ZLANSB(3)

okay bestie, this is ZLANSB(3) 💅 from the Library Functions Manual. file-path energy at the top: /home/abui...RC/zlansb.f(3). no cap, we're about to get into a double precision function that measures norms of a symmetric band matrix. 🦋

🎀 NAME 🎀

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zlansb.f — that's the source file this page is serving. 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. 💖

The full signature with all the types is giving very specific:

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

🛠️ Function/Subroutine Documentation 🛠️

Same function, now with the full type-coded signature:

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.

🎯 Purpose 🎯

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 whole assignment. 👑

📦 Returns 📦

The return value is literally ZLANSB, and the original spells out the menu like this:

!>
!>    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.
!>

🚨 real talk: max(abs(A(i,j))) is not a consistent matrix norm. The original says it, I'm not making it up. 💀

🧚 Parameters 🧚

NORM

NORM is CHARACTER*1. It specifies the value to be returned in ZLANSB as described above. (Yes, the above is the whole norm menu. Choose your fighter. 💅)

UPLO

UPLO is CHARACTER*1. It says 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. tiny matrix? zero matrix? respected either way. 🫶

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). It holds 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. (Not a human, just Doxygen doing its little auto-gen thing. 💖)

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💖 cute sign-off: source/version = LAPACK Version 3.12.0; footer path = /home/abui...RC/zlansb.f(3); and the footer's date stamp — acknowledged with love, not copied. mwah, bye bestie! 🎀✨