SLANHS(3)

🌸 SLANHS(3) — it's giving "norm energy" ✨

okay bestie, so this page lives at /home/abui...RC/slanhs.f(3) in the Library Functions Manual and it's all about a lil Fortran function called SLANHS from LAPACK. she's lowkey iconic: she measures how "big" an upper Hessenberg matrix is 💅 and honestly? we stan a queen who knows her own norms.

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slanhs.f — that's the whole name, no cap, she's just a file path and she's thriving 🎀

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🦋 SYNOPSIS 🦋

Functions/Subroutines

• real function SLANHS (norm, n, a, lda, work) — SLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix. that's the whole job description bestie, she does one thing and she ATE 🔥

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👑 Function/Subroutine Documentation 👑

real function SLANHS (character norm, integer n, real, dimension( lda, * )
    a, integer lda, real, dimension( * ) work)

SLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix. periodt. ✨

💖 Purpose:

!>
!> SLANHS  returns the value of the one norm,  or the Frobenius norm, or
!> the  infinity norm,  or the  element of  largest absolute value  of a
!> Hessenberg matrix A.
!>

like, she looks at your Hessenberg matrix A and hands you back one single number that tells you how chunky it is. which number? depends on NORM, babes. keep reading 💜

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🌈 Returns 🌈

!>
!>    SLANHS = ( max(abs(A(i,j))), NORM = 'M' or 'm'
!>             (
!>             ( norm1(A),         NORM = '1', 'O' or 'o'
!>             (
!>             ( normI(A),         NORM = 'I' or 'i'
!>             (
!>             ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
!>
!> where  norm1  denotes the  one norm of a matrix (maximum column sum),
!> normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
!> normF  denotes the  Frobenius norm of a matrix (square root of sum of
!> squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
!>

so the return value is literally pick your fighter based on NORM 🔥:

• 'M' / 'm' → max(abs(A(i,j)))
• '1', 'O', 'o' → norm1(A), the one norm (maximum column sum)
• 'I', 'i' → normI(A), the infinity norm (maximum row sum)
• 'F', 'f', 'E', 'e' → normF(A), the Frobenius norm (square root of sum of squares)

⚠️ heads up bestie: max(abs(A(i,j))) is not a consistent matrix norm. that's a real caveat, not me being dramatic. write it in your notes 💀

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🎀 Parameters 🎀

NORM

!>          NORM is CHARACTER*1
!>          Specifies the value to be returned in SLANHS as described
!>          above.
!>

she's a CHARACTER*1 and she's the main character — she decides which norm you get back, per the little menu above 👆

N

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.  When N = 0, SLANHS is
!>          set to zero.
!>

INTEGER, the order of matrix A, and it's N >= 0. and if N = 0? SLANHS is set to zero, no thoughts, head empty, zero 🙈

A

!>          A is REAL array, dimension (LDA,N)
!>          The n by n upper Hessenberg matrix A; the part of A below the
!>          first sub-diagonal is not referenced.
!>

REAL array, dimension (LDA,N). it's the n by n upper Hessenberg matrix A — and important: everything below the first sub-diagonal is not referenced, so don't stress about that part ✨

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(N,1).
!>

INTEGER, the leading dimension of array A, and bestie the rule is LDA >= max(N,1) 🫶

WORK

!>          WORK is REAL array, dimension (MAX(1,LWORK)),
!>          where LWORK >= N when NORM = 'I'; otherwise, WORK is not
!>          referenced.
!>

REAL array, dimension (MAX(1,LWORK)), where LWORK >= N only when NORM = 'I'. otherwise? WORK is not referenced — she's just there for moral support 💅

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⭐ Author ⭐

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

(genuinely a whole squad, we love a collaborative slay 👑)

Definition at line 107 of file slanhs.f. 📍

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💫 Author (the other one) 💫

Generated automatically by Doxygen for LAPACK from the source code. so nobody hand-wrote that bit — the robots did it 🤖✨

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🌸 ok that's the whole page, you understood it, i'm obsessed with you, go forth and compute norms responsibly 🦋💖

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✨ sign-off ✨ — this lil beauty is from LAPACK, Version 3.12.0, footer friend /home/abui...RC/slanhs.f(3), and mwah, that's the vibe check complete 🎀💅🌟