SRC/zlanhb.f(3)

💅 NAME

Okay bestie, this is SRC/zlanhb.f(3) from the Library Functions Manual — LAPACK business, specifically the zlanhb function page. No cap, it's giving Fortran realness. 🫶

✨ SYNOPSIS

Functions/Subroutines

       double precision function zlanhb (norm, uplo, n, k, ab, ldab, work)

ZLANHB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian band matrix. Iconic behavior, honestly. 💅

🌸 Function/Subroutine Documentation

   double precision function zlanhb (character norm, character uplo, integer n,
       integer k, complex*16, dimension( ldab, * ) ab, integer ldab, double
       precision, dimension( * ) work)

ZLANHB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian band matrix. That's the whole mood. ✨

🎯 Purpose

!>
!> ZLANHB  returns the value of the one norm,  or the Frobenius norm, or
!> the  infinity norm,  or the element of  largest absolute value  of an
!> n by n hermitian band matrix A,  with k super-diagonals.
!>

Literally the purpose section, served fresh. 🍓

🔥 Returns

!>
!>    ZLANHB = ( 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.
!>

Heads up bestie: max(abs(A(i,j))) is not a consistent matrix norm. The page said it, so I'm saying it. 💀

🧸 Parameters

NORM

NORM is CHARACTER*1. It specifies the value to be returned in ZLANHB as described above. Choose your fighter. 🎀

UPLO

UPLO is CHARACTER*1. It specifies whether the upper or lower triangular part of the band matrix A is supplied.

• = 'U': Upper triangular
• = 'L': Lower triangular

Upper or lower, pick one, bestie. 🦋

N

N is INTEGER. The order of the matrix A. N >= 0. When N = 0, ZLANHB is set to zero. Zero matrix? Zero answer. Periodt. ✨

K

K is INTEGER. The number of super-diagonals or sub-diagonals of the band matrix A. K >= 0. Band matrix bandwidth energy. 🎸

AB

AB is COMPLEX*16 array, dimension (LDAB,N). The upper or lower triangle of the hermitian band matrix A, stored in the first K+1 rows of AB. The j-th column of A is stored in the j-th column of the array AB as follows:

if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)   = A(i,j) for j<=i<=min(n,j+k).

Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero. So don't stress those diagonal imaginary bits, okay? 🫶

LDAB

LDAB is INTEGER. The leading dimension of the array AB. LDAB >= K+1. Respect the leading dimension. 💅

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. Sometimes workspace is booked and busy, sometimes it's not invited. 🎀

👑 Author

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

Definition at line 130 of file zlanhb.f. Line 130, noted. ⭐

💖 Author

Generated automatically by Doxygen for LAPACK from the source code. Auto-generated but still cute. 🌸

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Okay that's the whole page, bestie! Signing off with LAPACK Version 3.12.0 and the page id SRC/zlanhb.f(3) — mwah 💋✨