SRC/clanhb.f(3)

🌸 NAME 🌸

okay so bestie, this is the Library Functions Manual entry for SRC/clanhb.f — yes, that's the (3) section vibe, and we're about to get into Hermitian band matrix norm energy 💅✨

✨ SYNOPSIS ✨

Functions/Subroutines

       real function clanhb (norm, uplo, n, k, ab, ldab, work)

CLANHB 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. 🦋

💻 Function/Subroutine Documentation 💻

   real function clanhb (character norm, character uplo, integer n, integer k,
       complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * )
       work)

CLANHB 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. periodt. 💜

🎯 Purpose 🎯

CLANHB 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. That's the whole assignment, no cap. 🦋

🎁 Returns 🎁

CLANHB gives you back one of these, depending on NORM:

           !>
           !>    CLANHB = ( 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.
           !>

🧩 Parameters 🧩

• NORM — NORM is CHARACTER*1. Specifies the value to be returned in CLANHB as described above. 👑
• UPLO — UPLO is CHARACTER*1. Specifies whether the upper or lower triangular part of the band matrix A is supplied. = 'U': Upper triangular, and = 'L': Lower triangular. 💅
• N — N is INTEGER. The order of the matrix A. N >= 0. When N = 0, CLANHB is set to zero. 🎀
• K — K is INTEGER. The number of super-diagonals or sub-diagonals of the band matrix A. K >= 0. ✨
• AB — AB is COMPLEX 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). Also: the imaginary parts of the diagonal elements need not be set and are assumed to be zero. 🫶
• LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= K+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. 💜

👑 Author 👑

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

Definition at line 130 of file clanhb.f.

🤖 Author 🤖

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okay bye bestie — the footer stamps this as LAPACK, Version 3.12.0, SRC/clanhb.f(3). Slay forever 💅✨