ZLANGE(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 ZLANGE(3) 💅

okay so this is a page from the Library Functions Manual and honestly? it's giving linear algebra royalty. LAPACK said "let me cook" and dropped ZLANGE on us, bestie. let's get into it 🫶

✨ NAME ✨

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

like, yes, the NAME section is literally just the file path. it's iconic in a chaotic way. that's the whole vibe. 💀

🌈 SYNOPSIS 🌈

Functions/Subroutines

double precision function ZLANGE (norm, m, n, a, lda, work)

ZLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix. no cap, that's the whole job and she does it flawlessly. 👑

🦋 Function/Subroutine Documentation 🦋

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

ZLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix. main character energy, zero notes. ✨

🎀 Purpose 🎀

so the actual purpose text is this:

!>
!> ZLANGE  returns the value of the one norm,  or the Frobenius norm, or
!> the  infinity norm,  or the  element of  largest absolute value  of a
!> complex matrix A.
!>

short, sweet, slays. four different norms, one function. she contains multitudes. 💜

⭐ Returns ⭐

ZLANGE returns:

!>
!>    ZLANGE = ( 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.
!>

okay the nested-parens ASCII art is a whole aesthetic and i respect it. read it like a little flowchart: pick your NORM letter, get your answer.

🚨 real talk though: max(abs(A(i,j))) is not a consistent matrix norm. the manpage says it, i'm saying it, we're all saying it. don't come for her. 🙈

💖 Parameters 💖

  • NORM — NORM is CHARACTER*1. it specifies the value to be returned in ZLANGE as described above. yes, just one character. she's low maintenance, she's decisive. 💅
  • M — M is INTEGER. the number of rows of the matrix A. M >= 0. when M = 0, ZLANGE is set to zero. empty vibes, zero result, we move on. 🍓
  • N — N is INTEGER. the number of columns of the matrix A. N >= 0. when N = 0, ZLANGE is set to zero. same energy, same slay. 🌸
  • A — A is COMPLEX*16 array, dimension (LDA,N). the m by n matrix A. this is the moment, this is the main event, the matrix herself. 👑
  • LDA — LDA is INTEGER. the leading dimension of the array A. LDA >= max(M,1). respect the leading dimension bestie, she is load-bearing. 🔥
  • WORK — WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= M when NORM = 'I'; otherwise, WORK is not referenced. so like… only the infinity norm even acknowledges she exists. rude but factual. 😭

🌟 Author 🌟

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

the whole squad really showed up for this one 🫶

Definition at line 114 of file zlange.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. not a human, just vibes and a parser. 🤖✨

and that's the whole page!! that's her!! 🎀

sign-off time 🌈💖 — this lil artifact is from LAPACK, Version 3.12.0, and it lives at /home/abui...RC/zlange.f(3) (the file header and footer both said so, and i would never gatekeep). mwah, go compute a norm, bestie 💅🦋

📦 where this page comes from