SRC/zlanhe.f(3)

🎀 NAME 🎀

SRC/zlanhe.f — from the Library Functions Manual, bestie. This is the page for zlanhe, and it's lowkey iconic. 💅

✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

• 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. 🫶

💜 Function/Subroutine Documentation 💜

🦋 Signature 🦋

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. ✨

🎯 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. No cap. 💖

🧮 Returns 🧮

ZLANHE returns ZLANHE, and here's the exact mapping from NORM to the result:

!>
!>    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.
!>

So: norm1 is the one norm of a matrix (maximum column sum), normI is the infinity norm of a matrix (maximum row sum), and normF is the Frobenius norm of a matrix (square root of sum of squares). And bestie, real talk: max(abs(A(i,j))) is not a consistent matrix norm. 🫶

🎛️ Parameters 🎛️

• NORM is CHARACTER*1 — specifies the value to be returned in ZLANHE as described above.
• 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 is INTEGER — the order of the matrix A. N >= 0. When N = 0, ZLANHE is set to 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 is INTEGER — the leading dimension of the array A. LDA >= max(N,1).
• 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. 💜

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. 🫶

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Sign-off time: this page is from LAPACK, Version 3.12.0, and the source path is SRC/zlanhe.f(3). The footer didn't list a date, so that's the whole footer vibe — iconic, honestly. 💖✨