SRC/zlansb.f(3)

🌸 NAME 🌸

okay so bestie, welcome to the SRC/zlansb.f page from the Library Functions Manual 💖 — yes, that’s the manual-page name folded in right here at the top, and we are not copy-pasting the header line, periodt 💅.

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

• double precision function zlansb (norm, uplo, n, k, ab, ldab, work) — ZLANSB 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. slay 💅

🦋 Function/Subroutine Documentation 🦋

double precision function zlansb (character norm, character uplo, integer n,
    integer k, complex*16, dimension( ldab, * ) ab, integer ldab, double
    precision, dimension( * ) work)

ZLANSB 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, that’s the whole function vibe ✨

🌈 Purpose 🌈

okay so ZLANSB 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. that’s the assignment, bestie 🫶

💖 Returns — ZLANSB 💖

ZLANSB = ( 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. that last bit is a real note, not just vibes 💅

🌟 Parameters 🌟

• NORM — NORM is CHARACTER*1. Specifies the value to be returned in ZLANSB 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, ZLANSB 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*16 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 at line 128 of file zlansb.f.

💅 Author 💅

Generated automatically by Doxygen for LAPACK from the source code.

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and that’s the whole page, bestie 🫶 — this one lives under LAPACK, Version 3.12.0, and the footer vibe is SRC/zlansb.f(3). mwah 💋✨