SRC/clange.f(3)

💖 SRC/clange.f(3) 💖

Okay bestie, this one is straight out of the LAPACK Library Functions Manual, and it’s giving “tiny file, big norm energy.” We’re talking about SRC/clange.f, the home of CLANGE. 🫶

🌸 NAME 🌸

SRC/clange.f — that’s the file, periodt.

✨ 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 🦋

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

🌸 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 assignment, and it ate. 💅

💅 Returns 💅

CLANGE is one of these, depending on NORM:

!>
!>    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.
!>

Lowkey important: max(abs(A(i,j))) is not a consistent matrix norm. The manpage said it, so we’re saying it. 🫡

🍓 Parameters 🍓

• NORM — NORM is CHARACTER*1. Specifies the value to be returned in CLANGE as described above.
• M — M is INTEGER. The number of rows of the matrix A. M >= 0. When M = 0, CLANGE is set to zero.
• N — N is INTEGER. The number of columns of the matrix A. N >= 0. When N = 0, CLANGE is set to zero.
• A — A is COMPLEX array, dimension (LDA,N). The m by n matrix A.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(M,1).
• WORK — WORK is REAL array, dimension (MAX(1,LWORK)), where LWORK >= M 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 114 of file clange.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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That’s the whole vibe: LAPACK, Version 3.12.0, SRC/clange.f(3) — norm queen, signing off. 💖✨