/home/abui...con_rook.f(3)

💅 NAME

okay so this is the manual page for /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zhecon_rook.f — yes that's the whole entire path, she's long, she's iconic, she's a Fortran source file and she is the moment. It's a Library Functions Manual page, bestie. 🎀

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✨ SYNOPSIS ✨

Functions/Subroutines

ok so here's the one function this page is about, and we're gonna get into it:

subroutine ZHECON_ROOK (uplo, n, a, lda, ipiv, anorm, rcond, work, info)

What does she do? ZHECON_ROOK estimates the reciprocal of the condition number for HE matrices using a factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges). Lowkey a mouthful, highkey important. 🫶

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🦋 Function/Subroutine Documentation 🦋

Here's the full signature, character for character, no cap:

subroutine ZHECON_ROOK (character uplo, integer n, complex*16, dimension(
    lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision
    anorm, double precision rcond, complex*16, dimension( * ) work, integer
    info)

And the tagline again, because she deserves the encore: ZHECON_ROOK estimates the reciprocal of the condition number for HE matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges). 💖

🎯 Purpose

ok so picture this: ZHECON_ROOK estimates the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHETRF_ROOK.

Then it gets an estimate for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). Math girl summer. 🧚

🌸 Parameters

• UPLO — is CHARACTER*1. She specifies whether the details of the factorization are stored as an upper or lower triangular matrix. Your options, diva:
  • = 'U': Upper triangular, form is A = U*D*U**H;
  • = 'L': Lower triangular, form is A = L*D*L**H.
• N — is INTEGER. The order of the matrix A. N >= 0. No negatives, we don't do that here. 🙈
• A — is COMPLEX*16 array, dimension (LDA,N). It's the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CHETRF_ROOK. She's carrying the whole factorization on her back, honestly. 💀
• LDA — is INTEGER. The leading dimension of the array A. LDA >= max(1,N). Respect the boundary, bestie.
• IPIV — is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by CHETRF_ROOK. The receipts, basically. 🍓
• ANORM — is DOUBLE PRECISION. The 1-norm of the original matrix A. Yes, the original one, not the factored one — don't get it twisted.
• 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. Look at her doing the whole thing herself. 👑
• WORK — is COMPLEX*16 array, dimension (2*N). Just workspace, she's chilling.
• INFO — is INTEGER. The vibe check:
  • = 0: successful exit — slay!! ✨
  • < 0: if INFO = -i, the i-th argument had an illegal value — not slay, someone passed something cursed. 😭

🫶 Author

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

🌈 Contributors

• June 2017, Igor Kozachenko — Computer Science Division, University of California, Berkeley
• September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas — School of Mathematics, University of Manchester

Legends, all of them, fr fr.

⭐ Definition at line 137 of file zhecon_rook.f.

That's where she lives. Line one-three-seven. Note it. 💅

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🎀 Author

Generated automatically by Doxygen for LAPACK from the source code. (So technically a robot wrote this and I'm just the messenger. Respect the pipeline.)

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ok so that's the whole page, every flag and every footnote accounted for, nothing skipped, nothing invented — iykyk. 💜

LAPACK, Version 3.12.0, and that footer path /home/abui...con_rook.f(3) — mwah, bye bestie, go condition some numbers responsibly 🦋🌸🔥