SRC/dlanhs.f(3)

💅 NAME 💅

SRC/dlanhs.f — literally the Fortran file that gives you dlanhs, bestie. It's the source for the LAPACK Library Functions Manual entry, and it's giving "quiet but essential," no cap.

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✨ SYNOPSIS ✨

Functions/Subroutines 🎀

double precision function dlanhs (norm, n, a, lda, work)

So what does it do? 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. That's the whole vibe. 🦋

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🌸 Function/Subroutine Documentation 🌸

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

Okay so real talk: 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. Four norms, one function, main character energy fr fr. 👑

🧚 PURPOSE 🧚

!> !> 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 ⭐

DLANHS — and here's the exact map of which norm you get back, bestie, copy it into your notes:

!> !> 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. !>

⚠️ Heads up: that last line is a real caveat, not decorative. max(abs(A(i,j))) is not a consistent matrix norm. The manpage said it, I'm saying it, write it on your mirror. 💀

🫶 PARAMETERS 🫶

• NORM — NORM is CHARACTER*1. Specifies the value to be returned in DLANHS as described above. That's it, that's the whole job. ✨

!> 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. Empty matrix? Still slays, returns zero. 🎀

!> 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. So don't stress about what's down there, it's not being read. 🙈

!> 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). Respect the constraint or else. 😭

!> 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. So it's only doing something for one specific NORM, and the rest of the time it's just sitting there being iconic and unused. 💜

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

👑 AUTHOR 👑

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

Definition at line 107 of file dlanhs.f. 📍

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💖 AUTHOR (the meta one) 💖

Generated automatically by Doxygen for LAPACK from the source code. Not a human, just a very diligent little doc generator doing its thing. 🦋

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🌈 And that's the whole page, bestie! LAPACK, Version 3.12.0, SRC/dlanhs.f(3) — go forth and norm responsibly. 💅✨🎀