SLANSB(3)

💅 NAME

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

okay so real talk, bestie, you're in the LAPACK corner of the manual and this whole page is literally just that one file. that's the name. that's the whole name section. iconic minimalism, no notes 🎀

---

✨ SYNOPSIS

🦋 Functions/Subroutines

real function SLANSB (norm, uplo, n, k, ab, ldab, work)
    SLANSB 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.

---

🌸 Function/Subroutine Documentation

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

SLANSB 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. that's the whole gig. it does not solve anything, it does not factor anything, it just looks at your matrix and reports a number. main character energy tbh 👑

🍓 Purpose

!>
!> SLANSB  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.
!>

so like. an n by n symmetric band matrix A, with k super-diagonals. it measures it. that's it. that's the function. 🫶

🧚 Returns

SLANSB — and here's exactly what comes back, depending on the NORM you picked, no cap:

!>
!>    SLANSB = ( 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.
!>

breaking that down for you because the ASCII art is giving ancient runes:

• NORM = 'M' or 'm' → max(abs(A(i,j)))
• NORM = '1', 'O' or 'o' → norm1(A), the one norm (maximum column sum)
• NORM = 'I' or 'i' → normI(A), the infinity norm (maximum row sum)
• NORM = 'F', 'f', 'E' or 'e' → normF(A), the Frobenius norm (square root of sum of squares)

⚠️ heads up bestie, and this is important: max(abs(A(i,j))) is not a consistent matrix norm. the manpage says it, i'm saying it, we're all saying it. do not come for me in the replies. 💀

💖 Parameters

🌟 NORM

NORM is CHARACTER*1. it specifies the value to be returned in SLANSB as described above. it's the little switch that decides which norm you get, so pick your fighter wisely. ✨

🌟 UPLO

UPLO is CHARACTER*1. it 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. and when N = 0, SLANSB is set to zero — like, it just returns zero, that's the vibe, nothing to measure, nothing to report. 🦋

🌟 K

K is INTEGER. the number of super-diagonals or sub-diagonals of the band matrix A. K >= 0. this is the band width, the thing that makes it a band matrix and not a whole entire square. 🌈

🌟 AB

AB is REAL array, dimension (LDAB,N). it's 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).

read those index expressions slowly, they're the whole personality of the function. 💅

🌟 LDAB

LDAB is INTEGER. the leading dimension of the array AB. LDAB >= K+1. it's a constraint, it's non-negotiable, it's giving boundaries. 🎀

🌟 WORK

WORK is REAL array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is not referenced. so sometimes it's the hardest-working array in the room and sometimes it's literally just sitting there unused, and honestly? relatable. 😭

👑 Author

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

four whole institutions. a whole squad. the group chat that raised this function. 🫶

Definition at line 127 of file slansb.f.

---

⭐ Author

(yes, another one, we love a double author credit ✨)

Generated automatically by Doxygen for LAPACK from the source code. not a human, not a poet, just Doxygen doing its little thing. 🤖

---

okay bestie that's the whole page!! go forth and norm your symmetric band matrices 💖

— signed off with love by LAPACK, Version 3.12.0, from /home/abui...RC/slansb.f(3) 🎀💅🦋