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

💖 CHECON_ROOK — the LAPACK girlie's guide to condition numbers 💖

okay so bestie, this one lives in the LAPACK library manual, and the file is literally:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/checon_rook.f

no cap, that's the whole path. and it's checon_rook.f(3) in the manual, section 3, bestie. 🎀

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✨ SYNOPSIS ✨

Functions/Subroutines

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

CHECON_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). 💅

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🦋 Function/Subroutine Documentation 🦋

subroutine CHECON_ROOK (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real anorm, real rcond, complex, dimension( * ) work, integer info)

CHECON_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). so iconic honestly.

Purpose:

CHECON_ROOK estimates the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U*D*UH or A = L*D*LH computed by CHETRF_ROOK. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

bestie it's giving "how trustworthy is my matrix" energy. it takes your CHETRF_ROOK factorization and tells you how close to singular you are, via the reciprocal condition number. lowkey crucial. 🔥

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🌸 Parameters 🌸

• UPLO — UPLO is CHARACTER*1, and it specifies whether the details of the factorization are stored as an upper or lower triangular matrix. the tea:
  • = '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. N >= 0. periodt.
• A — A is COMPLEX 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. her main character moment honestly 💅
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N). don't skimp on her, she needs the space.
• IPIV — 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 — ANORM is REAL. The 1-norm of the original matrix A. ngl she's just the original vibe before any factorization happened.
• 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. this is the whole point of the function, she's the star ⭐
• WORK — WORK is COMPLEX array, dimension (2*N). that's it, that's the option. two Ns worth of scratch space, no drama.
• INFO — INFO is INTEGER, and here's the vibe check:
  • = 0: successful exit 🎉
  • < 0: if INFO = -i, the i-th argument had an illegal value 💀

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👑 Author 👑

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

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🧚 Contributors: 🧚

December 2016, Igor Kozachenko, Computer Science Division, University of California, Berkeley September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, School of Mathematics, University of Manchester

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💜 Definition at line 137 of file checon_rook.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. she wrote herself, fr fr. 🤖✨

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and that's the whole page bestie 🫶 — filed under LAPACK, Version 3.12.0, dated /home/abui...con_rook.f(3), brought to you by the LAPACK girlies and Doxygen doing its little autogen thing. mwah 💋🌸