CLANGB(3)

📦 version 3.12.0, in opensuse-leap 16.0

🦋 CLANGB — Library Functions Manual 🦋

okay so bestie, welcome to the CLANGB page 💅 this is the manual for /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/clangb.f and honestly? it's giving math girlie vibes and we're obsessed ✨

🌸 SYNOPSIS 🌸

Functions/Subroutines

real function CLANGB (norm, n, kl, ku, ab, ldab, work)

CLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix. no cap, that's the whole gig 🎀

🧚 Function/Subroutine Documentation 🧚

real function CLANGB (character norm, integer n, integer kl, integer ku,
    complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * )
    work)

CLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix. literally what it says on the tin, bestie 💖

✨ Purpose ✨

!> CLANGB returns the value of the one norm, or the Frobenius norm, or !> the infinity norm, or the element of largest absolute value of an !> n by n band matrix A, with kl sub-diagonals and ku super-diagonals.

so it's a norm girlie for a band matrix A that's n by n, with kl sub-diagonals and ku super-diagonals. she does four different norms and she does them well 😭🔥

💜 Returns 💜

CLANGB

!> CLANGB = ( 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 so the vibe check on the return value is: you pick your NORM letter and she gives you the matching norm. periodt 💅 but bestie, note that max(abs(A(i,j))) is not a consistent matrix norm — that's a warning, not a suggestion, okay? ⚠️

🌈 Parameters 🌈 (all the deets, no skipping)

  • NORM — NORM is CHARACTER*1. Specifies the value to be returned in CLANGB as described above. this is the "which norm do u want" button, pick your fighter 🎀
  • N — N is INTEGER. The order of the matrix A. N >= 0. When N = 0, CLANGB is set to zero. zero matrix? zero norm. it's giving minimalist queen ✨
  • KL — KL is INTEGER. The number of sub-diagonals of the matrix A. KL >= 0. the down-below diagonals, keep it non-negative bestie 💜
  • KU — KU is INTEGER. The number of super-diagonals of the matrix A. KU >= 0. the up-above diagonals, also non-negative, we don't do negative here 🙅‍♀️
  • AB — AB is COMPLEX array, dimension (LDAB,N). The band matrix A, stored in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows:
AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl)

this is the storage tea — the indexing is doing a little dance and you gotta respect it 🩰

  • LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KL+KU+1. the leading dimension gotta be at least KL+KU+1, no exceptions, she said what she said 💀
  • WORK — WORK is REAL array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced.

okay so WORK only gets invited to the party when NORM = 'I' and even then she needs LWORK >= N. otherwise she's literally not referenced. unbothered. moisturized. in her lane. 💅✨

👑 Author 👑

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

the academic icons behind the math, we stan 🫶

Definition at line 123 of file clangb.f.

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Generated automatically by Doxygen for LAPACK from the source code. this page is from LAPACK Version 3.12.0, dated the /home/abui...RC/clangb.f(3) era, and honestly? slay. go compute those norms bestie, you got this 💖✨🎀🦋

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