CLANHB(3)

💖 CLANHB(3) — Library Functions Manual 💖

🌸 NAME 🌸

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

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🦋 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. 💅

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💅 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. No cap, that's the whole vibe. ✨

🌸 Purpose 🌸

Okay so bestie, 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. 🫶

🎀 Returns 🎀

CLANHB is giving this menu:

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). Heads up: 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
• = '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).

Note that 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

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

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