprocal of the
!> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
!>

so basically: she's estimating how close to trouble your matrix is, using the factorization A = U*D*U**H or A = L*D*L**H that CHPTRF already did for you. she estimates norm(inv(A)), then does RCOND = 1 / (ANORM * norm(inv(A))). that's the vibe. that's the whole algorithm. iconic. 🌈

🌟 Parameters

• UPLO — UPLO is CHARACTER*1. tells her whether the factorization details are stored as an upper or lower triangular matrix, bestie. options are:
  • = 'U': Upper triangular, form is A = U*D*U**H;
  • = 'L': Lower triangular, form is A = L*D*L**H.
• N — N is INTEGER. the order of the matrix A. and like, N >= 0 obviously, we don't do negative orders here 🫶
• AP — AP is COMPLEX array, dimension (N*(N+1)/2). this is the block diagonal matrix D plus the multipliers used to get the factor U or L as computed by CHPTRF, all stored as a packed triangular matrix. packed! like a little suitcase of math ✨
• IPIV — IPIV is INTEGER array, dimension (N). the deets on the interchanges and the block structure of D, as determined by CHPTRF. iykyk 💅
• ANORM — ANORM is REAL. the 1-norm of the original matrix A. that's it, that's the number 🍓
• RCOND — RCOND is REAL. the reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine. she does the estimating herself, main character energy fr fr 👑
• WORK — WORK is COMPLEX array, dimension (2*N). scratch space, no notes 🌸
• INFO — INFO is INTEGER. the receipts:
  • = 0: successful exit 🎉
  • < 0: if INFO = -i, the i-th argument had an illegal value 💀

🧚 Author

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

Definition at line 117 of file chpcon.f. ⭐

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💖 Author 💖

Generated automatically by Doxygen for LAPACK from the source code. not me being auto-generated 🙈

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ok bye bestie, go estimate some condition numbers 💜

LAPACK — Version 3.12.0 — /home/abui...RC/chpcon.f(3) — mwah, that's the source, the version and the date all in one cute little sign-off 🎀✨🫶