ZHPCON(3)

💅 NAME

Bestie, this is the manual page for zhpcon.f — like, the actual source file living at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zhpcon.f. Yes the whole path, no we're not shortening it, it's part of Library Functions Manual energy and we respect the lore. 🫶

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✨ SYNOPSIS

Functions/Subroutines

subroutine ZHPCON (uplo, n, ap, ipiv, anorm, rcond, work, info)
    ZHPCON

That's the whole vibe. She's a subroutine. She's called ZHPCON. That's it, that's the girl. 💅

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🎀 Function/Subroutine Documentation

subroutine ZHPCON (character uplo, integer n, complex*16, dimension( * ) ap,
    integer, dimension( * ) ipiv, double precision anorm, double precision
    rcond, complex*16, dimension( * ) work, integer info)
    ZHPCON

🌸 Purpose

!>
!> ZHPCON 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 ZHPTRF.
!>
!> An estimate is obtained for norm(inv(A)), and the reciprocal of the
!> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
!>

Okay so real talk: ZHPCON gives you an estimate of the reciprocal of the condition number of a complex Hermitian packed matrix A. She's doing this using the factorization A = U*D*U**H or A = L*D*L**H that was already computed by ZHPTRF — so like, she's building on somebody else's work, we love efficiency. ✨

The way it works is lowkey iconic: an estimate is obtained for norm(inv(A)), and then the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). Math ate, honestly. 🧮

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🦋 Parameters

• UPLO — this one is CHARACTER*1 and it's giving "which triangle are we in". It specifies whether the details of the factorization are stored as an upper or lower triangular matrix.
  • = '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. Constraint check: N >= 0. Don't come at her with a negative, she will not be engaging. 🙈
• AP — AP is COMPLEX*16 array, dimension (N*(N+1)/2). This holds the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZHPTRF, stored as a packed triangular matrix. Packed. Like, tightly. No wasted space. Queen of efficiency. 👑
• IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by ZHPTRF. Receipts from the previous routine, basically. 🧾
• ANORM — ANORM is DOUBLE PRECISION. The 1-norm of the original matrix A. The before picture, if you will. 📸
• RCOND — RCOND is DOUBLE PRECISION. 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's the output. She's the moment. She's the main character. 🌟
• WORK — WORK is COMPLEX*16 array, dimension (2*N). Just her little scratchpad, no thoughts needed. 🍓
• INFO — INFO is INTEGER. The vibe check, formally:
  • = 0: successful exit (slay 💖)
  • < 0: if INFO = -i, the i-th argument had an illegal value (not slay 😭)

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👑 Author

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

All the legends, credited, periodt. 🫡

Definition at line 117 of file zhpcon.f. Bookmark it, iykyk. 🔖

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🌈 Author

Generated automatically by Doxygen for LAPACK from the source code. Not a human, just a very diligent little robot doing her thing. 🤖💜

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Okay bestie, that's the whole page — go forth and estimate those condition numbers responsibly. Fr fr. 🎀

LAPACK — Version 3.12.0 — and the file is zhpcon.f(3), okurrr? 💅✨🦋