CTRCON(3)

✨ CTRCON ✨

okay bestie, so this is the LAPACK tea from ctrcon.f in the /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/ directory — it's giving very specific, but we're gonna make it make sense 💅

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🌀 SYNOPSIS 🌀

subroutine CTRCON (norm, uplo, diag, n, a, lda, rcond, work, rwork, info)

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🫶 FUNCTION/SUBROUTINE DOCUMENTATION 🫶

🌸 The Full Signature (slay, literally) 🌸

subroutine CTRCON (character norm, character uplo, character diag, integer n, complex, dimension( lda, * ) a, integer lda, real rcond, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)

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💖 PURPOSE 💖

okay so picture this: CTRCON estimates the reciprocal of the condition number of a triangular matrix A — and it can do it in either the 1-norm or the infinity-norm, because we contain multitudes ✨

It computes the norm of A, gets an estimate for norm(inv(A)), and then does the cute little math:

RCOND = 1 / ( norm(A) * norm(inv(A)) ).

no cap, that's the whole vibe 🎀

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🌈 PARAMETERS 🌈

• NORM — CHARACTER*1. This one tells us whether we're doing the 1-norm condition number or the infinity-norm condition number, and she's very particular:
  • = '1' or 'O': 1-norm
  • = 'I': Infinity-norm
• UPLO — CHARACTER*1. Which triangle are we working with, bestie?
  • = 'U': A is upper triangular
  • = 'L': A is lower triangular
• DIAG — CHARACTER*1. Is the diagonal doing its own thing or are we assuming it's all ones?
  • = 'N': A is non-unit triangular
  • = 'U': A is unit triangular
• N — INTEGER. The order of the matrix A. And she said N >= 0, periodt.
• A — COMPLEX array, dimension (LDA,N). The triangular matrix A herself, the main character. Here's the tea:
  • If UPLO = 'U', the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced (we don't look at her, she's not invited).
  • If UPLO = 'L', the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. same energy.
  • If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1. iconic behavior honestly.
• LDA — INTEGER. The leading dimension of the array A. Must be LDA >= max(1,N). no exceptions, bestie, that's the rule 🦋
• RCOND — REAL. The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))). this is the moment, the whole reason we're here 💅
• WORK — COMPLEX array, dimension (2*N). just vibes and workspace.
• RWORK — REAL array, dimension (N). more workspace, but real this time.
• INFO — INTEGER. The receipts:
  • = 0: successful exit 🎉
  • < 0: if INFO = -i, the i-th argument had an illegal value. not cute, fix it.

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👑 AUTHOR 👑

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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⭐ DEFINITION ⭐

Defined at line 135 of file ctrcon.f.

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and that's the whole breakdown, bestie — generated automatically by Doxygen for LAPACK from the source code, from LAPACK Version 3.12.0, dated /home/abui...RC/ctrcon.f(3). we love a technically accurate slay 💜