CLANHS(3)

🎀 CLANHS(3) — the upper Hessenberg norm girlie 🎀

ok so real talk, bestie: this page came out of /home/abui...RC/clanhs.f(3), and the manual it lives in is the Library Functions Manual. That's the vibe. Let's get into it 💅

---

✨ SYNOPSIS ✨

Functions/Subroutines

• real function CLANHS (norm, n, a, lda, work) — 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 🫶

---

💖 Function/Subroutine Documentation 💖

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

CLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix. no cap, that's literally the whole job 🌸

🔥 Purpose 🔥

!>
!> CLANHS  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.
!>

⭐ Returns ⭐

CLANHS

!>
!>    CLANHS = ( 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 you pick your norm with NORM and CLANHS hands it right back to you, and if you're the 'M'/'m' girlie you get max(abs(A(i,j))) — and heads up, that one is not a consistent matrix norm, that's just the rules 💀

🌈 Parameters 🌈

• NORM — NORM is CHARACTER*1. Specifies the value to be returned in CLANHS as described above. that's it, that's the assignment ✨
• N — N is INTEGER. The order of the matrix A. N >= 0. When N = 0, CLANHS is set to zero. tiny matrix, tiny answer, we love a clean edge case 💜
• A — A is COMPLEX array, dimension (LDA,N). The n by n upper Hessenberg matrix A; the part of A below the first sub-diagonal is not referenced. so don't stress about what's down there, she's not looking 🙈
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(N,1). respect the leading dimension or perish 🎀
• WORK — WORK is REAL array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced. so bestie, if you're doing the infinity norm you NEED your workspace, otherwise you can literally leave it 🦋

👑 Author 👑

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

Definition at line 108 of file clanhs.f. iykyk 📍

---

💫 Author 💫

Generated automatically by Doxygen for LAPACK from the source code. it's giving "nobody hand-wrote me and yet I'm iconic" 😭

---

friendly reminder that every single one of these details is load-bearing: NORM picks the norm, N = 0 gives you zero, and WORK only matters for 'I'. don't come for me if you skip that 💅

---

LAPACK, Version 3.12.0 — mwah, that's the whole page, go forth and compute your norms, bestie 🧚💖✨