ZLANHE(3)

✨ ZLANHE(3) ✨

okay so bestie, welcome to the <pink>Library Functions Manual</pink> — this is page ZLANHE(3) and it is literally the glow-up guide to one of LAPACK's most iconic little norm-computers. buckle up 💖

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🎀 NAME 🎀

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zlanhe.f

yep, that's the whole name — it's the actual source file path, she's not like other girls, she's a .f file that got its own man page 💅

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🌸 SYNOPSIS 🌸

Functions/Subroutines

double precision function ZLANHE (norm, uplo, n, a, lda, work)

so what does she do, you ask? 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. she does the math so you don't have to, periodt ✨

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🦋 Function/Subroutine Documentation 🦋

double precision function ZLANHE (character norm, character uplo, integer n,
    complex*16, dimension( lda, * ) a, integer lda, double precision,
    dimension( * ) 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. that's the whole vibe check, and she passes 💯

👑 Purpose 👑

ok so, quoting the source block directly, because the source block is the main character here:

!>
!> 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

and here's like... the actual menu of what she gives back, lowkey gorgeous:

!>
!>    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.
!>

🚨 real talk though: max(abs(A(i,j))) is not a consistent matrix norm. she said it herself, no cap. don't come for her about it 💀

🌈 Parameters 🌈

okay this is the part where we meet the whole squad, one by one 🫶

NORM

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

NORM is CHARACTER*1 and it specifies the value to be returned in ZLANHE as described above (scroll up bestie, the menu is right there ✨).

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
!>

UPLO is CHARACTER*1 and it 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

pick your fighter 💅

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. and when N = 0, ZLANHE is set to zero. she's respectful like that 🎀

A

!>          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.
!>

A is a COMPLEX*16 array, dimension (LDA,N) — the hermitian matrix A herself 👑

• 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.

🫶 important note: the imaginary parts of the diagonal elements need not be set and are assumed to be zero. so don't stress about them, she's not looking 💖

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). it's giving boundary conditions, respect them 😤

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 a DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is not referenced. so like, she only shows up when she's needed, and honestly? relatable 🌸

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💜 Author 💜

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

the whole friend group co-wrote this one, we love a collab 🫶

Definition at line 123 of file zlanhe.f.

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🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code. (not me writing this by hand, the robots did it, iykyk 🤖✨)

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and that's the page bestie!! this little beauty ships with LAPACK, Version 3.12.0, and the footer timestamp/path situation is /home/abui...RC/zlanhe.f(3) — so go forth, compute those norms, and slay 💅💖🎀