SRC/clanhs.f(3)

💖 SRC/clanhs.f 💖

Okay so bestie, welcome to the LAPACK Library Functions Manual page for SRC/clanhs.f! This is literally the glow-up of a Fortran function that computes matrix norms for upper Hessenberg matrices, and it's giving main character energy. 🦋✨

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✨ NAME ✨

SRC/clanhs.f

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🌸 SYNOPSIS 🌸

🎀 Functions/Subroutines

• real function clanhs (norm, n, a, lda, 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.

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🎀 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.

🔥 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.
!>

💀 Just a heads-up, bestie: max(abs(A(i,j))) is not a consistent matrix norm, so don't come for me when it doesn't behave like a real norm. It's just the biggest absolute value, periodt. No cap.

🧚 Parameters

💅 NORM

NORM is CHARACTER*1. Specifies the value to be returned in CLANHS as described above. You pick the vibe ('M', '1', 'O', 'I', 'F', 'E', etc.) and it returns the matching norm. Slay.

🌟 N

N is INTEGER. The order of the matrix A. N >= 0. When N = 0, CLANHS is set to zero. So if your matrix is empty, you get a big fat zero, no cap. 🫶

🦋 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 like, only the upper Hessenberg part matters, the rest is giving extra and we're not checking for it. 💅

🎀 LDA

LDA is INTEGER. The leading dimension of the array A. LDA >= max(N,1). Don't try to be slick with a smaller LDA, bestie, it's not the move. 😭

⭐ WORK

WORK is REAL array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced. So only the infinity norm needs workspace, the others are lowkey freeloaders. iykyk 🙈

👑 Author

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

⭐ Definition

Definition at line 108 of file clanhs.f.

💜 Author (again, yes really)

Generated automatically by Doxygen for LAPACK from the source code.

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This page was brought to you by LAPACK Version 3.12.0 and the date is whatever Doxygen stamped on it. Bye bestie, go compute some norms! 💖✨🦋