SRC/ssycon_rook.f(3)

🌸 SRC/ssycon_rook.f(3) — from the Library Functions Manual 💅

okay so bestie, welcome to the glow-up of a genuinely iconic LAPACK page 🎀 this is SRC/ssycon_rook.f and she is that girl — a Fortran file that estimates condition numbers and does it flawlessly. let's get into it ✨

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✨ NAME ✨

SRC/ssycon_rook.f — literally the file, that's her name, no notes 💖

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🦋 SYNOPSIS 🦋

Functions/Subroutines

• subroutine ssycon_rook (uplo, n, a, lda, ipiv, anorm, rcond, work, iwork, info) — this is the main character right here 👑
• SSYCON_ROOK — the label, the name, the brand ✨

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👑 Function/Subroutine Documentation 👑

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

SSYCON_ROOK — say it with your chest 💅

🎯 Purpose

!> !> SSYCON_ROOK estimates the reciprocal of the condition number (in the !> 1-norm) of a real symmetric matrix A using the factorization !> A = U*D*U**T or A = L*D*L**T computed by SSYTRF_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))). !>

so like. the whole vibe is: you already ran SSYTRF_ROOK, you got your factorization A = U*D*U**T or A = L*D*L**T, and now this routine slides in to give you RCOND — the reciprocal of the condition number in the 1-norm 🧚 it estimates norm(inv(A)) and then hits you with RCOND = 1 / (ANORM * norm(inv(A))). math but make it cute 😭💜

🌈 Parameters

• UPLO — is CHARACTER*1. tells us whether the factorization details are chilling as an upper or lower triangular matrix, bestie:
  • = 'U': upper triangular, form is A = U*D*U**T;
  • = 'L': lower triangular, form is A = L*D*L**T.
• N — is INTEGER. the order of the matrix A. N >= 0. periodt ✨
• A — is REAL array, dimension (LDA,N). the block diagonal matrix D plus the multipliers used to obtain the factor U or L, as computed by SSYTRF_ROOK. iconic 🔥
• LDA — is INTEGER. the leading dimension of the array A. LDA >= max(1,N). don't skip this one 🙈
• IPIV — is INTEGER array, dimension (N). all the tea about the interchanges and the block structure of D, as determined by SSYTRF_ROOK 🍓
• ANORM — is REAL. the 1-norm of the original matrix A 💖
• 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's the output, she's the moment ⭐
• WORK — is REAL array, dimension (2*N). workspace, doing her thing 💅
• IWORK — is INTEGER array, dimension (N). more workspace, integer flavored 🎀
• INFO — is INTEGER:
  • = 0: successful exit, we love a win 🌸
  • < 0: if INFO = -i, the i-th argument had an illegal value — bestie someone passed a bad argument, call it out 💀

🌟 Author

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

the whole squad showed up 🫶

💜 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 !> !>

shoutout to everyone who built her 😭💖

📍 Definition at line 142 of file ssycon_rook.f.

go look, she's literally right there 👑

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🎀 Author 🎀

Generated automatically by Doxygen for LAPACK from the source code. the robots did this one 🤖✨

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and that's the whole page bestie, no cap, every flag and every line accounted for 💅 this cutie is from LAPACK, Version 3.12.0 and her file is SRC/ssycon_rook.f(3) — go estimate some condition numbers, you're gonna slay 🦋🌈💖