CLANGE(3)

📦 version 3.12.0, in opensuse-leap 16.0

💖 NAME 💖

okay so this is the Library Functions Manual page for CLANGE(3) — and the source file it points at is the iconic:

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

it's giving "we are deep in the LAPACK source tree and honestly? slay." 💅

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

  • real function CLANGE (norm, m, n, a, lda, work) — CLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix.

🦋 Function/Subroutine Documentation 🦋

the full signature is right here, bestie:

real function CLANGE (character norm, integer m, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) work)

and yes, same energy: CLANGE 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.

🎯 Purpose

CLANGE 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. that's the whole mission. 💖

💫 Returns 💫

CLANGE — here's the exact formula vibe:

!>
!>    CLANGE = ( 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.
!>

quick translation: norm1 is the maximum column sum, normI is the maximum row sum, and normF is the square root of the sum of squares.

important: max(abs(A(i,j))) is not a consistent matrix norm. periodt. 💀

🔧 Parameters 🔧

  • NORM — NORM is CHARACTER*1. it specifies the value to be returned in CLANGE as described above. choose your norm era wisely. ✨
  • M — M is INTEGER. the number of rows of the matrix A. M >= 0. when M = 0, CLANGE is set to zero. no rows, no drama. 🫶
  • N — N is INTEGER. the number of columns of the matrix A. N >= 0. when N = 0, CLANGE is set to zero. empty matrix? still valid, bestie. 🌸
  • A — A is COMPLEX array, dimension (LDA,N). the m by n matrix A. the main character matrix, literally. 👑
  • LDA — LDA is INTEGER. the leading dimension of the array A. LDA >= max(M,1). do not mess with the leading dimension, iykyk. 💅
  • WORK — WORK is REAL array, dimension (MAX(1,LWORK)), where LWORK >= M when NORM = 'I'; otherwise, WORK is not referenced. so if you're not doing the infinity-norm thing, WORK can just chill. 🧚

👑 Author 👑

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

Definition at line 114 of file clange.f.

🌸 Author 🌸

Generated automatically by Doxygen for LAPACK from the source code. 💖

and that's the sign-off, bestie: LAPACK Version 3.12.0, source path /home/abui...RC/clange.f(3). the footer doesn't print a date on this page, so we're not inventing one — no cap, no fake timestamp, just the version and source vibe. 🎀✨

📦 where this page comes from