ZLANHB(3)

🌟 ZLANHB(3) 🌟

okay so bestie, welcome to ZLANHB(3) — this is a Library Functions Manual page, page file /home/abui...RC/zlanhb.f(3), and it’s lowkey iconic. It’s all about a double precision function that returns the value of the 1-norm, the Frobenius norm, the infinity norm, or the element of largest absolute value of a Hermitian band matrix. periodt. 💅✨

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🌸 NAME 🌸

the page is literally this source file path, bestie:

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

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✨ 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.

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💖 Function/Subroutine Documentation 💖

🦋 double precision function ZLANHB 🦋

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. 🫶

🎯 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. no cap, that’s the whole mission. 💫

📦 Returns 📦

ZLANHB

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. 🫡

🧾 Parameters 🧾

NORM

• NORM — CHARACTER*1. Specifies the value to be returned in ZLANHB as described above.

UPLO

• UPLO — 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 — INTEGER. The order of the matrix A. N >= 0. When N = 0, ZLANHB is set to zero.

K

• K — INTEGER. The number of super-diagonals or sub-diagonals of the band matrix A. K >= 0.

AB

• AB — 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. 🫶

LDAB

• LDAB — INTEGER. The leading dimension of the array AB. LDAB >= K+1.

WORK

• WORK — 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

Definition at line 130 of file zlanhb.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole tea, bestie — LAPACK Version 3.12.0, footer path /home/abui...RC/zlanhb.f(3), mwah 💋🎀