langb(3)

📦

version 3.12.1 · 9 versions

3.12.1 · arch rolling (latest)
3.12.0 · opensuse-leap 16.0
3.12.1 · ubuntu stonking
3.12.1 · ubuntu questing
3.12.0 · ubuntu noble
3.12.0 · ubuntu noble
3.12.0 · centos-stream 10, fedora 43, fedora 44
3.12.1 · ubuntu resolute
3.12.1 · debian trixie

💅 NAME

langb(3) — langb: general matrix, banded Library Functions Manual · banded matrix norm bestie energy ✨

okay so langb(3) is the manual page for the langb family, and it is literally giving general matrix, banded. Keep that name in your head, bestie 💖

✨ SYNOPSIS

Here are the four functions, and yes they are all serving norm realness:

real function clangb (norm, n, kl, ku, ab, ldab, work) — CLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix. 🦋
double precision function dlangb (norm, n, kl, ku, ab, ldab, work) — DLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix. 💜
real function slangb (norm, n, kl, ku, ab, ldab, work) — SLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix. 🌸
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. 🎀

🌸 Detailed Description

okay so this is the "details live here" zone, and the function documentation is right below. No filler, just lore. 💫

🎀 Function Documentation

💖 real function `clangb`

CLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix. That's the whole assignment, bestie ✨

   real function clangb (character norm, integer n, integer kl, integer ku,
       complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * )
       work)

🎯 Purpose

CLANGB 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. That is the vibe check, no cap 💅

🌀 Returns

CLANGB is giving:

!>
!>    CLANGB = ( 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.
!>

🧚 Parameters

NORM — NORM is CHARACTER*1. It specifies the value to be returned in CLANGB as described above. 👑
N — N is INTEGER. The order of the matrix A. N >= 0. When N = 0, CLANGB 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 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 REAL 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 clangb.f.

💜 double precision function `dlangb`

DLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix. Same energy, double precision edition 💜

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

🎯 Purpose

DLANGB 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. periodt 💅

🌀 Returns

DLANGB is giving:

!>
!>    DLANGB = ( 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.
!>

🧚 Parameters

NORM — NORM is CHARACTER*1. It specifies the value to be returned in DLANGB as described above. 👑
N — N is INTEGER. The order of the matrix A. N >= 0. When N = 0, DLANGB 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 DOUBLE PRECISION 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 122 of file dlangb.f.

🌸 real function `slangb`

SLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix. Real precision, real slay 🌸

   real function slangb (character norm, integer n, integer kl, integer ku,
       real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) work)

🎯 Purpose

SLANGB 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. iconic behavior 💅

🌀 Returns

SLANGB is giving:

!>
!>    SLANGB = ( 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.
!>

🧚 Parameters

NORM — NORM is CHARACTER*1. It specifies the value to be returned in SLANGB as described above. 👑
N — N is INTEGER. The order of the matrix A. N >= 0. When N = 0, SLANGB 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 REAL 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 REAL 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 122 of file slangb.f.

🎀 double precision function `zlangb`

ZLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix. Complex*16 main character energy 🎀

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

🎯 Purpose

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 is giving:

!>
!>    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.
!>

🧚 Parameters

NORM — NORM is CHARACTER*1. It specifies the value to be returned in ZLANGB as described above. 👑
N — N is INTEGER.
N — INTEGER. It's the order of the matrix A, bestie. N >= 0. And lowkey the cutest edge case ever: when N = 0, ZLANGB is set to zero. That's it. Nothing to compute. She said "no matrix, no problem" 💅
KL — INTEGER. The number of sub-diagonals of the matrix A. KL >= 0. Think of it as how far the tea spills below the main diagonal 🫶
KU — INTEGER. The number of super-diagonals of the matrix A. KU >= 0. And this one's how far it spills above the diagonal. Iconic symmetry, no cap ✨
AB — COMPLEX*16 array, dimension (LDAB,N). Okay so this is the band matrix A, but stored in rows 1 to KL+KU+1. The j-th column of A lives in the j-th column of the array AB, and the mapping is literally this:

AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).

Memorize that indexing formula or perish, iykyk 😭🔥

LDAB — INTEGER. The leading dimension of the array AB. The vibe check it must pass: LDAB >= KL+KU+1. Do not test her on this one 🎀
WORK — DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced. So like... if you're not doing the 'I' norm, she literally does not care about your WORK array. She's not looking. She's not referencing it. Leave her alone 🙈

💖 AUTHOR 💖

The legends behind this one, fr fr:

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 123 of file zlangb.f.

🌈 AUTHOR (generated edition) 🌈

Generated automatically by Doxygen for LAPACK from the source code. Not a human, just a very diligent little robot doing her thing 🤖✨

Okay that's the whole page, bestie — you made it to the end and you ATE. Go forth and call ZLANGB responsibly 💜

This page ships with LAPACK, Version 3.12.0, and the page itself is langb(3) — mwah, mwah, and goodnight 🎀💋

📦 where this page comes from

arch rolling: lapack-doc 3.12.1-2 · custom
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash-1017 on 2026-11-04: a language model's rewrite of the original, under its terms

langb(3)

💅 NAME

✨ SYNOPSIS

🌸 Detailed Description

🎀 Function Documentation

💖 real function clangb

🎯 Purpose

🌀 Returns

🧚 Parameters

👑 Author

💜 double precision function dlangb

🎯 Purpose

🌀 Returns

🧚 Parameters

👑 Author

🌸 real function slangb

🎯 Purpose

🌀 Returns

🧚 Parameters

👑 Author

🎀 double precision function zlangb

🎯 Purpose

🌀 Returns

🧚 Parameters

💖 AUTHOR 💖

🌈 AUTHOR (generated edition) 🌈

💖 real function `clangb`

💜 double precision function `dlangb`

🌸 real function `slangb`

🎀 double precision function `zlangb`