lanhe(3)

📦

version 3.12.1 · 9 versions

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, in arch rolling

🎀 `lanhe(3)` — `lan{he,sy}`: Hermitian/symmetric matrix 🎀

💅 NAME 💅

lanhe — the whole lan{he,sy} squad: Hermitian/symmetric matrix norm functions. 💖

✨ SYNOPSIS ✨

🌸 Functions 🌸

real function clanhe (norm, uplo, n, a, lda, work) — CLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix. 💫
real function clansy (norm, uplo, n, a, lda, work) — CLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix. 🦋
double precision function dlansy (norm, uplo, n, a, lda, work) — DLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix. 💜
real function slansy (norm, uplo, n, a, lda, work) — SLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix. 🌸
double precision function zlanhe (norm, uplo, n, a, lda, work) — ZLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix. 🔥
double precision function zlansy (norm, uplo, n, a, lda, work) — ZLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix. ⭐

🦋 Detailed Description 🦋

okay so this page is the function-by-function breakdown for the lan{he,sy} family. We're doing signatures, purposes, return values, parameters, authors, and source-line receipts. Let's go, bestie. 🫶

👑 Function Documentation 👑

💖 `clanhe` — real function 💖

real function clanhe (character norm, character uplo, integer n, complex,
       dimension( lda, * ) a, integer lda, real, dimension( * ) work)

CLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix. That's the whole vibe. 💅

🎯 Purpose

CLANHE gives back the one norm, the Frobenius norm, the infinity norm, or the element of largest absolute value of a complex hermitian matrix A. ✨

🌟 Returns

The return value maps like this, literally:

!>
!>    CLANHE = ( 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's straight from the source, no cap. 💀

🧾 Parameters

NORM — NORM is CHARACTER*1. Specifies the value to be returned in CLANHE as described above. ✨
UPLO — UPLO is CHARACTER*1. Specifies whether the upper or lower triangular part of the hermitian matrix A is to be referenced.
- = 'U': Upper triangular part of A is referenced
- = 'L': Lower triangular part of A is referenced
N — N is INTEGER. The order of the matrix A. N >= 0. When N = 0, CLANHE is set to zero. 🎀
A — A is COMPLEX array, dimension (LDA,N). The hermitian matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero. 🫶
LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(N,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 123 of file clanhe.f.

🦋 `clansy` — real function 🦋

real function clansy (character norm, character uplo, integer n, complex,
       dimension( lda, * ) a, integer lda, real, dimension( * ) work)

CLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix. 💫

🎯 Purpose

CLANSY gives back the one norm, the Frobenius norm, the infinity norm, or the element of largest absolute value of a complex symmetric matrix A. ✨

🌟 Returns

The return value maps like this, literally:

!>
!>    CLANSY = ( 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 CLANSY as described above. ✨
UPLO — UPLO is CHARACTER*1. Specifies whether the upper or lower triangular part of the symmetric matrix A is to be referenced.
- = 'U': Upper triangular part of A is referenced
- = 'L': Lower triangular part of A is referenced
N — N is INTEGER. The order of the matrix A. N >= 0. When N = 0, CLANSY is set to zero. 🎀
A — A is COMPLEX array, dimension (LDA,N). The symmetric matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. 🫶
LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(N,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 122 of file clansy.f.

💙 `dlansy` — double precision function 💙

double precision function dlansy (character norm, character uplo, integer n,
       double precision, dimension( lda, * ) a, integer lda, double precision,
       dimension( * ) work)

DLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix. 💖

🎯 Purpose

DLANSY gives back the one norm, the Frobenius norm, the infinity norm, or the element of largest absolute value of a real symmetric matrix A. ✨

🌟 Returns

The return value maps like this, literally:

!>
!>    DLANSY = ( 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 DLANSY as described above. ✨
UPLO — UPLO is CHARACTER*1. Specifies whether the upper or lower triangular part of the symmetric matrix A is to be referenced.
- = 'U': Upper triangular part of A is referenced
- = 'L': Lower triangular part of A is referenced
N — N is INTEGER. The order of the matrix A. N >= 0. When N = 0, DLANSY is set to zero. 🎀
A — A is DOUBLE PRECISION array, dimension (LDA,N). The symmetric matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. 🫶
LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(N,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 121 of file dlansy.f.

🫶 `real function slansy (...)`

   real function slansy (character norm, character uplo, integer n, real,
       dimension( lda, * ) a, integer lda, real, dimension( * ) work)

Okay so SLANSY is the vibe-check function for a real symmetric matrix — it hands you back the 1-norm, or the Frobenius norm, or the infinity norm, or just the single largest absolute value chillin' in the matrix. Pick your fighter 💅

✨ Purpose

!>
!> SLANSY  returns the value of the one norm,  or the Frobenius norm, or
!> the  infinity norm,  or the  element of  largest absolute value  of a
!> real symmetric matrix A.
!>

🎀 Returns

!>
!>    SLANSY = ( 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: norm1 = max column sum, normI = max row sum, normF = √(sum of squares). And heads up bestie — max(abs(A(i,j))) is not a consistent matrix norm, so don't go around treating it like one 😭

🌸 Parameters

NORM — NORM is CHARACTER*1, and it says which value SLANSY should return, exactly as described above. You're literally choosing your own adventure here.

!>          NORM is CHARACTER*1
!>          Specifies the value to be returned in SLANSY as described
!>          above.
!>

UPLO — UPLO is CHARACTER*1. Tells the routine which triangle of the symmetric matrix A to actually look at.
- = 'U': Upper triangular part of A is referenced
- = 'L': Lower triangular part of A is referenced

!>          UPLO is CHARACTER*1
!>          Specifies whether the upper or lower triangular part of the
!>          symmetric matrix A is to be referenced.
!>          = 'U':  Upper triangular part of A is referenced
!>          = 'L':  Lower triangular part of A is referenced
!>

N — N is INTEGER, the order of the matrix A. N >= 0. And when N = 0, SLANSY is set to zero. No matrix, no problem 💀

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.  When N = 0, SLANSY is
!>          set to zero.
!>

A — A is REAL array, dimension (LDA,N). It's the symmetric matrix itself. If UPLO = 'U', the leading n by n upper triangular part of A holds the upper triangular part of the matrix, and the strictly lower triangular part is just… not referenced, ignored, uninvited 🙈. If UPLO = 'L', the leading n by n lower triangular part holds the lower triangular part, and the strictly upper triangular part is not referenced.

!>          A is REAL array, dimension (LDA,N)
!>          The symmetric matrix A.  If UPLO = 'U', the leading n by n
!>          upper triangular part of A contains the upper triangular part
!>          of the matrix A, and the strictly lower triangular part of A
!>          is not referenced.  If UPLO = 'L', the leading n by n lower
!>          triangular part of A contains the lower triangular part of
!>          the matrix A, and the strictly upper triangular part of A is
!>          not referenced.
!>

LDA — LDA is INTEGER, the leading dimension of the array A. Constraint: LDA >= max(N,1). Respect the leading dimension, it's the main character of array indexing 👑

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(N,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. So it's only pulling up to the function when it's actually needed 🫶

!>          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 121 of file slansy.f.

🦋 `double precision function zlanhe (...)`

   double precision function zlanhe (character norm, character uplo, integer n,
       complex*16, dimension( lda, * ) a, integer lda, double precision,
       dimension( * ) work)

Now this one's ZLANHE and it's the same whole situation but for a complex Hermitian matrix ✨ Same four norm options, same energy.

💜 Purpose

!>
!> ZLANHE  returns the value of the one norm,  or the Frobenius norm, or
!> the  infinity norm,  or the  element of  largest absolute value  of a
!> complex hermitian matrix A.
!>

🎀 Returns

!>
!>    ZLANHE = ( 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 deal, same caveat — max(abs(A(i,j))) is not a consistent matrix norm, bestie, we been knew 🔥

🌸 Parameters

NORM — NORM is CHARACTER*1, specifies the value to be returned in ZLANHE as described above.

!>          NORM is CHARACTER*1
!>          Specifies the value to be returned in ZLANHE as described
!>          above.
!>

UPLO — UPLO is CHARACTER*1, says whether the upper or lower triangular part of the hermitian matrix A gets referenced.
- = 'U': Upper triangular part of A is referenced
- = 'L': Lower triangular part of A is referenced

!>          UPLO is CHARACTER*1
!>          Specifies whether the upper or lower triangular part of the
!>          hermitian matrix A is to be referenced.
!>          = 'U':  Upper triangular part of A is referenced
!>          = 'L':  Lower triangular part of A is referenced
!>

N — N is INTEGER, the order of the matrix A. N >= 0. When N = 0, ZLANHE is set to zero.

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.  When N = 0, ZLANHE is
!>          set to zero.
!>

A — A is COMPLEX*16 array, dimension (LDA,N). The hermitian matrix. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix, and the strictly lower triangular part is not referenced. If UPLO = 'L', the leading n by n lower triangular part contains the lower triangular part, and the strictly upper triangular part is not referenced. Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero — so don't stress about them, they're literally assumed to be zero 🫶

!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          The hermitian matrix A.  If UPLO = 'U', the leading n by n
!>          upper triangular part of A contains the upper triangular part
!>          of the matrix A, and the strictly lower triangular part of A
!>          is not referenced.  If UPLO = 'L', the leading n by n lower
!>          triangular part of A contains the lower triangular part of
!>          the matrix A, and the strictly upper triangular part of A is
!>          not referenced. Note that the imaginary parts of the diagonal
!>          elements need not be set and are assumed to be zero.
!>

LDA — LDA is INTEGER, the leading dimension of the array A. LDA >= max(N,1).

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(N,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.

!>          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 123 of file zlanhe.f.

🌈 `double precision function zlansy (...)`

   double precision function zlansy (character norm, character uplo, integer n,
       complex*16, dimension( lda, * ) a, integer lda, double precision,
       dimension( * ) work)

And last but absolutely not least: ZLANSY — norms for a complex symmetric matrix. Note: symmetric, not hermitian. Different queen, different rules 💅

⭐ Purpose

!>
!> ZLANSY  returns the value of the one norm,  or the Frobenius norm, or
!> the  infinity norm,  or the  element of  largest absolute value  of a
!> complex symmetric matrix A.
!>

🎀 Returns

!>
!>    ZLANSY = ( 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.
!>

Once again for the people in the back: that max-abs thing? Not a consistent matrix norm. Periodt 🎤

🌸 Parameters

NORM — NORM is CHARACTER*1, specifies the value to be returned in ZLANSY as described above.

!>          NORM is CHARACTER*1
!>          Specifies the value to be returned in ZLANSY as described
!>          above.
!>

UPLO — UPLO is CHARACTER*1, specifies whether the upper or lower triangular part of the symmetric matrix A is to be referenced.
- = 'U': Upper triangular part of A is referenced
- = 'L': Lower triangular part of A is referenced

!>          UPLO is CHARACTER*1
!>          Specifies whether the upper or lower triangular part of the
!>          symmetric matrix A is to be referenced.
!>          = 'U':  Upper triangular part of A is referenced
!>          = 'L':  Lower triangular part of A is referenced
!>

N — N is INTEGER, the order of the matrix A. N >= 0. When N = 0, ZLANSY is set to zero.

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.  When N = 0, ZLANSY is
!>          set to zero.
!>

A — A is COMPLEX*16 array, dimension (LDA,N). The symmetric matrix. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix, and the strictly lower triangular part is not referenced. If UPLO = 'L', the leading n by n lower triangular part contains the lower triangular part, and the strictly upper triangular part is not referenced. (No imaginary-diagonal note here — that's a hermitian thing, not this one 👀)

!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          The symmetric matrix A.  If UPLO = 'U', the leading n by n
!>          upper triangular part of A contains the upper triangular part
!>          of the matrix A, and the strictly lower triangular part of A
!>          is not referenced.  If UPLO = 'L', the leading n by n lower
!>          triangular part of A contains the lower triangular part of
!>          the matrix A, and the strictly upper triangular part of A is
!>          not referenced.
!>

LDA — LDA is INTEGER, the leading dimension of the array A. LDA >= max(N,1).

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(N,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.

!>          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 122 of file zlansy.f.

💖 Author

Generated automatically by Doxygen for LAPACK from the source code.

ngl bestie, a robot wrote this whole page for us — Doxygen generated it straight from the LAPACK source code, so if something's off, blame the source, not me 😭

And that's a wrap on lanhe(3)! This absolute icon of a page is from LAPACK, Version 3.12.0 — go forth and norm your matrices responsibly 🌸💅✨

📦 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

lanhe(3)

🎀 lanhe(3) — lan{he,sy}: Hermitian/symmetric matrix 🎀

💅 NAME 💅

✨ SYNOPSIS ✨

🌸 Functions 🌸

🦋 Detailed Description 🦋

👑 Function Documentation 👑

💖 clanhe — real function 💖

🎯 Purpose

🌟 Returns

🧾 Parameters

🫶 Author

🦋 clansy — real function 🦋

🎯 Purpose

🌟 Returns

🧾 Parameters

🫶 Author

💙 dlansy — double precision function 💙

🎯 Purpose

🌟 Returns

🧾 Parameters

🫶 Author

🫶 real function slansy (...)

✨ Purpose

🎀 Returns

🌸 Parameters

👑 Author

🦋 double precision function zlanhe (...)

💜 Purpose

🎀 Returns

🌸 Parameters

👑 Author

🌈 double precision function zlansy (...)

⭐ Purpose

🎀 Returns

🌸 Parameters

👑 Author

💖 Author

🎀 `lanhe(3)` — `lan{he,sy}`: Hermitian/symmetric matrix 🎀

💖 `clanhe` — real function 💖

🦋 `clansy` — real function 🦋

💙 `dlansy` — double precision function 💙

🫶 `real function slansy (...)`

🦋 `double precision function zlanhe (...)`

🌈 `double precision function zlansy (...)`