CLANHE(3)

🦋 CLANHE(3) — Library Functions Manual 🦋

okay bestie, welcome to the clanhe.f(3) page — it’s giving LAPACK library function realness, and we’re gonna get through every single detail together. no cap. 💅

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🌸 NAME 🌸

The exact file path is:

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

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✨ SYNOPSIS ✨

💅 Functions/Subroutines

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. iconic behavior, honestly. 🫶

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🌈 Function/Subroutine Documentation 🌈

🧚 real function CLANHE

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. literally the whole main character energy of this page. ✨

💖 Purpose

okay so, for real: CLANHE 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. that’s the vibe check. 🦋

🎀 Returns

The return value is CLANHE, and here’s the exact formula situation:

!>    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.
!>

Translation for the besties: norm1 is the one norm of a matrix, aka the maximum column sum. normI is the infinity norm of a matrix, aka the maximum row sum. normF is the Frobenius norm of a matrix, aka the square root of sum of squares. And important: max(abs(A(i,j))) is not a consistent matrix norm. periodt. 💀

🍓 Parameters

• NORM — NORM is CHARACTER*1. It specifies the value to be returned in CLANHE as described above. ✨
• UPLO — UPLO is CHARACTER*1. 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
• 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. 💜

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👑 Author

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

Definition at line 123 of file clanhe.f.

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💜 Author

Generated automatically by Doxygen for LAPACK from the source code.

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💖 cute sign-off: this is LAPACK Version 3.12.0, with footer path /home/abui...RC/clanhe.f(3) — and that’s the whole page, bestie. mwah! 🎀✨