lanhb(3)

📦

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💖 lanhb(3) — lan{hb,sb}: Hermitian/symmetric matrix, banded 💖

okay so bestie, welcome to the Library Functions Manual ✨ this is the page for lanhb and honestly it's giving "norm energy" and we are obsessed. it's a long one so buckle up 🎀

🌸 NAME 🌸

lanhb — lan{hb,sb}: Hermitian/symmetric matrix, banded

✨ SYNOPSIS ✨

🔥 Functions 🔥

real function clanhb (norm, uplo, n, k, ab, ldab, work) — CLANHB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian band matrix. 💅
real function clansb (norm, uplo, n, k, ab, ldab, work) — CLANSB 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. ✨
double precision function dlansb (norm, uplo, n, k, ab, ldab, work) — 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. 🦋
real function slansb (norm, uplo, n, k, ab, ldab, work) — SLANSB 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. 🌸
double precision function zlanhb (norm, uplo, n, k, ab, ldab, work) — ZLANHB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian band matrix. 👑
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. ⭐

🌈 Detailed Description 🌈

(no cap: there's literally nothing extra here, the detailed tea is all in the function docs below 👇)

💜 Function Documentation 💜

🧚 real function clanhb (character norm, character uplo, integer n, integer k, complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) work) 🧚

CLANHB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian band matrix. main character of the whole page, honestly. 💅

🎀 Purpose 🎀

CLANHB 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 hermitian band matrix A, with k super-diagonals.

okay so it's literally just "what's the size of this matrix, bestie" — pick your flavor of norm and it hands it to you 🫶

⭐ Returns ⭐

here's the whole menu, keep it exact because the vibe check on this table is real:

   !>
   !>    CLANHB = ( 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.
   !>

ngl that last line is important: max(abs(A(i,j))) is not a consistent matrix norm. it said what it said 💀

🌸 Parameters 🌸

NORM — NORM is CHARACTER*1. it tells CLANHB which value to return, exactly like the menu up there says. ✨
UPLO — UPLO is CHARACTER*1. tells it whether the upper or lower triangular part of the band matrix A is supplied.
- = 'U': Upper triangular
- = 'L': Lower triangular
N — N is INTEGER. the order of the matrix A. N >= 0. and when N = 0, CLANHB is set to zero. periodt. 🎀
K — K is INTEGER. the number of super-diagonals or sub-diagonals of the band matrix A. K >= 0. 💅
AB — AB is COMPLEX array, dimension (LDAB,N). it holds the upper or lower triangle of the hermitian band matrix A, stored in the first K+1 rows of AB. the j-th column of A lives in the j-th column of the array AB like this:
- 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).

⚠️ and heads up: the imaginary parts of the diagonal elements need not be set and are assumed to be zero. so don't come for me if you left them blank, it's fine 🙈

LDAB — LDAB is INTEGER. the leading dimension of the array AB. LDAB >= K+1. fr fr. 🔥
WORK — WORK is REAL 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 130 of file clanhb.f.

🦋 real function clansb (character norm, character uplo, integer n, integer k, complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) work) 🦋

CLANSB 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. same energy, but symmetric this time — lowkey the chill twin of CLANHB 💜

🎀 Purpose 🎀

CLANSB 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 ⭐

   !>
   !>    CLANSB = ( 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.
   !>

same warning as before and it still matters: max(abs(A(i,j))) is not a consistent matrix norm. 😭

🌸 Parameters 🌸

NORM — NORM is CHARACTER*1. specifies the value to be returned in CLANSB, as described above. 💅
UPLO — UPLO is CHARACTER*1. tells it 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, CLANSB 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 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 sits in the j-th column of the array AB, like:
- 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 REAL 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 clansb.f.

💀 double precision function dlansb (character norm, character uplo, integer n, integer k, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) work) 💀

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. it's the double-precision sibling — more bits, same slay 🫶

🎀 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 = ( 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.
   !>

again: max(abs(A(i,j))) is not a consistent matrix norm. this is not me being dramatic, this is just facts 💅

🌸 Parameters 🌸

NORM — NORM is CHARACTER*1. specifies the value to be returned in DLANSB, as described above. ✨
UPLO — UPLO is CHARACTER*1. 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:
- 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

...and the last author-block crumbs for dlansb: big ups to Univ. of Colorado Denver and NAG Ltd. — and the receipt says Definition at line 127 of file dlansb.f. 🫶

🩷 real function `slansb`

real function slansb (character norm, character uplo, integer n, integer k, real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) work)

SLANSB 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

SLANSB 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

SLANSB

SLANSB = ( 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 — iconic behavior, but still not a consistent matrix norm. 😭

Parameters

NORM — NORM is CHARACTER*1. Specifies the value to be returned in SLANSB 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, SLANSB 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 REAL 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 REAL 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 127 of file slansb.f.

🧚 double precision function `zlanhb`

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

ZLANHB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian band matrix. 🔥

Purpose

ZLANHB 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 hermitian band matrix A, with k super-diagonals. 👑

Returns

ZLANHB

ZLANHB = ( 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'

Parameters

NORM — NORM is CHARACTER*1. Specifies the value to be returned in ZLANHB 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; = 'L': Lower triangular. ⭐
N — N is INTEGER. The order of the matrix A. N >= 0. When N = 0, ZLANHB 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 hermitian 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).

Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero. 🙈

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 130 of file zlanhb.f.

🦋 double precision function `zlansb`

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. 💜

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'

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. 🤖✨

Okay that’s the whole sparkly saga, bestie: LAPACK Version 3.12.0, manual page lanhb(3) — and the original footer didn’t print a date, so no cap, that’s the receipt. 💖👑

📦 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

lanhb(3)

💖 lanhb(3) — lan{hb,sb}: Hermitian/symmetric matrix, banded 💖

🌸 NAME 🌸

✨ SYNOPSIS ✨

🔥 Functions 🔥

🌈 Detailed Description 🌈

💜 Function Documentation 💜

🧚 real function clanhb (character norm, character uplo, integer n, integer k, complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) work) 🧚

🎀 Purpose 🎀

⭐ Returns ⭐

🌸 Parameters 🌸

👑 Author 👑

🦋 real function clansb (character norm, character uplo, integer n, integer k, complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) work) 🦋

🎀 Purpose 🎀

⭐ Returns ⭐

🌸 Parameters 🌸

👑 Author 👑

💀 double precision function dlansb (character norm, character uplo, integer n, integer k, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) work) 💀

🎀 Purpose 🎀

⭐ Returns ⭐

🌸 Parameters 🌸

👑 Author 👑

🩷 real function slansb

🧚 double precision function zlanhb

🦋 double precision function zlansb

🩷 real function `slansb`

🧚 double precision function `zlanhb`

🦋 double precision function `zlansb`