DLANHS(3)

💅 NAME 💅

okay so bestie, welcome to DLANHS(3) from the Library Functions Manual — and the “name” on this page is literally this whole file path:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlanhs.f

It’s the Fortran routine that returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix. slay. 💖

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

• double precision function DLANHS (norm, n, a, lda, work) — DLANHS 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 🌈

The full signature is exactly this, no cap:

double precision function DLANHS (character norm, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) work)

🎀 Purpose 🎀

Here’s the actual Doxygen block, preserved character-for-character so nobody comes for me:

           !>
           !> DLANHS  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 ⭐

It returns DLANHS, and the definition is giving very specific math-girl energy:

           !>
           !>    DLANHS = ( 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.
           !>

That last line matters, bestie: max(abs(A(i,j))) is not a consistent matrix norm. The manpage said it, so I’m saying it. 💀

🦋 Parameters 🦋

• NORM — NORM is CHARACTER*1. Specifies the value to be returned in DLANHS as described above.
• N — N is INTEGER. The order of the matrix A. N >= 0. When N = 0, DLANHS is set to zero.
• A — A is DOUBLE PRECISION array, dimension (LDA,N). The n by n upper Hessenberg matrix A; the part of A below the first sub-diagonal is not referenced.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(N,1).
• WORK — WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced.

🫶 Author 🫶

These absolute legends:

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

Definition at line 107 of file dlanhs.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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byeee 💖 — this cutie is from LAPACK Version 3.12.0, footer path /home/abui...RC/dlanhs.f(3), and the date slot is literally not printed on this page, so I’m not inventing one for you 🌸