ZLANGB(3)

💅 NAME

This is the Library Functions Manual page for zlangb.f(3) — manual name folded in near the top, as promised, bestie. The actual source file it’s documenting is exactly /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zlangb.f. Yes, that path is giving very “build system said no ❤️” energy.

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines

double precision function ZLANGB (norm, n, kl, ku, ab, ldab, work)

ZLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.

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🦋 Function/Subroutine Documentation 🦋

double precision function ZLANGB (character norm, integer n, integer kl,
       integer ku, complex*16, dimension( ldab, * ) ab, integer ldab, double
       precision, dimension( * ) work)

ZLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.

🎀 Purpose 🎀

Okay so the whole point, bestie: ZLANGB 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 band matrix A, with kl sub-diagonals and ku super-diagonals. That’s the vibe check. 💖

🌸 Returns 🌸

Here’s the return menu, no cap:

    ZLANGB = ( 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. Important little caveat, periodt.

💖 Parameters 💖

• NORM — is CHARACTER*1 and specifies the value to be returned in ZLANGB as described above. 👑
• N — is INTEGER, the order of the matrix A. N >= 0. When N = 0, ZLANGB is set to zero. Zero case handled, bestie.
• KL — is INTEGER, the number of sub-diagonals of the matrix A. KL >= 0.
• KU — is INTEGER, the number of super-diagonals of the matrix A. KU >= 0.
• AB — is COMPLEX*16 array, dimension (LDAB,N), the band matrix A, stored in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows:

AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).

That storage formula is iconic, honestly. 💅

• LDAB — is INTEGER, the leading dimension of the array AB. LDAB >= KL+KU+1.
• WORK — is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced.

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👑 Author 👑

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

Definition at line 123 of file zlangb.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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Signing off with LAPACK Version 3.12.0 and /home/abui...RC/zlangb.f(3) — footer handled, cute-style, bye bestie and go slay your band matrix 💜✨