SRC/zlanhs.f(3)

okay so bestie, welcome to SRC/zlanhs.f(3) from the Library Functions Manual. This is the page for zlanhs, and it’s lowkey iconic: we’re measuring norms of an upper Hessenberg matrix and doing it with main character energy. Let’s go. 💅✨

💖 NAME

SRC/zlanhs.f — yes, that’s the name. Short, sweet, and absolutely serving file-path realness. 🎀

✨ SYNOPSIS

Functions/Subroutines

• double precision function zlanhs (norm, n, a, lda, work) — ZLANHS 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 the whole assignment. 🦋

🛠️ Function/Subroutine Documentation

Full signature, exactly as it appears:

double precision function zlanhs (character norm, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) work)

ZLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix. Again for the people in the back. 💖

🎯 Purpose

ZLANHS 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. It’s giving norm buffet, pick your fave. ✨

📦 Returns

ZLANHS comes back with this mapping, exactly:

ZLANHS = ( 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.

🧸 Parameters

okay, parameter time — every single one is a main character, so let’s give them their moment:

NORM

NORM is CHARACTER*1. It specifies the value to be returned in ZLANHS as described above. It’s basically the vibe selector for the return value. 💅

N

N is INTEGER. It’s the order of the matrix A. N >= 0. When N = 0, ZLANHS is set to zero. Literally zero, periodt. 🫶

A

A is COMPLEX*16 array, dimension (LDA,N). It’s the n by n upper Hessenberg matrix A; the part of A below the first sub-diagonal is not referenced. So that lower part can chill, bestie. 🌸

LDA

LDA is INTEGER. It’s the leading dimension of the array A. LDA >= max(N,1). It’s the stride queen and we respect her. 👑

WORK

WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced. So it only gets called up for the infinity-norm situation, iykyk. 🔥

👑 Author

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

Definition at line 108 of file zlanhs.f. 📍

👑 Author

Generated automatically by Doxygen for LAPACK from the source code. The robots handled this one, and honestly? They ate. 🤖✨

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source/version check, bestie: LAPACK, Version 3.12.0, page SRC/zlanhs.f(3). The original footer didn’t give a date, so I’m not inventing one — we keep it factual and cute. slay responsibly. 💖🎀