lanhs(3)

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version 3.12.1 · 9 versions
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🌸 NAME 🌸

Okay bestie, this is lanhs(3) from the Library Functions Manual — the page for lanhs - lanhs: Hessenberg. Yes, the NAME line is a little redundant, but she's iconic. 💅

🌈 SYNOPSIS 🌈

Functions — four norm besties, all serving upper Hessenberg matrix realness. Signatures are exact, no cap:

real function clanhs (norm, n, a, lda, work)
double precision function dlanhs (norm, n, a, lda, work)
real function slanhs (norm, n, a, lda, work)
double precision function zlanhs (norm, n, a, lda, work)
  • clanhs — CLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix. 💖
  • dlanhs — DLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix. ✨
  • slanhs — SLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix. 🎀
  • zlanhs — ZLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix. 🦋

🦋 Detailed Description 🦋

Okay so the detailed description is basically the doorway to Function Documentation — no extra lore here, just the four norm besties below. 🫶

💖 Function Documentation 💖

🌟 real function clanhs 🌟

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

CLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix. She's giving norm energy. ✨

Purpose:

!>
!> CLANHS  returns the value of the one norm,  or the Frobenius norm, or
!> the  infinity norm,  or the  element of  largest absolute value  of a
!> Hessenberg matrix A.
!>

Returns:

CLANHS

!>
!>    CLANHS = ( 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.
!>

Translation, bestie: norm1 is the one norm (maximum column sum), normI is the infinity norm (maximum row sum), and normF is the Frobenius norm (square root of sum of squares). 🧮✨

🚨 Note from the source: max(abs(A(i,j))) is not a consistent matrix norm. We don't make the rules, we just report them.

Parameters:

  • NORM — NORM is CHARACTER*1. Specifies the value to be returned in CLANHS as described above.
  • N — N is INTEGER. The order of the matrix A. N >= 0. When N = 0, CLANHS is set to zero.
  • A — A is COMPLEX array, dimension (LDA,N). The n by n upper Hessenberg matrix A; the part of A below the first sub-diagonal 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'; otherwise, WORK is not referenced.

Author:

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

Definition at line 108 of file clanhs.f.

🌟 double precision function dlanhs 🌟

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

DLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix. Double precision, double slay. 💅

Purpose:

!>
!> DLANHS  returns the value of the one norm,  or the Frobenius norm, or
!> the  infinity norm,  or the  element of  largest absolute value  of a
!> Hessenberg matrix A.
!>

Returns:

DLANHS

!>
!>    DLANHS = ( 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 definitions as above, just with DLANHS in the main character seat: norm1 = one norm (maximum column sum), normI = infinity norm (maximum row sum), normF = Frobenius norm (square root of sum of squares). 🔥

🚨 Again for the people in the back: max(abs(A(i,j))) is not a consistent matrix norm.

Parameters:

  • NORM — NORM is CHARACTER*1. Specifies the value to be returned in DLANHS as described above.
  • N — N is INTEGER. The order of the matrix A. N >= 0. When N = 0, DLANHS is set to zero.
  • A — A is DOUBLE PRECISION array, dimension (LDA,N). The n by n upper Hessenberg matrix A; the part of A below the first sub-diagonal 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'; otherwise, WORK is not referenced.

Author:

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

Definition at line 107 of file dlanhs.f.

🌟 real function slanhs 🌟

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

SLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix. Real values, real vibes. 🌸

Purpose:

!>
!> SLANHS  returns the value of the one norm,  or the Frobenius norm, or
!> the  infinity norm,  or the  element of  largest absolute value  of a
!> Hessenberg matrix A.
!>

Returns:

SLANHS

!>
!>    SLANHS = ( 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.
!>

The lore: norm1 = one norm (maximum column sum), normI = infinity norm (maximum row sum), normF = Frobenius norm (square root of sum of squares). 🧚

🚨 Technical caveat, bestie: max(abs(A(i,j))) is not a consistent matrix norm.

Parameters:

  • NORM — NORM is CHARACTER*1. Specifies the value to be returned in SLANHS as described above.
  • N — N is INTEGER. The order of the matrix A. N >= 0. When N = 0, SLANHS is set to zero.
  • A — A is REAL array, dimension (LDA,N). The n by n upper Hessenberg matrix A; the part of A below the first sub-diagonal 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'; otherwise, WORK is not referenced.

Author:

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

Definition at line 107 of file slanhs.f.

🌟 double precision function zlanhs 🌟

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

ZLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix. Complex*16 energy, but make it norm. 💜

Purpose:

!>
!> ZLANHS  returns the value of the one norm,  or the Frobenius norm, or
!> the  infinity norm,  or the  element of  largest absolute value  of a
!> Hessenberg matrix A.
!>

Returns:

ZLANHS

!>
!>    ZLANHS = ( 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.
!>

Definitions stay iconic: norm1 = one norm (maximum column sum), normI = infinity norm (maximum row sum), normF = Frobenius norm (square root of sum of squares). 🌈

🚨 Final reminder from the source: max(abs(A(i,j))) is not a consistent matrix norm. Periodt.

Parameters:

  • NORM — NORM is CHARACTER*1. Specifies the value to be returned in ZLANHS as described above.
  • N — N is INTEGER. The order of the matrix A. N >= 0. When N = 0, ZLANHS is set to zero.
  • A — A is COMPLEX*16 array, dimension (LDA,N). The n by n upper Hessenberg matrix A; the part of A below the first sub-diagonal 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'; otherwise, WORK is not referenced.

Author:

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

Definition at line 108 of file zlanhs.f.

👑 Author 👑

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💖 Sign-off szn: source/version is LAPACK, Version 3.12.0; the original footer didn't print a date, so we're not inventing one, bestie. This is lanhs(3), and she ate. 🎀✨

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