DLANSB(3)

💖 NAME 💖

okay so bestie, this whole page is literally about this file path:

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

and yes, we’re in the Library Functions Manual for dlansb.f(3) — iconic.

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✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

• double precision function DLANSB (norm, uplo, n, k, ab, ldab, work) — no cap, 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.

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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)

okay so again, for the people in the back 💅 — 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 🎀

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

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.

iykyk, that last bit matters 🫶

🌸 Parameters 🌸

• NORM — NORM is CHARACTER*1. Specifies the value to be returned in DLANSB as described above.
• 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, DLANSB 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 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 — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= K+1.
• WORK — WORK is 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 🦋

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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mwah 💋 and that’s the whole vibe, bestie: this page is from LAPACK, Version 3.12.0, source footer path /home/abui...RC/dlansb.f(3) — and the footer didn’t list a date, so no fake date energy here 🙈✨