SRC/dlansb.f(3)

💖 NAME 💖

Okay so this page is SRC/dlansb.f(3) from the Library Functions Manual, and it's literally the group-chat explainer for DLANSB, bestie. SRC/dlansb.f is the file, and the function is giving main-character linear-algebra energy. 💅

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✨ SYNOPSIS ✨

🧸 Functions/Subroutines

double precision function dlansb (norm, uplo, n, k, ab, ldab, work)

DLANSB 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. No cap. ✨

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🫶 Function/Subroutine Documentation 🫶

double precision function dlansb (character norm, character uplo, integer n,
     integer k, double precision, dimension( ldab, * ) ab, integer ldab,
     double precision, dimension( * ) work)

Same vibe, full signature: DLANSB 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

Bestie, here's the exact purpose block, preserved because we do not play with technical details:

!>
!> DLANSB  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

DLANSB returns one of these, depending on NORM:

!>
!>    DLANSB = ( 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.
!>

Heads up, bestie: max(abs(A(i,j))) is not a consistent matrix norm. That's not me being dramatic, that's literally in the page. 💀

🧩 Parameters

• NORM — CHARACTER*1. Specifies the value to be returned in DLANSB as described above. 👑
• UPLO — 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 — INTEGER. The order of the matrix A. N >= 0. When N = 0, DLANSB is set to zero. 🫶
• K — INTEGER. The number of super-diagonals or sub-diagonals of the band matrix A. K >= 0. ✨
• AB — DOUBLE PRECISION 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 — INTEGER. The leading dimension of the array AB. LDAB >= K+1. 🌸
• WORK — DOUBLE PRECISION 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 127 of file dlansb.f.

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🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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Cute sign-off: source/version is LAPACK, Version 3.12.0, page SRC/dlansb.f(3) — and the original footer doesn't print a date, so we're not inventing one, bestie. Periodt. 💖✨