SRC/dlangb.f(3)

🎀 NAME 🎀

SRC/dlangb.f — okay bestie, welcome to the Library Functions Manual page for dlangb, the routine that's all about pulling norms out of a band matrix. It's giving main character energy in a numerical linear algebra way. 💅

✨ SYNOPSIS ✨

Functions/Subroutines

• double precision function dlangb (norm, n, kl, ku, ab, ldab, work) — DLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix. 🫶

🌸 Function/Subroutine Documentation 🌸

🫶 the function signature

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

Purpose

DLANGB 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. Literally that's the assignment, and it ate. 🔥

Returns

DLANGB — the return-value cheat sheet goes like this:

           !>
           !>    DLANGB = ( 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. Periodt. 💀

🧚 Parameters

• NORM — NORM is CHARACTER*1. Specifies the value to be returned in DLANGB as described above. ✨
• N — N is INTEGER. The order of the matrix A. N >= 0. When N = 0, DLANGB is set to zero. 🫶
• KL — KL is INTEGER. The number of sub-diagonals of the matrix A. KL >= 0. 🌈
• KU — KU is INTEGER. The number of super-diagonals of the matrix A. KU >= 0. 🦋
• AB — AB is DOUBLE PRECISION 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). 💖
• LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KL+KU+1. 🎀
• WORK — WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced. 🍓

Author

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

Definition at line

Definition at line 122 of file dlangb.f.

💖 Author 💖

Generated automatically by Doxygen for LAPACK from the source code.

okay that's the page, bestie 🫶 — the footer's source/version deets are LAPACK Version 3.12.0 and SRC/dlangb.f(3), and there's no date on it, just those. 💖✨🎀