SRC/zlangb.f(3)

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version 3.12.1 · 7 versions
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💅 SRC/zlangb.f(3) — Library Functions Manual 💅

okay bestie, welcome to the SRC/zlangb.f(3) page from the Library Functions Manual. This is the whole vibe for ZLANGB, a double precision function that hands you a norm-ish value for a general band matrix. Band matrix storage is the main character here, and yes, she has rules.

✨ NAME ✨

SRC/zlangb.f — the LAPACK source page for zlangb, the norm-returning bestie for general band matrices.

🦋 SYNOPSIS 🦋

🫶 Functions/Subroutines 🫶

  • double precision function zlangb (norm, n, kl, ku, ab, ldab, work) — ZLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.

🌸 Function/Subroutine Documentation 🌸

double precision function zlangb (character norm, integer n, integer kl,
     integer ku, complex*16, dimension( ldab, * ) ab, integer ldab, double
     precision, dimension( * ) work)

ZLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.

🎀 Purpose 🎀

okay so here's the purpose, no cap: ZLANGB 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 band matrix A, with kl sub-diagonals and ku super-diagonals.

💖 Returns 💖

ZLANGB

ZLANGB = ( 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.

Lowkey important: max(abs(A(i,j))) is not a consistent matrix norm. The doc says it, I'm just making sure you saw it. 👀

🌈 Parameters 🌈

  • NORM — NORM is CHARACTER*1. Specifies the value to be returned in ZLANGB as described above.
  • N — N is INTEGER. The order of the matrix A. N >= 0. When N = 0, ZLANGB is set to zero.
  • KL — KL is INTEGER. The number of sub-diagonals of the matrix A. KL >= 0.
  • KU — KU is INTEGER. The number of super-diagonals of the matrix A. KU >= 0.
  • AB — AB is COMPLEX*16 array, dimension (LDAB,N). The band matrix A, stored in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows: AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
  • LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KL+KU+1.
  • WORK — WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced.

👑 Author 👑

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 123 of file zlangb.f.

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

xoxo, your LAPACK bestie 💖 — this iconic little page is from LAPACK Version 3.12.0, SRC/zlangb.f(3). stay hydrated and may your matrices always be banded correctly 🫶✨

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