CLANSB(3)

💖 NAME 💖

Okay bestie, welcome to the clansb.f(3) page — header vibe is /home/abui...RC/clansb.f(3) and it lives in the Library Functions Manual. The NAME section is literally this whole path, no extra lore:

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

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

real function CLANSB (norm, uplo, n, k, ab, ldab, work)
    CLANSB returns the value of the 1-norm, or the Frobenius norm, or
    the infinity norm, or the element of largest absolute value of a
    symmetric band matrix.

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🦋 Function/Subroutine Documentation 🦋

This is the full signature, bestie — copy it exactly, no autocorrect:

real function CLANSB (character norm, character uplo, integer n, integer k,
    complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * )
    work)

And the one-liner is: CLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix.

💜 Purpose 💜

Here's the exact purpose block, untouched because it's doing main character work:

!>
!> CLANSB  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 symmetric band matrix A,  with k super-diagonals.
!>

🎀 Returns 🎀

Returns: CLANSB. And the return menu is exactly this:

!>
!>    CLANSB = ( 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.
!>

🍓 Parameters 🍓

• NORM — NORM is CHARACTER*1; specifies the value to be returned in CLANSB as described above. It's the norm selector, iykyk.
• UPLO — UPLO is CHARACTER*1; specifies whether the upper or lower triangular part of the band matrix A is supplied:

= 'U':  Upper triangular part is supplied
= 'L':  Lower triangular part is supplied

• N — N is INTEGER; the order of the matrix A. N >= 0. When N = 0, CLANSB is set to zero.
• K — K is INTEGER; the number of super-diagonals or sub-diagonals of the band matrix A. K >= 0.
• AB — AB is COMPLEX array, dimension (LDAB,N); the upper or lower triangle of the symmetric band matrix A, stored in the first K+1 rows of AB. The j-th column of A is stored in the j-th column of the array AB as follows:

if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)   = A(i,j) for j<=i<=min(n,j+k).

• LDAB — LDAB is INTEGER; the leading dimension of the array AB. LDAB >= K+1.
• WORK — WORK is REAL array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is not referenced.

👑 Author 👑

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

Definition at line 128 of file clansb.f.

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🫶 Author 🫶

This page was Generated automatically by Doxygen for LAPACK from the source code. Slay, automation.

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Cute lil sign-off: this is LAPACK Version 3.12.0, and the footer path is /home/abui...RC/clansb.f(3). Byeee, go compute those norms responsibly 💅✨